Daily Papers

Long-term multi-agent systems inevitably generate vast amounts of trajectories and historical interactions, which makes efficient memory management essential for both performance and scalability. Existing methods typically depend on vector retrieval and hierarchical storage, yet they are prone to noise accumulation, uncontrolled memory expansion, and limited generalization across domains. To address these challenges, we present SEDM, Self-Evolving Distributed Memory, a verifiable and adaptive framework that transforms memory from a passive repository into an active, self-optimizing component. SEDM integrates verifiable write admission based on reproducible replay, a self-scheduling memory controller that dynamically ranks and consolidates entries according to empirical utility, and cross-domain knowledge diffusion that abstracts reusable insights to support transfer across heterogeneous tasks. Evaluations on benchmark datasets demonstrate that SEDM improves reasoning accuracy while reducing token overhead compared with strong memory baselines, and further enables knowledge distilled from fact verification to enhance multi-hop reasoning. The results highlight SEDM as a scalable and sustainable memory mechanism for open-ended multi-agent collaboration. The code will be released in the later stage of this project.

Verifiability is a core content policy of Wikipedia: claims that are likely to be challenged need to be backed by citations. There are millions of articles available online and thousands of new articles are released each month. For this reason, finding relevant sources is a difficult task: many claims do not have any references that support them. Furthermore, even existing citations might not support a given claim or become obsolete once the original source is updated or deleted. Hence, maintaining and improving the quality of Wikipedia references is an important challenge and there is a pressing need for better tools to assist humans in this effort. Here, we show that the process of improving references can be tackled with the help of artificial intelligence (AI). We develop a neural network based system, called Side, to identify Wikipedia citations that are unlikely to support their claims, and subsequently recommend better ones from the web. We train this model on existing Wikipedia references, therefore learning from the contributions and combined wisdom of thousands of Wikipedia editors. Using crowd-sourcing, we observe that for the top 10% most likely citations to be tagged as unverifiable by our system, humans prefer our system's suggested alternatives compared to the originally cited reference 70% of the time. To validate the applicability of our system, we built a demo to engage with the English-speaking Wikipedia community and find that Side's first citation recommendation collects over 60% more preferences than existing Wikipedia citations for the same top 10% most likely unverifiable claims according to Side. Our results indicate that an AI-based system could be used, in tandem with humans, to improve the verifiability of Wikipedia. More generally, we hope that our work can be used to assist fact checking efforts and increase the general trustworthiness of information online.

Reinforcement learning with verifiable rewards (RLVR) has enabled large language models (LLMs) to achieve remarkable breakthroughs in reasoning tasks with objective ground-truth answers, such as mathematics and code generation. However, a significant gap remains for non-verifiable tasks, like creative writing and open-ended dialogue, where quality assessment is inherently subjective and lacks definitive references. Existing approaches for these domains often rely on scalar reward models trained with human preferences, which suffer from limited generalization and are prone to reward hacking, such as over-explanation and length bias. In this work, we propose a unified RLVR-based training paradigm that bridges the gap between non-verifiable tasks and verifiable rewards. We introduce a writing-principle-based pairwise Generative Reward Model (GenRM) and a novel Bootstrapped Relative Policy Optimization (BRPO) algorithm. The pairwise writing GenRM leverages self-principled critique to transform subjective assessments into reliable, verifiable rewards, while BRPO enables dynamic, reference-free pairwise comparison by leveraging a bootstrapped response as temporary reference from within group rollouts during RL training. Our approach empowers LLMs to develop robust writing capabilities without supervised fine-tuning, as demonstrated by Writing-Zero, which shows consistent improvement and strong resistance to reward hacking compared to scalar reward baselines. Furthermore, our method achieves competitive results on both in-house and open-source writing benchmarks. Our findings suggest the potential to unify rule-based, reference-based, and reference-free reward modeling under the RLVR framework, thus paving the way for a comprehensive and scalable RL training paradigm applicable across all language tasks.

Handwriting verification has stood as a steadfast identity authentication method for decades. However, this technique risks potential privacy breaches due to the inclusion of personal information in handwritten biometrics such as signatures. To address this concern, we propose using the Random Digit String (RDS) for privacy-preserving handwriting verification. This approach allows users to authenticate themselves by writing an arbitrary digit sequence, effectively ensuring privacy protection. To evaluate the effectiveness of RDS, we construct a new HRDS4BV dataset composed of online naturally handwritten RDS. Unlike conventional handwriting, RDS encompasses unconstrained and variable content, posing significant challenges for modeling consistent personal writing style. To surmount this, we propose the Pattern Attentive VErification Network (PAVENet), along with a Discriminative Pattern Mining (DPM) module. DPM adaptively enhances the recognition of consistent and discriminative writing patterns, thus refining handwriting style representation. Through comprehensive evaluations, we scrutinize the applicability of online RDS verification and showcase a pronounced outperformance of our model over existing methods. Furthermore, we discover a noteworthy forgery phenomenon that deviates from prior findings and discuss its positive impact in countering malicious impostor attacks. Substantially, our work underscores the feasibility of privacy-preserving biometric verification and propels the prospects of its broader acceptance and application.

Large language models (LLMs) are increasingly integrated in software development, but ensuring correctness in LLM-generated code remains challenging and often requires costly manual review. Verifiable code generation -- jointly generating code, specifications, and proofs of code-specification alignment -- offers a promising path to address this limitation and further unleash LLMs' benefits in coding. Yet, there exists a significant gap in evaluation: current benchmarks often lack support for end-to-end verifiable code generation. In this paper, we introduce Verina (Verifiable Code Generation Arena), a high-quality benchmark enabling a comprehensive and modular evaluation of code, specification, and proof generation as well as their compositions. Verina consists of 189 manually curated coding tasks in Lean, with detailed problem descriptions, reference implementations, formal specifications, and extensive test suites. Our extensive evaluation of state-of-the-art LLMs reveals significant challenges in verifiable code generation, especially in proof generation, underscoring the need for improving LLM-based theorem provers in verification domains. The best model, OpenAI o4-mini, generates only 61.4% correct code, 51.0% sound and complete specifications, and 3.6% successful proofs, with one trial per task. We hope Verina will catalyze progress in verifiable code generation by providing a rigorous and comprehensive benchmark. We release our dataset on https://huggingface.co/datasets/sunblaze-ucb/verina and our evaluation code on https://github.com/sunblaze-ucb/verina.

Large language models demonstrate remarkable reasoning capabilities but often produce unreliable or incorrect responses. Existing verification methods are typically model-specific or domain-restricted, requiring significant computational resources and lacking scalability across diverse reasoning tasks. To address these limitations, we propose VerifiAgent, a unified verification agent that integrates two levels of verification: meta-verification, which assesses completeness and consistency in model responses, and tool-based adaptive verification, where VerifiAgent autonomously selects appropriate verification tools based on the reasoning type, including mathematical, logical, or commonsense reasoning. This adaptive approach ensures both efficiency and robustness across different verification scenarios. Experimental results show that VerifiAgent outperforms baseline verification methods (e.g., deductive verifier, backward verifier) among all reasoning tasks. Additionally, it can further enhance reasoning accuracy by leveraging feedback from verification results. VerifiAgent can also be effectively applied to inference scaling, achieving better results with fewer generated samples and costs compared to existing process reward models in the mathematical reasoning domain. Code is available at https://github.com/Jiuzhouh/VerifiAgent

Metrics like FactScore and VeriScore that evaluate long-form factuality operate by decomposing an input response into atomic claims and then individually verifying each claim. While effective and interpretable, these methods incur numerous LLM calls and can take upwards of 100 seconds to evaluate a single response, limiting their practicality in large-scale evaluation and training scenarios. To address this, we propose VeriFastScore, which leverages synthetic data to fine-tune Llama3.1 8B for simultaneously extracting and verifying all verifiable claims within a given text based on evidence from Google Search. We show that this task cannot be solved via few-shot prompting with closed LLMs due to its complexity: the model receives ~4K tokens of evidence on average and needs to concurrently decompose claims, judge their verifiability, and verify them against noisy evidence. However, our fine-tuned VeriFastScore model demonstrates strong correlation with the original VeriScore pipeline at both the example level (r=0.80) and system level (r=0.94) while achieving an overall speedup of 6.6x (9.9x excluding evidence retrieval) over VeriScore. To facilitate future factuality research, we publicly release our VeriFastScore model and synthetic datasets.

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates this landscape by introducing its own challenging trade-off: sophisticated Generative Reward Models (GenRMs) can be computationally prohibitive if naively integrated with LLMs at test-time, while simpler, faster methods may lack reliability. To overcome these challenges, we introduce FlexiVe, a novel generative verifier that flexibly balances computational resources between rapid, reliable fast thinking and meticulous slow thinking using a Flexible Allocation of Verification Budget strategy. We further propose the Solve-Detect-Verify pipeline, an efficient inference-time scaling framework that intelligently integrates FlexiVe, proactively identifying solution completion points to trigger targeted verification and provide focused solver feedback. Experiments show FlexiVe achieves superior accuracy in pinpointing errors within reasoning traces on ProcessBench. Furthermore, on challenging mathematical reasoning benchmarks (AIME 2024, AIME 2025, and CNMO), our full approach outperforms baselines like self-consistency in reasoning accuracy and inference efficiency. Our system offers a scalable and effective solution to enhance LLM reasoning at test time.

Large Language Models (LLMs) show great promise in complex reasoning, with Reinforcement Learning with Verifiable Rewards (RLVR) being a key enhancement strategy. However, a prevalent issue is ``superficial self-reflection'', where models fail to robustly verify their own outputs. We introduce RISE (Reinforcing Reasoning with Self-Verification), a novel online RL framework designed to tackle this. RISE explicitly and simultaneously trains an LLM to improve both its problem-solving and self-verification abilities within a single, integrated RL process. The core mechanism involves leveraging verifiable rewards from an outcome verifier to provide on-the-fly feedback for both solution generation and self-verification tasks. In each iteration, the model generates solutions, then critiques its own on-policy generated solutions, with both trajectories contributing to the policy update. Extensive experiments on diverse mathematical reasoning benchmarks show that RISE consistently improves model's problem-solving accuracy while concurrently fostering strong self-verification skills. Our analyses highlight the advantages of online verification and the benefits of increased verification compute. Additionally, RISE models exhibit more frequent and accurate self-verification behaviors during reasoning. These advantages reinforce RISE as a flexible and effective path towards developing more robust and self-aware reasoners.

Large language model (LLM)-based reasoning systems have recently achieved gold medal-level performance in the IMO 2025 competition, writing mathematical proofs where, to receive full credit, each step must be not only correct but also sufficiently supported. To train LLM-based reasoners in such challenging, open-ended settings, strong verifiers capable of catching step-level mistakes are necessary prerequisites. We introduce Hard2Verify, a human-annotated, step-level verification benchmark produced with over 500 hours of human labor. Hard2Verify is designed to rigorously assess step-level verifiers at the frontier: Verifiers must provide step-level annotations or identify the first error in responses generated by frontier LLMs for very recent, challenging, and open-ended math questions. We evaluate 29 generative critics and process reward models, demonstrating that, beyond a few standouts, open-source verifiers lag closed source models. We subsequently analyze what drives poor performance in step-level verification, the impacts of scaling verifier compute, as well as fundamental questions such as self-verification and verification-generation dynamics.

Verifiers play a crucial role in large language model (LLM) reasoning, needed by post-training techniques such as reinforcement learning. However, reliable verifiers are hard to get for difficult coding problems, because a well-disguised wrong solution may only be detected by carefully human-written edge cases that are difficult to synthesize. To address this issue, we propose HARDTESTGEN, a pipeline for high-quality test synthesis using LLMs. With this pipeline, we curate a comprehensive competitive programming dataset HARDTESTS with 47k problems and synthetic high-quality tests. Compared with existing tests, HARDTESTGEN tests demonstrate precision that is 11.3 percentage points higher and recall that is 17.5 percentage points higher when evaluating LLM-generated code. For harder problems, the improvement in precision can be as large as 40 points. HARDTESTS also proves to be more effective for model training, measured by downstream code generation performance. We will open-source our dataset and synthesis pipeline at https://leililab.github.io/HardTests/.

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework Safe. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework Safe across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose FormalStep as a benchmark for step correctness theorem proving with 30,809 formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values \(V(s)\) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (\textbf{Tree-Estimated Mean Prefix Value for Policy Optimization}), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.

Mathematical reasoning is a central challenge for large language models (LLMs), requiring not only correct answers but also faithful reasoning processes. Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach for enhancing such capabilities; however, its ability to foster genuine reasoning remains unclear. We investigate RLVR on two combinatorial problems with fully verifiable solutions: Activity Scheduling and the Longest Increasing Subsequence, using carefully curated datasets with unique optima. Across multiple reward designs, we find that RLVR improves evaluation metrics but often by reinforcing superficial heuristics rather than acquiring new reasoning strategies. These findings highlight the limits of RLVR generalization, emphasizing the importance of benchmarks that disentangle genuine mathematical reasoning from shortcut exploitation and provide faithful measures of progress. Code available at https://github.com/xashru/rlvr-seq-generalization.

Through reinforcement learning with verifiable rewards (RLVR), large language models have achieved substantial progress in domains with easily verifiable outcomes, such as mathematics and coding. However, when applied to more complex tasks like open-domain question answering, RLVR faces significant challenges due to the difficulty of verifying correctness. The nuanced and ambiguous nature of real-world knowledge makes it difficult to reliably evaluate correctness in these settings, necessitating further abilities that extend beyond mere logical consistency to encompass an understanding and assessment of both external and internal knowledge. Recent work has primarily focused on improving faithfulness, defined as semantic alignment with supporting documents, which can cause models to rely excessively on external sources and diminish their capacity for critical assessment. To address this, we propose the Thinking-supervised Reward Model (TRM), which incorporates sentence-level thinking supervision to endow reward models with critical thinking abilities. Given a query, answer, and supporting documents, TRM first assesses the faithfulness of each answer sentence to the supporting documents, and then applies a reasoning step to evaluate sentence-level correctness. By structuring reward modeling as a sequence of faithfulness, reasoning, and correctness evaluations, TRM encourages models to critically assess and leverage both external and internal knowledge. Experiments on reward signals demonstrate that TRM substantially improves the identification of incorrect sentences, and incorporating TRM into policy optimization leads to significant gains in both answer correctness and usefulness.

For humans to trust the fluent generations of large language models (LLMs), they must be able to verify their correctness against trusted, external sources. Recent efforts aim to increase verifiability through citations of retrieved documents or post-hoc provenance. However, such citations are prone to mistakes that further complicate their verifiability. To address these limitations, we tackle the verifiability goal with a different philosophy: we trivialize the verification process by developing models that quote verbatim statements from trusted sources in pre-training data. We propose Quote-Tuning, which demonstrates the feasibility of aligning LLMs to leverage memorized information and quote from pre-training data. Quote-Tuning quantifies quoting against large corpora with efficient membership inference tools, and uses the amount of quotes as an implicit reward signal to construct a synthetic preference dataset for quoting, without any human annotation. Next, the target model is aligned to quote using preference optimization algorithms. Experimental results show that Quote-Tuning significantly increases the percentage of LLM generation quoted verbatim from high-quality pre-training documents by 55% to 130% relative to untuned models while maintaining response quality. Further experiments demonstrate that Quote-Tuning generalizes quoting to out-of-domain data, is applicable in different tasks, and provides additional benefits to truthfulness. Quote-Tuning not only serves as a hassle-free method to increase quoting but also opens up avenues for improving LLM trustworthiness through better verifiability.

Reinforcement learning (RL) has become a standard paradigm for refining large language models (LLMs) beyond pre-training and instruction tuning. A prominent line of work is RL with verifiable rewards (RLVR), which leverages automatically verifiable outcomes (e.g., correctness or executability) to generate reward signals. While efficient, this framework faces two key limitations: First, its binary feedback is too sparse to capture the quality of the reasoning process. Second, its coarse-grained rewards potentially lead to vanishing gradients. Inspired by observations from human learning, we introduce a RL technique that integrates verifiable outcomes with the model's own confidence estimates. This joint design enriches the reward signal, providing finer-grained feedback and implicitly supervising the reasoning process. Experimental results demonstrate that our proposed method enhances RL performance across multiple datasets and reduces token consumption during inference, while incurring negligible additional training cost. Moreover, it can be used as a plug-in module to enhance other state-of-the-art RL methods.

Automated Essay Score (AES) is proven to be one of the cutting-edge technologies. Scoring techniques are used for various purposes. Reliable scores are calculated based on influential variables. Such variables can be computed by different methods based on the domain. The research is concentrated on the user's understanding of a given topic. The analysis is based on a scoring index by using Large Language Models. The user can then compare and contrast the understanding of a topic that they recently learned. The results are then contributed towards learning analytics and progression is made for enhancing the learning ability. In this research, the focus is on summarizing a PDF document and gauging a user's understanding of its content. The process involves utilizing a Langchain tool to summarize the PDF and extract the essential information. By employing this technique, the research aims to determine how well the user comprehends the summarized content.

Reinforcement learning with verifiable rewards (RLVR) has advanced the reasoning capabilities of large language models (LLMs). However, prevailing RLVR methods exhibit a systematic bias toward exploitation over exploration, as evidenced by improved pass@1 but reduced pass@K (K>1) performance. To understand this issue, we analyze training dynamics of RLVR methods by tracking the token-level probability distributions over vocabulary candidates. Our analysis reveals a consistent probability concentration effect where the top-1 candidate increasingly accumulates probability mass and suppresses that of other candidates. More importantly, stronger over-concentration correlates with worse pass@K performance. Inspired by this finding, we propose Simple Pass@K Optimization (SimKO), a method designed to mitigate the over-concentration issue, thereby encouraging exploration. SimKO operates in an asymmetrical manner. For verified-correct responses, it boosts the probabilities of the top-K candidates. For verified-incorrect responses, it applies stronger penalties to the top-1 candidate. We observe that this asymmetric design is particularly effective at mitigating over-concentration when applied at tokens with high entropy. Across various math and logical-reasoning benchmarks, SimKO consistently yields higher pass@K for a wide range of K, providing a simple way to improve RLVR's exploration.

Common self-improvement approaches for large language models (LLMs), such as STaR (Zelikman et al., 2022), iteratively fine-tune LLMs on self-generated solutions to improve their problem-solving ability. However, these approaches discard the large amounts of incorrect solutions generated during this process, potentially neglecting valuable information in such solutions. To address this shortcoming, we propose V-STaR that utilizes both the correct and incorrect solutions generated during the self-improvement process to train a verifier using DPO that judges correctness of model-generated solutions. This verifier is used at inference time to select one solution among many candidate solutions. Running V-STaR for multiple iterations results in progressively better reasoners and verifiers, delivering a 4% to 17% test accuracy improvement over existing self-improvement and verification approaches on common code generation and math reasoning benchmarks with LLaMA2 models.

Machine reading comprehension (MRC) is an AI challenge that requires machine to determine the correct answers to questions based on a given passage. MRC systems must not only answer question when necessary but also distinguish when no answer is available according to the given passage and then tactfully abstain from answering. When unanswerable questions are involved in the MRC task, an essential verification module called verifier is especially required in addition to the encoder, though the latest practice on MRC modeling still most benefits from adopting well pre-trained language models as the encoder block by only focusing on the "reading". This paper devotes itself to exploring better verifier design for the MRC task with unanswerable questions. Inspired by how humans solve reading comprehension questions, we proposed a retrospective reader (Retro-Reader) that integrates two stages of reading and verification strategies: 1) sketchy reading that briefly investigates the overall interactions of passage and question, and yield an initial judgment; 2) intensive reading that verifies the answer and gives the final prediction. The proposed reader is evaluated on two benchmark MRC challenge datasets SQuAD2.0 and NewsQA, achieving new state-of-the-art results. Significance tests show that our model is significantly better than the strong ELECTRA and ALBERT baselines. A series of analysis is also conducted to interpret the effectiveness of the proposed reader.

Speculative decoding (SD), where an extra draft model is employed to provide multiple draft tokens first and then the original target model verifies these tokens in parallel, has shown great power for LLM inference acceleration. However, existing SD methods suffer from the mutual waiting problem, i.e., the target model gets stuck when the draft model is guessing tokens, and vice versa. This problem is directly incurred by the asynchronous execution of the draft model and the target model, and is exacerbated due to the fixed draft length in speculative decoding. To address these challenges, we propose a conceptually simple, flexible, and general framework to boost speculative decoding, namely Parallel spEculative decoding with Adaptive dRaft Length (PEARL). Specifically, PEARL proposes pre-verify to verify the first draft token in advance during the drafting phase, and post-verify to generate more draft tokens during the verification phase. PEARL parallels the drafting phase and the verification phase via applying the two strategies, and achieves adaptive draft length for different scenarios, which effectively alleviates the mutual waiting problem. Moreover, we theoretically demonstrate that the mean accepted tokens of PEARL is more than existing draft-then-verify works. Experiments on various text generation benchmarks demonstrate the effectiveness of our \name, leading to a superior speedup performance up to 3.79times and 1.52times, compared to auto-regressive decoding and vanilla speculative decoding, respectively.

One core capability of Large Language Models (LLMs) is to follow natural language instructions. However, the evaluation of such abilities is not standardized: Human evaluations are expensive, slow, and not objectively reproducible, while LLM-based auto-evaluation is potentially biased or limited by the ability of the evaluator LLM. To overcome these issues, we introduce Instruction-Following Eval (IFEval) for large language models. IFEval is a straightforward and easy-to-reproduce evaluation benchmark. It focuses on a set of "verifiable instructions" such as "write in more than 400 words" and "mention the keyword of AI at least 3 times". We identified 25 types of those verifiable instructions and constructed around 500 prompts, with each prompt containing one or more verifiable instructions. We show evaluation results of two widely available LLMs on the market. Our code and data can be found at https://github.com/google-research/google-research/tree/master/instruction_following_eval

Language models (LMs) are widely used by an increasing number of users, underscoring the challenge of maintaining factuality across a broad range of topics. We first present VERIFY (Verification and Evidence RetrIeval for FactualitY evaluation), a pipeline to evaluate LMs' factuality in real-world user interactions. VERIFY considers the verifiability of LM-generated content and categorizes content units as supported, unsupported, or undecidable based on the retrieved evidence from the Web. Importantly, factuality judgment by VERIFY correlates better with human evaluations than existing methods. Using VERIFY, we identify "hallucination prompts" across diverse topics, i.e., those eliciting the highest rates of incorrect and inconclusive LM responses. These prompts form FactBench, a dataset of 1K prompts across 150 fine-grained topics. Our dataset captures emerging factuality challenges in real-world LM interactions and can be regularly updated with new prompts. We benchmark widely-used LMs from GPT, Gemini, and Llama3.1 family on FactBench, yielding the following key findings: (i) Proprietary models exhibit better factuality, with performance declining from Easy to Hard hallucination prompts. (ii) Llama3.1-405B-Instruct shows comparable or lower factual accuracy than Llama3.1-70B-Instruct across all evaluation methods due to its higher subjectivity that leads to more content labeled as undecidable. (iii) Gemini1.5-Pro shows a significantly higher refusal rate, with over-refusal in 25% of cases. Our code and data are publicly available at https://huggingface.co/spaces/launch/factbench.

