Daily Papers

Large Language Models (LLMs), constrained by limited context windows, often face significant performance degradation when reasoning over long contexts. To address this, Retrieval-Augmented Generation (RAG) retrieves and reasons over chunks but frequently sacrifices logical coherence due to its reliance on similarity-based rankings. Similarly, divide-and-conquer frameworks (DCF) split documents into small chunks for independent reasoning and aggregation. While effective for local reasoning, DCF struggles to capture long-range dependencies and risks inducing conflicts by processing chunks in isolation. To overcome these limitations, we propose ToM, a novel Tree-oriented MapReduce framework for long-context reasoning. ToM leverages the inherent hierarchical structure of long documents (e.g., main headings and subheadings) by constructing a DocTree through hierarchical semantic parsing and performing bottom-up aggregation. Using a Tree MapReduce approach, ToM enables recursive reasoning: in the Map step, rationales are generated at child nodes; in the Reduce step, these rationales are aggregated across sibling nodes to resolve conflicts or reach consensus at parent nodes. Experimental results on 70B+ LLMs show that ToM significantly outperforms existing divide-and-conquer frameworks and retrieval-augmented generation methods, achieving better logical coherence and long-context reasoning. Our code is available at https://github.com/gjn12-31/ToM .

Enlarging the context window of large language models (LLMs) has become a crucial research area, particularly for applications involving extremely long texts. In this work, we propose a novel training-free framework for processing long texts, utilizing a divide-and-conquer strategy to achieve comprehensive document understanding. The proposed LLMtimesMapReduce framework splits the entire document into several chunks for LLMs to read and then aggregates the intermediate answers to produce the final output. The main challenge for divide-and-conquer long text processing frameworks lies in the risk of losing essential long-range information when splitting the document, which can lead the model to produce incomplete or incorrect answers based on the segmented texts. Disrupted long-range information can be classified into two categories: inter-chunk dependency and inter-chunk conflict. We design a structured information protocol to better cope with inter-chunk dependency and an in-context confidence calibration mechanism to resolve inter-chunk conflicts. Experimental results demonstrate that LLMtimesMapReduce can outperform representative open-source and commercial long-context LLMs, and is applicable to several different models.

Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without requiring expert knowledge. However, these solvers exhibit significant performance degradation when applied to large-scale CO problems. Recently, two-stage neural methods motivated by divide-and-conquer strategies have shown efficiency in addressing large-scale CO problems. Nevertheless, the performance of these methods highly relies on problem-specific heuristics in either the dividing or the conquering procedure, which limits their applicability to general CO problems. Moreover, these methods employ separate training schemes and ignore the interdependencies between the dividing and conquering strategies, often leading to sub-optimal solutions. To tackle these drawbacks, this article develops a unified neural divide-and-conquer framework (i.e., UDC) for solving general large-scale CO problems. UDC offers a Divide-Conquer-Reunion (DCR) training method to eliminate the negative impact of a sub-optimal dividing policy. Employing a high-efficiency Graph Neural Network (GNN) for global instance dividing and a fixed-length sub-path solver for conquering divided sub-problems, the proposed UDC framework demonstrates extensive applicability, achieving superior performance in 10 representative large-scale CO problems. The code is available at https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/UDC-Large-scale-CO-master.

Retrieve-then-read and generate-then-read are two typical solutions to handle unknown and known questions in open-domain question-answering, while the former retrieves necessary external knowledge and the later prompt the large language models to generate internal known knowledge encoded in the parameters. However, few of previous works consider the compositional unknown questions, which consist of several known or unknown sub-questions. Thus, simple binary classification (known or unknown) becomes sub-optimal and inefficient since it will call external retrieval excessively for each compositional unknown question. To this end, we propose the first Compositional unknown Question-Answering dataset (CuQA), and introduce a Self Divide-and-Conquer (Self-DC) framework to empower LLMs to adaptively call different methods on-demand, resulting in better performance and efficiency. Experimental results on two datasets (CuQA and FreshQA) demonstrate that Self-DC can achieve comparable or even better performance with much more less retrieval times compared with several strong baselines.

Most existing GUI agents typically depend on non-vision inputs like HTML source code or accessibility trees, limiting their flexibility across diverse software environments and platforms. Current multimodal large language models (MLLMs), which excel at using vision to ground real-world objects, offer a potential alternative. However, they often struggle with accurately localizing GUI elements -- a critical requirement for effective GUI automation -- due to the semantic gap between real-world objects and GUI elements. In this work, we introduce Ponder & Press, a divide-and-conquer framework for general computer control using only visual input. Our approach combines an general-purpose MLLM as an 'interpreter', responsible for translating high-level user instructions into detailed action descriptions, with a GUI-specific MLLM as a 'locator' that precisely locates GUI elements for action placement. By leveraging a purely visual input, our agent offers a versatile, human-like interaction paradigm applicable to a wide range of applications. Ponder & Press locator outperforms existing models by +22.5% on the ScreenSpot GUI grounding benchmark. Both offline and interactive agent benchmarks across various GUI environments -- including web pages, desktop software, and mobile UIs -- demonstrate that Ponder & Press framework achieves state-of-the-art performance, highlighting the potential of visual GUI agents. Refer to the project homepage https://invinciblewyq.github.io/ponder-press-page/

Pretrained Vision-Language Models (VLMs) have achieved remarkable performance in image retrieval from text. However, their performance drops drastically when confronted with linguistically complex texts that they struggle to comprehend. Inspired by the Divide-and-Conquer algorithm and dual-process theory, in this paper, we regard linguistically complex texts as compound proposition texts composed of multiple simple proposition sentences and propose an end-to-end Neural Divide-and-Conquer Reasoning framework, dubbed NDCR. It contains three main components: 1) Divide: a proposition generator divides the compound proposition text into simple proposition sentences and produces their corresponding representations, 2) Conquer: a pretrained VLMs-based visual-linguistic interactor achieves the interaction between decomposed proposition sentences and images, 3) Combine: a neural-symbolic reasoner combines the above reasoning states to obtain the final solution via a neural logic reasoning approach. According to the dual-process theory, the visual-linguistic interactor and neural-symbolic reasoner could be regarded as analogical reasoning System 1 and logical reasoning System 2. We conduct extensive experiments on a challenging image retrieval from contextual descriptions data set. Experimental results and analyses indicate NDCR significantly improves performance in the complex image-text reasoning problem. Code link: https://github.com/YunxinLi/NDCR.

Recent advancements in Large Language Models (LLMs) have expanded their capabilities to multimodal contexts, including comprehensive video understanding. However, processing extensive videos such as 24-hour CCTV footage or full-length films presents significant challenges due to the vast data and processing demands. Traditional methods, like extracting key frames or converting frames to text, often result in substantial information loss. To address these shortcomings, we develop OmAgent, efficiently stores and retrieves relevant video frames for specific queries, preserving the detailed content of videos. Additionally, it features an Divide-and-Conquer Loop capable of autonomous reasoning, dynamically invoking APIs and tools to enhance query processing and accuracy. This approach ensures robust video understanding, significantly reducing information loss. Experimental results affirm OmAgent's efficacy in handling various types of videos and complex tasks. Moreover, we have endowed it with greater autonomy and a robust tool-calling system, enabling it to accomplish even more intricate tasks.

We develop a novel, general and computationally efficient framework, called Divide and Conquer Dynamic Programming (DCDP), for localizing change points in time series data with high-dimensional features. DCDP deploys a class of greedy algorithms that are applicable to a broad variety of high-dimensional statistical models and can enjoy almost linear computational complexity. We investigate the performance of DCDP in three commonly studied change point settings in high dimensions: the mean model, the Gaussian graphical model, and the linear regression model. In all three cases, we derive non-asymptotic bounds for the accuracy of the DCDP change point estimators. We demonstrate that the DCDP procedures consistently estimate the change points with sharp, and in some cases, optimal rates while incurring significantly smaller computational costs than the best available algorithms. Our findings are supported by extensive numerical experiments on both synthetic and real data.

Despite recent progress made by large language models in code generation, they still struggle with programs that meet complex requirements. Recent work utilizes plan-and-solve decomposition to decrease the complexity and leverage self-tests to refine the generated program. Yet, planning deep-inside requirements in advance can be challenging, and the tests need to be accurate to accomplish self-improvement. To this end, we propose FunCoder, a code generation framework incorporating the divide-and-conquer strategy with functional consensus. Specifically, FunCoder recursively branches off sub-functions as smaller goals during code generation, represented by a tree hierarchy. These sub-functions are then composited to attain more complex objectives. Additionally, we designate functions via a consensus formed by identifying similarities in program behavior, mitigating error propagation. FunCoder outperforms state-of-the-art methods by +9.8% on average in HumanEval, MBPP, xCodeEval and MATH with GPT-3.5 and GPT-4. Moreover, our method demonstrates superiority on smaller models: With FunCoder, StableCode-3b surpasses GPT-3.5 by +18.6% and achieves 97.7% of GPT-4's performance on HumanEval. Further analysis reveals that our proposed dynamic function decomposition is capable of handling complex requirements, and the functional consensus prevails over self-testing in correctness evaluation.

While showing sophisticated reasoning abilities, large language models (LLMs) still struggle with long-horizon decision-making tasks due to deficient exploration and long-term credit assignment, especially in sparse-reward scenarios. Inspired by the divide-and-conquer principle, we propose an innovative framework **GLIDER** (**G**rounding **L**anguage Models as Eff**I**cient **D**ecision-Making Agents via Offline Hi**E**rarchical **R**einforcement Learning) that introduces a parameter-efficient and generally applicable hierarchy to LLM policies. We develop a scheme where the low-level controller is supervised with abstract, step-by-step plans that are learned and instructed by the high-level policy. This design decomposes complicated problems into a series of coherent chain-of-thought reasoning sub-tasks, providing flexible temporal abstraction to significantly enhance exploration and learning for long-horizon tasks. Furthermore, GLIDER facilitates fast online adaptation to non-stationary environments owing to the strong transferability of its task-agnostic low-level skills. Experiments on ScienceWorld and ALFWorld benchmarks show that GLIDER achieves consistent performance gains, along with enhanced generalization capabilities.