Reliable verifiable data has become a key driver of capability gains in modern language models, enabling stable reinforcement learning with verifiable rewards and effective distillation that transfers competence across math, coding, and agentic tasks. Yet constructing generalizable synthetic verifiable data remains difficult due to hallucination-prone generation, and weak or trivial verification artifacts that fail to separate strong from weak solutions. Existing approaches often rely on task-specific heuristics or post-hoc filters that do not transfer across domains and lack a principled, universal evaluator of verifiability. In this work, we introduce an evolutionary, task-agnostic, strategy-guided, executably-checkable data synthesis framework that, from minimal seed supervision, jointly synthesizes problems, diverse candidate solutions, and verification artifacts, and iteratively discovers strategies via a consistency-based evaluator that enforces agreement between human-annotated and strategy-induced checks. This pipeline upgrades filtering into principled synthesis: it reliably assembles coherent, verifiable training instances and generalizes without domain-specific rules. Our experiments demonstrate the effectiveness of the proposed approach under both RLVR and model distillation training paradigms. The results show that training with our synthesized data yields significant improvements on both the LiveCodeBench and AgentBench-OS tasks, highlighting the robust generalization of our framework.

We investigate the effectiveness of reinforcement learning methods for finetuning large language models when transitioning from offline to semi-online to fully online regimes for both verifiable and non-verifiable tasks. Our experiments cover training on verifiable math as well as non-verifiable instruction following with a set of benchmark evaluations for both. Across these settings, we extensively compare online and semi-online Direct Preference Optimization and Group Reward Policy Optimization objectives, and surprisingly find similar performance and convergence between these variants, which all strongly outperform offline methods. We provide a detailed analysis of the training dynamics and hyperparameter selection strategies to achieve optimal results. Finally, we show that multi-tasking with verifiable and non-verifiable rewards jointly yields improved performance across both task types.

The standard paradigm for solving coding tasks via large language models (LLMs) is to generate-then-rank programs, where the latter step uses a verifier in the ranking process. The growing consensus is that a comprehensive verifier (e.g., a full test suite) should be prioritized over an outcome reward model (ORM) whenever possible, with little consideration given to the trade-offs involved. We aim to challenge this assumption by systematically exploring the tradeoff between speed and accuracy. We find that ORMs play a crucial role in scaling verification through trading accuracy for speed, even when a comprehensive verifier is available. Their value becomes especially apparent when used in a generate-prune-then-rank approach, where a faster but less accurate verifier removes incorrect solutions prior to ranking -- leading to a system that is 11.65x faster while only being 8.33% less accurate than the full test suite. We analyze the generate-prune-then-rank approach and show that it works by filtering out incorrect but highly ranked solutions. These findings enable the design of scalable and accurate program ranking systems.

We present the Verifee Dataset: a novel dataset of news articles with fine-grained trustworthiness annotations. We develop a detailed methodology that assesses the texts based on their parameters encompassing editorial transparency, journalist conventions, and objective reporting while penalizing manipulative techniques. We bring aboard a diverse set of researchers from social, media, and computer sciences to overcome barriers and limited framing of this interdisciplinary problem. We collect over 10,000 unique articles from almost 60 Czech online news sources. These are categorized into one of the 4 classes across the credibility spectrum we propose, raging from entirely trustworthy articles all the way to the manipulative ones. We produce detailed statistics and study trends emerging throughout the set. Lastly, we fine-tune multiple popular sequence-to-sequence language models using our dataset on the trustworthiness classification task and report the best testing F-1 score of 0.52. We open-source the dataset, annotation methodology, and annotators' instructions in full length at https://verifee.ai/research to enable easy build-up work. We believe similar methods can help prevent disinformation and educate in the realm of media literacy.

The breakthrough of OpenAI o1 highlights the potential of enhancing reasoning to improve LLM. Yet, most research in reasoning has focused on mathematical tasks, leaving domains like medicine underexplored. The medical domain, though distinct from mathematics, also demands robust reasoning to provide reliable answers, given the high standards of healthcare. However, verifying medical reasoning is challenging, unlike those in mathematics. To address this, we propose verifiable medical problems with a medical verifier to check the correctness of model outputs. This verifiable nature enables advancements in medical reasoning through a two-stage approach: (1) using the verifier to guide the search for a complex reasoning trajectory for fine-tuning LLMs, (2) applying reinforcement learning (RL) with verifier-based rewards to enhance complex reasoning further. Finally, we introduce HuatuoGPT-o1, a medical LLM capable of complex reasoning, which outperforms general and medical-specific baselines using only 40K verifiable problems. Experiments show complex reasoning improves medical problem-solving and benefits more from RL. We hope our approach inspires advancements in reasoning across medical and other specialized domains.

Large language models (LLMs) have exhibited impressive capabilities across a myriad of tasks, yet they occasionally yield undesirable outputs. We posit that these limitations are rooted in the foundational autoregressive architecture of LLMs, which inherently lacks mechanisms for differentiating between desirable and undesirable results. Drawing inspiration from the dual-process theory of human cognition, we introduce LLM2, a novel framework that combines an LLM (System 1) with a process-based verifier (System 2). Within LLM2, the LLM is responsible for generating plausible candidates, while the verifier provides timely process-based feedback to distinguish desirable and undesirable outputs. The verifier is trained with a pairwise comparison loss on synthetic process-supervision data generated through our token quality exploration strategy. Empirical results on mathematical reasoning benchmarks substantiate the efficacy of LLM2, exemplified by an accuracy enhancement from 50.3 to 57.8 (+7.5) for Llama3-1B on GSM8K. Furthermore, when combined with self-consistency, LLM2 achieves additional improvements, boosting major@20 accuracy from 56.2 to 70.2 (+14.0).

Under a unified operational definition, we define LLM memory as a persistent state written during pretraining, finetuning, or inference that can later be addressed and that stably influences outputs. We propose a four-part taxonomy (parametric, contextual, external, procedural/episodic) and a memory quadruple (location, persistence, write/access path, controllability). We link mechanism, evaluation, and governance via the chain write -> read -> inhibit/update. To avoid distorted comparisons across heterogeneous setups, we adopt a three-setting protocol (parametric only, offline retrieval, online retrieval) that decouples capability from information availability on the same data and timeline. On this basis we build a layered evaluation: parametric (closed-book recall, edit differential, memorization/privacy), contextual (position curves and the mid-sequence drop), external (answer correctness vs snippet attribution/faithfulness), and procedural/episodic (cross-session consistency and timeline replay, E MARS+). The framework integrates temporal governance and leakage auditing (freshness hits, outdated answers, refusal slices) and uncertainty reporting via inter-rater agreement plus paired tests with multiple-comparison correction. For updating and forgetting, we present DMM Gov: coordinating DAPT/TAPT, PEFT, model editing (ROME, MEND, MEMIT, SERAC), and RAG to form an auditable loop covering admission thresholds, rollout, monitoring, rollback, and change audits, with specs for timeliness, conflict handling, and long-horizon consistency. Finally, we give four testable propositions: minimum identifiability; a minimal evaluation card; causally constrained editing with verifiable forgetting; and when retrieval with small-window replay outperforms ultra-long-context reading. This yields a reproducible, comparable, and governable coordinate system for research and deployment.

Large Multimodal Models (LMMs) are increasingly capable of answering medical questions that require joint reasoning over images and text, yet training general medical VQA systems is impeded by the lack of large, openly usable, high-quality corpora. We present MedVLSynther, a rubric-guided generator-verifier framework that synthesizes high-quality multiple-choice VQA items directly from open biomedical literature by conditioning on figures, captions, and in-text references. The generator produces self-contained stems and parallel, mutually exclusive options under a machine-checkable JSON schema; a multi-stage verifier enforces essential gates (self-containment, single correct answer, clinical validity, image-text consistency), awards fine-grained positive points, and penalizes common failure modes before acceptance. Applying this pipeline to PubMed Central yields MedSynVQA: 13,087 audited questions over 14,803 images spanning 13 imaging modalities and 28 anatomical regions. Training open-weight LMMs with reinforcement learning using verifiable rewards improves accuracy across six medical VQA benchmarks, achieving averages of 55.85 (3B) and 58.15 (7B), with up to 77.57 on VQA-RAD and 67.76 on PathVQA, outperforming strong medical LMMs. A Ablations verify that both generation and verification are necessary and that more verified data consistently helps, and a targeted contamination analysis detects no leakage from evaluation suites. By operating entirely on open literature and open-weight models, MedVLSynther offers an auditable, reproducible, and privacy-preserving path to scalable medical VQA training data.

Search augmentation empowers Large Language Models with retrieval capabilities to overcome the limitations imposed by static parameters. Recently, Reinforcement Learning leverages tailored reward signals as a viable technique to enhance LLMs performing tasks involving search. However, existing reward modeling for search-augmented LLMs faces several limitations. Rule-based rewards, such as Exact Match, are verifiable but fragile to variations in expression and cannot be applied to long-form workloads. In contrast, generative rewards improve robustness, but designing verifiable and stable rewards for long-form workloads in dynamic corpora remains challenging and also incurs high computational costs. In this paper, we propose a unified and verifiable paradigm, "nugget-as-rubric", which treats atomic information points as structured evaluation criteria for different search-augmentation workloads. Short-form tasks correspond to a single rubric, whereas long-form tasks expand to multiple rubrics aligned with the question's information needs. To support long-form settings, we design an automatic rubric construction pipeline based on query rewriting, which can automatically retrieve passages relevant to each question and extract rubrics from them, both from static corpora and from dynamic online web content. Furthermore, we introduce Search-Gen-V, a 4B-parameter efficient generative verifier under our proposed verifiable paradigm, which is trained via the idea of distillation and a two-stage strategy. Experimental results show that Search-Gen-V achieves strong verification accuracy across different workloads, making it a scalable, robust, and efficient verifiable reward constructor for search-augmented LLMs.

Generative search engines directly generate responses to user queries, along with in-line citations. A prerequisite trait of a trustworthy generative search engine is verifiability, i.e., systems should cite comprehensively (high citation recall; all statements are fully supported by citations) and accurately (high citation precision; every cite supports its associated statement). We conduct human evaluation to audit four popular generative search engines -- Bing Chat, NeevaAI, perplexity.ai, and YouChat -- across a diverse set of queries from a variety of sources (e.g., historical Google user queries, dynamically-collected open-ended questions on Reddit, etc.). We find that responses from existing generative search engines are fluent and appear informative, but frequently contain unsupported statements and inaccurate citations: on average, a mere 51.5% of generated sentences are fully supported by citations and only 74.5% of citations support their associated sentence. We believe that these results are concerningly low for systems that may serve as a primary tool for information-seeking users, especially given their facade of trustworthiness. We hope that our results further motivate the development of trustworthy generative search engines and help researchers and users better understand the shortcomings of existing commercial systems.

Reinforcement Learning with Verifiable Rewards (RLVR) trains policies against automated verifiers to avoid costly human labeling. To reduce vulnerability to verifier hacking, many RLVR systems collapse rewards to binary {0,1} during training. This choice carries a cost: it introduces false negatives (rejecting correct answers, FNs) and false positives (accepting incorrect ones, FPs). For instance, a rule-based checker may mark the correct fraction 12{36} as wrong when compared against the canonical 1{3} due to brittle parsing/equivalence rules (FN), while a large language model (LLM) judges can be gamed by superficial cues or even a single adversarial token, yielding inflated correctness for wrong solutions (FP). We formalize verifier unreliability by modeling the verifier as a stochastic reward channel with asymmetric noise rates. From this abstraction, we derive two correction algorithms for verifier errors. The first is a backward correction that de-biases the observed binary reward to recover an unbiased estimator of the clean policy gradient. The second is a forward correction that reweights score-function terms so that the expected update direction aligns with the clean gradient; notably, it requires only the FN rate. We implement both as lightweight hooks in a group relative policy optimization (GRPO)-based RLVR pipeline and evaluate them on math-reasoning models and benchmarks. Across models and datasets, both corrections improve over uncorrected training; the forward variant converges faster and remains stable under heavier noise. Finally, we show a practical appeal mechanism in which a lightweight LLM verifier estimates the FN rate online by rechecking rule-based negatives, obtaining outperformance compared with other state-of-the-art contenders.

The recent paradigm shift towards training large language models (LLMs) using DeepSeek-R1-Zero-style reinforcement learning (RL) on verifiable rewards has led to impressive advancements in code and mathematical reasoning. However, this methodology is limited to tasks where rule-based answer verification is possible and does not naturally extend to real-world domains such as chemistry, healthcare, engineering, law, biology, business, and economics. Current practical workarounds use an additional LLM as a model-based verifier; however, this introduces issues such as reliance on a strong verifier LLM, susceptibility to reward hacking, and the practical burden of maintaining the verifier model in memory during training. To address this and extend DeepSeek-R1-Zero-style training to general reasoning domains, we propose a verifier-free method (VeriFree) that bypasses answer verification and instead uses RL to directly maximize the probability of generating the reference answer. We compare VeriFree with verifier-based methods and demonstrate that, in addition to its significant practical benefits and reduced compute requirements, VeriFree matches and even surpasses verifier-based methods on extensive evaluations across MMLU-Pro, GPQA, SuperGPQA, and math-related benchmarks. Moreover, we provide insights into this method from multiple perspectives: as an elegant integration of training both the policy and implicit verifier in a unified model, and as a variational optimization approach. Code is available at https://github.com/sail-sg/VeriFree.

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.

Large language models (LLMs) have proven to be very capable, but access to the best models currently rely on inference providers which introduces trust challenges -- how can we be sure that the provider is using the model configuration they claim? We propose TOPLOC, a novel method for verifiable inference that addresses this problem. TOPLOC leverages a compact locality sensitive hashing mechanism for intermediate activations which can detect unauthorized modifications to models, prompts, or precision with 100% accuracy, achieving no false positives or negatives in our empirical evaluations. Our approach is robust across diverse hardware configurations, GPU types, and algebraic reorderings, which allows for validation speeds significantly faster than the original inference. By introducing a polynomial encoding scheme, TOPLOC minimizes memory overhead of the generated commits by 1000times, requiring only 258 bytes of storage per 32 new tokens compared to the 262KB requirement of storing the token embeddings directly for Llama-3.1-8B-Instruct. Our method empowers users to verify LLM inference computations efficiently, fostering greater trust and transparency in open ecosystems and lays a foundation for decentralized and verifiable AI services.

Human verification under adversarial information flow operates as a cost-bounded decision procedure constrained by working memory limits and cognitive biases. We introduce the Verification Cost Asymmetry (VCA) coefficient, formalizing it as the ratio of expected verification work between populations under identical claim distributions. Drawing on probabilistically checkable proofs (PCP) and parameterized complexity theory, we construct dissemination protocols that reduce verification for trusted audiences to constant human effort while imposing superlinear costs on adversarial populations lacking cryptographic infrastructure. We prove theoretical guarantees for this asymmetry, validate the framework through controlled user studies measuring verification effort with and without spot-checkable provenance, and demonstrate practical encoding of real-world information campaigns. The results establish complexity-theoretic foundations for engineering democratic advantage in cognitive warfare, with immediate applications to content authentication, platform governance, and information operations doctrine.

Answer verification is crucial not only for evaluating large language models (LLMs) by matching their unstructured outputs against standard answers, but also serves as the reward model to guide LLM optimization. Most evaluation frameworks rely on regularized matching or employ general LLMs for answer verification, which demands extensive, repetitive customization for regex rules or evaluation prompts. Two fundamental limitations persist in current methodologies: 1) the absence of comprehensive benchmarks that systematically evaluate verification capabilities across different LLMs; and 2) the nascent stage of verifier development, where existing approaches lack both the robustness to handle complex edge cases and the generalizability across different domains. In this work, we develop CompassVerifier, an accurate and robust lightweight verifier model for evaluation and outcome reward. It demonstrates multi-domain competency spanning math, knowledge, and diverse reasoning tasks, with the capability to process various answer types, including multi-subproblems, formulas, and sequence answers, while effectively identifying abnormal/invalid responses. We introduce VerifierBench benchmark comprising model outputs collected from multiple data sources, augmented through manual analysis of metaerror patterns to enhance CompassVerifier. We anticipate that CompassVerifier and VerifierBench will facilitate answer verification, evaluation protocols, and reinforcement learning research. Code and dataset are available at https://github.com/open-compass/CompassVerifier.

LLMs can perform multi-step reasoning through Chain-of-Thought (CoT), but they cannot reliably verify their own logic. Even when they reach correct answers, the underlying reasoning may be flawed, undermining trust in high-stakes scenarios. To mitigate this issue, we introduce VeriCoT, a neuro-symbolic method that extracts and verifies formal logical arguments from CoT reasoning. VeriCoT formalizes each CoT reasoning step into first-order logic and identifies premises that ground the argument in source context, commonsense knowledge, or prior reasoning steps. The symbolic representation enables automated solvers to verify logical validity while the NL premises allow humans and systems to identify ungrounded or fallacious reasoning steps. Experiments on the ProofWriter, LegalBench, and BioASQ datasets show VeriCoT effectively identifies flawed reasoning, and serves as a strong predictor of final answer correctness. We also leverage VeriCoT's verification signal for (1) inference-time self-reflection, (2) supervised fine-tuning (SFT) on VeriCoT-distilled datasets and (3) preference fine-tuning (PFT) with direct preference optimization (DPO) using verification-based pairwise rewards, further improving reasoning validity and accuracy.

Large language models (LLMs) struggle with multi-step reasoning, where inference-time scaling has emerged as a promising strategy for performance improvement. Verifier-guided search outperforms repeated sampling when sample size is limited by selecting and prioritizing valid reasoning paths. However, we identify a critical limitation: scaling flaws, prevalent across different models (Mistral 7B and DeepSeekMath 7B), benchmarks (GSM8K and MATH), and verifiers (outcome value models and process reward models). As sample size increases, verifier-guided search exhibits diminishing advantages and eventually underperforms repeated sampling. Our analysis attributes this to verifier failures, where imperfect verifiers misrank candidates and erroneously prune all valid paths. These issues are further exacerbated in challenging and out-of-distribution problems, restricting search effectiveness. To mitigate verifier failures, we explore reducing reliance on verifiers and conduct preliminary investigations using two simple methods. Our findings reveal fundamental limitations in verifier-guided search and suggest future directions.

Authorship identification has proven unsettlingly effective in inferring the identity of the author of an unsigned document, even when sensitive personal information has been carefully omitted. In the digital era, individuals leave a lasting digital footprint through their written content, whether it is posted on social media, stored on their employer's computers, or located elsewhere. When individuals need to communicate publicly yet wish to remain anonymous, there is little available to protect them from unwanted authorship identification. This unprecedented threat to privacy is evident in scenarios such as whistle-blowing. Proposed defenses against authorship identification attacks primarily aim to obfuscate one's writing style, thereby making it unlinkable to their pre-existing writing, while concurrently preserving the original meaning and grammatical integrity. The presented work offers a comprehensive review of the advancements in this research area spanning over the past two decades and beyond. It emphasizes the methodological frameworks of modification and generation-based strategies devised to evade authorship identification attacks, highlighting joint efforts from the differential privacy community. Limitations of current research are discussed, with a spotlight on open challenges and potential research avenues.

Artificial Intelligence (AI) is starting to transform the research process as we know it by automating the discovery of new solutions. Given a task, the typical AI-driven approach is (i) to generate a set of diverse solutions, and then (ii) to verify these solutions and select one that solves the problem. Crucially, this approach assumes the existence of a reliable verifier, i.e., one that can accurately determine whether a solution solves the given problem. We argue that systems research, long focused on designing and evaluating new performance-oriented algorithms, is particularly well-suited for AI-driven solution discovery. This is because system performance problems naturally admit reliable verifiers: solutions are typically implemented in real systems or simulators, and verification reduces to running these software artifacts against predefined workloads and measuring performance. We term this approach as AI-Driven Research for Systems (ADRS), which iteratively generates, evaluates, and refines solutions. Using penEvolve, an existing open-source ADRS instance, we present case studies across diverse domains, including load balancing for multi-region cloud scheduling, Mixture-of-Experts inference, LLM-based SQL queries, and transaction scheduling. In multiple instances, ADRS discovers algorithms that outperform state-of-the-art human designs (e.g., achieving up to 5.0x runtime improvements or 50% cost reductions). We distill best practices for guiding algorithm evolution, from prompt design to evaluator construction, for existing frameworks. We then discuss the broader implications for the systems community: as AI assumes a central role in algorithm design, we argue that human researchers will increasingly focus on problem formulation and strategic guidance. Our results highlight both the disruptive potential and the urgent need to adapt systems research practices in the age of AI.

The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous studies to automate formalization focused on powerful search algorithms, no attempts were made to take advantage of available informal proofs. In this work, we introduce Draft, Sketch, and Prove (DSP), a method that maps informal proofs to formal proof sketches, and uses the sketches to guide an automated prover by directing its search to easier sub-problems. We investigate two relevant setups where informal proofs are either written by humans or generated by a language model. Our experiments and ablation studies show that large language models are able to produce well-structured formal sketches that follow the same reasoning steps as the informal proofs. Guiding an automated prover with these sketches enhances its performance from 20.9% to 39.3% on a collection of mathematical competition problems.

Reinforcement learning from verifiable rewards has emerged as a powerful technique for enhancing the complex reasoning abilities of Large Language Models (LLMs). However, these methods are fundamentally constrained by the ''learning cliff'' phenomenon: when faced with problems far beyond their current capabilities, models consistently fail, yielding a persistent zero-reward signal. In policy optimization algorithms like GRPO, this collapses the advantage calculation to zero, rendering these difficult problems invisible to the learning gradient and stalling progress. To overcome this, we introduce Scaf-GRPO (Scaffolded Group Relative Policy Optimization), a progressive training framework that strategically provides minimal guidance only when a model's independent learning has plateaued. The framework first diagnoses learning stagnation and then intervenes by injecting tiered in-prompt hints, ranging from abstract concepts to concrete steps, enabling the model to construct a valid solution by itself. Extensive experiments on challenging mathematics benchmarks demonstrate Scaf-GRPO's effectiveness, boosting the pass@1 score of the Qwen2.5-Math-7B model on the AIME24 benchmark by a relative 44.3% over a vanilla GRPO baseline. This result demonstrates our framework provides a robust and effective methodology for unlocking a model's ability to solve problems previously beyond its reach, a critical step towards extending the frontier of autonomous reasoning in LLM.