We present MicroCinema, a straightforward yet effective framework for high-quality and coherent text-to-video generation. Unlike existing approaches that align text prompts with video directly, MicroCinema introduces a Divide-and-Conquer strategy which divides the text-to-video into a two-stage process: text-to-image generation and image\&text-to-video generation. This strategy offers two significant advantages. a) It allows us to take full advantage of the recent advances in text-to-image models, such as Stable Diffusion, Midjourney, and DALLE, to generate photorealistic and highly detailed images. b) Leveraging the generated image, the model can allocate less focus to fine-grained appearance details, prioritizing the efficient learning of motion dynamics. To implement this strategy effectively, we introduce two core designs. First, we propose the Appearance Injection Network, enhancing the preservation of the appearance of the given image. Second, we introduce the Appearance Noise Prior, a novel mechanism aimed at maintaining the capabilities of pre-trained 2D diffusion models. These design elements empower MicroCinema to generate high-quality videos with precise motion, guided by the provided text prompts. Extensive experiments demonstrate the superiority of the proposed framework. Concretely, MicroCinema achieves SOTA zero-shot FVD of 342.86 on UCF-101 and 377.40 on MSR-VTT. See https://wangyanhui666.github.io/MicroCinema.github.io/ for video samples.

Single-view 3D reconstruction is currently approached from two dominant perspectives: reconstruction of scenes with limited diversity using 3D data supervision or reconstruction of diverse singular objects using large image priors. However, real-world scenarios are far more complex and exceed the capabilities of these methods. We therefore propose a hybrid method following a divide-and-conquer strategy. We first process the scene holistically, extracting depth and semantic information, and then leverage a single-shot object-level method for the detailed reconstruction of individual components. By following a compositional processing approach, the overall framework achieves full reconstruction of complex 3D scenes from a single image. We purposely design our pipeline to be highly modular by carefully integrating specific procedures for each processing step, without requiring an end-to-end training of the whole system. This enables the pipeline to naturally improve as future methods can replace the individual modules. We demonstrate the reconstruction performance of our approach on both synthetic and real-world scenes, comparing favorable against prior works. Project page: https://andreeadogaru.github.io/Gen3DSR.

Unified multimodal models have recently attracted considerable attention for their remarkable abilities in jointly understanding and generating diverse content. However, as contexts integrate increasingly numerous interleaved multimodal tokens, the iterative processes of diffusion denoising and autoregressive decoding impose significant computational overhead. To address this, we propose Hyper-Bagel, a unified acceleration framework designed to simultaneously speed up both multimodal understanding and generation tasks. Our approach uses a divide-and-conquer strategy, employing speculative decoding for next-token prediction and a multi-stage distillation process for diffusion denoising. The framework delivers substantial performance gains, achieving over a 2x speedup in multimodal understanding. For generative tasks, our resulting lossless 6-NFE model yields a 16.67x speedup in text-to-image generation and a 22x speedup in image editing, all while preserving the high-quality output of the original model. We further develop a highly efficient 1-NFE model that enables near real-time interactive editing and generation. By combining advanced adversarial distillation with human feedback learning, this model achieves ultimate cost-effectiveness and responsiveness, making complex multimodal interactions seamless and instantaneous.

Long document summarization systems are critical for domains with lengthy and jargonladen text, yet they present significant challenges to researchers and developers with limited computing resources. Existing solutions mainly focus on efficient attentions or divide-and-conquer strategies. The former reduces theoretical time complexity, but is still memory-heavy. The latter methods sacrifice global context, leading to uninformative and incoherent summaries. This work aims to leverage the memory-efficient nature of divide-and-conquer methods while preserving global context. Concretely, our framework AWESOME uses two novel mechanisms: (1) External memory mechanisms track previously encoded document segments and their corresponding summaries, to enhance global document understanding and summary coherence. (2) Global salient content is further identified beforehand to augment each document segment to support its summarization. Extensive experiments on diverse genres of text, including government reports, transcripts, scientific papers, and novels, show that AWESOME produces summaries with improved informativeness, faithfulness, and coherence than competitive baselines on longer documents, while having a similar or smaller GPU memory footprint.

The network pruning algorithm based on evolutionary multi-objective (EMO) can balance the pruning rate and performance of the network. However, its population-based nature often suffers from the complex pruning optimization space and the highly resource-consuming pruning structure verification process, which limits its application. To this end, this paper proposes an EMO joint pruning with multiple sub-networks (EMO-PMS) to reduce space complexity and resource consumption. First, a divide-and-conquer EMO network pruning framework is proposed, which decomposes the complex EMO pruning task on the whole network into easier sub-tasks on multiple sub-networks. On the one hand, this decomposition reduces the pruning optimization space and decreases the optimization difficulty; on the other hand, the smaller network structure converges faster, so the computational resource consumption of the proposed algorithm is lower. Secondly, a sub-network training method based on cross-network constraints is designed so that the sub-network can process the features generated by the previous one through feature constraints. This method allows sub-networks optimized independently to collaborate better and improves the overall performance of the pruned network. Finally, a multiple sub-networks joint pruning method based on EMO is proposed. For one thing, it can accurately measure the feature processing capability of the sub-networks with the pre-trained feature selector. For another, it can combine multi-objective pruning results on multiple sub-networks through global performance impairment ranking to design a joint pruning scheme. The proposed algorithm is validated on three datasets with different challenging. Compared with fifteen advanced pruning algorithms, the experiment results exhibit the effectiveness and efficiency of the proposed algorithm.

Recent advancements in human video generation and animation tasks, driven by diffusion models, have achieved significant progress. However, expressive and realistic human animation remains challenging due to the trade-off between motion naturalness and visual fidelity. To address this, we propose AlignHuman, a framework that combines Preference Optimization as a post-training technique with a divide-and-conquer training strategy to jointly optimize these competing objectives. Our key insight stems from an analysis of the denoising process across timesteps: (1) early denoising timesteps primarily control motion dynamics, while (2) fidelity and human structure can be effectively managed by later timesteps, even if early steps are skipped. Building on this observation, we propose timestep-segment preference optimization (TPO) and introduce two specialized LoRAs as expert alignment modules, each targeting a specific dimension in its corresponding timestep interval. The LoRAs are trained using their respective preference data and activated in the corresponding intervals during inference to enhance motion naturalness and fidelity. Extensive experiments demonstrate that AlignHuman improves strong baselines and reduces NFEs during inference, achieving a 3.3times speedup (from 100 NFEs to 30 NFEs) with minimal impact on generation quality. Homepage: https://alignhuman.github.io/{https://alignhuman.github.io/}

While Large Language Models (LLMs) demonstrate impressive capabilities, they still struggle with generating factually incorrect content (i.e., hallucinations). A promising approach to mitigate this issue is enabling models to express uncertainty when unsure. Previous research on uncertainty modeling has primarily focused on short-form QA, but realworld applications often require much longer responses. In this work, we introduce the task of Long-form Generation with Uncertainty(LoGU). We identify two key challenges: Uncertainty Suppression, where models hesitate to express uncertainty, and Uncertainty Misalignment, where models convey uncertainty inaccurately. To tackle these challenges, we propose a refinement-based data collection framework and a two-stage training pipeline. Our framework adopts a divide-and-conquer strategy, refining uncertainty based on atomic claims. The collected data are then used in training through supervised fine-tuning (SFT) and direct preference optimization (DPO) to enhance uncertainty expression. Extensive experiments on three long-form instruction following datasets show that our method significantly improves accuracy, reduces hallucinations, and maintains the comprehensiveness of responses.

Recently, significant progress has been made in text-based motion generation, enabling the generation of diverse and high-quality human motions that conform to textual descriptions. However, it remains challenging to generate fine-grained or stylized motions due to the lack of datasets annotated with detailed textual descriptions. By adopting a divide-and-conquer strategy, we propose a new framework named Fine-Grained Human Motion Diffusion Model (FG-MDM) for human motion generation. Specifically, we first parse previous vague textual annotation into fine-grained description of different body parts by leveraging a large language model (GPT-3.5). We then use these fine-grained descriptions to guide a transformer-based diffusion model. FG-MDM can generate fine-grained and stylized motions even outside of the distribution of the training data. Our experimental results demonstrate the superiority of FG-MDM over previous methods, especially the strong generalization capability. We will release our fine-grained textual annotations for HumanML3D and KIT.

Developing a general robot manipulation system capable of performing a wide range of tasks in complex, dynamic, and unstructured real-world environments has long been a challenging task. It is widely recognized that achieving human-like efficiency and robustness manipulation requires the robotic brain to integrate a comprehensive set of functions, such as task planning, policy generation, anomaly monitoring and handling, and long-term memory, achieving high-efficiency operation across all functions. Vision-Language Models (VLMs), pretrained on massive multimodal data, have acquired rich world knowledge, exhibiting exceptional scene understanding and multimodal reasoning capabilities. However, existing methods typically focus on realizing only a single function or a subset of functions within the robotic brain, without integrating them into a unified cognitive architecture. Inspired by a divide-and-conquer strategy and the architecture of the human brain, we propose FrankenBot, a VLM-driven, brain-morphic robotic manipulation framework that achieves both comprehensive functionality and high operational efficiency. Our framework includes a suite of components, decoupling a part of key functions from frequent VLM calls, striking an optimal balance between functional completeness and system efficiency. Specifically, we map task planning, policy generation, memory management, and low-level interfacing to the cortex, cerebellum, temporal lobe-hippocampus complex, and brainstem, respectively, and design efficient coordination mechanisms for the modules. We conducted comprehensive experiments in both simulation and real-world robotic environments, demonstrating that our method offers significant advantages in anomaly detection and handling, long-term memory, operational efficiency, and stability -- all without requiring any fine-tuning or retraining.

We introduce a framework for translating game descriptions in natural language into extensive-form representations in game theory, leveraging Large Language Models (LLMs) and in-context learning. Given the varying levels of strategic complexity in games, such as perfect versus imperfect information, directly applying in-context learning would be insufficient. To address this, we introduce a two-stage framework with specialized modules to enhance in-context learning, enabling it to divide and conquer the problem effectively. In the first stage, we tackle the challenge of imperfect information by developing a module that identifies information sets along and the corresponding partial tree structure. With this information, the second stage leverages in-context learning alongside a self-debugging module to produce a complete extensive-form game tree represented using pygambit, the Python API of a recognized game-theoretic analysis tool called Gambit. Using this python representation enables the automation of tasks such as computing Nash equilibria directly from natural language descriptions. We evaluate the performance of the full framework, as well as its individual components, using various LLMs on games with different levels of strategic complexity. Our experimental results show that the framework significantly outperforms baseline models in generating accurate extensive-form games, with each module playing a critical role in its success.

In-Context Learning (ICL) emerges as a key feature for Large Language Models (LLMs), allowing them to adapt to new tasks by leveraging task-specific examples without updating model parameters. However, ICL faces challenges with increasing numbers of examples due to performance degradation and quadratic computational costs. In this paper, we propose Logit Arithmetic Reweighting Approach (LARA), a novel framework that enhances ICL by using logit-based ensembling of multiple demonstrations. Our approach divides long input demonstrations into parallelizable shorter inputs to significantly reduce memory requirements, and then effectively aggregate the information by reweighting logits of each group via a non-gradient optimization approach. We further introduce Binary LARA (B-LARA), a variant that constrains weights to binary values to simplify the search space and reduces memory usage by filtering out less informative demonstration groups. Experiments on BBH and MMLU demonstrate that LARA and B-LARA outperform all baseline methods in both accuracy and memory efficiency. We also conduct extensive analysis to show that LARA generalizes well to scenarios of varying numbers of examples from limited to many-shot demonstrations.

Multimodal large language models (MLLMs) have experienced significant advancements recently, but still struggle to recognize and interpret intricate details in high-resolution (HR) images effectively. While state-of-the-art (SOTA) MLLMs claim to process images at 4K resolution, existing MLLM benchmarks only support up to 2K, leaving the capabilities of SOTA models on true HR images largely untested. Furthermore, existing methods for enhancing HR image perception in MLLMs rely on computationally expensive visual instruction tuning. To address these limitations, we introduce HR-Bench, the first deliberately designed benchmark to rigorously evaluate MLLM performance on 4K&8K images. Through extensive experiments, we demonstrate that while downsampling HR images leads to vision information loss, leveraging complementary modalities, e.g., text, can effectively compensate for this loss. Building upon this insight, we propose Divide, Conquer and Combine (DC^2), a novel training-free framework for enhancing MLLM perception of HR images. DC^2 follows a three-staged approach: 1) Divide: recursively partitioning the HR image into patches and merging similar patches to minimize computational overhead, 2) Conquer: leveraging the MLLM to generate accurate textual descriptions for each image patch, and 3) Combine: utilizing the generated text descriptions to enhance the MLLM's understanding of the overall HR image. Extensive experiments show that: 1) the SOTA MLLM achieves 63% accuracy, which is markedly lower than the 87% accuracy achieved by humans on HR-Bench; 2) our DC^2 brings consistent and significant improvements (a relative increase of +6% on HR-Bench and +8% on general multimodal benchmarks). The benchmark and code will be released to facilitate the multimodal R&D community.

Evaluating the quality and variability of text generated by Large Language Models (LLMs) poses a significant, yet unresolved research challenge. Traditional evaluation methods, such as ROUGE and BERTScore, which measure token similarity, often fail to capture the holistic semantic equivalence. This results in a low correlation with human judgments and intuition, which is especially problematic in high-stakes applications like healthcare and finance where reliability, safety, and robust decision-making are highly critical. This work proposes DCR, an automated framework for evaluating and improving the consistency of LLM-generated texts using a divide-conquer-reasoning approach. Unlike existing LLM-based evaluators that operate at the paragraph level, our method employs a divide-and-conquer evaluator (DCE) that breaks down the paragraph-to-paragraph comparison between two generated responses into individual sentence-to-paragraph comparisons, each evaluated based on predefined criteria. To facilitate this approach, we introduce an automatic metric converter (AMC) that translates the output from DCE into an interpretable numeric score. Beyond the consistency evaluation, we further present a reason-assisted improver (RAI) that leverages the analytical reasons with explanations identified by DCE to generate new responses aimed at reducing these inconsistencies. Through comprehensive and systematic empirical analysis, we show that our approach outperforms state-of-the-art methods by a large margin (e.g., +19.3% and +24.3% on the SummEval dataset) in evaluating the consistency of LLM generation across multiple benchmarks in semantic, factual, and summarization consistency tasks. Our approach also substantially reduces nearly 90% of output inconsistencies, showing promise for effective hallucination mitigation.

Customized generation aims to incorporate a novel concept into a pre-trained text-to-image model, enabling new generations of the concept in novel contexts guided by textual prompts. However, customized generation suffers from an inherent trade-off between concept fidelity and editability, i.e., between precisely modeling the concept and faithfully adhering to the prompts. Previous methods reluctantly seek a compromise and struggle to achieve both high concept fidelity and ideal prompt alignment simultaneously. In this paper, we propose a Divide, Conquer, then Integrate (DCI) framework, which performs a surgical adjustment in the early stage of denoising to liberate the fine-tuned model from the fidelity-editability trade-off at inference. The two conflicting components in the trade-off are decoupled and individually conquered by two collaborative branches, which are then selectively integrated to preserve high concept fidelity while achieving faithful prompt adherence. To obtain a better fine-tuned model, we introduce an Image-specific Context Optimization} (ICO) strategy for model customization. ICO replaces manual prompt templates with learnable image-specific contexts, providing an adaptive and precise fine-tuning direction to promote the overall performance. Extensive experiments demonstrate the effectiveness of our method in reconciling the fidelity-editability trade-off.

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

Large deep learning models have achieved remarkable success in many scenarios. However, training large models is usually challenging, e.g., due to the high computational cost, the unstable and painfully slow optimization procedure, and the vulnerability to overfitting. To alleviate these problems, this work studies a divide-and-conquer strategy, i.e., dividing a large model into smaller modules, training them independently, and reassembling the trained modules to obtain the target model. This approach is promising since it avoids directly training large models from scratch. Nevertheless, implementing this idea is non-trivial, as it is difficult to ensure the compatibility of the independently trained modules. In this paper, we present an elegant solution to address this issue, i.e., we introduce a global, shared meta model to implicitly link all the modules together. This enables us to train highly compatible modules that collaborate effectively when they are assembled together. We further propose a module incubation mechanism that enables the meta model to be designed as an extremely shallow network. As a result, the additional overhead introduced by the meta model is minimalized. Though conceptually simple, our method significantly outperforms end-to-end (E2E) training in terms of both final accuracy and training efficiency. For example, on top of ViT-Huge, it improves the accuracy by 2.7% compared to the E2E baseline on ImageNet-1K, while saving the training cost by 43% in the meantime. Code is available at https://github.com/LeapLabTHU/Model-Assembling.

This work investigates the reasoning and planning capabilities of foundation models and their scalability in complex, dynamic environments. We introduce PuzzlePlex, a benchmark designed to assess these capabilities through a diverse set of puzzles. PuzzlePlex consists of 15 types of puzzles, including deterministic and stochastic games of varying difficulty, as well as single-player and two-player scenarios. The PuzzlePlex framework provides a comprehensive environment for each game, and supports extensibility to generate more challenging instances as foundation models evolve. Additionally, we implement customized game-playing strategies for comparison. Building on this benchmark, we develop fine-grained metrics to measure performance and conduct an in-depth analysis of frontier foundation models across two settings: instruction-based and code-based. Furthermore, we systematically investigate their scaling limits. Our findings show that reasoning models outperform others in instruction-based settings, while code-based execution presents greater challenges but offers a scalable and efficient alternative. PuzzlePlex enables targeted evaluation and guides future improvements in reasoning, planning, and generalization for foundation models.

We present ControlLLM, a novel framework that enables large language models (LLMs) to utilize multi-modal tools for solving complex real-world tasks. Despite the remarkable performance of LLMs, they still struggle with tool invocation due to ambiguous user prompts, inaccurate tool selection and parameterization, and inefficient tool scheduling. To overcome these challenges, our framework comprises three key components: (1) a task decomposer that breaks down a complex task into clear subtasks with well-defined inputs and outputs; (2) a Thoughts-on-Graph (ToG) paradigm that searches the optimal solution path on a pre-built tool graph, which specifies the parameter and dependency relations among different tools; and (3) an execution engine with a rich toolbox that interprets the solution path and runs the tools efficiently on different computational devices. We evaluate our framework on diverse tasks involving image, audio, and video processing, demonstrating its superior accuracy, efficiency, and versatility compared to existing methods.

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.

The field of vision-and-language (VL) understanding has made unprecedented progress with end-to-end large pre-trained VL models (VLMs). However, they still fall short in zero-shot reasoning tasks that require multi-step inferencing. To achieve this goal, previous works resort to a divide-and-conquer pipeline. In this paper, we argue that previous efforts have several inherent shortcomings: 1) They rely on domain-specific sub-question decomposing models. 2) They force models to predict the final answer even if the sub-questions or sub-answers provide insufficient information. We address these limitations via IdealGPT, a framework that iteratively decomposes VL reasoning using large language models (LLMs). Specifically, IdealGPT utilizes an LLM to generate sub-questions, a VLM to provide corresponding sub-answers, and another LLM to reason to achieve the final answer. These three modules perform the divide-and-conquer procedure iteratively until the model is confident about the final answer to the main question. We evaluate IdealGPT on multiple challenging VL reasoning tasks under a zero-shot setting. In particular, our IdealGPT outperforms the best existing GPT-4-like models by an absolute 10% on VCR and 15% on SNLI-VE. Code is available at https://github.com/Hxyou/IdealGPT

Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating proof search spaces. While the existing approaches primarily rely on value functions and Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Search (BFS) remains underexplored. This paper investigates whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM's policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a score of 71.31 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.