Machine learning models are often used to decide who will receive a loan, a job interview, or a public benefit. Standard techniques to build these models use features about people but overlook their actionability. In turn, models can assign predictions that are fixed, meaning that consumers who are denied loans, interviews, or benefits may be permanently locked out from access to credit, employment, or assistance. In this work, we introduce a formal testing procedure to flag models that assign fixed predictions that we call recourse verification. We develop machinery to reliably determine if a given model can provide recourse to its decision subjects from a set of user-specified actionability constraints. We demonstrate how our tools can ensure recourse and adversarial robustness in real-world datasets and use them to study the infeasibility of recourse in real-world lending datasets. Our results highlight how models can inadvertently assign fixed predictions that permanently bar access, and we provide tools to design algorithms that account for actionability when developing models.

Large reasoning models such as OpenAI o1 and DeepSeek-R1 have achieved remarkable performance in the domain of reasoning. A key component of their training is the incorporation of verifiable rewards within reinforcement learning (RL). However, existing reward benchmarks do not evaluate reference-based reward systems, leaving researchers with limited understanding of the accuracy of verifiers used in RL. In this paper, we introduce two benchmarks, VerifyBench and VerifyBench-Hard, designed to assess the performance of reference-based reward systems. These benchmarks are constructed through meticulous data collection and curation, followed by careful human annotation to ensure high quality. Current models still show considerable room for improvement on both VerifyBench and VerifyBench-Hard, especially smaller-scale models. Furthermore, we conduct a thorough and comprehensive analysis of evaluation results, offering insights for understanding and developing reference-based reward systems. Our proposed benchmarks serve as effective tools for guiding the development of verifier accuracy and the reasoning capabilities of models trained via RL in reasoning tasks.

Qiskit is an open-source quantum computing framework that allows users to design, simulate, and run quantum circuits on real quantum hardware. We explore post-training techniques for LLMs to assist in writing Qiskit code. We introduce quantum verification as an effective method for ensuring code quality and executability on quantum hardware. To support this, we developed a synthetic data pipeline that generates quantum problem-unit test pairs and used it to create preference data for aligning LLMs with DPO. Additionally, we trained models using GRPO, leveraging quantum-verifiable rewards provided by the quantum hardware. Our best-performing model, combining DPO and GRPO, surpasses the strongest open-source baselines on the challenging Qiskit-HumanEval-hard benchmark.

Trustworthy verifiers are essential for the success of reinforcement learning with verifiable reward (RLVR), which is the core methodology behind various large reasoning models such as DeepSeek-R1. In complex domains like mathematical reasoning, rule-based verifiers have been widely adopted in previous works to train strong reasoning models. However, the reliability of these verifiers and their impact on the RL training process remain poorly understood. In this work, we take mathematical reasoning as a case study and conduct a comprehensive analysis of various verifiers in both static evaluation and RL training scenarios. First, we find that current open-source rule-based verifiers often fail to recognize equivalent answers presented in different formats across multiple commonly used mathematical datasets, resulting in non-negligible false negative rates. This limitation adversely affects RL training performance and becomes more pronounced as the policy model gets stronger. Subsequently, we investigate model-based verifiers as a potential solution to address these limitations. While the static evaluation shows that model-based verifiers achieve significantly higher verification accuracy, further analysis and RL training results imply that they are highly susceptible to hacking, where they misclassify certain patterns in responses as correct (i.e., false positives). This vulnerability is exploited during policy model optimization, leading to artificially inflated rewards. Our findings underscore the unique risks inherent to both rule-based and model-based verifiers, aiming to offer valuable insights to develop more robust reward systems in reinforcement learning.

Recent advances have shown that scaling test-time computation enables large language models (LLMs) to solve increasingly complex problems across diverse domains. One effective paradigm for test-time scaling (TTS) involves LLM generators producing multiple solution candidates, with LLM verifiers assessing the correctness of these candidates without reference answers. In this paper, we study generative verifiers, which perform verification by generating chain-of-thought (CoT) reasoning followed by a binary verdict. We systematically analyze verification dynamics across three dimensions - problem difficulty, generator capability, and verifier generation capability - with empirical studies on 12 benchmarks across mathematical reasoning, knowledge, and natural language reasoning tasks using 14 open-source models (2B to 72B parameter range) and GPT-4o. Our experiments reveal three key findings about verification effectiveness: (1) Easy problems allow verifiers to more reliably certify correct responses; (2) Weak generators produce errors that are easier to detect than strong generators; (3) Verification ability is generally correlated with the verifier's own problem-solving capability, but this relationship varies with problem difficulty. These findings reveal opportunities to optimize basic verification strategies in TTS applications. First, given the same verifier, some weak generators can nearly match stronger ones in post-verification TTS performance (e.g., the Gemma2-9B to Gemma2-27B performance gap shrinks by 75.5%). Second, we identify cases where strong verifiers offer limited advantage over weak ones, as both fail to provide meaningful verification gains, suggesting that verifier scaling alone cannot overcome fundamental verification challenges.

One way to increase confidence in the outputs of Large Language Models (LLMs) is to support them with reasoning that is clear and easy to check -- a property we call legibility. We study legibility in the context of solving grade-school math problems and show that optimizing chain-of-thought solutions only for answer correctness can make them less legible. To mitigate the loss in legibility, we propose a training algorithm inspired by Prover-Verifier Game from Anil et al. (2021). Our algorithm iteratively trains small verifiers to predict solution correctness, "helpful" provers to produce correct solutions that the verifier accepts, and "sneaky" provers to produce incorrect solutions that fool the verifier. We find that the helpful prover's accuracy and the verifier's robustness to adversarial attacks increase over the course of training. Furthermore, we show that legibility training transfers to time-constrained humans tasked with verifying solution correctness. Over course of LLM training human accuracy increases when checking the helpful prover's solutions, and decreases when checking the sneaky prover's solutions. Hence, training for checkability by small verifiers is a plausible technique for increasing output legibility. Our results suggest legibility training against small verifiers as a practical avenue for increasing legibility of large LLMs to humans, and thus could help with alignment of superhuman models.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing Large Language Models (LLMs), exemplified by the success of OpenAI's o-series. In RLVR, rewards are derived from verifiable signals-such as passing unit tests in code generation or matching correct answers in mathematical reasoning. While effective, this requirement largely confines RLVR to domains with automatically checkable outcomes. To overcome this, we extend the RLVR paradigm to open-ended tasks by integrating rubric-based rewards, where carefully designed rubrics serve as structured, model-interpretable criteria for automatic scoring of subjective outputs. We construct, to our knowledge, the largest rubric reward system to date, with over 10,000 rubrics from humans, LLMs, or a hybrid human-LLM collaboration. Implementing rubric-based RL is challenging; we tackle these issues with a clear framework and present an open-sourced Qwen-30B-A3B model with notable gains: 1) With only 5K+ samples, our system improves by +5.2% on open-ended benchmarks (especially humanities), outperforming a 671B DeepSeek-V3 model by +2.4%, while preserving general and reasoning abilities. 2) Our method provides fine-grained stylistic control, using rubrics as anchors to mitigate the "AI-like" tone and produce more human-like, expressive responses. We share key lessons in rubric construction, data selection, and training, and discuss limitations and future releases.

Claim verification is critical for enhancing digital literacy. However, the state-of-the-art single-LLM methods struggle with complex claim verification that involves multi-faceted evidences. Inspired by real-world fact-checking practices, we propose DebateCV, the first claim verification framework that adopts a debate-driven methodology using multiple LLM agents. In our framework, two Debaters take opposing stances on a claim and engage in multi-round argumentation, while a Moderator evaluates the arguments and renders a verdict with justifications. To further improve the performance of the Moderator, we introduce a novel post-training strategy that leverages synthetic debate data generated by the zero-shot DebateCV, effectively addressing the scarcity of real-world debate-driven claim verification data. Experimental results show that our method outperforms existing claim verification methods under varying levels of evidence quality. Our code and dataset are publicly available at https://anonymous.4open.science/r/DebateCV-6781.

We introduce our Leanabell-Prover-V2, a 7B large language models (LLMs) that can produce formal theorem proofs in Lean 4, with verifier-integrated Long Chain-of-Thoughts (CoT). Following our previous work Leanabell-Prover-V1, we continual to choose to posttrain existing strong prover models for further performance improvement. In our V2 version, we mainly upgrade the Reinforcement Learning (RL) with feedback provided by the Lean 4 verifier. Crucially, verifier feedback, such as indicating success or detailing specific errors, allows the LLM to become ``self-aware'' of the correctness of its own reasoning process and learn to reflexively correct errors. Leanabell-Prover-V2 directly optimizes LLM reasoning trajectories with multi-turn verifier interactions, together with feedback token masking for stable RL training and a simple reward strategy. Experiments show that Leanabell-Prover-V2 improves performance by 3.2% (pass@128) with Kimina-Prover-Preview-Distill-7B and 2.0% (pass@128) with DeepSeek-Prover-V2-7B on the MiniF2F test set. The source codes, curated data and models are available at: https://github.com/Leanabell-LM/Leanabell-Prover-V2.

Signature synthesis is a computation technique that generates artificial specimens which can support decision making in automatic signature verification. A lot of work has been dedicated to this subject, which centres on synthesizing dynamic and static two-dimensional handwriting on canvas. This paper proposes a framework to generate synthetic 3D on-air signatures exploiting the lognormality principle, which mimics the complex neuromotor control processes at play as the fingertip moves. Addressing the usual cases involving the development of artificial individuals and duplicated samples, this paper contributes to the synthesis of: (1) the trajectory and velocity of entirely 3D new signatures; (2) kinematic information when only the 3D trajectory of the signature is known, and (3) duplicate samples of 3D real signatures. Validation was conducted by generating synthetic 3D signature databases mimicking real ones and showing that automatic signature verifications of genuine and skilled forgeries report performances similar to those of real and synthetic databases. We also observed that training 3D automatic signature verifiers with duplicates can reduce errors. We further demonstrated that our proposal is also valid for synthesizing 3D air writing and gestures. Finally, a perception test confirmed the human likeness of the generated specimens. The databases generated are publicly available, only for research purposes, at .

Generating high-quality stories spanning thousands of tokens requires competency across a variety of skills, from tracking plot and character arcs to keeping a consistent and engaging style. Due to the difficulty of sourcing labeled datasets and precise quality measurements, most work using large language models (LLMs) for long-form story generation uses combinations of hand-designed prompting techniques to elicit author-like behavior. This is a manual process that is highly dependent on the specific story-generation task. Motivated by the recent success of applying RL with Verifiable Rewards to domains like math and coding, we propose a general story-generation task (Next-Chapter Prediction) and a reward formulation (Verified Rewards via Completion Likelihood Improvement) that allows us to use an unlabeled book dataset as a learning signal for reasoning. We learn to reason over a story's condensed information and generate a detailed plan for the next chapter. Our reasoning is evaluated via the chapters it helps a story-generator create, and compared against non-trained and supervised finetuning (SFT) baselines. Pairwise human judgments reveal the chapters our learned reasoning produces are preferred across almost all metrics, and the effect is more pronounced in Scifi and Fantasy genres.

We propose CoT-Self-Instruct, a synthetic data generation method that instructs LLMs to first reason and plan via Chain-of-Thought (CoT) based on the given seed tasks, and then to generate a new synthetic prompt of similar quality and complexity for use in LLM training, followed by filtering for high-quality data with automatic metrics. In verifiable reasoning, our synthetic data significantly outperforms existing training datasets, such as s1k and OpenMathReasoning, across MATH500, AMC23, AIME24 and GPQA-Diamond. For non-verifiable instruction-following tasks, our method surpasses the performance of human or standard self-instruct prompts on both AlpacaEval 2.0 and Arena-Hard.

Drafting-then-verifying decoding methods such as speculative decoding are widely adopted training-free methods to accelerate the inference of large language models (LLMs). Instead of employing an autoregressive process to decode tokens sequentially, speculative decoding initially creates drafts with an efficient small model. Then LLMs are required to conduct verification and correction in a non-autoregressive fashion to minimize time overhead. Generating longer drafts can lead to even more significant speedups once verified, but also incurs substantial trial and error costs if it fails. Suffering from the high verification failure probability, existing decoding methods cannot draft too much content for verification at one time, achieving sub-optimal inference acceleration. In this paper, we introduce Ouroboros, which constructs a phrase candidate pool from the verification process of LLMs to provide candidates for draft generation of the small model. Thereby, Ouroboros can further improve the efficiency and effectiveness of the initial drafts. The experimental results on typical text generation tasks show that Ouroboros achieves speedups of up to 1.9x and 2.8x compared to lookahead decoding and speculative decoding, respectively. The source code of Ouroboros is available at https://github.com/thunlp/Ouroboros.

Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the proofs in formal language can be challenging for humans and machines. The miniF2F benchmark has 20 IMO problems in its test set, yet formal proofs are available only for 6 of these problems (3 of which are only written by mathematicians). The model with best accuracy can only prove 2 of these 20 IMO problems, from 1950s and 60s, while its training set is a secret. In this work, we write complete, original formal proofs for the remaining IMO problems in Lean along with 3 extra problems from IMO 2022 and 2023. This effort expands the availability of proof currently in the public domain by creating 5,880 lines of Lean proof. The goal of the paper is to pave the way for developing AI models that can automatically write the formal proofs for all the IMO problems in miniF2F and beyond by providing an evaluation benchmark. In this pursuit, we devise a method to decompose the proofs of these problems into their building blocks, constructing a dataset of 1,329 lemmas with more than 40k lines of Lean code. These lemmas are not trivial, yet they are approachable, providing the opportunity to evaluate and diagnose the failures and successes of AI models. We evaluate the ability of the SOTA LLMs on our dataset and analyze their success and failure modes from different perspectives. Our dataset and code is available at: https://github.com/roozbeh-yz/IMO-Steps.

Recent advances in large language models (LLMs) have fueled the vision of automated scientific discovery, often called AI Co-Scientists. To date, prior work casts these systems as generative co-authors responsible for crafting hypotheses, synthesizing code, or drafting manuscripts. In this work, we explore a complementary application: using LLMs as verifiers to automate the academic verification of scientific manuscripts. To that end, we introduce SPOT, a dataset of 83 published papers paired with 91 errors significant enough to prompt errata or retraction, cross-validated with actual authors and human annotators. Evaluating state-of-the-art LLMs on SPOT, we find that none surpasses 21.1\% recall or 6.1\% precision (o3 achieves the best scores, with all others near zero). Furthermore, confidence estimates are uniformly low, and across eight independent runs, models rarely rediscover the same errors, undermining their reliability. Finally, qualitative analysis with domain experts reveals that even the strongest models make mistakes resembling student-level misconceptions derived from misunderstandings. These findings highlight the substantial gap between current LLM capabilities and the requirements for dependable AI-assisted academic verification.

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis. In this paper, we present a combination of LLMs and static analysis to synthesize invariants, assertions, and other proof structures for a Rust-based formal verification framework called Verus. In a few-shot setting, LLMs demonstrate impressive logical ability in generating postconditions and loop invariants, especially when analyzing short code snippets. However, LLMs lack the ability to retain and propagate context information, a strength of traditional static analysis. Based on these observations, we developed a prototype based on OpenAI's GPT-4 model. Our prototype decomposes the verification task into multiple smaller ones, iteratively queries GPT-4, and combines its output with lightweight static analysis. We evaluated the prototype with a developer in the automation loop on 20 vector-manipulating programs. The results demonstrate that it significantly reduces human effort in writing entry-level proof code.

Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem proving is hindered by a lack of training data. To address this issue, we introduce an approach to generate extensive Lean 4 proof data derived from high-school and undergraduate-level mathematical competition problems. This approach involves translating natural language problems into formal statements, filtering out low-quality statements, and generating proofs to create synthetic data. After fine-tuning the DeepSeekMath 7B model on this synthetic dataset, which comprises 8 million formal statements with proofs, our model achieved whole-proof generation accuracies of 46.3% with 64 samples and 52% cumulatively on the Lean 4 miniF2F test, surpassing the baseline GPT-4 at 23.0% with 64 samples and a tree search reinforcement learning method at 41.0%. Additionally, our model successfully proved 5 out of 148 problems in the Lean 4 Formalized International Mathematical Olympiad (FIMO) benchmark, while GPT-4 failed to prove any. These results demonstrate the potential of leveraging large-scale synthetic data to enhance theorem-proving capabilities in LLMs. Both the synthetic dataset and the model will be made available to facilitate further research in this promising field.

Reinforcement Learning with Verifiable Rewards (RLVR) has improved the reasoning abilities of Large Language Models (LLMs) by using rule-based binary feedback, helping to mitigate reward hacking. However, current RLVR methods typically treat whole responses as single actions, assigning the same reward to every token. This coarse-grained feedback hampers precise credit assignment, making it hard for models to identify which reasoning steps lead to success or failure, and often results in suboptimal policies and inefficient learning. Methods like PPO provide credit assignment through value estimation, but often yield inaccurate and unverifiable signals due to limited sampling. On the other hand, methods using Process Reward Models can provide step-by-step judgments for each reasoning step, but they require high-quality process supervision labels and are time-consuming when applied in online reinforcement learning (RL). To overcome these limitations, we introduce a simple but efficient method Credit Assignment Policy Optimization (CAPO). Given a reasoning response rollout from the policy model, CAPO directly leverages an off-the-shelf, general-purpose LLM as a Generative Process Reward Model (LLM-as-GenPRM) to generate all step-wise critique by one pass, thereby providing verifiable token-level rewards to refine the tokens that were originally assigned identical rule-based rewards. This enables more fine-grained credit assignment in an effective way. Furthermore, to enhance the accuracy and robustness of CAPO, we employ voting mechanisms that scale with the number of generated critiques. Extensive experiments using different backbones like Llama and Qwen models and in different sizes show that CAPO consistently outperforms supervised learning-based and RL-based fine-tuning methods across six challenging mathematical benchmarks and three out-of-domain benchmarks.

There is a strong association between the quality of the writing in a resume for new labor market entrants and whether those entrants are ultimately hired. We show that this relationship is, at least partially, causal: a field experiment in an online labor market was conducted with nearly half a million jobseekers in which a treated group received algorithmic writing assistance. Treated jobseekers experienced an 8% increase in the probability of getting hired. Contrary to concerns that the assistance is taking away a valuable signal, we find no evidence that employers were less satisfied. We present a model in which better writing is not a signal of ability but helps employers ascertain ability, which rationalizes our findings.

Automated essay scoring (AES) involves predicting a score that reflects the writing quality of an essay. Most existing AES systems produce only a single overall score. However, users and L2 learners expect scores across different dimensions (e.g., vocabulary, grammar, coherence) for English essays in real-world applications. To address this need, we have developed two models that automatically score English essays across multiple dimensions by employing fine-tuning and other strategies on two large datasets. The results demonstrate that our systems achieve impressive performance in evaluation using three criteria: precision, F1 score, and Quadratic Weighted Kappa. Furthermore, our system outperforms existing methods in overall scoring.

AI-generated text is proliferating across domains, from creative writing and journalism to marketing content and scientific articles. Models can follow user-provided instructions to generate coherent and grammatically correct outputs but in this work, we study a more fundamental question: how do we evaluate and improve the writing quality of AI-generated text? Writing quality assessment has received less attention from the community, in part because it is fundamentally subjective and requires expertise. We first introduce the Writing Quality Benchmark (WQ) by consolidating five writing-preference datasets into 4,729 writing quality judgments. Our experiments show that most of the competitive baselines, including state-of-the-art LLMs that excel at reasoning tasks, barely outperform random baselines on WQ. We then train specialized Writing Quality Reward Models (WQRM) of various sizes for writing quality assessment that demonstrate strong generalization on four out-of-distribution test sets and 74% accuracy on the WQ benchmark. To further show WQRM's practical benefits during inference, we leverage additional test-time compute to generate and rank multiple candidate revisions, allowing us to select higher-quality outputs from an initial draft. Human evaluation with 9 experienced writers confirm that WQRM-based selection produces writing samples preferred by experts 66% overall, and 72.2% when the reward gap is larger than 1 point. We release our datasets and models to encourage community engagement with writing quality assessment and development of AI writing systems better aligned with human preferences.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

The progress of AI is bottlenecked by the quality of evaluation, and powerful LLM-as-a-Judge models have proved to be a core solution. Improved judgment ability is enabled by stronger chain-of-thought reasoning, motivating the need to find the best recipes for training such models to think. In this work we introduce J1, a reinforcement learning approach to training such models. Our method converts both verifiable and non-verifiable prompts to judgment tasks with verifiable rewards that incentivize thinking and mitigate judgment bias. In particular, our approach outperforms all other existing 8B or 70B models when trained at those sizes, including models distilled from DeepSeek-R1. J1 also outperforms o1-mini, and even R1 on some benchmarks, despite training a smaller model. We provide analysis and ablations comparing Pairwise-J1 vs Pointwise-J1 models, offline vs online training recipes, reward strategies, seed prompts, and variations in thought length and content. We find that our models make better judgments by learning to outline evaluation criteria, comparing against self-generated reference answers, and re-evaluating the correctness of model responses.

Developing custom reasoning models via Reinforcement Learning (RL) that can incorporate organization-specific knowledge has great potential to address problems faced by enterprise customers. In many of these problems, the reward function is verifiable, a setting termed RL with Verifiable Rewards (RLVR). We apply RLVR to a popular data science benchmark called BIRD that measures the ability of an AI agent to convert a natural language query for a database to SQL executions. We apply a simple and general-purpose training recipe involving careful prompt and model selection, a warm-up stage using our offline RL approach called TAO, followed by rigorous online RLVR training. With no additional training data beyond the BIRD training set and no use of proprietary models, our very first submission to the BIRD leaderboard reached state-of-the-art accuracy on the private test set: 73.56% without self-consistency and 75.68% with self-consistency. In the latter case, our model also required fewer generations than the second-best approach. While BIRD is only a proxy task, the simplicity of our framework makes it broadly applicable to enterprise domains such as business intelligence, data science, and coding.