Test-time compute scaling has emerged as a powerful paradigm for enhancing mathematical reasoning in large language models (LLMs) by allocating additional computational resources during inference. However, current methods employ uniform resource distribution across all reasoning sub-problems, creating fundamental bottlenecks where challenging sub-problems receive insufficient attention while routine operations consume disproportionate resources. This uniform allocation creates performance bottlenecks where additional computational resources yield diminishing returns. Inspired by dual-process theory, we propose SCALE (Selective Resource Allocation), a framework that selectively allocates computational resources based on sub-problem difficulty. SCALE operates through four stages: (1) problem decomposition into sequential reasoning sub-problems, (2) difficulty assessment of each sub-problem to distinguish between routine operations and computationally challenging sub-problems, (3) selective processing mode assignment between System 1 for simple sub-problems and System 2 for complex ones, and (4) sequential execution with context propagation. By concentrating resources on challenging sub-problems while processing routine operations efficiently, SCALE achieves substantial performance improvements with superior resource utilization. Extensive experiments demonstrate that SCALE significantly outperforms uniform scaling baselines, achieving accuracy improvements of up to 13.75 percentage points (57.50% to 71.25% on AIME25) while reducing computational costs by 33%-53%, representing a major advance in test-time scaling that addresses fundamental limitations of current approaches.

Quizzes play a crucial role in education by reinforcing students' understanding of key concepts and encouraging self-directed exploration. However, compiling high-quality quizzes can be challenging and require deep expertise and insight into specific subject matter. Although LLMs have greatly enhanced the efficiency of quiz generation, concerns remain regarding the quality of these AI-generated quizzes and their educational impact on students. To address these issues, we introduce ConQuer, a concept-based quiz generation framework that leverages external knowledge sources. We employ comprehensive evaluation dimensions to assess the quality of the generated quizzes, using LLMs as judges. Our experiment results demonstrate a 4.8% improvement in evaluation scores and a 77.52% win rate in pairwise comparisons against baseline quiz sets. Ablation studies further underscore the effectiveness of each component in our framework. Code available at https://github.com/sofyc/ConQuer.

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.

The integration of Large Language Models (LLMs) into automated theorem proving has shown immense promise, yet is fundamentally constrained by challenges in scaling up both training-time reinforcement learning (RL) and inference-time compute. This paper introduces BFS-Prover-V2, a system designed to address this dual scaling problem. We present two primary innovations. The first is a novel multi-turn off-policy RL framework for continually improving the performance of LLM step-prover at training time. This framework, inspired by the principles of AlphaZero, utilizes a multi-stage expert iteration pipeline featuring adaptive tactic-level data filtering and periodic retraining to surmount the performance plateaus that typically curtail long-term RL in LLM-based agents. The second innovation is a planner-enhanced multi-agent search architecture that scales reasoning capabilities at inference time. This architecture employs a general reasoning model as a high-level planner to iteratively decompose complex theorems into a sequence of simpler subgoals. This hierarchical approach substantially reduces the search space, enabling a team of parallel prover agents to collaborate efficiently by leveraging a shared proof cache. We demonstrate that this dual approach to scaling yields state-of-the-art results on established formal mathematics benchmarks. BFS-Prover-V2 achieves 95.08\% and 41.4\% on the MiniF2F and ProofNet test sets respectively. While demonstrated in the domain of formal mathematics, the RL and inference techniques presented in this work are of broader interest and may be applied to other domains requiring long-horizon multi-turn reasoning and complex search.

In large-scale AI training, Sparse Mixture-of-Experts (s-MoE) layers enable scaling by activating only a small subset of experts per token. An operational challenge in this design is load balancing: routing tokens to minimize the number of idle experts, which is important for the efficient utilization of (costly) GPUs. We provide a theoretical framework for analyzing the Auxiliary-Loss-Free Load Balancing (ALF-LB) procedure -- proposed by DeepSeek's Wang et al. (2024) -- by casting it as a one-step-per-iteration primal-dual method for an assignment problem. First, in a stylized deterministic setting, our framework yields several insightful structural properties: (i) a monotonic improvement of a Lagrangian objective, (ii) a preference rule that moves tokens from overloaded to underloaded experts, and (iii) an approximate-balancing guarantee. Then, we incorporate the stochastic and dynamic nature of AI training using a generalized online optimization formulation. In the online setting, we derive a strong convexity property of the objective that leads to a logarithmic expected regret bound under certain step-size choices. Additionally, we present real experiments on 1B-parameter DeepSeekMoE models to complement our theoretical findings. Together, these results build a principled framework for analyzing the Auxiliary-Loss-Free Load Balancing of s-MoE in AI models.

The Polymorphic Combinatorial Framework (PCF) leverages Large Language Models (LLMs) and mathematical frameworks to guide the meta-prompt enabled design of solution spaces and adaptive AI agents for complex, dynamic environments. Unlike static agent architectures, PCF enables real-time parameter reconfiguration through mathematically-grounded combinatorial spaces, allowing agents to adapt their core behavioral traits dynamically. Grounded in combinatorial logic, topos theory, and rough fuzzy set theory, PCF defines a multidimensional SPARK parameter space (Skills, Personalities, Approaches, Resources, Knowledge) to capture agent behaviors. This paper demonstrates how LLMs can parameterize complex spaces and estimate likely parameter values/variabilities. Using PCF, we parameterized mock caf\'e domains (five levels of complexity), estimated variables/variabilities, and conducted over 1.25 million Monte Carlo simulations. The results revealed trends in agent adaptability and performance across the five complexity tiers, with diminishing returns at higher complexity levels highlighting thresholds for scalable designs. PCF enables the generation of optimized agent configurations for specific scenarios while maintaining logical consistency. This framework supports scalable, dynamic, explainable, and ethical AI applications in domains like customer service, healthcare, robotics, and collaborative systems, paving the way for adaptable and cooperative next-generation polymorphic agents.

Developing autonomous LLM agents capable of making a series of intelligent decisions to solve complex, real-world tasks is a fast-evolving frontier. Like human cognitive development, agents are expected to acquire knowledge and skills through exploration and interaction with the environment. Despite advances, the community still lacks a unified, interactive reinforcement learning (RL) framework that can effectively train such agents from scratch -- without relying on supervised fine-tuning (SFT) -- across diverse and realistic environments. To bridge this gap, we introduce AgentGym-RL, a new framework to train LLM agents for multi-turn interactive decision-making through RL. The framework features a modular and decoupled architecture, ensuring high flexibility and extensibility. It encompasses a wide variety of real-world scenarios, and supports mainstream RL algorithms. Furthermore, we propose ScalingInter-RL, a training approach designed for exploration-exploitation balance and stable RL optimization. In early stages, it emphasizes exploitation by restricting the number of interactions, and gradually shifts towards exploration with larger horizons to encourage diverse problem-solving strategies. In this way, the agent develops more diverse behaviors and is less prone to collapse under long horizons. We perform extensive experiments to validate the stability and effectiveness of both the AgentGym-RL framework and the ScalingInter-RL approach. Our agents match or surpass commercial models on 27 tasks across diverse environments. We offer key insights and will open-source the complete AgentGym-RL framework -- including code and datasets -- to empower the research community in developing the next generation of intelligent agents.

Mixed integer linear programs are commonly solved by Branch and Bound algorithms. A key factor of the efficiency of the most successful commercial solvers is their fine-tuned heuristics. In this paper, we leverage patterns in real-world instances to learn from scratch a new branching strategy optimised for a given problem and compare it with a commercial solver. We propose FMSTS, a novel Reinforcement Learning approach specifically designed for this task. The strength of our method lies in the consistency between a local value function and a global metric of interest. In addition, we provide insights for adapting known RL techniques to the Branch and Bound setting, and present a new neural network architecture inspired from the literature. To our knowledge, it is the first time Reinforcement Learning has been used to fully optimise the branching strategy. Computational experiments show that our method is appropriate and able to generalise well to new instances.

LLMs have achieved remarkable breakthroughs in reasoning, insights, and tool use, but chaining these abilities into extended processes at the scale of those routinely executed by humans, organizations, and societies has remained out of reach. The models have a persistent error rate that prevents scale-up: for instance, recent experiments in the Towers of Hanoi benchmark domain showed that the process inevitably becomes derailed after at most a few hundred steps. Thus, although LLM research is often still benchmarked on tasks with relatively few dependent logical steps, there is increasing attention on the ability (or inability) of LLMs to perform long range tasks. This paper describes MAKER, the first system that successfully solves a task with over one million LLM steps with zero errors, and, in principle, scales far beyond this level. The approach relies on an extreme decomposition of a task into subtasks, each of which can be tackled by focused microagents. The high level of modularity resulting from the decomposition allows error correction to be applied at each step through an efficient multi-agent voting scheme. This combination of extreme decomposition and error correction makes scaling possible. Thus, the results suggest that instead of relying on continual improvement of current LLMs, massively decomposed agentic processes (MDAPs) may provide a way to efficiently solve problems at the level of organizations and societies.

Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations research and mathematical optimization, which restricts non-experts' accessibility to MILP. To address this challenge, we propose a framework for automatically formulating MILP models from unstructured natural language descriptions of decision problems, which integrates Large Language Models (LLMs) and mathematical modeling techniques. This framework consists of three phases: i) identification of decision variables, ii) classification of objective and constraints, and iii) finally, generation of MILP models. In this study, we present a constraint classification scheme and a set of constraint templates that can guide the LLMs in synthesizing a complete MILP model. After fine-tuning LLMs, our approach can identify and synthesize logic constraints in addition to classic demand and resource constraints. The logic constraints have not been studied in existing work. To evaluate the performance of the proposed framework, we extend the NL4Opt dataset with more problem descriptions and constraint types, and with the new dataset, we compare our framework with one-step model generation methods offered by LLMs. The experimental results reveal that with respect to the accuracies of generating the correct model, objective, and constraints, our method which integrates constraint classification and templates with LLMs significantly outperforms the others. The prototype system that we developed has a great potential to capture more constraints for more complex MILPs. It opens up opportunities for developing training tools for operations research practitioners and has the potential to be a powerful tool for automatic decision problem modeling and solving in practice.

Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes subgoal-based proofs with expert learning to enhance LLMs' capabilities in formal theorem proving within the Isabelle environment. SubgoalXL addresses two critical challenges: the scarcity of specialized mathematics and theorem-proving data, and the need for improved multi-step reasoning abilities in LLMs. By optimizing data efficiency and employing subgoal-level supervision, SubgoalXL extracts richer information from limited human-generated proofs. The framework integrates subgoal-oriented proof strategies with an expert learning system, iteratively refining formal statement, proof, and subgoal generators. Leveraging the Isabelle environment's advantages in subgoal-based proofs, SubgoalXL achieves a new state-of-the-art performance of 56.1\% in Isabelle on the standard miniF2F dataset, marking an absolute improvement of 4.9\%. Notably, SubgoalXL successfully solves 41 AMC12, 9 AIME, and 3 IMO problems from miniF2F. These results underscore the effectiveness of maximizing limited data utility and employing targeted guidance for complex reasoning in formal theorem proving, contributing to the ongoing advancement of AI reasoning capabilities. The implementation is available at https://github.com/zhaoxlpku/SubgoalXL.

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although effective in improving accuracy, these methods are not optimal in terms of efficiency: they perform simple decomposition on the reasoning process, but ignore the planning-execution nature of tasks such as math reasoning or code generation. This results in inefficient exploration of reasoning process. To address this, we propose a dual-phase test-time scaling framework that explicitly separates reasoning into planning and execution, and performs search over the two phases individually. Specifically, we decompose reasoning trajectories and develop reward models for each phase, enabling the search to explore and prune plans and executions separately. We further introduce a dynamic budget allocation mechanism that adaptively redistributes sampling effort based on reward feedback, allowing early stopping on confident steps and reallocation of computation to more challenging parts of the reasoning process. Experiments on both mathematical reasoning and code generation benchmarks demonstrate that our approach consistently improves accuracy while reducing redundant computation.

Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of this approach, there is a lack of a common repository that provides distributions of similar MILP instances across different domains, at different hardness levels, with standardized test sets. In this paper, we introduce Distributional MIPLIB, a multi-domain library of problem distributions for advancing ML-guided MILP methods. We curate MILP distributions from existing work in this area as well as real-world problems that have not been used, and classify them into different hardness levels. It will facilitate research in this area by enabling comprehensive evaluation on diverse and realistic domains. We empirically illustrate the benefits of using Distributional MIPLIB as a research vehicle in two ways. We evaluate the performance of ML-guided variable branching on previously unused distributions to identify potential areas for improvement. Moreover, we propose to learn branching policies from a mix of distributions, demonstrating that mixed distributions achieve better performance compared to homogeneous distributions when there is limited data and generalize well to larger instances. The dataset is publicly available at https://sites.google.com/usc.edu/distributional-miplib/home.

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and their weak formal proving performance. Recent studies show that the informal accuracy exceeds 80% while formal success remains below 8% on benchmarks like PutnamBench. We argue this gap persists because current state-of-the-art provers, by tightly coupling reasoning and proving, are trained with paradigms that inadvertently punish deep reasoning in favor of shallow, tactic-based strategies. To bridge this fundamental gap, we propose a novel framework that decouples high-level reasoning from low-level proof generation. Our approach utilizes two distinct, specialized models: a powerful, general-purpose Reasoner to generate diverse, strategic subgoal lemmas, and an efficient Prover to rigorously verify them. This modular design liberates the model's full reasoning potential and bypasses the pitfalls of end-to-end training. We evaluate our method on a challenging set of post-2000 IMO problems, a problem set on which no prior open-source prover has reported success. Our decoupled framework successfully solves 5 of these problems, demonstrating a significant step towards automated reasoning on exceptionally difficult mathematical challenges. To foster future research, we release our full dataset of generated and verified lemmas for a wide range of IMO problems, available at https://tencent-imo.github.io/ .

Agents, language model (LM)-based systems that are capable of reasoning, planning, and acting are becoming the dominant paradigm for real-world AI applications. Despite this widespread adoption, the principles that determine their performance remain underexplored, leaving practitioners to rely on heuristics rather than principled design choices. We address this gap by deriving quantitative scaling principles for agent systems. We evaluate this across four diverse benchmarks: Finance-Agent, BrowseComp-Plus, PlanCraft, and Workbench. Using five canonical architectures (Single, Independent, Centralized, Decentralized, Hybrid) instantiated across three LLM families, we perform a controlled evaluation spanning 180 configurations with standardized tools and token budgets. We derive a predictive model using empirical coordination metrics, including efficiency, overhead, error amplification, and redundancy, that achieves cross-validated R^2=0.513. We identify three dominant effects: (1) a tool-coordination trade-off: under fixed computational budgets, tool-heavy tasks suffer disproportionately from multi-agent overhead. (2) a capability saturation: coordination yields diminishing or negative returns (beta=-0.408, p<0.001) once single-agent baselines exceed ~45%. (3) topology-dependent error amplification: independent agents amplify errors 17.2x through unchecked propagation, while centralized coordination contains this to 4.4x. Centralized coordination improves performance by 80.9% on parallelizable tasks like financial reasoning, while decentralized coordination excels on dynamic web navigation (+9.2% vs. +0.2%). Yet for sequential reasoning tasks, all multi-agent variants degraded performance by 39-70%. The framework predicts the optimal coordination strategy for 87% of held-out configurations, providing a predictive principle of agentic scaling based on measurable task properties.

Automated analysis for engineering structures offers considerable potential for boosting efficiency by minimizing repetitive tasks. Although AI-driven methods are increasingly common, no systematic framework yet leverages Large Language Models (LLMs) for automatic structural analysis. To address this gap, we propose a novel framework that integrates LLMs with structural analysis software. LLMs serve as the core engine: they parse structural descriptions from text and translate them into executable Python scripts. Moreover, the framework integrates the generative capabilities of LLMs with code-based finite element (FE) tools like OpenSeesPy. It employs domain-specific prompt design and in-context learning strategies to enhance the LLM's problem-solving capabilities and generative stability, enabling fully automated structural analysis from descriptive text to model outputs. In our experiments, we introduce a well-curated small-scale benchmark dataset of 20 structural analysis word problems (SAWPs) with ground-truth solutions and evaluate the performance of different LLMs within our framework in solving these SAWPs. The role of system instructions, crafted by structural engineers, is also investigated to understand their impact on LLM-driven structural analysis. Additionally, the generative stability of our framework is examined. Through multiple validation experiments on the benchmark, our results demonstrate that the proposed framework can substantially increase the level of automation in solving SAWPs compared to traditional methods. Quantitatively, the framework, built on GPT-4o, achieved 100% accuracy, surpassing GPT-4 (85%), Gemini 1.5 Pro (80%), and Llama-3.3 (30%) on the test examples. Furthermore, integrating domain-specific instructions enhanced performance by 30% on problems with asymmetrical structural configurations.

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling Pareto of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.

Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. Occurring, for instance, in distributed 'big data' problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then find either an analytical approximation or sample approximation of the resulting (product-pooled) posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form, such as being approximately Gaussian. Recently, a Fusion approach has been proposed which finds an exact Monte Carlo approximation of the posterior, circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors. In this paper, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is robust to increasing numbers of sub-posteriors.

Efficient performance estimation of architectures drawn from large search spaces is essential to Neural Architecture Search. One-Shot methods tackle this challenge by training one supernet to approximate the performance of every architecture in the search space via weight-sharing, thereby drastically reducing the search cost. However, due to coupled optimization between child architectures caused by weight-sharing, One-Shot supernet's performance estimation could be inaccurate, leading to degraded search outcomes. To address this issue, Few-Shot NAS reduces the level of weight-sharing by splitting the One-Shot supernet into multiple separated sub-supernets via edge-wise (layer-wise) exhaustive partitioning. Since each partition of the supernet is not equally important, it necessitates the design of a more effective splitting criterion. In this work, we propose a gradient matching score (GM) that leverages gradient information at the shared weight for making informed splitting decisions. Intuitively, gradients from different child models can be used to identify whether they agree on how to update the shared modules, and subsequently to decide if they should share the same weight. Compared with exhaustive partitioning, the proposed criterion significantly reduces the branching factor per edge. This allows us to split more edges (layers) for a given budget, resulting in substantially improved performance as NAS search spaces usually include dozens of edges (layers). Extensive empirical evaluations of the proposed method on a wide range of search spaces (NASBench-201, DARTS, MobileNet Space), datasets (cifar10, cifar100, ImageNet) and search algorithms (DARTS, SNAS, RSPS, ProxylessNAS, OFA) demonstrate that it significantly outperforms its Few-Shot counterparts while surpassing previous comparable methods in terms of the accuracy of derived architectures.

Solving Mixed-Integer Programming (MIP) problems often requires substantial computational resources due to their combinatorial nature. Parallelization has emerged as a critical strategy to accelerate solution times and enhance scalability to tackle large, complex instances. This paper investigates the parallelization capabilities of Balans, a recently proposed multi-armed bandits-based adaptive large neighborhood search for MIPs. While Balans's modular architecture inherently supports parallel exploration of diverse parameter configurations, this potential has not been thoroughly examined. To address this gap, we introduce ParBalans, an extension that leverages both solver-level and algorithmic-level parallelism to improve performance on challenging MIP instances. Our experimental results demonstrate that ParBalans exhibits competitive performance compared to the state-of-the-art commercial solver Gurobi, particularly on hard optimization benchmarks.

Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the generation of DPMs usually consumes much time due to the large number of function evaluations (NFE). Though recent works have accelerated the sampling to around 20 steps with high-order solvers, the sample quality with less than 10 NFE can still be improved. In this paper, we propose a unified sampling framework (USF) to study the optional strategies for solver. Under this framework, we further reveal that taking different solving strategies at different timesteps may help further decrease the truncation error, and a carefully designed solver schedule has the potential to improve the sample quality by a large margin. Therefore, we propose a new sampling framework based on the exponential integral formulation that allows free choices of solver strategy at each step and design specific decisions for the framework. Moreover, we propose S^3, a predictor-based search method that automatically optimizes the solver schedule to get a better time-quality trade-off of sampling. We demonstrate that S^3 can find outstanding solver schedules which outperform the state-of-the-art sampling methods on CIFAR-10, CelebA, ImageNet, and LSUN-Bedroom datasets. Specifically, we achieve 2.69 FID with 10 NFE and 6.86 FID with 5 NFE on CIFAR-10 dataset, outperforming the SOTA method significantly. We further apply S^3 to Stable-Diffusion model and get an acceleration ratio of 2times, showing the feasibility of sampling in very few steps without retraining the neural network.

We initiate a formal investigation into the design and analysis of LLM-based algorithms, i.e. algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of LLMs. While LLM-based algorithms, ranging from basic LLM calls with prompt engineering to complicated LLM-powered agent systems and compound AI systems, have achieved remarkable empirical success, the design and optimization of them have mostly relied on heuristics and trial-and-errors, which is largely due to a lack of formal and analytical study for these algorithms. To fill this gap, we start by identifying the computational-graph representation of LLM-based algorithms, the design principle of task decomposition, and some key abstractions, which then facilitate our formal analysis for the accuracy and efficiency of LLM-based algorithms, despite the black-box nature of LLMs. Through extensive analytical and empirical investigation in a series of case studies, we demonstrate that the proposed framework is broadly applicable to a wide range of scenarios and diverse patterns of LLM-based algorithms, such as parallel, hierarchical and recursive task decomposition. Our proposed framework holds promise for advancing LLM-based algorithms, by revealing the reasons behind curious empirical phenomena, guiding the choices of hyperparameters, predicting the empirical performance of algorithms, and inspiring new algorithm design. To promote further study of LLM-based algorithms, we release our source code at https://github.com/modelscope/agentscope/tree/main/examples/paper_llm_based_algorithm.

Multi-agent systems powered by large language models exhibit strong capabilities in collaborative problem-solving. However, these systems suffer from substantial knowledge redundancy. Agents duplicate efforts in retrieval and reasoning processes. This inefficiency stems from a deeper issue: current architectures lack mechanisms to ensure agents share minimal sufficient information at each operational stage. Empirical analysis reveals an average knowledge duplication rate of 47.3\% across agent communications. We propose D3MAS (Decompose, Deduce, and Distribute), a hierarchical coordination framework addressing redundancy through structural design rather than explicit optimization. The framework organizes collaboration across three coordinated layers. Task decomposition filters irrelevant sub-problems early. Collaborative reasoning captures complementary inference paths across agents. Distributed memory provides access to non-redundant knowledge. These layers coordinate through structured message passing in a unified heterogeneous graph. This cross-layer alignment ensures information remains aligned with actual task needs. Experiments on four challenging datasets show that D3MAS consistently improves reasoning accuracy by 8.7\% to 15.6\% and reduces knowledge redundancy by 46\% on average.

Recent advances in LLM-guided evolutionary computation, particularly AlphaEvolve (Novikov et al., 2025; Georgiev et al., 2025), have demonstrated remarkable success in discovering novel mathematical constructions and solving challenging optimization problems. However, the high-level descriptions in published work leave many implementation details unspecified, hindering reproducibility and further research. In this report we present GigaEvo, an extensible open-source framework that enables researchers to study and experiment with hybrid LLM-evolution approaches inspired by AlphaEvolve. Our system provides modular implementations of key components: MAP-Elites quality-diversity algorithms, asynchronous DAG-based evaluation pipelines, LLM-driven mutation operators with insight generation and bidirectional lineage tracking, and flexible multi-island evolutionary strategies. In order to assess reproducibility and validate our implementation we evaluate GigaEvo on challenging problems from the AlphaEvolve paper: Heilbronn triangle placement, circle packing in squares, and high-dimensional kissing numbers. The framework emphasizes modularity, concurrency, and ease of experimentation, enabling rapid prototyping through declarative configuration. We provide detailed descriptions of system architecture, implementation decisions, and experimental methodology to support further research in LLM driven evolutionary methods. The GigaEvo framework and all experimental code are available at https://github.com/AIRI-Institute/gigaevo-core.

Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined with recursive decomposition of difficult theorems into simpler entailing propositions. These models are coordinated through a multi-agent architecture that orchestrates autoformalization (if required), proof generation, decomposition of difficult theorems into simpler entailing propositions, and recursive proof (and/or decomposition) of these propositions. Without decomposition, we achieve a 90.4% pass rate on miniF2F. With decomposition, this is significantly improved. A key technical contribution lies in our extension of the Kimina Lean Server with abstract syntax tree (AST) parsing capabilities to facilitate automated, recursive proof decomposition. The system is made available on PyPI as goedels-poetry (at https://pypi.org/project/goedels-poetry ), and the open-source implementation KellyJDavis/goedels-poetry (at https://github.com/KellyJDavis/goedels-poetry ) facilitates both adaptation to alternative language models and extension with custom functionality.

Mixture-of-Experts (MoE) architectures achieve parameter efficiency through conditional computation, yet contemporary designs suffer from two fundamental limitations: structural parameter isolation that causes catastrophic forgetting, and instruction-overfitting that degrades performance in instruction-free scenarios. We propose CDSP-MoE (Conflict-Driven Subspace Pruning MoE), a framework that addresses these issues through a paradigm shift from isolated expert containers to dynamic expert instantiation within a shared physical subspace. Grounded in the Universal Weight Subspace Hypothesis, CDSP-MoE maintains a super-complete parameter backbone where logical experts are carved out via learnable topology masks. Unlike prior work that uses gradient conflict for token reassignment or optimization surgery, we leverage it as a structural supervisory signal: a Lagged Gradient Game penalizes interfering connections in the shared manifold, enabling the topology to spontaneously prune conflicting pathways and evolve interpretable modular structures. Experimental results demonstrate that CDSP-MoE achieves robust content-driven routing without human-defined task labels, maintaining semantic specialization even under strict blind inference protocols where explicit instructions are absent. Code is available at: https://github.com/konodiodaaaaa1/Conflict-Driven-Subspace-Pruning-Mixture-of-Experts

Mathematical reasoning lies at the heart of artificial intelligence, underpinning applications in education, program verification, and research-level mathematical discovery. Mathematical competitions, in particular, present two challenging problem types: theorem proving, which requires rigorous proofs of stated conclusions, and answer construction, which involves hypothesizing and formally verifying mathematical objects. Large Language Models (LLMs) effectively generate creative candidate answers but struggle with formal verification, while symbolic provers ensure rigor but cannot efficiently handle creative conjecture generation. We introduce the Enumerate-Conjecture-Prove (ECP) framework, a modular neuro-symbolic method integrating LLM-based enumeration and pattern-driven conjecturing with formal theorem proving. We present ConstructiveBench, a dataset of 3,431 answer-construction problems in various math competitions with verified Lean formalizations. On the ConstructiveBench dataset, ECP improves the accuracy of answer construction from a Chain-of-Thought (CoT) baseline of 14.54% to 45.06% with the gpt-4.1-mini model. Moreover, combined with ECP's constructed answers, the state-of-the-art DeepSeek-Prover-V2-7B model generates correct proofs for 858 of the 3,431 constructive problems in Lean, achieving 25.01% accuracy compared to 9.86% for symbolic-only baselines. Our code and dataset are publicly available at https://github.com/JackSun200312/ECP.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

Evaluating language models fairly is becoming harder as static benchmarks available on the internet risk contamination by training data. This makes it unclear whether models are truly reasoning or just recalling answers. In this paper, we introduce BeyondBench, an evaluation framework that avoids this problem by using algorithmic problem generation. Unlike traditional benchmarks that risk contamination from internet-scale training data, BeyondBench creates mathematically grounded problems on the fly, ensuring each test remains fresh and uncontaminated. Our framework covers 44 algorithmic tasks with a total of 117 variations, grouped into three difficulty levels: the Easy Suite (29 tasks) for basic arithmetic and statistics, the Medium Suite (5 tasks, 49 variations) for sequence patterns and reasoning, and the Hard Suite (10 tasks, 68 variations) tackling NP-complete and constraint satisfaction problems. Each task generates problems from a combinatorial space larger than 10^15 unique instances, with solutions verified deterministically by mathematical proofs. We evaluated 101 language models, including 85 open-source and 16 closed-source models, spanning sizes from 0.5B to 141B parameters and multiple quantization schemes. Our results show consistent reasoning deficiencies across model families, with performance degrading sharply as problem complexity increases from polynomial to exponential. In our Hard Suite evaluations, models such as Gemini-2.5-pro, Llama-3.3-70B, and Qwen2.5-72B achieved average accuracies of 56.38%, 26.91%, and 33.60%, respectively. Moreover, we observe that performance drops drastically without tool usage, with GPT-5, GPT-5-mini, and GPT-5-nano showing a decline of 16.81%, 28.05%, and 47.59% accuracy on the hard suite. Our leaderboard is publicly available at https://ctrl-gaurav.github.io/BeyondBench/

Large Language Models (LLMs) prompted to generate chain-of-thought (CoT) exhibit impressive reasoning capabilities. Recent attempts at prompt decomposition toward solving complex, multi-step reasoning problems depend on the ability of the LLM to simultaneously decompose and solve the problem. A significant disadvantage is that foundational LLMs are typically not available for fine-tuning, making adaptation computationally prohibitive. We believe (and demonstrate) that problem decomposition and solution generation are distinct capabilites, better addressed in separate modules, than by one monolithic LLM. We introduce DaSLaM, which uses a decomposition generator to decompose complex problems into subproblems that require fewer reasoning steps. These subproblems are answered by a solver. We use a relatively small (13B parameters) LM as the decomposition generator, which we train using policy gradient optimization to interact with a solver LM (regarded as black-box) and guide it through subproblems, thereby rendering our method solver-agnostic. Evaluation on multiple different reasoning datasets reveal that with our method, a 175 billion parameter LM (text-davinci-003) can produce competitive or even better performance, compared to its orders-of-magnitude larger successor, GPT-4. Additionally, we show that DaSLaM is not limited by the solver's capabilities as a function of scale; e.g., solver LMs with diverse sizes give significant performance improvement with our solver-agnostic decomposition technique. Exhaustive ablation studies evince the superiority of our modular finetuning technique over exorbitantly large decomposer LLMs, based on prompting alone.