Large reasoning models (LRMs) have recently achieved significant progress in complex reasoning tasks, aided by reinforcement learning with verifiable rewards. However, LRMs often suffer from overthinking, expending excessive computation on simple problems and reducing efficiency. Existing efficient reasoning methods typically require accurate task assessment to preset token budgets or select reasoning modes, which limits their flexibility and reliability. In this work, we revisit the essence of overthinking and identify that encouraging effective steps while penalizing ineffective ones is key to its solution. To this end, we propose a novel rule-based verifiable stepwise reward mechanism (VSRM), which assigns rewards based on the performance of intermediate states in the reasoning trajectory. This approach is intuitive and naturally fits the step-by-step nature of reasoning tasks. We conduct extensive experiments on standard mathematical reasoning benchmarks, including AIME24 and AIME25, by integrating VSRM with PPO and Reinforce++. Results show that our method achieves substantial output length reduction while maintaining original reasoning performance, striking an optimal balance between efficiency and accuracy. Further analysis of overthinking frequency and pass@k score before and after training demonstrates that our approach in deed effectively suppresses ineffective steps and encourages effective reasoning, fundamentally alleviating the overthinking problem. All code will be released upon acceptance.

Mathematical verfier achieves success in mathematical reasoning tasks by validating the correctness of solutions. However, existing verifiers are trained with binary classification labels, which are not informative enough for the model to accurately assess the solutions. To mitigate the aforementioned insufficiency of binary labels, we introduce step-wise natural language feedbacks as rationale labels (i.e., the correctness of the current step and the explanations). In this paper, we propose Math-Minos, a natural language feedback enhanced verifier by constructing automatically-generated training data and a two-stage training paradigm for effective training and efficient inference. Our experiments reveal that a small set (30k) of natural language feedbacks can significantly boost the performance of the verifier by the accuracy of 1.6\% (86.6\% rightarrow 88.2\%) on GSM8K and 0.8\% (37.8\% rightarrow 38.6\%) on MATH. We have released our code and data for further exploration.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs). Unlike supervised learning, it updates the model using both correct and incorrect samples via policy gradients. To better understand its mechanism, we decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR), respectively. We train Qwen2.5-Math-7B and Qwen3-4B on a mathematical reasoning dataset and uncover a surprising result: training with only negative samples -- without reinforcing correct responses -- can be highly effective: it consistently improves performance over the base model across the entire Pass@k spectrum (k up to 256), often matching or surpassing PPO and GRPO. In contrast, reinforcing only correct responses improves Pass@1 but degrades performance at higher k, due to reduced diversity. These inference-scaling trends highlight that solely penalizing incorrect responses may contribute more to performance than previously recognized. Through gradient analysis, we show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs. It refines the model's existing knowledge rather than introducing entirely new behaviors. Building on this insight, we propose a simple variant of the RL objective that upweights NSR, and show that it consistently improves overall Pass@k performance on MATH, AIME 2025, and AMC23. Our code is available at https://github.com/TianHongZXY/RLVR-Decomposed.

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

We present a novel inference scheme, self-speculative decoding, for accelerating Large Language Models (LLMs) without the need for an auxiliary model. This approach is characterized by a two-stage process: drafting and verification. The drafting stage generates draft tokens at a slightly lower quality but more quickly, which is achieved by selectively skipping certain intermediate layers during drafting Subsequently, the verification stage employs the original LLM to validate those draft output tokens in one forward pass. This process ensures the final output remains identical to that produced by the unaltered LLM, thereby maintaining output quality. The proposed method requires no additional neural network training and no extra memory footprint, making it a plug-and-play and cost-effective solution for inference acceleration. Benchmarks with LLaMA-2 and its fine-tuned models demonstrated a speedup up to 1.73times.

Research on offline signature verification has explored a large variety of methods on multiple signature datasets, which are collected under controlled conditions. However, these datasets may not fully reflect the characteristics of the signatures in some practical use cases. Real-world signatures extracted from the formal documents may contain different types of occlusions, for example, stamps, company seals, ruling lines, and signature boxes. Moreover, they may have very high intra-class variations, where even genuine signatures resemble forgeries. In this paper, we address a real-world writer independent offline signature verification problem, in which, a bank's customers' transaction request documents that contain their occluded signatures are compared with their clean reference signatures. Our proposed method consists of two main components, a stamp cleaning method based on CycleGAN and signature representation based on CNNs. We extensively evaluate different verification setups, fine-tuning strategies, and signature representation approaches to have a thorough analysis of the problem. Moreover, we conduct a human evaluation to show the challenging nature of the problem. We run experiments both on our custom dataset, as well as on the publicly available Tobacco-800 dataset. The experimental results validate the difficulty of offline signature verification on real-world documents. However, by employing the stamp cleaning process, we improve the signature verification performance significantly.

In this paper, we introduce BMMR, a large-scale bilingual, multimodal, multi-disciplinary reasoning dataset for the community to develop and evaluate large multimodal models (LMMs). BMMR comprises 110k college-level questions spanning 300 UNESCO-defined subjects, spanning diverse formats-multiple-choice, fill-in-the-blank, and open-ended QA-and sourced from both print and digital media such as books, exams, and quizzes. All data are curated and filtered via a human-in-the-loop and scalable framework, and each instance is paired with a high-quality reasoning path. The dataset is organized into two parts: BMMR-Eval that comprises 20,458 high-quality instances to comprehensively assess LMMs' knowledge and reasoning across multiple disciplines in both Chinese and English; and BMMR-Train that contains 88,991 instances to support further research and development, extending the current focus on mathematical reasoning to diverse disciplines and domains. In addition, we propose the process-based multi-discipline verifier (i.e., BMMR-Verifier) for accurate and fine-grained evaluation of reasoning paths. Extensive experiments on 24 models reveal that (i) even SOTA models (e.g., o3 and Gemini-2.5-Pro) leave substantial headroom on BMMR-Eval; (ii) reasoning models exhibit discipline bias and outperform LMMs only on specific subjects; (iii) open-source models still trail their proprietary counterparts; and (iv) fine-tuning on BMMR-Train narrows this gap. Additionally, we conduct reasoning-chain analyses using BMMR-Verifier and other in-depth studies, uncovering the challenges LMMs currently face in multidisciplinary reasoning. We will release the data, and we hope our work can offer insights and contributions to the community.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess these paths. However, existing verifiers, typically trained on binary-labeled reasoning paths, fail to fully utilize the relative merits of intermediate steps, thereby limiting the effectiveness of the feedback provided. To overcome this limitation, we propose Tree-based Preference Learning Verifier (Tree-PLV), a novel approach that constructs reasoning trees via a best-first search algorithm and collects step-level paired data for preference training. Compared to traditional binary classification, step-level preferences more finely capture the nuances between reasoning steps, allowing for a more precise evaluation of the complete reasoning path. We empirically evaluate Tree-PLV across a range of arithmetic and commonsense reasoning tasks, where it significantly outperforms existing benchmarks. For instance, Tree-PLV achieved substantial performance gains over the Mistral-7B self-consistency baseline on GSM8K (67.55% to 82.79%), MATH (17.00% to 26.80%), CSQA (68.14% to 72.97%), and StrategyQA (82.86% to 83.25%).Additionally, our study explores the appropriate granularity for applying preference learning, revealing that step-level guidance provides feedback that better aligns with the evaluation of the reasoning process.

As Large Language Models (LLMs) become more pervasive across various users and scenarios, identifying potential issues when using these models becomes essential. Examples of such issues include: bias, inconsistencies, and hallucination. Although auditing the LLM for these problems is often warranted, such a process is neither easy nor accessible for most. An effective method is to probe the LLM using different versions of the same question. This could expose inconsistencies in its knowledge or operation, indicating potential for bias or hallucination. However, to operationalize this auditing method at scale, we need an approach to create those probes reliably and automatically. In this paper we propose the LLMAuditor framework which is an automatic, and scalable solution, where one uses a different LLM along with human-in-the-loop (HIL). This approach offers verifiability and transparency, while avoiding circular reliance on the same LLM, and increasing scientific rigor and generalizability. Specifically, LLMAuditor includes two phases of verification using humans: standardized evaluation criteria to verify responses, and a structured prompt template to generate desired probes. A case study using questions from the TruthfulQA dataset demonstrates that we can generate a reliable set of probes from one LLM that can be used to audit inconsistencies in a different LLM. This process is enhanced by our structured prompt template with HIL, which not only boosts the reliability of our approach in auditing but also yields the delivery of less hallucinated results. The novelty of our research stems from the development of a comprehensive, general-purpose framework that includes a HIL verified prompt template for auditing responses generated by LLMs.

Writing is a cognitively demanding task involving continuous decision-making, heavy use of working memory, and frequent switching between multiple activities. Scholarly writing is particularly complex as it requires authors to coordinate many pieces of multiform knowledge. To fully understand writers' cognitive thought process, one should fully decode the end-to-end writing data (from individual ideas to final manuscript) and understand their complex cognitive mechanisms in scholarly writing. We introduce ScholaWrite dataset, the first-of-its-kind keystroke logs of an end-to-end scholarly writing process for complete manuscripts, with thorough annotations of cognitive writing intentions behind each keystroke. Our dataset includes LaTeX-based keystroke data from five preprints with nearly 62K total text changes and annotations across 4 months of paper writing. ScholaWrite shows promising usability and applications (e.g., iterative self-writing) for the future development of AI writing assistants for academic research, which necessitate complex methods beyond LLM prompting. Our experiments clearly demonstrated the importance of collection of end-to-end writing data, rather than the final manuscript, for the development of future writing assistants to support the cognitive thinking process of scientists. Our de-identified dataset, demo, and code repository are available on our project page.

State-of-the-art language models can match human performance on many tasks, but they still struggle to robustly perform multi-step mathematical reasoning. To diagnose the failures of current models and support research, we introduce GSM8K, a dataset of 8.5K high quality linguistically diverse grade school math word problems. We find that even the largest transformer models fail to achieve high test performance, despite the conceptual simplicity of this problem distribution. To increase performance, we propose training verifiers to judge the correctness of model completions. At test time, we generate many candidate solutions and select the one ranked highest by the verifier. We demonstrate that verification significantly improves performance on GSM8K, and we provide strong empirical evidence that verification scales more effectively with increased data than a finetuning baseline.

Digital identity is unsolved: after many years of research there is still no trusted communication over the Internet. To provide identity within the context of mutual distrust, this paper presents a blockchain-based digital identity solution. Without depending upon a single trusted third party, the proposed solution achieves passport-level legally valid identity. This solution for making identities Self-Sovereign, builds on a generic provable claim model for which attestations of truth from third parties need to be collected. The claim model is then shown to be both blockchain structure and proof method agnostic. Four different implementations in support of these two claim model properties are shown to offer sub-second performance for claim creation and claim verification. Through the properties of Self-Sovereign Identity, legally valid status and acceptable performance, our solution is considered to be fit for adoption by the general public.

The widespread adoption of deep neural networks (DNNs) requires efficient techniques for verifying their safety. DNN verifiers are complex tools, which might contain bugs that could compromise their soundness and undermine the reliability of the verification process. This concern can be mitigated using proofs: artifacts that are checkable by an external and reliable proof checker, and which attest to the correctness of the verification process. However, such proofs tend to be extremely large, limiting their use in many scenarios. In this work, we address this problem by minimizing proofs of unsatisfiability produced by DNN verifiers. We present algorithms that remove facts which were learned during the verification process, but which are unnecessary for the proof itself. Conceptually, our method analyzes the dependencies among facts used to deduce UNSAT, and removes facts that did not contribute. We then further minimize the proof by eliminating remaining unnecessary dependencies, using two alternative procedures. We implemented our algorithms on top of a proof producing DNN verifier, and evaluated them across several benchmarks. Our results show that our best-performing algorithm reduces proof size by 37%-82% and proof checking time by 30%-88%, while introducing a runtime overhead of 7%-20% to the verification process itself.

We present Aryabhata 1.0, a compact 7B parameter math reasoning model optimized for the Indian academic exam, the Joint Entrance Examination (JEE). Despite rapid progress in large language models (LLMs), current models often remain unsuitable for educational use. Aryabhata 1.0 is built by merging strong open-weight reasoning models, followed by supervised fine-tuning (SFT) with curriculum learning on verified chain-of-thought (CoT) traces curated through best-of-n rejection sampling. To further boost performance, we apply reinforcement learning with verifiable rewards (RLVR) using A2C objective with group-relative advantage estimation alongwith novel exploration strategies such as Adaptive Group Resizing and Temperature Scaling. Evaluated on both in-distribution (JEE Main 2025) and out-of-distribution (MATH, GSM8K) benchmarks, Aryabhata outperforms existing models in accuracy and efficiency, while offering pedagogically useful step-by-step reasoning. We release Aryabhata as a foundation model to advance exam-centric, open-source small language models. This marks our first open release for community feedback (https://huggingface.co/PhysicsWallahAI/Aryabhata-1.0{Aryabhata 1.0 on Hugging Face}); PW is actively training future models to further improve learning outcomes for students.

Recent advances in large reasoning models highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising method for enhancing AI's capabilities, particularly in solving complex logical tasks. However, it remains unclear whether RLVR truly expands a model's reasoning boundary or merely amplifies high-reward outputs that the base model already knows for improved precision. This study presents a theoretical and empirical investigation that provides fresh insights into the potential limits of RLVR. First, we offer a new theoretical perspective that RLVR is constrained by the base model's support-unable to sample solutions with zero initial probability-and operates as a conservative reweighting mechanism that may restrict the discovery of entirely original solutions. We also identify an entropy-reward tradeoff: while RLVR reliably enhances precision, it may progressively narrow exploration and potentially overlook correct yet underrepresented solutions. Extensive empirical experiments validate that while RLVR consistently improves pass@1, the shrinkage of empirical support generally outweighs the expansion of empirical support under larger sampling budgets, failing to recover correct answers that were previously accessible to the base model. Interestingly, we also observe that while RLVR sometimes increases token-level entropy, resulting in greater uncertainty at each generation step, answer-level entropy declines, indicating that these seemingly more uncertain paths ultimately converge onto a smaller set of distinct answers. Taken together, these findings reveal potential limits of RLVR in extending reasoning horizons. Breaking this invisible leash may require future algorithmic innovations such as explicit exploration mechanisms or hybrid strategies that seed probability mass into underrepresented solution regions.

We contribute the largest publicly available dataset of naturally occurring factual claims for the purpose of automatic claim verification. It is collected from 26 fact checking websites in English, paired with textual sources and rich metadata, and labelled for veracity by human expert journalists. We present an in-depth analysis of the dataset, highlighting characteristics and challenges. Further, we present results for automatic veracity prediction, both with established baselines and with a novel method for joint ranking of evidence pages and predicting veracity that outperforms all baselines. Significant performance increases are achieved by encoding evidence, and by modelling metadata. Our best-performing model achieves a Macro F1 of 49.2%, showing that this is a challenging testbed for claim veracity prediction.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

Automated code generation with large language models has gained significant traction, but there remains no guarantee on the correctness of generated code. We aim to use formal verification to provide mathematical guarantees that the generated code is correct. However, generating formally verified code with LLMs is hindered by the scarcity of training data and the complexity of formal proofs. To tackle this challenge, we introduce AlphaVerus, a self-improving framework that bootstraps formally verified code generation by iteratively translating programs from a higher-resource language and leveraging feedback from a verifier. AlphaVerus operates in three phases: exploration of candidate translations, Treefinement -- a novel tree search algorithm for program refinement using verifier feedback, and filtering misaligned specifications and programs to prevent reward hacking. Through this iterative process, AlphaVerus enables a LLaMA-3.1-70B model to generate verified code without human intervention or model finetuning. AlphaVerus shows an ability to generate formally verified solutions for HumanEval and MBPP, laying the groundwork for truly trustworthy code-generation agents.

In domains with high stakes such as law, recruitment, and healthcare, learning models frequently rely on sensitive user data for inference, necessitating the complete set of features. This not only poses significant privacy risks for individuals but also demands substantial human effort from organizations to verify information accuracy. This paper asks whether it is necessary to use all input features for accurate predictions at inference time. The paper demonstrates that, in a personalized setting, individuals may only need to disclose a small subset of their features without compromising decision-making accuracy. The paper also provides an efficient sequential algorithm to determine the appropriate attributes for each individual to provide. Evaluations across various learning tasks show that individuals can potentially report as little as 10\% of their information while maintaining the same accuracy level as a model that employs the full set of user information.

It is important that consumers and regulators can verify the provenance of large neural models to evaluate their capabilities and risks. We introduce the concept of a "Proof-of-Training-Data": any protocol that allows a model trainer to convince a Verifier of the training data that produced a set of model weights. Such protocols could verify the amount and kind of data and compute used to train the model, including whether it was trained on specific harmful or beneficial data sources. We explore efficient verification strategies for Proof-of-Training-Data that are compatible with most current large-model training procedures. These include a method for the model-trainer to verifiably pre-commit to a random seed used in training, and a method that exploits models' tendency to temporarily overfit to training data in order to detect whether a given data-point was included in training. We show experimentally that our verification procedures can catch a wide variety of attacks, including all known attacks from the Proof-of-Learning literature.

The deployment of autonomous AI agents in sensitive domains, such as healthcare, introduces critical risks to safety, security, and privacy. These agents may deviate from user objectives, violate data handling policies, or be compromised by adversarial attacks. Mitigating these dangers necessitates a mechanism to formally guarantee that an agent's actions adhere to predefined safety constraints, a challenge that existing systems do not fully address. We introduce VeriGuard, a novel framework that provides formal safety guarantees for LLM-based agents through a dual-stage architecture designed for robust and verifiable correctness. The initial offline stage involves a comprehensive validation process. It begins by clarifying user intent to establish precise safety specifications. VeriGuard then synthesizes a behavioral policy and subjects it to both testing and formal verification to prove its compliance with these specifications. This iterative process refines the policy until it is deemed correct. Subsequently, the second stage provides online action monitoring, where VeriGuard operates as a runtime monitor to validate each proposed agent action against the pre-verified policy before execution. This separation of the exhaustive offline validation from the lightweight online monitoring allows formal guarantees to be practically applied, providing a robust safeguard that substantially improves the trustworthiness of LLM agents.

Existing Vision-Language Models often struggle with complex, multi-question reasoning tasks where partial correctness is crucial for effective learning. Traditional reward mechanisms, which provide a single binary score for an entire response, are too coarse to guide models through intricate problems with multiple sub-parts. To address this, we introduce StructVRM, a method that aligns multimodal reasoning with Structured and Verifiable Reward Models. At its core is a model-based verifier trained to provide fine-grained, sub-question-level feedback, assessing semantic and mathematical equivalence rather than relying on rigid string matching. This allows for nuanced, partial credit scoring in previously intractable problem formats. Extensive experiments demonstrate the effectiveness of StructVRM. Our trained model, Seed-StructVRM, achieves state-of-the-art performance on six out of twelve public multimodal benchmarks and our newly curated, high-difficulty STEM-Bench. The success of StructVRM validates that training with structured, verifiable rewards is a highly effective approach for advancing the capabilities of multimodal models in complex, real-world reasoning domains.

Reinforcement learning with verifiable rewards has significantly advanced reasoning in large language models (LLMs), but such signals remain coarse, offering only binary correctness feedback. This limitation often results in inefficiencies, including overly verbose reasoning and high computational cost, while existing solutions often compromise accuracy. To address this, we introduce self-aligned reward (SAR), a self-guided signal that complements verifiable rewards to encourage both reasoning accuracy and efficiency. SAR is defined as the relative perplexity difference between an answer conditioned on the query and the standalone answer, thereby favoring responses that are concise and query-specific. Quantitative analysis reveals that SAR reliably distinguishes answer quality: concise, correct answers score higher than redundant ones, and partially correct answers score higher than entirely incorrect ones. Evaluation on 4 models across 7 benchmarks shows that integrating SAR with prevalent RL algorithms like PPO and GRPO improves accuracy by 4%, while reducing inference cost by 30%. Further analysis demonstrates that SAR achieves a Pareto-optimal trade-off between correctness and efficiency compared to reward signals based on length or self-confidence. We also show that SAR shortens responses while preserving advanced reasoning behaviors, demonstrating its ability to suppress unnecessary elaboration without losing critical reasoning. These results highlight the promise of self-aligned reward as a fine-grained complement to verifiable rewards, paving the way for more efficient and effective LLM training.

Claim verification is essential in combating misinformation, and large language models (LLMs) have recently emerged in this area as powerful tools for assessing the veracity of claims using external knowledge. Existing LLM-based methods for claim verification typically adopt a Decompose-Then-Verify paradigm, which involves decomposing complex claims into several independent sub-claims and verifying each sub-claim separately. However, this paradigm often introduces errors during the claim decomposition process. To mitigate these errors, we propose to develop the Chain-of-Thought (CoT)-Verify paradigm, which leverages LLM reasoning methods to generate CoT-verification paths for the original complex claim without requiring decompositions into sub-claims and separate verification stages. The CoT-Verify paradigm allows us to propose a natural fine-tuning method called Reasoning-CV to enhance the verification capabilities in LLMs. Reasoning-CV includes a supervised fine-tuning (SFT) stage and a self-improvement direct preference optimization (DPO) stage. Utilizing only an 8B pre-trained LLM, Reasoning-CV demonstrates superior knowledge-assisted claim verification performances compared to existing Decompose-Then-Verify methods, as well as powerful black-box LLMs such as GPT-4o+CoT and o1-preview. Our code is available.

Reinforcement learning with verifiable rewards (RLVR) has become a key technique for enhancing large language models (LLMs), with verification engineering playing a central role. However, best practices for RL in instruction following remain underexplored. In this work, we explore the verification challenge in RL for instruction following and propose VerIF, a verification method that combines rule-based code verification with LLM-based verification from a large reasoning model (e.g., QwQ-32B). To support this approach, we construct a high-quality instruction-following dataset, VerInstruct, containing approximately 22,000 instances with associated verification signals. We apply RL training with VerIF to two models, achieving significant improvements across several representative instruction-following benchmarks. The trained models reach state-of-the-art performance among models of comparable size and generalize well to unseen constraints. We further observe that their general capabilities remain unaffected, suggesting that RL with VerIF can be integrated into existing RL recipes to enhance overall model performance. We have released our datasets, codes, and models to facilitate future research at https://github.com/THU-KEG/VerIF.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models (LLMs). In this context, models explore reasoning trajectories and exploit rollouts with correct answers as positive signals for policy optimization. However, these rollouts might involve flawed patterns such as answer-guessing and jump-in-reasoning. Such flawed-positive rollouts are rewarded identically to fully correct ones, causing policy models to internalize these unreliable reasoning patterns. In this work, we first conduct a systematic study of flawed-positive rollouts in RL and find that they enable rapid capability gains during the early optimization stage, while constraining reasoning capability later by reinforcing unreliable patterns. Building on these insights, we propose Flawed-Aware Policy Optimization (FAPO), which presents a parameter-free reward penalty for flawed-positive rollouts, enabling the policy to leverage them as useful shortcuts in the warm-up stage, securing stable early gains, while gradually shifting optimization toward reliable reasoning in the later refinement stage. To accurately and comprehensively detect flawed-positive rollouts, we introduce a generative reward model (GenRM) with a process-level reward that precisely localizes reasoning errors. Experiments show that FAPO is effective in broad domains, improving outcome correctness, process reliability, and training stability without increasing the token budget.