Chain-of-Thought (CoT) and its variants have markedly advanced the reasoning abilities of Large Language Models (LLMs), yet their monolithic and auto-regressive architecture inherently conflates high-level strategic planning with low-level step-by-step execution, leading to computational inefficiency, limited exploration of reasoning paths, and reduced interpretability. To overcome these issues, we propose the Explore-Execute Chain (E^2C), a structured reasoning framework that decouples reasoning into two distinct phases: an exploratory phase that stochastically generates succinct high-level plans, followed by an execution phase that deterministically carries out the chosen plan. Our approach incorporates a two-stage training methodology, which combines Supervised Fine-Tuning (SFT) - augmented by a novel data generation algorithm enforcing strict plan adherence - with a subsequent Reinforcement Learning (RL) stage that capitalizes on the informativeness of exploration and reinforces the determinism of execution. This decomposition enables an efficient test-time scaling strategy: on AIME'2024, E^2C Test Time Scaling reaches 58.1% accuracy using <10% of the decoding tokens required by comparable methods (e.g., Forest-of-Thought), sharply cutting self-consistency overhead. For cross-domain adaptation, our Exploration-Focused SFT (EF-SFT) fine-tunes with only 3.5% of the tokens used by standard SFT yet yields up to 14.5% higher accuracy than standard SFT on medical benchmarks, delivering state-of-the-art performance, strong generalization, and greater interpretability by separating planning from execution. The code and pre-trained models for the project are available at: https://github.com/yks23/Explore-Execute-Chain.git

General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in specialized languages like Lean 4 remains a significant challenge for these models, limiting their application in complex theorem proving and automated verification. Current approaches typically require specializing models through fine-tuning on dedicated formal corpora, incurring high costs for data collection and training. In this work, we introduce Delta Prover, an agent-based framework that orchestrates the interaction between a general-purpose LLM and the Lean 4 proof environment. Delta Prover leverages the reflection and reasoning capabilities of general-purpose LLMs to interactively construct formal proofs in Lean 4, circumventing the need for model specialization. At its core, the agent integrates two novel, interdependent components: an algorithmic framework for reflective decomposition and iterative proof repair, and a custom Domain-Specific Language (DSL) built upon Lean 4 for streamlined subproblem management. Delta Prover achieves a state-of-the-art 95.9\% success rate on the miniF2F-test benchmark, surpassing all existing approaches, including those requiring model specialization. Furthermore, Delta Prover exhibits a significantly stronger test-time scaling law compared to standard Best-of-N proof strategies. Crucially, our findings demonstrate that general-purpose LLMs, when guided by an effective agentic structure, possess substantial untapped theorem-proving capabilities. This presents a computationally efficient alternative to specialized models for robust automated reasoning in formal environments.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive (top-down) algorithms recursively partition the nodes into two communities, until a stopping rule indicates that no further split is needed. In contrast, agglomerative (bottom-up) algorithms first identify the smallest community structure and then repeatedly merge the communities using a linkage method. In this article, we establish theoretical guarantees for the recovery of the hierarchical tree and community structure of a Hierarchical Stochastic Block Model by a bottom-up algorithm. We also establish that this bottom-up algorithm attains the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy. Notably, these recovery conditions are less restrictive compared to those existing for top-down algorithms. This shows that bottom-up algorithms extend the feasible region for achieving exact recovery at intermediate levels. Numerical experiments on both synthetic and real data sets confirm the superiority of bottom-up algorithms over top-down algorithms. We also observe that top-down algorithms can produce dendrograms with inversions. These findings contribute to a better understanding of hierarchical clustering techniques and their applications in network analysis.

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

Large Language Models (LLMs) have already become quite proficient at solving simpler programming tasks like those in HumanEval or MBPP benchmarks. However, solving more complex and competitive programming tasks is still quite challenging for these models - possibly due to their tendency to generate solutions as monolithic code blocks instead of decomposing them into logical sub-tasks and sub-modules. On the other hand, experienced programmers instinctively write modularized code with abstraction for solving complex tasks, often reusing previously developed modules. To address this gap, we propose CodeChain, a novel framework for inference that elicits modularized code generation through a chain of self-revisions, each being guided by some representative sub-modules generated in previous iterations. Concretely, CodeChain first instructs the LLM to generate modularized codes through chain-of-thought prompting. Then it applies a chain of self-revisions by iterating the two steps: 1) extracting and clustering the generated sub-modules and selecting the cluster representatives as the more generic and re-usable implementations, and 2) augmenting the original chain-of-thought prompt with these selected module-implementations and instructing the LLM to re-generate new modularized solutions. We find that by naturally encouraging the LLM to reuse the previously developed and verified sub-modules, CodeChain can significantly boost both modularity as well as correctness of the generated solutions, achieving relative pass@1 improvements of 35% on APPS and 76% on CodeContests. It is shown to be effective on both OpenAI LLMs as well as open-sourced LLMs like WizardCoder. We also conduct comprehensive ablation studies with different methods of prompting, number of clusters, model sizes, program qualities, etc., to provide useful insights that underpin CodeChain's success.

The Branch-and-bound (B&B) algorithm is the main solver for Mixed Integer Linear Programs (MILPs), where the selection of branching variable is essential to computational efficiency. However, traditional heuristics for branching often fail to generalize across heterogeneous problem instances, while existing learning-based methods such as imitation learning (IL) suffers from dependence on expert demonstration quality, and reinforcement learning (RL) struggles with limitations in sparse rewards and dynamic state representation challenges. To address these issues, we propose ReviBranch, a novel deep RL framework that constructs revived trajectories by reviving explicit historical correspondences between branching decisions and their corresponding graph states along search-tree paths. During training, ReviBranch enables agents to learn from complete structural evolution and temporal dependencies within the branching process. Additionally, we introduce an importance-weighted reward redistribution mechanism that transforms sparse terminal rewards into dense stepwise feedback, addressing the sparse reward challenge. Extensive experiments on different MILP benchmarks demonstrate that ReviBranch outperforms state-of-the-art RL methods, reducing B&B nodes by 4.0% and LP iterations by 2.2% on large-scale instances. The results highlight the robustness and generalizability of ReviBranch across heterogeneous MILP problem classes.

Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks, but their inference remains computationally inefficient. We observe a common failure mode in many prevalent LLMs, overthinking, where models generate verbose and tangential reasoning traces even for simple queries. Recent works have tried to mitigate this by enforcing fixed token budgets, however, this can lead to underthinking, especially on harder problems. Through empirical analysis, we identify that this inefficiency often stems from unclear problem-solving strategies. To formalize this, we develop a theoretical model, BBAM (Bayesian Budget Allocation Model), which models reasoning as a sequence of sub-questions with varying uncertainty, and introduce the E^3 metric to capture the trade-off between correctness and computation efficiency. Building on theoretical results from BBAM, we propose Plan-and-Budget, a model-agnostic, test-time framework that decomposes complex queries into sub-questions and allocates token budgets based on estimated complexity using adaptive scheduling. Plan-and-Budget improves reasoning efficiency across a range of tasks and models, achieving up to +70% accuracy gains, -39% token reduction, and +187.5% improvement in E^3. Notably, it elevates a smaller model (DS-Qwen-32B) to match the efficiency of a larger model (DS-LLaMA-70B)-demonstrating Plan-and-Budget's ability to close performance gaps without retraining. Our code is available at anonymous.4open.science/r/P-and-B-6513/.

The rapid advancement of ML models in critical sectors such as healthcare, finance, and security has intensified the need for robust data security, model integrity, and reliable outputs. Large multimodal foundational models, while crucial for complex tasks, present challenges in scalability, reliability, and potential misuse. Decentralized systems offer a solution by distributing workload and mitigating central points of failure, but they introduce risks of unauthorized access to sensitive data across nodes. We address these challenges with a comprehensive framework designed for responsible AI development. Our approach incorporates: 1) Zero-knowledge proofs for secure model verification, enhancing trust without compromising privacy. 2) Consensus-based verification checks to ensure consistent outputs across nodes, mitigating hallucinations and maintaining model integrity. 3) Split Learning techniques that segment models across different nodes, preserving data privacy by preventing full data access at any point. 4) Hardware-based security through trusted execution environments (TEEs) to protect data and computations. This framework aims to enhance security and privacy and improve the reliability and fairness of multimodal AI systems. Promoting efficient resource utilization contributes to more sustainable AI development. Our state-of-the-art proofs and principles demonstrate the framework's effectiveness in responsibly democratizing artificial intelligence, offering a promising approach for building secure and private foundational models.