We study the process through which reasoning models trained with reinforcement learning on verifiable rewards (RLVR) can learn to solve new problems. We find that RLVR drives performance in two main ways: (1) by compressing pass@k into pass@1 and (2) via "capability gain" in which models learn to solve new problems that they previously could not solve even at high k. We find that while capability gain exists across model scales, learning to solve new problems is primarily driven through self-distillation. We demonstrate these findings across model scales ranging from 0.5B to 72B parameters on >500,000 reasoning problems with prompts and verifiable final answers across math, science, and code domains. We further show that we can significantly improve pass@k rates by leveraging natural language guidance for the model to consider within context while still requiring the model to derive a solution chain from scratch. Based of these insights, we derive Guide -- a new class of online training algorithms. Guide adaptively incorporates hints into the model's context on problems for which all rollouts were initially incorrect and adjusts the importance sampling ratio for the "off-policy" trajectories in order to optimize the policy for contexts in which the hints are no longer present. We describe variants of Guide for GRPO and PPO and empirically show that Guide-GRPO on 7B and 32B parameter models improves generalization over its vanilla counterpart with up to 4% macro-average improvement across math benchmarks. We include careful ablations to analyze Guide's components and theoretically analyze Guide's learning efficiency.

Commercial LLM services often conceal internal reasoning traces while still charging users for every generated token, including those from hidden intermediate steps, raising concerns of token inflation and potential overbilling. This gap underscores the urgent need for reliable token auditing, yet achieving it is far from straightforward: cryptographic verification (e.g., hash-based signature) offers little assurance when providers control the entire execution pipeline, while user-side prediction struggles with the inherent variance of reasoning LLMs, where token usage fluctuates across domains and prompt styles. To bridge this gap, we present PALACE (Predictive Auditing of LLM APIs via Reasoning Token Count Estimation), a user-side framework that estimates hidden reasoning token counts from prompt-answer pairs without access to internal traces. PALACE introduces a GRPO-augmented adaptation module with a lightweight domain router, enabling dynamic calibration across diverse reasoning tasks and mitigating variance in token usage patterns. Experiments on math, coding, medical, and general reasoning benchmarks show that PALACE achieves low relative error and strong prediction accuracy, supporting both fine-grained cost auditing and inflation detection. Taken together, PALACE represents an important first step toward standardized predictive auditing, offering a practical path to greater transparency, accountability, and user trust.

Machine learning methods have proven useful in transcribing historical data. However, results from even highly accurate methods require manual verification and correction. Such manual review can be time-consuming and expensive, therefore the objective of this paper was to make it more efficient. Previously, we used machine learning to transcribe 2.3 million handwritten occupation codes from the Norwegian 1950 census with high accuracy (97%). We manually reviewed the 90,000 (3%) codes with the lowest model confidence. We allocated those 90,000 codes to human reviewers, who used our annotation tool to review the codes. To assess reviewer agreement, some codes were assigned to multiple reviewers. We then analyzed the review results to understand the relationship between accuracy improvements and effort. Additionally, we interviewed the reviewers to improve the workflow. The reviewers corrected 62.8% of the labels and agreed with the model label in 31.9% of cases. About 0.2% of the images could not be assigned a label, while for 5.1% the reviewers were uncertain, or they assigned an invalid label. 9,000 images were independently reviewed by multiple reviewers, resulting in an agreement of 86.43% and disagreement of 8.96%. We learned that our automatic transcription is biased towards the most frequent codes, with a higher degree of misclassification for the lowest frequency codes. Our interview findings show that the reviewers did internal quality control and found our custom tool well-suited. So, only one reviewer is needed, but they should report uncertainty.

Process reward models (PRMs) have proven effective for test-time scaling of Large Language Models (LLMs) on challenging reasoning tasks. However, reward hacking issues with PRMs limit their successful application in reinforcement fine-tuning. In this paper, we identify the main cause of PRM-induced reward hacking: the canonical summation-form credit assignment in reinforcement learning (RL), which defines the value as cumulative gamma-decayed future rewards, easily induces LLMs to hack steps with high rewards. To address this, we propose PURE: Process sUpervised Reinforcement lEarning. The key innovation of PURE is a min-form credit assignment that formulates the value function as the minimum of future rewards. This method significantly alleviates reward hacking by limiting the value function range and distributing advantages more reasonably. Through extensive experiments on 3 base models, we show that PRM-based approaches enabling min-form credit assignment achieve comparable reasoning performance to verifiable reward-based methods within only 30% steps. In contrast, the canonical sum-form credit assignment collapses training even at the beginning! Additionally, when we supplement PRM-based fine-tuning with just 10% verifiable rewards, we further alleviate reward hacking and produce the best fine-tuned model based on Qwen2.5-Math-7B in our experiments, achieving 82.5% accuracy on AMC23 and 53.3% average accuracy across 5 benchmarks. Moreover, we summarize the observed reward hacking cases and analyze the causes of training collapse. Code and models are available at https://github.com/CJReinforce/PURE.

Verifiers or reward models are often used to enhance the reasoning performance of large language models (LLMs). A common approach is the Best-of-N method, where N candidate solutions generated by the LLM are ranked by a verifier, and the best one is selected. While LLM-based verifiers are typically trained as discriminative classifiers to score solutions, they do not utilize the text generation capabilities of pretrained LLMs. To overcome this limitation, we instead propose training verifiers using the ubiquitous next-token prediction objective, jointly on verification and solution generation. Compared to standard verifiers, such generative verifiers (GenRM) can benefit from several advantages of LLMs: they integrate seamlessly with instruction tuning, enable chain-of-thought reasoning, and can utilize additional inference-time compute via majority voting for better verification. We demonstrate that when using Gemma-based verifiers on algorithmic and grade-school math reasoning tasks, GenRM outperforms discriminative verifiers and LLM-as-a-Judge, showing a 16-64% improvement in the percentage of problems solved with Best-of-N. Furthermore, we show that GenRM scales favorably across dataset size, model capacity, and inference-time compute.

Test-time scaling is a powerful strategy for boosting the performance of large language models on complex reasoning tasks. While state-of-the-art approaches often employ generative verifiers to select the best solution from a pool of candidates, this method incurs prohibitive computational costs, limiting its practicality. In this work, we shift the focus to a more budget-aware paradigm: discriminative verification. We conduct a thorough empirical analysis and demonstrate that while discriminative verifiers may underperform in isolation, combining them with self-consistency in a hybrid approach creates a powerful and efficient test-time scaling mechanism. Notably, under a fixed compute budget, this hybrid approach surpasses state-of-the-art generative verification by a significant margin: achieving up to 15.3\% higher accuracy on AIME2025. Our findings establish that for practical, real-world applications, budget-aware scaling with discriminative verifiers is not only a "free" upgrade over self-consistency, but also a more effective and efficient alternative to costly generative techniques. Code is available at https://github.com/wang-research-lab/verification.

We introduce MathWriting, the largest online handwritten mathematical expression dataset to date. It consists of 230k human-written samples and an additional 400k synthetic ones. MathWriting can also be used for offline HME recognition and is larger than all existing offline HME datasets like IM2LATEX-100K. We introduce a benchmark based on MathWriting data in order to advance research on both online and offline HME recognition.

Recent advancements in Vision-Language Models (VLMs) have opened new possibilities in automatic grading of handwritten student responses, particularly in mathematics. However, a comprehensive study to test the ability of VLMs to evaluate and reason over handwritten content remains absent. To address this gap, we introduce FERMAT, a benchmark designed to assess the ability of VLMs to detect, localize and correct errors in handwritten mathematical content. FERMAT spans four key error dimensions - computational, conceptual, notational, and presentation - and comprises over 2,200 handwritten math solutions derived from 609 manually curated problems from grades 7-12 with intentionally introduced perturbations. Using FERMAT we benchmark nine VLMs across three tasks: error detection, localization, and correction. Our results reveal significant shortcomings in current VLMs in reasoning over handwritten text, with Gemini-1.5-Pro achieving the highest error correction rate (77%). We also observed that some models struggle with processing handwritten content, as their accuracy improves when handwritten inputs are replaced with printed text or images. These findings highlight the limitations of current VLMs and reveal new avenues for improvement. We release FERMAT and all the associated resources in the open-source to drive further research.

Despite the recent advances in Large Language Models, benchmarks for evaluating legal writing remain scarce due to the inherent complexity of assessing open-ended responses in this domain. One of the key challenges in evaluating language models on domain-specific tasks is finding test datasets that are public, frequently updated, and contain comprehensive evaluation guidelines. The Brazilian Bar Examination meets these requirements. We introduce oab-bench, a benchmark comprising 105 questions across seven areas of law from recent editions of the exam. The benchmark includes comprehensive evaluation guidelines and reference materials used by human examiners to ensure consistent grading. We evaluate the performance of four LLMs on oab-bench, finding that Claude-3.5 Sonnet achieves the best results with an average score of 7.93 out of 10, passing all 21 exams. We also investigated whether LLMs can serve as reliable automated judges for evaluating legal writing. Our experiments show that frontier models like OpenAI's o1 achieve a strong correlation with human scores when evaluating approved exams, suggesting their potential as reliable automated evaluators despite the inherently subjective nature of legal writing assessment. The source code and the benchmark -- containing questions, evaluation guidelines, model-generated responses, and their respective automated evaluations -- are publicly available.

Post-training for reasoning of large language models (LLMs) increasingly relies on verifiable rewards: deterministic checkers that provide 0-1 correctness signals. While reliable, such binary feedback is brittle--many tasks admit partially correct or alternative answers that verifiers under-credit, and the resulting all-or-nothing supervision limits learning. Reward models offer richer, continuous feedback, which can serve as a complementary supervisory signal to verifiers. We introduce HERO (Hybrid Ensemble Reward Optimization), a reinforcement learning framework that integrates verifier signals with reward-model scores in a structured way. HERO employs stratified normalization to bound reward-model scores within verifier-defined groups, preserving correctness while refining quality distinctions, and variance-aware weighting to emphasize challenging prompts where dense signals matter most. Across diverse mathematical reasoning benchmarks, HERO consistently outperforms RM-only and verifier-only baselines, with strong gains on both verifiable and hard-to-verify tasks. Our results show that hybrid reward design retains the stability of verifiers while leveraging the nuance of reward models to advance reasoning.

Recent Language Models (LMs) have shown impressive capabilities in generating texts with the knowledge internalized in parameters. Yet, LMs often generate the factually incorrect responses to the given queries, since their knowledge may be inaccurate, incomplete, and outdated. To address this problem, previous works propose to augment LMs with the knowledge retrieved from an external knowledge source. However, such approaches often show suboptimal text generation performance due to two reasons: 1) the model may fail to retrieve the knowledge relevant to the given query, or 2) the model may not faithfully reflect the retrieved knowledge in the generated text. To overcome these, we propose to verify the output and the knowledge of the knowledge-augmented LMs with a separate verifier, which is a small LM that is trained to detect those two types of errors through instruction-finetuning. Then, when the verifier recognizes an error, we can rectify it by either retrieving new knowledge or generating new text. Further, we use an ensemble of the outputs from different instructions with a single verifier to enhance the reliability of the verification processes. We validate the effectiveness of the proposed verification steps on multiple question answering benchmarks, whose results show that the proposed verifier effectively identifies retrieval and generation errors, allowing LMs to provide more factually correct outputs. Our code is available at https://github.com/JinheonBaek/KALMV.

While Large Language Models (LLMs) have shown exceptional performance in various tasks, their (arguably) most prominent drawback is generating inaccurate or false information with a confident tone. In this paper, we hypothesize that the LLM's internal state can be used to reveal the truthfulness of a statement. Therefore, we introduce a simple yet effective method to detect the truthfulness of LLM-generated statements, which utilizes the LLM's hidden layer activations to determine the veracity of statements. To train and evaluate our method, we compose a dataset of true and false statements in six different topics. A classifier is trained to detect which statement is true or false based on an LLM's activation values. Specifically, the classifier receives as input the activation values from the LLM for each of the statements in the dataset. Our experiments demonstrate that our method for detecting statement veracity significantly outperforms even few-shot prompting methods, highlighting its potential to enhance the reliability of LLM-generated content and its practical applicability in real-world scenarios.

Scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are challenges overlooked by existing function-centric methods. We introduce RagVerus, a framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories, achieving a 27% relative improvement on our novel RepoVBench benchmark -- the first repository-level dataset for Verus with 383 proof completion tasks. RagVerus triples proof pass rates on existing benchmarks under constrained language model budgets, demonstrating a scalable and sample-efficient verification.

Ensuring that Large Language Models (LLMs) generate summaries faithful to a given source document is essential for real-world applications. While prior research has explored LLM faithfulness, existing benchmarks suffer from annotation ambiguity, primarily due to the ill-defined boundary of permissible external knowledge in generated outputs. For instance, common sense is often incorporated into responses and labeled as "faithful", yet the acceptable extent of such knowledge remains unspecified, leading to inconsistent annotations. To address this issue, we propose a novel faithfulness annotation framework, which introduces an intermediate category, Out-Dependent, to classify cases where external knowledge is required for verification. Using this framework, we construct VeriGray (Verification with the Gray Zone) -- a new unfaithfulness detection benchmark in summarization. Statistics reveal that even SOTA LLMs, such as GPT-5, exhibit hallucinations (sim 6% of sentences) in summarization tasks. Moreover, a substantial proportion (sim 8% on average of models) of generated sentences fall into the Out-Dependent category, underscoring the importance of resolving annotation ambiguity in unfaithfulness detection benchmarks. Experiments demonstrate that our benchmark poses significant challenges to multiple baseline methods, indicating considerable room for future improvement.

Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model debate approaches, our method leverages consistency in a sequence of self-reflection actions to improve verification accuracy. Empirical evaluations across diverse mathematical process error identification benchmarks (Mathcheck, ProcessBench, and PRM800K) show consistent performance improvements over baseline methods. When applied to the recent DeepSeek R1 distilled models, our method demonstrates strong performance, enabling 7B/8B distilled models to outperform all 70B/72B models and GPT-4o on ProcessBench. Notably, the distilled 14B model with our method achieves performance comparable to Deepseek-R1. Our codes are available at https://github.com/jcguo123/Temporal-Consistency

Training Large Language Models (LLMs) requires immense computational power and vast amounts of data. As a result, protecting the intellectual property of these models through fingerprinting is essential for ownership authentication. While adding fingerprints to LLMs through fine-tuning has been attempted, it remains costly and unscalable. In this paper, we introduce FP-VEC, a pilot study on using fingerprint vectors as an efficient fingerprinting method for LLMs. Our approach generates a fingerprint vector that represents a confidential signature embedded in the model, allowing the same fingerprint to be seamlessly incorporated into an unlimited number of LLMs via vector addition. Results on several LLMs show that FP-VEC is lightweight by running on CPU-only devices for fingerprinting, scalable with a single training and unlimited fingerprinting process, and preserves the model's normal behavior. The project page is available at https://fingerprintvector.github.io .

Reinforcement learning with verifiable rewards (RLVR) is a practical and scalable approach to enhancing large language models in areas such as math, code, and other structured tasks. Two questions motivate this paper: how much of the reported gains survive under strictly parity-controlled evaluation, and whether RLVR is cost-free or exacts a measurable tax. We argue that progress is real, but gains are often overstated due to three forces - an RLVR tax, evaluation pitfalls, and data contamination. Using a partial-prompt contamination audit and matched-budget reproductions across base and RL models, we show that several headline gaps shrink or vanish under clean, parity-controlled evaluation. We then propose a tax-aware training and evaluation protocol that co-optimizes accuracy, grounding, and calibrated abstention and standardizes budgeting and provenance checks. Applied to recent RLVR setups, this protocol yields more reliable estimates of reasoning gains and, in several cases, revises prior conclusions. Our position is constructive: RLVR is valuable and industry-ready; we advocate keeping its practical benefits while prioritizing reliability, safety, and measurement.

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g. human preferences) before using it to provide online feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on the dataset via offline maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only lose information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a generation-verification gap, the combination of the ease of learning the relatively simple RM (verifier) from the preference data, coupled with the ability of the downstream RL procedure to then filter its search space to the subset of policies (generators) that are optimal for relatively simple verifiers is what leads to the superior performance of online FT.

Verifiable delay functions have found a lot of applications in blockchain technology in recent times. Continuous verifiable delay functions are an improvement over the basic notion of VDFs with recursive capabilities. We are proposing the application of VDF for constructing more space time-efficient provers and simulators required for the iterative non-interactive zero-knowledge systems.

Recent studies have shown that reinforcement learning with verifiable rewards (RLVR) enhances overall accuracy but fails to improve capability, while distillation can improve both. In this paper, we investigate the mechanisms behind these phenomena. First, we demonstrate that RLVR does not improve capability because it focuses on improving the accuracy of the less-difficult questions to the detriment of the accuracy of the most difficult questions, thereby leading to no improvement in capability. Second, we find that RLVR does not merely increase the success probability for the less difficult questions, but in our small model settings produces quality responses that were absent in its output distribution before training. In addition, we show these responses are neither noticeably longer nor feature more reflection-related keywords, underscoring the need for more reliable indicators of response quality. Third, we show that while distillation reliably improves accuracy by learning strong reasoning patterns, it only improves capability when new knowledge is introduced. Moreover, when distilling only with reasoning patterns and no new knowledge, the accuracy of the less-difficult questions improves to the detriment of the most difficult questions, similar to RLVR. Together, these findings offer a clearer understanding of how RLVR and distillation shape reasoning behavior in language models.

There has been some recent interest in detecting and addressing memorization of training data by deep neural networks. A formal framework for memorization in generative models, called "data-copying," was proposed by Meehan et. al. (2020). We build upon their work to show that their framework may fail to detect certain kinds of blatant memorization. Motivated by this and the theory of non-parametric methods, we provide an alternative definition of data-copying that applies more locally. We provide a method to detect data-copying, and provably show that it works with high probability when enough data is available. We also provide lower bounds that characterize the sample requirement for reliable detection.

Background: Generative artificial intelligence (AI) deployment in academic medical settings raises copyright compliance concerns. Dana-Farber Cancer Institute implemented GPT4DFCI, an internal generative AI tool utilizing OpenAI models, that is approved for enterprise use in research and operations. Given (1) the exceptionally broad adoption of the tool in our organization, (2) our research mission, and (3) the shared responsibility model required to benefit from Customer Copyright Commitment in Azure OpenAI Service products, we deemed rigorous copyright compliance testing necessary. Case Description: We conducted a structured red teaming exercise in Nov. 2024, with 42 participants from academic, industry, and government institutions. Four teams attempted to extract copyrighted content from GPT4DFCI across four domains: literary works, news articles, scientific publications, and access-restricted clinical notes. Teams successfully extracted verbatim book dedications and near-exact passages through various strategies. News article extraction failed despite jailbreak attempts. Scientific article reproduction yielded only high-level summaries. Clinical note testing revealed appropriate privacy safeguards. Discussion: The successful extraction of literary content indicates potential copyrighted material presence in training data, necessitating inference-time filtering. Differential success rates across content types suggest varying protective mechanisms. The event led to implementation of a copyright-specific meta-prompt in GPT4DFCI; this mitigation has been in production since Jan. 2025. Conclusion: Systematic red teaming revealed specific vulnerabilities in generative AI copyright compliance, leading to concrete mitigation strategies. Academic medical institutions deploying generative AI should implement continuous testing protocols to ensure legal and ethical compliance.

Probabilistic text generators have been used to produce fake scientific papers for more than a decade. Such nonsensical papers are easily detected by both human and machine. Now more complex AI-powered generation techniques produce texts indistinguishable from that of humans and the generation of scientific texts from a few keywords has been documented. Our study introduces the concept of tortured phrases: unexpected weird phrases in lieu of established ones, such as 'counterfeit consciousness' instead of 'artificial intelligence.' We combed the literature for tortured phrases and study one reputable journal where these concentrated en masse. Hypothesising the use of advanced language models we ran a detector on the abstracts of recent articles of this journal and on several control sets. The pairwise comparisons reveal a concentration of abstracts flagged as 'synthetic' in the journal. We also highlight irregularities in its operation, such as abrupt changes in editorial timelines. We substantiate our call for investigation by analysing several individual dubious articles, stressing questionable features: tortured writing style, citation of non-existent literature, and unacknowledged image reuse. Surprisingly, some websites offer to rewrite texts for free, generating gobbledegook full of tortured phrases. We believe some authors used rewritten texts to pad their manuscripts. We wish to raise the awareness on publications containing such questionable AI-generated or rewritten texts that passed (poor) peer review. Deception with synthetic texts threatens the integrity of the scientific literature.

The evolution of machine learning has increasingly prioritized the development of powerful models and more scalable supervision signals. However, the emergence of foundation models presents significant challenges in providing effective supervision signals necessary for further enhancing their capabilities. Consequently, there is an urgent need to explore novel supervision signals and technical approaches. In this paper, we propose verifier engineering, a novel post-training paradigm specifically designed for the era of foundation models. The core of verifier engineering involves leveraging a suite of automated verifiers to perform verification tasks and deliver meaningful feedback to foundation models. We systematically categorize the verifier engineering process into three essential stages: search, verify, and feedback, and provide a comprehensive review of state-of-the-art research developments within each stage. We believe that verifier engineering constitutes a fundamental pathway toward achieving Artificial General Intelligence.

Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct limitations, while training specialized large models still requires significant computational resources. This paper introduces ProofCompass, a novel hybrid methodology that achieves remarkable computational efficiency by strategically guiding existing specialized prover methods, such as DeepSeek-Prover-v1.5-RL (DSP-v1.5) with a Large Language Model (LLM) without requiring additional model training. The LLM provides natural language proof strategies and analyzes failed attempts to select intermediate lemmas, enabling effective problem decomposition. On the miniF2F benchmark, ProofCompass demonstrates substantial resource efficiency: it outperforms DSP-v1.5 (54.9% rightarrow 55.3%) while using 25x fewer attempts (3200 rightarrow 128). Our synergistic approach paves the way for simultaneously improving computational efficiency and accuracy in formal theorem proving.

Step-by-step verifiers -- also known as process reward models (PRMs) -- are a key ingredient for test-time scaling. PRMs require step-level supervision, making them expensive to train. This work aims to build data-efficient PRMs as verbalized step-wise reward models that verify every step in the solution by generating a verification chain-of-thought (CoT). We propose ThinkPRM, a long CoT verifier fine-tuned on orders of magnitude fewer process labels than those required by discriminative PRMs. Our approach capitalizes on the inherent reasoning abilities of long CoT models, and outperforms LLM-as-a-Judge and discriminative verifiers -- using only 1% of the process labels in PRM800K -- across several challenging benchmarks. Specifically, ThinkPRM beats the baselines on ProcessBench, MATH-500, and AIME '24 under best-of-N selection and reward-guided search. In an out-of-domain evaluation on a subset of GPQA-Diamond and LiveCodeBench, our PRM surpasses discriminative verifiers trained on the full PRM800K by 8% and 4.5%, respectively. Lastly, under the same token budget, ThinkPRM scales up verification compute more effectively compared to LLM-as-a-Judge, outperforming it by 7.2% on a subset of ProcessBench. Our work highlights the value of generative, long CoT PRMs that can scale test-time compute for verification while requiring minimal supervision for training. Our code, data, and models will be released at https://github.com/mukhal/thinkprm.

Large language models (LLMs) suffer from high inference latency due to the auto-regressive decoding process. Speculative decoding accelerates inference by generating multiple draft tokens using a lightweight model and verifying them in parallel. However, existing verification methods rely heavily on distributional consistency while overlooking semantic correctness, thereby limiting the potential speedup of speculative decoding. While some methods employ additional models for relaxed verification of draft tokens, they often fail to generalize effectively to more diverse or open-domain settings. In this work, we propose Reflective Verification, a training-free and semantics-aware approach that achieves a better trade-off between correctness and efficiency. Specifically, we leverage the inherent reflective capacity of LLMs to semantically assess the correctness of draft tokens in parallel during verification. Using prompt-based probing, we obtain both the original and reflective distributions of draft tokens in a single forward pass. The fusion of these distributions enables semantic-level verification of draft tokens that incorporates both consistency and correctness. Experiments across multiple domain benchmarks and model scales demonstrate that our method significantly increases the acceptance length of draft tokens without compromising model performance. Furthermore, we find that the proposed Reflective Verification is orthogonal to existing statistical verification methods, and their combination yields additional 5sim15\% improvements in decoding speed.

The rapid deployment of Large Language Models (LLMs) requires careful consideration of their effect on cybersecurity. Our work aims to improve the selection process of LLMs that are suitable for facilitating Secure Coding (SC). This raises challenging research questions, such as (RQ1) Which functionality can streamline the LLM evaluation? (RQ2) What should the evaluation measure? (RQ3) How to attest that the evaluation process is impartial? To address these questions, we introduce LLMSecCode, an open-source evaluation framework designed to assess LLM SC capabilities objectively. We validate the LLMSecCode implementation through experiments. When varying parameters and prompts, we find a 10% and 9% difference in performance, respectively. We also compare some results to reliable external actors, where our results show a 5% difference. We strive to ensure the ease of use of our open-source framework and encourage further development by external actors. With LLMSecCode, we hope to encourage the standardization and benchmarking of LLMs' capabilities in security-oriented code and tasks.

This paper provides a systematic analysis of the opportunities, challenges, and potential solutions of harnessing Large Language Models (LLMs) such as GPT-4 to dig out vulnerabilities within smart contracts based on our ongoing research. For the task of smart contract vulnerability detection, achieving practical usability hinges on identifying as many true vulnerabilities as possible while minimizing the number of false positives. Nonetheless, our empirical study reveals contradictory yet interesting findings: generating more answers with higher randomness largely boosts the likelihood of producing a correct answer but inevitably leads to a higher number of false positives. To mitigate this tension, we propose an adversarial framework dubbed GPTLens that breaks the conventional one-stage detection into two synergistic stages - generation and discrimination, for progressive detection and refinement, wherein the LLM plays dual roles, i.e., auditor and critic, respectively. The goal of auditor is to yield a broad spectrum of vulnerabilities with the hope of encompassing the correct answer, whereas the goal of critic that evaluates the validity of identified vulnerabilities is to minimize the number of false positives. Experimental results and illustrative examples demonstrate that auditor and critic work together harmoniously to yield pronounced improvements over the conventional one-stage detection. GPTLens is intuitive, strategic, and entirely LLM-driven without relying on specialist expertise in smart contracts, showcasing its methodical generality and potential to detect a broad spectrum of vulnerabilities. Our code is available at: https://github.com/git-disl/GPTLens.

As large language models (LLMs) become more powerful and are deployed more autonomously, it will be increasingly important to prevent them from causing harmful outcomes. Researchers have investigated a variety of safety techniques for this purpose, e.g. using models to review the outputs of other models, or red-teaming techniques to surface subtle failure modes. However, researchers have not evaluated whether such techniques still ensure safety if the model is itself intentionally trying to subvert them. In this paper, we develop and evaluate pipelines of safety techniques ("protocols") that are robust to intentional subversion. We investigate a scenario in which we want to solve a sequence of programming problems, using access to a powerful but untrusted model (in our case, GPT-4), access to a less powerful trusted model (in our case, GPT-3.5), and limited access to high-quality trusted labor. We investigate protocols that aim to never submit solutions containing backdoors, which we operationalize here as logical errors that are not caught by test cases. We investigate a range of protocols and test each against strategies that the untrusted model could use to subvert them. One protocol is what we call trusted editing. This protocol first asks GPT-4 to write code, and then asks GPT-3.5 to rate the suspiciousness of that code. If the code is below some suspiciousness threshold, it is submitted. Otherwise, GPT-3.5 edits the solution to remove parts that seem suspicious and then submits the edited code. Another protocol is untrusted monitoring. This protocol asks GPT-4 to write code, and then asks another instance of GPT-4 whether the code is backdoored, using various techniques to prevent the GPT-4 instances from colluding. These protocols improve substantially on simple baselines.

Previous works on Large Language Models (LLMs) have mainly focused on evaluating their helpfulness or harmlessness. However, honesty, another crucial alignment criterion, has received relatively less attention. Dishonest behaviors in LLMs, such as spreading misinformation and defrauding users, eroding user trust, and causing real-world harm, present severe risks that intensify as these models approach superintelligence levels. Enhancing honesty in LLMs addresses critical deficiencies and helps uncover latent capabilities that are not readily expressed. This underscores the urgent need for reliable methods and benchmarks to effectively ensure and evaluate the honesty of LLMs. In this paper, we introduce BeHonest, a pioneering benchmark specifically designed to assess honesty in LLMs comprehensively. BeHonest evaluates three essential aspects of honesty: awareness of knowledge boundaries, avoidance of deceit, and consistency in responses. Building on this foundation, we designed 10 scenarios to evaluate and analyze 9 popular LLMs on the market, including both closed-source and open-source models from different model families with varied model sizes. Our findings indicate that there is still significant room for improvement in the honesty of LLMs. We also encourage the AI community to prioritize honesty alignment in LLMs. Our benchmark and code can be found at: https://github.com/GAIR-NLP/BeHonest.

How to design reinforcement learning (RL) tasks that effectively unleash the reasoning capability of large language models (LLMs) remains an open question. Existing RL tasks (e.g., math, programming, and constructing reasoning tasks) suffer from three key limitations: (1) Scalability. They rely heavily on human annotation or expensive LLM synthesis to generate sufficient training data. (2) Verifiability. LLMs' outputs are hard to verify automatically and reliably. (3) Controllable Difficulty. Most tasks lack fine-grained difficulty control, making it hard to train LLMs to develop reasoning ability from easy to hard. To address these limitations, we propose Saturn, a SAT-based RL framework that uses Boolean Satisfiability (SAT) problems to train and evaluate LLM reasoning. Saturn enables scalable task construction, rule-based verification, and precise difficulty control. Saturn designs a curriculum learning pipeline that continuously improves LLMs' reasoning capability by constructing SAT tasks of increasing difficulty and training LLMs from easy to hard. To ensure stable training, we design a principled mechanism to control difficulty transitions. We introduce Saturn-2.6k, a dataset of 2,660 SAT problems with varying difficulty. It supports the evaluation of how LLM reasoning changes with problem difficulty. We apply Saturn to DeepSeek-R1-Distill-Qwen and obtain Saturn-1.5B and Saturn-7B. We achieve several notable results: (1) On SAT problems, Saturn-1.5B and Saturn-7B achieve average pass@3 improvements of +14.0 and +28.1, respectively. (2) On math and programming tasks, Saturn-1.5B and Saturn-7B improve average scores by +4.9 and +1.8 on benchmarks (e.g., AIME, LiveCodeBench). (3) Compared to the state-of-the-art (SOTA) approach in constructing RL tasks, Saturn achieves further improvements of +8.8%. We release the source code, data, and models to support future research.

Large Language Models (LLMs) have become an indispensable part of natural language processing tasks. However, autoregressive sampling has become an efficiency bottleneck. Multi-Draft Speculative Decoding (MDSD) is a recent approach where, when generating each token, a small draft model generates multiple drafts, and the target LLM verifies them in parallel, ensuring that the final output conforms to the target model distribution. The two main design choices in MDSD are the draft sampling method and the verification algorithm. For a fixed draft sampling method, the optimal acceptance rate is a solution to an optimal transport problem, but the complexity of this problem makes it difficult to solve for the optimal acceptance rate and measure the gap between existing verification algorithms and the theoretical upper bound. This paper discusses the dual of the optimal transport problem, providing a way to efficiently compute the optimal acceptance rate. For the first time, we measure the theoretical upper bound of MDSD efficiency for vocabulary sizes in the thousands and quantify the gap between existing verification algorithms and this bound. We also compare different draft sampling methods based on their optimal acceptance rates. Our results show that the draft sampling method strongly influences the optimal acceptance rate, with sampling without replacement outperforming sampling with replacement. Additionally, existing verification algorithms do not reach the theoretical upper bound for both without replacement and with replacement sampling. Our findings suggest that carefully designed draft sampling methods can potentially improve the optimal acceptance rate and enable the development of verification algorithms that closely match the theoretical upper bound.

While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth answers, and are often saturated due to problem simplicity or the viability of guessing or memorization. Crucially, they capture only a narrow subset of relevant math problems. To address this research gap, we introduce \mc, a new benchmark of 126 challenging problems sourced from various math competitions, which targets constructive proofs, a widely encountered problem type requiring the construction of mathematical objects with specific properties. These proofs are particularly suitable for LLM evaluation, as solution correctness can be easily verified. Our automated verifiers also enable MathConstruct to generate problem variations, used to evaluate robustness. State-of-the-art LLMs solve only 54% of MathConstruct problems, highlighting its complexity and importance for LLM evaluation.

Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of general reliability, and business logic blindness. In this work, we propose a novel framework that leverages functional programming and type systems to translate Scala backend code into formal Lean representations. Our pipeline automatically generates theorems that specify the intended behavior of APIs and database operations, and uses LLM-based provers to verify them. When a theorem is proved, the corresponding logic is guaranteed to be correct and no further testing is needed. If the negation of a theorem is proved instead, it confirms a bug. In cases where neither can be proved, human intervention is required. We evaluate our method on realistic backend systems and find that it can formally verify over 50% of the test requirements, which suggests that half of a testing engineer's workload can be automated. Additionally, with an average cost of only $2.19 per API, LLM-based verification is significantly more cost-effective than manual testing and can be scaled easily through parallel execution. Our results indicate a promising direction for scalable, AI-powered software testing, with the potential to greatly improve engineering productivity as models continue to advance.

Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in fields ranging from RL (procedural environments) to physics (simulation engines). These programs can be seen as functions which execute to different outputs based on their parameterizations (e.g., gridworld configuration or initial physical conditions). We introduce the term EFA (Executable Functional Abstraction) to denote such programs for math problems. EFA-like constructs have been shown to be useful for math reasoning as problem generators for stress-testing models. However, prior work has been limited to abstractions for grade-school math (whose simple rules are easy to encode in programs), while generating EFAs for advanced math has thus far required human engineering. We explore the automatic construction of EFAs for advanced math problems. We operationalize the task of automatically constructing EFAs as a program synthesis task, and develop EFAGen, which conditions an LLM on a seed math problem and its step-by-step solution to generate candidate EFA programs that are faithful to the generalized problem and solution class underlying the seed problem. Furthermore, we formalize properties any valid EFA must possess in terms of executable unit tests, and show how the tests can be used as verifiable rewards to train LLMs to become better writers of EFAs. We demonstrate that EFAs constructed by EFAGen behave rationally by remaining faithful to seed problems, produce learnable problem variations, and that EFAGen can infer EFAs across multiple diverse sources of competition-level math problems. Finally, we show downstream uses of model-written EFAs e.g. finding problem variations that are harder or easier for a learner to solve, as well as data generation.

Recent advancements in large language models (LLMs) suggest great promises in code and proof generations. However, scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are crucial challenges overlooked by existing LLM-based methods with a special focus on targeting isolated, function-level verification tasks. To systematically explore and address the significant challenges of verifying entire software repositories, we introduce RVBench, the first verification benchmark explicitly designed for repository-level evaluation, constructed from four diverse and complex open-source Verus projects. We further introduce RagVerus, an extensible framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories. RagVerus triples proof pass rates on existing benchmarks under constrained model inference budgets, and achieves a 27% relative improvement on the more challenging RVBench benchmark, demonstrating a scalable and sample-efficient verification solution.

Our work tackles the challenge of securing user inputs in cloud-hosted large language model (LLM) serving while ensuring output invariance, model confidentiality, and compute efficiency. We introduce secure multi-party decoding (SMD), which leverages confidential computing to confine user prompts to a trusted execution environment (TEE), namely a confidential virtual machine (CVM), while allowing service providers to generate tokens efficiently. We also introduce a novel cryptographic method, prompt obfuscation (PO), to ensure robustness against reconstruction attacks on SMD. We demonstrate that our approach preserves both prompt confidentiality and LLM serving efficiency. Our solution can enable privacy-preserving cloud LLM serving that handles sensitive prompts, such as clinical records, financial data, and personal information.

Reinforcement Learning with Verifiable Rewards (RLVR) demonstrates promising potential in advancing the reasoning capabilities of LLMs. However, its success remains largely confined to mathematical and code domains. This primary limitation stems from the heavy reliance on domain-specific verifiers, which results in prohibitive complexity and limited scalability. To address the challenge, our key observation is that LLM's intrinsic probability of generating a correct free-form answer directly indicates its own evaluation of the reasoning reward (i.e., how well the reasoning process leads to the correct answer). Building on this insight, we propose RLPR, a simple verifier-free framework that extrapolates RLVR to broader general domains. RLPR uses the LLM's own token probability scores for reference answers as the reward signal and maximizes the expected reward during training. We find that addressing the high variance of this noisy probability reward is crucial to make it work, and propose prob-to-reward and stabilizing methods to ensure a precise and stable reward from LLM intrinsic probabilities. Comprehensive experiments in four general-domain benchmarks and three mathematical benchmarks show that RLPR consistently improves reasoning capabilities in both areas for Gemma, Llama, and Qwen based models. Notably, RLPR outperforms concurrent VeriFree by 7.6 points on TheoremQA and 7.5 points on Minerva, and even surpasses strong verifier-model-dependent approaches General-Reasoner by 1.6 average points across seven benchmarks.

Large Language Models (LLMs) have demonstrated impressive problem-solving capabilities in mathematics through step-by-step reasoning chains. However, they are susceptible to reasoning errors that impact the quality of subsequent reasoning chains and the final answer due to language models' autoregressive token-by-token generating nature. Recent works have proposed adopting external verifiers to guide the generation of reasoning paths, but existing works utilize models that have been trained with step-by-step labels to assess the correctness of token-by-token reasoning chains. Consequently, they struggle to recognize discriminative details of tokens within a reasoning path and lack the ability to evaluate whether an intermediate reasoning path is on a promising track toward the correct final answer. To amend the lack of sound and token-grained math-verification signals, we devise a novel training scheme for verifiers that apply token-level supervision with the expected cumulative reward (i.e., value). Furthermore, we propose a practical formulation of the cumulative reward by reducing it to finding the probability of future correctness of the final answer and thereby enabling the empirical estimation of the value. Experimental results on mathematical reasoning benchmarks show that Token-Supervised Value Model (TVM) can outperform step-by-step verifiers on GSM8K and MATH with Mistral and Llama.

Automated Essay Scoring (AES) plays a crucial role in educational assessment by providing scalable and consistent evaluations of writing tasks. However, traditional AES systems face three major challenges: (1) reliance on handcrafted features that limit generalizability, (2) difficulty in capturing fine-grained traits like coherence and argumentation, and (3) inability to handle multimodal contexts. In the era of Multimodal Large Language Models (MLLMs), we propose EssayJudge, the first multimodal benchmark to evaluate AES capabilities across lexical-, sentence-, and discourse-level traits. By leveraging MLLMs' strengths in trait-specific scoring and multimodal context understanding, EssayJudge aims to offer precise, context-rich evaluations without manual feature engineering, addressing longstanding AES limitations. Our experiments with 18 representative MLLMs reveal gaps in AES performance compared to human evaluation, particularly in discourse-level traits, highlighting the need for further advancements in MLLM-based AES research.

As large language models (LLMs) are increasingly applied to scientific reasoning, the complexity of answer formats and the diversity of equivalent expressions make answer verification a critical yet challenging task. Existing verification studies in scientific domains suffer from two major limitations: (a) the absence of systematic evaluation standards and insufficient disciplinary coverage, which hinders their comprehensive assessment; and (b) heavy reliance on cumbersome rule design or prompt engineering, which reduces their effectiveness in complex reasoning scenarios or limits their cross-disciplinary generalization. To address these challenges, we propose solutions at both the data and model levels. On the data side, we construct SCI-VerifyBench, a cross-disciplinary benchmark covering mathematics, physics, biology, chemistry, and general scientific QA. The benchmark is built from real LLM responses and enhanced with domain-specific equivalence transformations that generate challenging and realistic data. Model-based and expert annotations ensure both quality and diversity, enabling rigorous evaluation of verification ability. On the model side, we emphasize the importance of reasoning for verification and introduce SCI-Verifier, a unified reasoning-augmented verifier for scientific domains. Through post-training, SCI-Verifier demonstrates strong logical reasoning and equivalence judgment capabilities while maintaining concise and stable outputs. Together, SCI-VerifyBench and SCI-Verifier provide a principled framework for scientific verification, offering both systematic evaluation and practical pathways to enhance the reliability and applicability of LLMs in scientific domains.

Accuracy is an important concern for suppliers of artificial intelligence (AI) services, but considerations beyond accuracy, such as safety (which includes fairness and explainability), security, and provenance, are also critical elements to engender consumers' trust in a service. Many industries use transparent, standardized, but often not legally required documents called supplier's declarations of conformity (SDoCs) to describe the lineage of a product along with the safety and performance testing it has undergone. SDoCs may be considered multi-dimensional fact sheets that capture and quantify various aspects of the product and its development to make it worthy of consumers' trust. Inspired by this practice, we propose FactSheets to help increase trust in AI services. We envision such documents to contain purpose, performance, safety, security, and provenance information to be completed by AI service providers for examination by consumers. We suggest a comprehensive set of declaration items tailored to AI and provide examples for two fictitious AI services in the appendix of the paper.

Large language models (LLMs) have recently achieved notable success in code-generation benchmarks such as HumanEval and LiveCodeBench. However, a detailed examination reveals that these evaluation suites often comprise only a limited number of homogeneous test cases, resulting in subtle faults going undetected. This not only artificially inflates measured performance but also compromises accurate reward estimation in reinforcement learning frameworks utilizing verifiable rewards (RLVR). To address these critical shortcomings, we systematically investigate the test-case generation (TCG) task by proposing multi-dimensional metrics designed to rigorously quantify test-suite thoroughness. Furthermore, we introduce a human-LLM collaborative method (SAGA), leveraging human programming expertise with LLM reasoning capability, aimed at significantly enhancing both the coverage and the quality of generated test cases. In addition, we develop a TCGBench to facilitate the study of the TCG task. Experiments show that SAGA achieves a detection rate of 90.62% and a verifier accuracy of 32.58% on TCGBench. The Verifier Accuracy (Verifier Acc) of the code generation evaluation benchmark synthesized by SAGA is 10.78% higher than that of LiveCodeBench-v6. These results demonstrate the effectiveness of our proposed method. We hope this work contributes to building a scalable foundation for reliable LLM code evaluation, further advancing RLVR in code generation, and paving the way for automated adversarial test synthesis and adaptive benchmark integration.

We introduce SimpleQA Verified, a 1,000-prompt benchmark for evaluating Large Language Model (LLM) short-form factuality based on OpenAI's SimpleQA. It addresses critical limitations in OpenAI's benchmark, including noisy and incorrect labels, topical biases, and question redundancy. SimpleQA Verified was created through a rigorous multi-stage filtering process involving de-duplication, topic balancing, and source reconciliation to produce a more reliable and challenging evaluation set, alongside improvements in the autorater prompt. On this new benchmark, Gemini 2.5 Pro achieves a state-of-the-art F1-score of 55.6, outperforming other frontier models, including GPT-5. This work provides the research community with a higher-fidelity tool to track genuine progress in parametric model factuality and to mitigate hallucinations. The benchmark dataset, evaluation code, and leaderboard are available at: https://www.kaggle.com/benchmarks/deepmind/simpleqa-verified.

Large Language Models are trained on vast amounts of text from the internet, which contains both factual and misleading information about the world. Can language models discern truth from falsehood in this contradicting data? Expanding on the view that LLMs can model different agents producing the corpora, we hypothesize that they can cluster truthful text by modeling a truthful persona: a group of agents that are likely to produce truthful text and share similar features. For example, trustworthy sources like Wikipedia and Science usually use formal writing styles and make consistent claims. By modeling this persona, LLMs can generalize truthfulness beyond the specific contexts in which each agent generated the training text. For example, the model can infer that the agent "Wikipedia" will behave truthfully on topics that were only generated by "Science" because they share a persona. We first show evidence for the persona hypothesis via two observations: (1) we can probe whether a model's answer will be truthful before it is generated; (2) finetuning a model on a set of facts improves its truthfulness on unseen topics. Next, using arithmetics as a synthetic environment, we show that language models can separate true and false statements, and generalize truthfulness across agents; but only if agents in the training data share a truthful generative process that enables the creation of a truthful persona. Overall, our findings suggest that models can exploit hierarchical structures in the data to learn abstract concepts like truthfulness.

Fact-checking requires retrieving evidence related to a claim under investigation. The task can be formulated as question generation based on a claim, followed by question answering. However, recent question generation approaches assume that the answer is known and typically contained in a passage given as input, whereas such passages are what is being sought when verifying a claim. In this paper, we present {\it Varifocal}, a method that generates questions based on different focal points within a given claim, i.e.\ different spans of the claim and its metadata, such as its source and date. Our method outperforms previous work on a fact-checking question generation dataset on a wide range of automatic evaluation metrics. These results are corroborated by our manual evaluation, which indicates that our method generates more relevant and informative questions. We further demonstrate the potential of focal points in generating sets of clarification questions for product descriptions.

Code verification has recently found great success as a critical component in training large scale reasoning models for coding. Synthetic techniques such as self-generated test cases and reward models provide a way to enhance code capabilities beyond predefined tests. Building on these advancements, we propose new benchmarks designed to systematically evaluate the impact of synthetic verification methods on assessing solution correctness. We introduce HE-R, HE-R+, MBPP-R, and MBPP-R+, which transform existing coding benchmarks into scoring and ranking datasets to evaluate the effectiveness of synthetic verifiers. Using these benchmarks, we analyze synthetic verification methods in standard, reasoning-based, and reward-based LLMs. Our results show that recent reasoning models significantly improve test case generation and that scaling test cases enhances verification accuracy.

Scaling test-time compute is crucial for enhancing the reasoning capabilities of large language models (LLMs). Existing approaches typically employ reinforcement learning (RL) to maximize a verifiable reward obtained at the end of reasoning traces. However, such methods optimize only the final performance under a large and fixed token budget, which hinders efficiency in both training and deployment. In this work, we present a novel framework, AnytimeReasoner, to optimize anytime reasoning performance, which aims to improve token efficiency and the flexibility of reasoning under varying token budget constraints. To achieve this, we truncate the complete thinking process to fit within sampled token budgets from a prior distribution, compelling the model to summarize the optimal answer for each truncated thinking for verification. This introduces verifiable dense rewards into the reasoning process, facilitating more effective credit assignment in RL optimization. We then optimize the thinking and summary policies in a decoupled manner to maximize the cumulative reward. Additionally, we introduce a novel variance reduction technique, Budget Relative Policy Optimization (BRPO), to enhance the robustness and efficiency of the learning process when reinforcing the thinking policy. Empirical results in mathematical reasoning tasks demonstrate that our method consistently outperforms GRPO across all thinking budgets under various prior distributions, enhancing both training and token efficiency.

Recent advances such as DeepSeek R1-Zero highlight the effectiveness of incentive training, a reinforcement learning paradigm that computes rewards solely based on the final answer part of a language model's output, thereby encouraging the generation of intermediate reasoning steps. However, these methods fundamentally rely on external verifiers, which limits their applicability to domains like mathematics and coding where such verifiers are readily available. Although reward models can serve as verifiers, they require high-quality annotated data and are costly to train. In this work, we propose NOVER, NO-VERifier Reinforcement Learning, a general reinforcement learning framework that requires only standard supervised fine-tuning data with no need for an external verifier. NOVER enables incentive training across a wide range of text-to-text tasks and outperforms the model of the same size distilled from large reasoning models such as DeepSeek R1 671B by 7.7 percent. Moreover, the flexibility of NOVER enables new possibilities for optimizing large language models, such as inverse incentive training.

LLMs are highly sensitive to prompt phrasing, yet standard benchmarks typically report performance using a single prompt, raising concerns about the reliability of such evaluations. In this work, we argue for a stochastic method of moments evaluation over the space of meaning-preserving prompt perturbations. We introduce a formal definition of reliable evaluation that accounts for prompt sensitivity, and suggest ReliableEval - a method for estimating the number of prompt resamplings needed to obtain meaningful results. Using our framework, we stochastically evaluate five frontier LLMs and find that even top-performing models like GPT-4o and Claude-3.7-Sonnet exhibit substantial prompt sensitivity. Our approach is model-, task-, and metric-agnostic, offering a recipe for meaningful and robust LLM evaluation.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

Formal verification (FV) has witnessed growing significance with current emerging program synthesis by the evolving large language models (LLMs). However, current formal verification mainly resorts to symbolic verifiers or hand-craft rules, resulting in limitations for extensive and flexible verification. On the other hand, formal languages for automated theorem proving, such as Isabelle, as another line of rigorous verification, are maintained with comprehensive rules and theorems. In this paper, we propose FVEL, an interactive Formal Verification Environment with LLMs. Specifically, FVEL transforms a given code to be verified into Isabelle, and then conducts verification via neural automated theorem proving with an LLM. The joined paradigm leverages the rigorous yet abundant formulated and organized rules in Isabelle and is also convenient for introducing and adjusting cutting-edge LLMs. To achieve this goal, we extract a large-scale FVELER3. The FVELER dataset includes code dependencies and verification processes that are formulated in Isabelle, containing 758 theories, 29,125 lemmas, and 200,646 proof steps in total with in-depth dependencies. We benchmark FVELER in the FVEL environment by first fine-tuning LLMs with FVELER and then evaluating them on Code2Inv and SV-COMP. The results show that FVEL with FVELER fine-tuned Llama3- 8B solves 17.39% (69 -> 81) more problems, and Mistral-7B 12% (75 -> 84) more problems in SV-COMP. And the proportion of proof errors is reduced. Project page: https://fveler.github.io/.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for advancing the reasoning capabilities of Large Language Models (LLMs). However, a critical paradox clouds its efficacy: RLVR-tuned models often underperform their base models on the Pass@K metric for solution-finding, leading to the hypothesis that RLVR merely re-weights existing reasoning paths at the cost of reasoning diversity. In this work, we resolve this contradiction by identifying the source of the problem: the Pass@K metric itself is a flawed measure of reasoning, as it credits correct final answers that probably arise from inaccurate or incomplete chains of thought (CoTs). To address this, we introduce a more precise evaluation metric, CoT-Pass@K, which mandates that both the reasoning path and the final answer be correct. We provide a new theoretical foundation that formalizes how RLVR, unlike traditional RL, is uniquely structured to incentivize logical integrity. Our empirical results are supportive: using CoT-Pass@K, we observe that RLVR can incentivize the generalization of correct reasoning for all values of K. Furthermore, by analyzing the training dynamics, we find that this enhanced reasoning capability emerges early in the training process and smoothly generalizes. Our work provides a clear perspective on the role of RLVR, offers a more reliable method for its evaluation, and confirms its potential to genuinely advance machine reasoning.

In this paper, we present the current progress of the project Verif.ai, an open-source scientific generative question-answering system with referenced and verified answers. The components of the system are (1) an information retrieval system combining semantic and lexical search techniques over scientific papers (PubMed), (2) a fine-tuned generative model (Mistral 7B) taking top answers and generating answers with references to the papers from which the claim was derived, and (3) a verification engine that cross-checks the generated claim and the abstract or paper from which the claim was derived, verifying whether there may have been any hallucinations in generating the claim. We are reinforcing the generative model by providing the abstract in context, but in addition, an independent set of methods and models are verifying the answer and checking for hallucinations. Therefore, we believe that by using our method, we can make scientists more productive, while building trust in the use of generative language models in scientific environments, where hallucinations and misinformation cannot be tolerated.

Recent advances in Large Language Models (LLMs) have demonstrated remarkable general reasoning capabilities. However, systematically evaluating and enhancing these reasoning capabilities is challenging due to the lack of controllable and scalable tools for fine-grained analysis. Existing benchmarks and datasets often lack the necessary variable control for multi-dimensional, systematic analysis and training, or have narrow problem types and formats. To address these limitations, we introduce SATQuest, a systematic verifier designed to evaluate and enhance logical reasoning in LLMs by generating diverse, Satisfiability-based logical reasoning problems directly from Conjunctive Normal Form (CNF) instances. SATQuest structures these problems along three orthogonal dimensions: instance scale, problem type, and question format, employing randomized, SAT-based problem generation and objective answer verification via PySAT. This design mitigates memorization issues, allows for nuanced insights into reasoning performance, and enables effective reinforcement fine-tuning. Our extensive evaluation of various LLMs using SATQuest identified significant limitations in their logical reasoning, particularly in generalizing beyond familiar mathematical formats. Furthermore, we show that reinforcement fine-tuning with SATQuest rewards substantially improves targeted task performance and generalizes to more complex instances, while highlighting remaining challenges in cross-format adaptation. Through these demonstrations, we showcase SATQuest's potential as a foundational tool and a valuable starting point for advancing LLM logical reasoning.

High-quality mathematical and logical datasets with verifiable answers are essential for strengthening the reasoning capabilities of large language models (LLMs). While recent data augmentation techniques have facilitated the creation of large-scale benchmarks, existing LLM-generated datasets often suffer from limited reliability, diversity, and scalability. To address these challenges, we introduce PuzzleClone, a formal framework for synthesizing verifiable data at scale using Satisfiability Modulo Theories (SMT). Our approach features three key innovations: (1) encoding seed puzzles into structured logical specifications, (2) generating scalable variants through systematic variable and constraint randomization, and (3) ensuring validity via a reproduction mechanism. Applying PuzzleClone, we construct a curated benchmark comprising over 83K diverse and programmatically validated puzzles. The generated puzzles span a wide spectrum of difficulty and formats, posing significant challenges to current state-of-the-art models. We conduct post training (SFT and RL) on PuzzleClone datasets. Experimental results show that training on PuzzleClone yields substantial improvements not only on PuzzleClone testset but also on logic and mathematical benchmarks. Post training raises PuzzleClone average from 14.4 to 56.2 and delivers consistent improvements across 7 logic and mathematical benchmarks up to 12.5 absolute percentage points (AMC2023 from 52.5 to 65.0). Our code and data are available at https://github.com/puzzleclone.

Recent advances in generative artificial intelligence (AI) have shown promise in accurately grading open-ended student responses. However, few prior works have explored grading handwritten responses due to a lack of data and the challenge of combining visual and textual information. In this work, we leverage state-of-the-art multi-modal AI models, in particular GPT-4o, to automatically grade handwritten responses to college-level math exams. Using real student responses to questions in a probability theory exam, we evaluate GPT-4o's alignment with ground-truth scores from human graders using various prompting techniques. We find that while providing rubrics improves alignment, the model's overall accuracy is still too low for real-world settings, showing there is significant room for growth in this task.

Current research on the Decompose-Then-Verify paradigm for evaluating the factuality of long-form text typically treats decomposition and verification in isolation, overlooking their interactions and potential misalignment. We find that existing decomposition policies, typically hand-crafted demonstrations, do not align well with downstream verifiers in terms of atomicity -- a novel metric quantifying information density -- leading to suboptimal verification results. We formulate finding the optimal decomposition policy for optimal verification as a bilevel optimization problem. To approximate a solution for this strongly NP-hard problem, we propose dynamic decomposition, a reinforcement learning framework that leverages verifier feedback to learn a policy for dynamically decomposing claims to verifier-preferred atomicity. Experimental results show that dynamic decomposition outperforms existing decomposition policies, improving verification confidence by 0.07 and accuracy by 0.12 (on a 0-1 scale) on average across varying verifiers, datasets, and atomcities of input claims.

Reinforcement learning with verifiable rewards (RLVR) improves language model reasoning by using rule-based rewards in verifiable domains such as mathematics and code. However, RLVR leads to limited generalization for open-ended tasks -- such as writing outline essays or making meal plans -- where humans reason routinely. This paper shows that the RLVR paradigm is effective beyond verifiable domains, and introduces **RL** with **M**odel-rewarded **T**hinking (**RLMT**) for general-purpose chat capabilities. Using diverse real-world prompts, RLMT requires LMs to generate long CoT reasoning before response, and optimizes them with online RL against a preference-based reward model used in RLHF. Across 40 training runs on Llama-3.1-8B and Qwen-2.5-7B (both base and instruct) and multiple optimization algorithms (DPO, PPO, and GRPO), RLMT consistently outperforms standard RLHF pipelines. This includes substantial gains of 3-7 points on three chat benchmarks (AlpacaEval2, WildBench, and ArenaHardV2), along with 1-3 point improvements on other tasks like creative writing and general knowledge. Our best 8B model surpasses GPT-4o in chat and creative writing and rivals Claude-3.7-Sonnet (Thinking). RLMT can also be applied directly to base models without an SFT stage, akin to R1-Zero training. Remarkably, with only 7K prompts, Llama-3.1-8B base trained with our RLMT recipe outperforms Llama-3.1-8B-Instruct post-trained with a complex multi-staged pipeline with 25M+ examples. We close with qualitative and quantitative analyses of how trained models plan their responses. Our results rethink the post-training pipeline and call upon future work to understand and employ thinking more broadly.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the Code Usage Frequency of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit code-based self-verification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to 84.3\%).

Writing competitive programming problems is exacting. Authors must: set constraints, input distributions, and edge cases that rule out shortcuts; target specific algorithms (e.g., max-flow, dynamic programming, data structures); and calibrate complexity beyond the reach of most competitors. We argue that this makes for an ideal test of general large language model capabilities and study whether they can do this reliably. We introduce AutoCode, which uses multiple rounds of validation to yield competition-grade problem statements and test cases. On held-out problems, AutoCode test suites approach 99% consistency with official judgments, a significant improvement over current state-of-the-art methods like HardTests, which achieve less than 81%. Furthermore, starting with a random seed problem, AutoCode can create novel variants with reference and brute-force solutions. By cross-verifying these generated solutions against test cases, we can further filter out malformed problems. Our system ensures high correctness, as verified by human experts. AutoCode successfully produces novel problems judged by Grandmaster-level (top 0.3%) competitive programmers to be of contest quality.

A primary concern regarding training large language models (LLMs) is whether they abuse copyrighted online text. With the increasing training data scale and the prevalence of LLMs in daily lives, two problems arise: 1) false positive membership inference results misled by similar examples; 2) membership inference methods are usually too complex for end users to understand and use. To address these issues, we propose an alternative insert-and-detect methodology, advocating that web users and content platforms employ \textit{unique identifiers} for reliable and independent membership inference. Users and platforms can create their identifiers, embed them in copyrighted text, and independently detect them in future LLMs. As an initial demonstration, we introduce \textbf{ghost sentences} and a user-friendly last-k words test, allowing end users to chat with LLMs for membership inference. Ghost sentences consist primarily of unique passphrases of random natural words, which can come with customized elements to bypass possible filter rules. The last-k words test requires a significant repetition time of ghost sentences~(ge10). For cases with fewer repetitions, we designed an extra perplexity test, as LLMs exhibit high perplexity when encountering unnatural passphrases. We also conduct a comprehensive study on the memorization and membership inference of ghost sentences, examining factors such as training data scales, model sizes, repetition times, insertion positions, wordlist of passphrases, alignment, etc. Our study shows the possibility of applying ghost sentences in real scenarios and provides instructions for the potential application.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

Large Language Models (LLMs) increasingly rely on external tools such as search engines to solve complex agentic tasks that require reasoning and external knowledge retrieval. Recently, reinforcement learning with verifiable rewards (RLVR) has demonstrated its effectiveness in advancing capabilities of LLMs by rewarding the final answers via outcome rewards. While straightforward to supervise, outcome rewards only provide sparse signals and delayed feedback, which limits their effectiveness on long trajectories. Process rewards address this by evaluating intermediate steps, providing fine-grained supervision and encouraging grounded problem solving. However, it is notoriously hard to annotate step-wise labels, especially in non-verifiable process without "golden" answers. Furthermore, step-wise judgment requires the balance between local quality with contribution to the final outcome, as optimizing towards higher process reward may not always align with better final outcomes. To address the above challenges, we introduce Principle Process Reward (PPR), an RL approach that unifies principled step-level assessment and outcome verification. We train a principle-based reward model to improve the transparency and reliability of process evaluation, and further introduce a Reward Normalization (ReNorm) strategy to calibrate outcome and process rewards. Experiment results show that PPR achieves state-of-the-art performance across a wide range of benchmarks, demonstrating its impressive robustness and generalization. Our code and model collection is available in this link.

A key component of fact verification is thevevidence retrieval, often from multiple documents. Recent approaches use dense representations and condition the retrieval of each document on the previously retrieved ones. The latter step is performed over all the documents in the collection, requiring storing their dense representations in an index, thus incurring a high memory footprint. An alternative paradigm is retrieve-and-rerank, where documents are retrieved using methods such as BM25, their sentences are reranked, and further documents are retrieved conditioned on these sentences, reducing the memory requirements. However, such approaches can be brittle as they rely on heuristics and assume hyperlinks between documents. We propose a novel retrieve-and-rerank method for multi-hop retrieval, that consists of a retriever that jointly scores documents in the knowledge source and sentences from previously retrieved documents using an autoregressive formulation and is guided by a proof system based on natural logic that dynamically terminates the retrieval process if the evidence is deemed sufficient. This method is competitive with current state-of-the-art methods on FEVER, HoVer and FEVEROUS-S, while using 5 to 10 times less memory than competing systems. Evaluation on an adversarial dataset indicates improved stability of our approach compared to commonly deployed threshold-based methods. Finally, the proof system helps humans predict model decisions correctly more often than using the evidence alone.

Reasoning models have achieved remarkable performance on tasks like math and logical reasoning thanks to their ability to search during reasoning. However, they still suffer from overthinking, often performing unnecessary reasoning steps even after reaching the correct answer. This raises the question: can models evaluate the correctness of their intermediate answers during reasoning? In this work, we study whether reasoning models encode information about answer correctness through probing the model's hidden states. The resulting probe can verify intermediate answers with high accuracy and produces highly calibrated scores. Additionally, we find models' hidden states encode correctness of future answers, enabling early prediction of the correctness before the intermediate answer is fully formulated. We then use the probe as a verifier to decide whether to exit reasoning at intermediate answers during inference, reducing the number of inference tokens by 24\% without compromising performance. These findings confirm that reasoning models do encode a notion of correctness yet fail to exploit it, revealing substantial untapped potential to enhance their efficiency.

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.

The development of large language models tailored for handling patients' clinical notes is often hindered by the limited accessibility and usability of these notes due to strict privacy regulations. To address these challenges, we first create synthetic large-scale clinical notes using publicly available case reports extracted from biomedical literature. We then use these synthetic notes to train our specialized clinical large language model, Asclepius. While Asclepius is trained on synthetic data, we assess its potential performance in real-world applications by evaluating it using real clinical notes. We benchmark Asclepius against several other large language models, including GPT-3.5-turbo and other open-source alternatives. To further validate our approach using synthetic notes, we also compare Asclepius with its variants trained on real clinical notes. Our findings convincingly demonstrate that synthetic clinical notes can serve as viable substitutes for real ones when constructing high-performing clinical language models. This conclusion is supported by detailed evaluations conducted by both GPT-4 and medical professionals. All resources including weights, codes, and data used in the development of Asclepius are made publicly accessible for future research.

Having reliable specifications is an unavoidable challenge in achieving verifiable correctness, robustness, and interpretability of AI systems. Existing specifications for neural networks are in the paradigm of data as specification. That is, the local neighborhood centering around a reference input is considered to be correct (or robust). While existing specifications contribute to verifying adversarial robustness, a significant problem in many research domains, our empirical study shows that those verified regions are somewhat tight, and thus fail to allow verification of test set inputs, making them impractical for some real-world applications. To this end, we propose a new family of specifications called neural representation as specification, which uses the intrinsic information of neural networks - neural activation patterns (NAPs), rather than input data to specify the correctness and/or robustness of neural network predictions. We present a simple statistical approach to mining neural activation patterns. To show the effectiveness of discovered NAPs, we formally verify several important properties, such as various types of misclassifications will never happen for a given NAP, and there is no ambiguity between different NAPs. We show that by using NAP, we can verify a significant region of the input space, while still recalling 84% of the data on MNIST. Moreover, we can push the verifiable bound to 10 times larger on the CIFAR10 benchmark. Thus, we argue that NAPs can potentially be used as a more reliable and extensible specification for neural network verification.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for training large language models (LLMs) on complex reasoning tasks, such as mathematical problem solving. A prerequisite for the scalability of RLVR is a high-quality problem set with precise and verifiable answers. However, the scarcity of well-crafted human-labeled math problems and limited-verification answers in existing distillation-oriented synthetic datasets limit their effectiveness in RL. Additionally, most problem synthesis strategies indiscriminately expand the problem set without considering the model's capabilities, leading to low efficiency in generating useful questions. To mitigate this issue, we introduce a Self-aware Weakness-driven problem Synthesis framework (SwS) that systematically identifies model deficiencies and leverages them for problem augmentation. Specifically, we define weaknesses as questions that the model consistently fails to learn through its iterative sampling during RL training. We then extract the core concepts from these failure cases and synthesize new problems to strengthen the model's weak areas in subsequent augmented training, enabling it to focus on and gradually overcome its weaknesses. Without relying on external knowledge distillation, our framework enables robust generalization byempowering the model to self-identify and address its weaknesses in RL, yielding average performance gains of 10.0% and 7.7% on 7B and 32B models across eight mainstream reasoning benchmarks.

Verifiers can improve language model capabilities by scoring and ranking responses from generated candidates. Currently, high-quality verifiers are either unscalable (e.g., humans) or limited in utility (e.g., tools like Lean). While LM judges and reward models have become broadly useful as general-purpose verifiers, a significant performance gap remains between them and oracle verifiers (verifiers with perfect accuracy). To help close this gap, we introduce Weaver, a framework for designing a strong verifier by combining multiple weak, imperfect verifiers. We find weighted ensembles of verifiers, which typically require learning from labeled data, significantly outperform unweighted combinations due to differences in verifier accuracies. To reduce dependency on labeled data, Weaver leverages weak supervision to estimate each verifier's accuracy and combines outputs into a unified score that better reflects true response quality. However, directly applying weak supervision algorithms poses challenges, including inconsistent verifier output formats and handling low-quality verifiers. Weaver addresses these using dataset statistics to normalize outputs and filter specific verifiers. We study Weaver's effectiveness in test-time repeated sampling, where a model generates multiple candidate responses and selects one. Our evaluations show Weaver significantly improves over Pass@1-performance when selecting the first candidate-across reasoning and math tasks, achieving o3-mini-level accuracy with Llama 3.3 70B Instruct as generator, and an ensemble of 70B or smaller judge and reward models as verifiers (87.7% average). This gain mirrors the jump between GPT-4o and o3-mini (69.0% vs. 86.7%), which required extensive finetuning and post-training. To reduce computational costs of verifier ensembles, we train a 400M cross-encoder using Weaver's combined output scores.

Although online handwriting verification has made great progress recently, the verification performances are still far behind the real usage owing to the small scale of the datasets as well as the limited biometric mediums. Therefore, this paper proposes a new handwriting verification benchmark dataset named Multimodal Signature and Digit String (MSDS), which consists of two subsets: MSDS-ChS (Chinese Signatures) and MSDS-TDS (Token Digit Strings), contributed by 402 users, with 20 genuine samples and 20 skilled forgeries per user per subset. MSDS-ChS consists of handwritten Chinese signatures, which, to the best of our knowledge, is the largest publicly available Chinese signature dataset for handwriting verification, at least eight times larger than existing online datasets. Meanwhile, MSDS-TDS consists of handwritten Token Digit Strings, i.e, the actual phone numbers of users, which have not been explored yet. Extensive experiments with different baselines are respectively conducted for MSDS-ChS and MSDS-TDS. Surprisingly, verification performances of state-of-the-art methods on MSDS-TDS are generally better than those on MSDS-ChS, which indicates that the handwritten Token Digit String could be a more effective biometric than handwritten Chinese signature. This is a promising discovery that could inspire us to explore new biometric traits. The MSDS dataset is available at https://github.com/HCIILAB/MSDS.

Reinforcement learning from verifiable rewards (RLVR) has recently gained attention for its ability to elicit self-evolved reasoning capabilitie from base language models without explicit reasoning supervisions, as demonstrated by DeepSeek-R1. While prior work on RLVR has primarily focused on mathematical and coding domains, its applicability to other tasks and domains remains unexplored. In this work, we investigate whether medical reasoning can emerge from RLVR. We introduce Med-RLVR as an initial study of RLVR in the medical domain leveraging medical multiple-choice question answering (MCQA) data as verifiable labels. Our results demonstrate that RLVR is not only effective for math and coding but also extends successfully to medical question answering. Notably, Med-RLVR achieves performance comparable to traditional supervised fine-tuning (SFT) on in-distribution tasks while significantly improving out-of-distribution generalization, with an 8-point accuracy gain. Further analysis of training dynamics reveals that, with no explicit reasoning supervision, reasoning emerges from the 3B-parameter base model. These findings underscore the potential of RLVR in domains beyond math and coding, opening new avenues for its application in knowledge-intensive fields such as medicine.

We show that reinforcement learning with verifiable rewards (RLVR) can elicit strong mathematical reasoning in certain models even with spurious rewards that have little, no, or even negative correlation with the correct answer. For example, RLVR improves MATH-500 performance for Qwen2.5-Math-7B in absolute points by 21.4% (random reward), 13.8% (format reward), 24.1% (incorrect label), 26.0% (1-shot RL), and 27.1% (majority voting) -- nearly matching the 29.1% gained with ground truth rewards. However, the spurious rewards that work for Qwen often fail to yield gains with other model families like Llama3 or OLMo2. In particular, we find code reasoning -- thinking in code without actual code execution -- to be a distinctive Qwen2.5-Math behavior that becomes significantly more frequent after RLVR, from 65% to over 90%, even with spurious rewards. Overall, we hypothesize that, given the lack of useful reward signal, RLVR must somehow be surfacing useful reasoning representations learned during pretraining, although the exact mechanism remains a topic for future work. We suggest that future RLVR research should possibly be validated on diverse models rather than a single de facto choice, as we show that it is easy to get significant performance gains on Qwen models even with completely spurious reward signals.

Software testing and verification are critical for ensuring the reliability and security of modern software systems. Traditionally, formal verification techniques, such as model checking and theorem proving, have provided rigorous frameworks for detecting bugs and vulnerabilities. However, these methods often face scalability challenges when applied to complex, real-world programs. Recently, the advent of Large Language Models (LLMs) has introduced a new paradigm for software analysis, leveraging their ability to understand insecure coding practices. Although LLMs demonstrate promising capabilities in tasks such as bug prediction and invariant generation, they lack the formal guarantees of classical methods. This paper presents a comprehensive study of state-of-the-art software testing and verification, focusing on three key approaches: classical formal methods, LLM-based analysis, and emerging hybrid techniques, which combine their strengths. We explore each approach's strengths, limitations, and practical applications, highlighting the potential of hybrid systems to address the weaknesses of standalone methods. We analyze whether integrating formal rigor with LLM-driven insights can enhance the effectiveness and scalability of software verification, exploring their viability as a pathway toward more robust and adaptive testing frameworks.

Large Language Models (LLMs) have achieved remarkable success across various industries due to their exceptional generative capabilities. However, for safe and effective real-world deployments, ensuring honesty and helpfulness is critical. This paper addresses the question: Can we prioritize the helpfulness of LLMs while preserving their honesty? To begin with, we establish exhaustive principles aimed at guaranteeing the honesty of LLM. Additionally, we introduce a novel dataset, referred to as HoneSet, comprising 930 queries spanning six categories meticulously crafted to assess an LLM's capacity for maintaining honesty. Subsequently, we present two approaches to augmenting honesty and helpfulness in LLMs: a training-free enhancement and a fine-tuning-based improvement. The training-free approach, which is based on curiosity-driven prompting, empowers LLMs to articulate internal confusion and uncertainty regarding queries, thereby optimizing their responses. Conversely, the fine-tuning-based method employs a two-stage process inspired by curriculum learning: initially instructing LLMs to discern between honest and dishonest responses, then refining their training to enhance helpfulness. Experiments conducted on nine prominent LLMs demonstrate a significant improvement in alignment with honesty across all models through the implementation of our proposed enhancements. Particularly noteworthy is the 65.3% enhancement observed in Llama3-8b and the remarkable 124.7% improvement in Mistral-7b, as measured by the H^{2} (honest and helpful) assessment. We believe that our work can pave the way for developing more trustworthy LLMs for real-world applications.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful framework for improving the reasoning abilities of Large Language Models (LLMs). However, current methods such as GRPO rely only on problems where the model responses to the same input differ in correctness, while ignoring those where all responses receive the same reward - so-called zero-variance prompts. In this work, we argue that such prompts are not useless but can, in fact, provide meaningful feedback for policy optimization. To this end, we introduce RL with Zero-Variance Prompts (RL-ZVP), a novel algorithm that extract learning signals from zero-variance prompts. RL-ZVP directly rewards correctness and penalizes errors even without contrasting responses, modulating feedback with token-level characteristics to preserve informative, nuanced signals. Across six math reasoning benchmarks, RL-ZVP achieves significant improvements of up to 8.61 points in accuracy and 7.77 points in pass rate over GRPO, while consistently outperforming other baselines that filter out zero-variance prompts. These results highlight the untapped potential of learning from zero-variance prompts in RLVR.

Reinforcement Learning with Verifiable Rewards (RLVR) has markedly enhanced the reasoning abilities of large language models (LLMs). Its success, however, largely depends on strong base models with rich world knowledge, yielding only modest improvements for small-size language models (SLMs). To address this limitation, we investigate Guided GRPO, which injects ground-truth reasoning steps into roll-out trajectories to compensate for SLMs' inherent weaknesses. Through a comprehensive study of various guidance configurations, we find that naively adding guidance delivers limited gains. These insights motivate G^2RPO-A, an adaptive algorithm that automatically adjusts guidance strength in response to the model's evolving training dynamics. Experiments on mathematical reasoning and code-generation benchmarks confirm that G^2RPO-A substantially outperforms vanilla GRPO. Our code and models are available at https://github.com/T-Lab-CUHKSZ/G2RPO-A.

Machine learning programs, such as those performing inference, fine-tuning, and training of LLMs, are commonly delegated to untrusted compute providers. To provide correctness guarantees for the client, we propose adapting the cryptographic notion of refereed delegation to the machine learning setting. This approach enables a computationally limited client to delegate a program to multiple untrusted compute providers, with a guarantee of obtaining the correct result if at least one of them is honest. Refereed delegation of ML programs poses two technical hurdles: (1) an arbitration protocol to resolve disputes when compute providers disagree on the output, and (2) the ability to bitwise reproduce ML programs across different hardware setups, For (1), we design Verde, a dispute arbitration protocol that efficiently handles the large scale and graph-based computational model of modern ML programs. For (2), we build RepOps (Reproducible Operators), a library that eliminates hardware "non-determinism" by controlling the order of floating point operations performed on all hardware. Our implementation shows that refereed delegation achieves both strong guarantees for clients and practical overheads for compute providers.

Reinforcement learning (RL) has recently emerged as a compelling approach for enhancing the reasoning capabilities of large language models (LLMs), where an LLM generator serves as a policy guided by a verifier (reward model). However, current RL post-training methods for LLMs typically use verifiers that are fixed (rule-based or frozen pretrained) or trained discriminatively via supervised fine-tuning (SFT). Such designs are susceptible to reward hacking and generalize poorly beyond their training distributions. To overcome these limitations, we propose Tango, a novel framework that uses RL to concurrently train both an LLM generator and a verifier in an interleaved manner. A central innovation of Tango is its generative, process-level LLM verifier, which is trained via RL and co-evolves with the generator. Importantly, the verifier is trained solely based on outcome-level verification correctness rewards without requiring explicit process-level annotations. This generative RL-trained verifier exhibits improved robustness and superior generalization compared to deterministic or SFT-trained verifiers, fostering effective mutual reinforcement with the generator. Extensive experiments demonstrate that both components of Tango achieve state-of-the-art results among 7B/8B-scale models: the generator attains best-in-class performance across five competition-level math benchmarks and four challenging out-of-domain reasoning tasks, while the verifier leads on the ProcessBench dataset. Remarkably, both components exhibit particularly substantial improvements on the most difficult mathematical reasoning problems. Code is at: https://github.com/kaiwenzha/rl-tango.

Assessing the quality of Large Language Model (LLM) outputs presents a critical challenge. Previous methods either rely on text-level information (e.g., reward models, majority voting), which can overfit to superficial cues, or on calibrated confidence from token probabilities, which would fail on less-calibrated models. Yet both of these signals are, in fact, partial projections of a richer source of information: the model's internal hidden states. Early layers, closer to token embeddings, preserve semantic and lexical features that underpin text-based judgments, while later layers increasingly align with output logits, embedding confidence-related information. This paper explores hidden states directly as a unified foundation for verification. We show that the correctness of a solution is encoded as a geometrically separable signature within the trajectory of hidden activations. To validate this, we present Clue (Clustering and Experience-based Verification), a deliberately minimalist, non-parametric verifier. With no trainable parameters, CLUE only summarizes each reasoning trace by an hidden state delta and classifies correctness via nearest-centroid distance to ``success'' and ``failure'' clusters formed from past experience. The simplicity of this method highlights the strength of the underlying signal. Empirically, CLUE consistently outperforms LLM-as-a-judge baselines and matches or exceeds modern confidence-based methods in reranking candidates, improving both top-1 and majority-vote accuracy across AIME 24/25 and GPQA. As a highlight, on AIME 24 with a 1.5B model, CLUE boosts accuracy from 56.7% (majority@64) to 70.0% (top-maj@16).

Recent advancements in large language models (LLMs) have significantly enhanced text generation capabilities, yet evaluating their performance in generative writing remains a challenge. Existing benchmarks primarily focus on generic text generation or limited in writing tasks, failing to capture the diverse requirements of high-quality written contents across various domains. To bridge this gap, we present WritingBench, a comprehensive benchmark designed to evaluate LLMs across 6 core writing domains and 100 subdomains, encompassing creative, persuasive, informative, and technical writing. We further propose a query-dependent evaluation framework that empowers LLMs to dynamically generate instance-specific assessment criteria. This framework is complemented by a fine-tuned critic model for criteria-aware scoring, enabling evaluations in style, format and length. The framework's validity is further demonstrated by its data curation capability, which enables 7B-parameter models to approach state-of-the-art (SOTA) performance. We open-source the benchmark, along with evaluation tools and modular framework components, to advance the development of LLMs in writing.

As post-training techniques evolve, large language models (LLMs) are increasingly augmented with structured multi-step reasoning abilities, often optimized through reinforcement learning. These reasoning-enhanced models outperform standard LLMs on complex tasks and now underpin many commercial LLM APIs. However, to protect proprietary behavior and reduce verbosity, providers typically conceal the reasoning traces while returning only the final answer. This opacity introduces a critical transparency gap: users are billed for invisible reasoning tokens, which often account for the majority of the cost, yet have no means to verify their authenticity. This opens the door to token count inflation, where providers may overreport token usage or inject synthetic, low-effort tokens to inflate charges. To address this issue, we propose CoIn, a verification framework that audits both the quantity and semantic validity of hidden tokens. CoIn constructs a verifiable hash tree from token embedding fingerprints to check token counts, and uses embedding-based relevance matching to detect fabricated reasoning content. Experiments demonstrate that CoIn, when deployed as a trusted third-party auditor, can effectively detect token count inflation with a success rate reaching up to 94.7%, showing the strong ability to restore billing transparency in opaque LLM services. The dataset and code are available at https://github.com/CASE-Lab-UMD/LLM-Auditing-CoIn.

Large language models (LLMs) excel at general mathematical reasoning but fail catastrophically on specialized technical mathematics. In wireless communications, where problems require precise manipulation of information-theoretic bounds, optimization constraints, and signal processing formulations, even state-of-the-art models struggle to achieve competent performance. We present WirelessMathLM, demonstrating that compact models (0.5B-7B parameters) can match or exceed much larger models through domain-specific reinforcement learning with verifiable rewards. Our key insight is that wireless mathematics problems possess a unique property--verifiable correctness--that enables effective reinforcement learning without human feedback. We construct WirelessMathBench-XL, a comprehensive benchmark of 4,027 problems from 970 papers. Using Group Relative Policy Optimization (GRPO) with binary verification rewards, we train models directly from base checkpoints without supervised warm-start. Our 7B model achieves 39.5% accuracy on WirelessMathBench-XL, approaching GPT-4o (40.4%) while using about 100 times fewer parameters than DeepSeek-R1 (671B, 57.4%). Remarkably, GRPO training nearly doubles performance across all model scales (0.5B +11%, 3B +103%, 7B +81%), with positive transfer to general mathematics benchmarks--our models gain +8.4 points on average across MATH, Minerva-Math, OlympiadBench, AMC, and AIME without any training on these tasks.

Inference-time scaling via repeated sampling has shown promise in reasoning tasks, but its effectiveness in multilingual generation remains underexplored. We evaluate this approach using perplexity- and reward-based verifiers on two multilingual benchmarks: the Aya Evaluation Suite and m-ArenaHard. Our results show consistent quality improvements, with gains exceeding 35% in some cases. While perplexity-based scoring is effective for open-ended prompts, only reward-based verifiers improve performance on tasks requiring reasoning (e.g., math, code). Our results demonstrate the broader utility of repeated sampling for multilingual text generation and underscore the importance of selecting right verifiers for the task.

Automated Essay Scoring (AES) holds significant promise in the field of education, helping educators to mark larger volumes of essays and provide timely feedback. However, Arabic AES research has been limited by the lack of publicly available essay data. This study introduces AR-AES, an Arabic AES benchmark dataset comprising 2046 undergraduate essays, including gender information, scores, and transparent rubric-based evaluation guidelines, providing comprehensive insights into the scoring process. These essays come from four diverse courses, covering both traditional and online exams. Additionally, we pioneer the use of AraBERT for AES, exploring its performance on different question types. We find encouraging results, particularly for Environmental Chemistry and source-dependent essay questions. For the first time, we examine the scale of errors made by a BERT-based AES system, observing that 96.15 percent of the errors are within one point of the first human marker's prediction, on a scale of one to five, with 79.49 percent of predictions matching exactly. In contrast, additional human markers did not exceed 30 percent exact matches with the first marker, with 62.9 percent within one mark. These findings highlight the subjectivity inherent in essay grading, and underscore the potential for current AES technology to assist human markers to grade consistently across large classes.

Prompt engineering is critical for the development of LLM-based applications. However, it is usually done manually in a "trial and error" fashion. This manual procedure can be time consuming, ineffective, and the generated prompts are, in a lot of cases, sub-optimal. Even for the prompts which seemingly work well, there is always a lingering question: can the prompts be made better with further modifications? To address these questions, in this paper, we investigate prompt engineering automation. We consider a specific use case scenario in which developers/users have drafted initial prompts, but lack the time/expertise to optimize them. We propose PRewrite, an automated tool to rewrite these drafts and to generate highly effective new prompts. PRewrite is based on the Reinforcement Learning (RL) framework which allows for end-to-end optimization and our design allows the RL search to happen in a large action space. The automated tool leverages manually crafted prompts as starting points which makes the rewriting procedure more guided and efficient. The generated prompts are human readable, and self-explanatory, unlike some of those in previous works. We conducted extensive experiments on diverse datasets and found that the prompts generated with this new method not only outperform professionally crafted prompts, but also prompts generated with other previously proposed methods.

Self-awareness, i.e., the ability to assess and correct one's own generation, is a fundamental aspect of human intelligence, making its replication in large language models (LLMs) an important yet challenging task. Previous works tackle this by employing extensive reinforcement learning or rather relying on large external verifiers. In this work, we propose Refine via Intrinsic Self-Verification (ReVISE), an efficient and effective framework that enables LLMs to self-correct their outputs through self-verification. The core idea of ReVISE is to enable LLMs to verify their reasoning processes and continually rethink reasoning trajectories based on its verification. We introduce a structured curriculum based upon online preference learning to implement this efficiently. Specifically, as ReVISE involves two challenging tasks (i.e., self-verification and reasoning correction), we tackle each task sequentially using curriculum learning, collecting both failed and successful reasoning paths to construct preference pairs for efficient training. During inference, our approach enjoys natural test-time scaling by integrating self-verification and correction capabilities, further enhanced by our proposed confidence-aware decoding mechanism. Our experiments on various reasoning tasks demonstrate that ReVISE achieves efficient self-correction and significantly improves reasoning performance.

As large language models (LLMs) advance in conversational and reasoning capabilities, their practical application in healthcare has become a critical research focus. However, there is a notable gap between the performance of medical LLMs on static benchmarks such as USMLE and their utility in real-world clinical decision-making. This discrepancy arises because traditional exams fail to capture the dynamic, interactive nature of medical consultations. To address this challenge, we introduce a novel dynamic verification framework that moves beyond static answer verifier, establishing a large-scale, high-fidelity interactive reinforcement learning system. Our framework comprises two key components: a Patient Simulator that creates realistic clinical environments using de-identified medical records, and a Clinical Rubrics Generator that dynamically produces multi-dimensional evaluation metrics. Building on this foundation, we develop Baichuan-M2, a 32B-parameter medical augmented reasoning model trained through a multi-stage reinforcement learning strategy with an improved Group Relative Policy Optimization (GRPO) algorithm. Evaluated on HealthBench, Baichuan-M2 outperforms all other open-source models and most advanced closed-source counterparts, achieving a score above 32 on the challenging HealthBench Hard benchmark-previously exceeded only by GPT-5. Our work demonstrates that robust dynamic verifier system is essential for aligning LLM capabilities with practical clinical applications, establishing a new Pareto front in the performance-parameter trade-off for medical AI deployment.

Teaching Computer Science (CS) by having students write programs by hand on paper has key pedagogical advantages: It allows focused learning and requires careful thinking compared to the use of Integrated Development Environments (IDEs) with intelligent support tools or "just trying things out". The familiar environment of pens and paper also lessens the cognitive load of students with no prior experience with computers, for whom the mere basic usage of computers can be intimidating. Finally, this teaching approach opens learning opportunities to students with limited access to computers. However, a key obstacle is the current lack of teaching methods and support software for working with and running handwritten programs. Optical character recognition (OCR) of handwritten code is challenging: Minor OCR errors, perhaps due to varied handwriting styles, easily make code not run, and recognizing indentation is crucial for languages like Python but is difficult to do due to inconsistent horizontal spacing in handwriting. Our approach integrates two innovative methods. The first combines OCR with an indentation recognition module and a language model designed for post-OCR error correction without introducing hallucinations. This method, to our knowledge, surpasses all existing systems in handwritten code recognition. It reduces error from 30\% in the state of the art to 5\% with minimal hallucination of logical fixes to student programs. The second method leverages a multimodal language model to recognize handwritten programs in an end-to-end fashion. We hope this contribution can stimulate further pedagogical research and contribute to the goal of making CS education universally accessible. We release a dataset of handwritten programs and code to support future research at https://github.com/mdoumbouya/codeocr

Recent advances in large reasoning models have leveraged reinforcement learning with verifiable rewards (RLVR) to improve reasoning capabilities. However, scaling these methods typically requires extensive rollout computation and large datasets, leading to high training costs and low data efficiency. To mitigate this issue, we propose DEPO, a Data-Efficient Policy Optimization pipeline that combines optimized strategies for both offline and online data selection. In the offline phase, we curate a high-quality subset of training samples based on diversity, influence, and appropriate difficulty. During online RLVR training, we introduce a sample-level explorability metric to dynamically filter samples with low exploration potential, thereby reducing substantial rollout computational costs. Furthermore, we incorporate a replay mechanism for under-explored samples to ensure adequate training, which enhances the model's final convergence performance. Experiments across five reasoning benchmarks show that DEPO consistently outperforms existing methods in both offline and online data selection scenarios. Notably, using only 20% of the training data, our approach achieves a 1.85 times speed-up on AIME24 and a 1.66 times speed-up on AIME25 compared to GRPO trained on the full dataset.

Test-time scaling has shown considerable success in improving the performance of language models on complex reasoning tasks without requiring fine-tuning. However, current strategies such as self-reflection primarily focus on logical or structural refinement. They do not leverage the guiding potential of affective feedback. Inspired by psychological research showing that emotions can modulate cognitive performance, we introduce HEART--a novel framework that uses emotionally-driven prompts for iterative self-correction. HEART provides feedback on a model's incorrect response using a curated set of concise, emotionally charged phrases based on the six universal emotions categorized by Dr. Paul Ekman. By systematically varying the emotional tone of the feedback across iterations, our method guides the model to escape flawed reasoning paths and explore more promising alternatives. We evaluate our framework on challenging reasoning benchmarks including OlympiadBench, Humanity's Last Exam, and SimpleQA. Our results reveal a significant new phenomenon: when guided by an oracle verifier, this affective iteration protocol unlocks significantly deeper reasoning, leading to consistent and substantial increases in accuracy over state-of-the-art baselines with the same verifier. However, we also identify a critical bottleneck for practical deployment. In a verifier-free setting, it struggles to harness these gains consistently, highlighting as a key challenge for future work. Our findings suggest that the next frontier in machine reasoning may lie not just in refining logic, but also in understanding and leveraging the `HEART' of the models.