The integration of knowledge extracted from diverse models, whether described by domain experts or generated by machine learning algorithms, has historically been challenged by the absence of a suitable framework for specifying and integrating structures, learning processes, data transformations, and data models or rules. In this work, we extend algebraic specification methods to address these challenges within such a framework. In our work, we tackle the challenging task of developing a comprehensive framework for defining and analyzing deep learning architectures. We believe that previous efforts have fallen short by failing to establish a clear connection between the constraints a model must adhere to and its actual implementation. Our methodology employs graphical structures that resemble Ehresmann's sketches, interpreted within a universe of fuzzy sets. This approach offers a unified theory that elegantly encompasses both deterministic and non-deterministic neural network designs. Furthermore, we highlight how this theory naturally incorporates fundamental concepts from computer science and automata theory. Our extended algebraic specification framework, grounded in graphical structures akin to Ehresmann's sketches, offers a promising solution for integrating knowledge across disparate models and domains. By bridging the gap between domain-specific expertise and machine-generated insights, we pave the way for more comprehensive, collaborative, and effective approaches to knowledge integration and modeling.

We propose an abstract framework to establish the convergence of the iterates of stochastic versions of a broad range of monotone operator splitting methods in Hilbert spaces. This framework allows for the introduction of stochasticity at several levels: approximation of operators, selection of coordinates and operators in block-iterative implementations, and relaxation parameters. The proposed analysis involves a reduced inclusion model with two operators. At each iteration, stochastic approximations to points in the graphs of these two operators are used to form the update. The results are applied to derive the almost sure and L^2 convergence of stochastic versions of the proximal point algorithm, as well as of randomized block-iterative projective splitting methods for solving systems of coupled inclusions involving a mix of set-valued, cocoercive, and Lipschitzian monotone operators combined via various monotonicity-preserving operations.

Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large language models (LLMs), offering insights beyond general mathematical problem-solving. Progress in this area is hampered by existing datasets that are often scarce, synthetic, or rigidly formal. We address this by proposing an informal yet verifiable task formulation, recasting inequality proving into two automatically checkable subtasks: bound estimation and relation prediction. Building on this, we release IneqMath, an expert-curated dataset of Olympiad-level inequalities, including a test set and training corpus enriched with step-wise solutions and theorem annotations. We also develop a novel LLM-as-judge evaluation framework, combining a final-answer judge with four step-wise judges designed to detect common reasoning flaws. A systematic evaluation of 29 leading LLMs on IneqMath reveals a surprising reality: even top models like o1 achieve less than 10% overall accuracy under step-wise scrutiny; this is a drop of up to 65.5% from their accuracy considering only final answer equivalence. This discrepancy exposes fragile deductive chains and a critical gap for current LLMs between merely finding an answer and constructing a rigorous proof. Scaling model size and increasing test-time computation yield limited gains in overall proof correctness. Instead, our findings highlight promising research directions such as theorem-guided reasoning and self-refinement. Code and data are available at https://ineqmath.github.io/.

Cutting-edge large language models (LLMs) demonstrate promising performance in solving complex math problems with a divide-and-conquer pipeline and the assistance of in-context learning (ICL) examples. However, their potential for improvement is limited by two critical problems within their ICL examples: granularity-mismatch and the ensuing negative-effect noise problem. Specifically, the LLMs are capable of the dividing process yet mostly failed by inaccurate reasoning within a few conquer steps, while the ICL examples retrieved in question-grained sometimes lack relevant steps for a specific challenging reasoning step. Further, this disconnect may hinder the correct reasoning due to its irrelevance. To this end, we focus on improving the reasoning quality within each step and present BoostStep. BoostStep aligns the granularity between the retrieving and reasoning on step grained, and provides highly related ICL examples for each reasoning step with a novel `first-try' strategy. BoostStep provides more relevant examples than the coarse question-grained strategy, enhancing the model reasoning quality within each step steadily. BoostStep is a general and robust reasoning-enhancing method that not only improves standalone reasoning performance but also integrates seamlessly with Monte Carlo Tree Search methods (MCTS) to refine both candidate generation and decision-making. Quantitatively, it improves GPT-4o and Qwen2.5-Math-72B by 3.6\% and 2.0\% respectively on various mathematical benchmarks, and 7.5\% gain combined with MCTS.

This paper presents an advanced mathematical problem-solving framework, LLaMA-Berry, for enhancing the mathematical reasoning ability of Large Language Models (LLMs). The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path and utilizes a pairwise reward model to evaluate different paths globally. By leveraging the self-critic and rewriting capabilities of LLMs, Self-Refine applied to MCTS (SR-MCTS) overcomes the inefficiencies and limitations of conventional step-wise and greedy search algorithms by fostering a more efficient exploration of solution spaces. Pairwise Preference Reward Model~(PPRM), inspired by Reinforcement Learning from Human Feedback (RLHF), is then used to model pairwise preferences between solutions, utilizing an Enhanced Borda Count (EBC) method to synthesize these preferences into a global ranking score to find better answers. This approach addresses the challenges of scoring variability and non-independent distributions in mathematical reasoning tasks. The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability compared to existing methods like ToT and rStar, particularly in complex Olympiad-level benchmarks, including GPQA, AIME24 and AMC23.

With the rapid development of large language models (LLMs), distributed training and inference frameworks like DeepSpeed have become essential for scaling model training and inference across multiple GPUs or nodes. However, the increasing complexity of these frameworks brings non-trivial software bugs, which may degrade training performance, cause unexpected failures, and result in significant resource waste. Understanding framework bugs' characteristics is fundamental for quality assurance, allowing the design of more effective debugging and repair methods. Thus, our paper conducts the first large-scale empirical analysis of 308 fixed bugs across three popular distributed training/inference frameworks: DeepSpeed, Megatron-LM, and Colossal-AI. We examine bug symptoms, root causes, bug identification and fixing efforts, and common low-effort fixing strategies. Additionally, the distributed nature of these frameworks introduces unique bug root causes, such as allocation strategy error and distributed communication error. Diagnosing and fixing complex bugs remains challenging due to factors like the disconnect between symptoms and root causes, high bug reproduction costs, and low-level or cross-component interactions. Interestingly, we observe that 48% of bug fixes require minimal code changes (<=10 LOC) and follow simple strategies such as conditional logic optimization, parameter handling enhancement, or version compatibility handling, indicating potential for automation. Based on these insights, we offer several implications for improving the reliability of both distributed training and inference frameworks and their dependent LLM projects, while also identifying opportunities to leverage LLM-based tools for automated debugging and repair.

Recent advancements have introduced machine learning frameworks to enhance the Branch and Bound (B\&B) branching policies for solving Mixed Integer Linear Programming (MILP). These methods, primarily relying on imitation learning of Strong Branching, have shown superior performance. However, collecting expert samples for imitation learning, particularly for Strong Branching, is a time-consuming endeavor. To address this challenge, we propose Contrastive Learning with Augmented MILPs for Branching (CAMBranch), a framework that generates Augmented MILPs (AMILPs) by applying variable shifting to limited expert data from their original MILPs. This approach enables the acquisition of a considerable number of labeled expert samples. CAMBranch leverages both MILPs and AMILPs for imitation learning and employs contrastive learning to enhance the model's ability to capture MILP features, thereby improving the quality of branching decisions. Experimental results demonstrate that CAMBranch, trained with only 10\% of the complete dataset, exhibits superior performance. Ablation studies further validate the effectiveness of our method.

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear alpha-regret methods that only require bandit feedback, achieving Oleft(T^2{3}log(T)^1{3}right) expected cumulative alpha-regret dependence on the horizon T. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to multiple problems in submodular maximization, adapting approximation algorithms for cardinality and for knapsack constraints. The new CMAB algorithms for knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet their direct application to NP-hard combinatorial problems (CPs) remains underexplored. In this work, we systematically investigate the reasoning abilities of LLMs on a variety of NP-hard combinatorial optimization tasks and introduce ACCORD: Autoregressive Constraint-satisfying generation for COmbinatorial optimization with Routing and Dynamic attention. ACCORD features a novel dataset representation and model architecture that leverage the autoregressive nature of LLMs to dynamically enforce feasibility constraints, coupled with attention-based routing to activate problem-specific LoRA modules. We also present the ACCORD-90k supervised dataset, covering six NP-hard combinatorial problems: TSP, VRP, Knapsack, FlowShop, JSSP, and BinPacking. Extensive experiments demonstrate that our ACCORD model, built on an 8B-parameter Llama backbone, consistently outperforms standard prompting and input-output methods, even when compared to much larger LLMs, such as gpt-4. Ablation studies further show that our output structure enhances solution feasibility. To the best of our knowledge, this is the first large-scale, end-to-end framework for exploring the applications of LLMs to a broad spectrum of combinatorial optimization problems. The codes are publicly available at https://github.com/starjob42/ACCORD

Humans possess an extraordinary ability to create and utilize tools, allowing them to overcome physical limitations and explore new frontiers. With the advent of foundation models, AI systems have the potential to be equally adept in tool use as humans. This paradigm, i.e., tool learning with foundation models, combines the strengths of specialized tools and foundation models to achieve enhanced accuracy, efficiency, and automation in problem-solving. Despite its immense potential, there is still a lack of a comprehensive understanding of key challenges, opportunities, and future endeavors in this field. To this end, we present a systematic investigation of tool learning in this paper. We first introduce the background of tool learning, including its cognitive origins, the paradigm shift of foundation models, and the complementary roles of tools and models. Then we recapitulate existing tool learning research into tool-augmented and tool-oriented learning. We formulate a general tool learning framework: starting from understanding the user instruction, models should learn to decompose a complex task into several subtasks, dynamically adjust their plan through reasoning, and effectively conquer each sub-task by selecting appropriate tools. We also discuss how to train models for improved tool-use capabilities and facilitate the generalization in tool learning. Considering the lack of a systematic tool learning evaluation in prior works, we experiment with 18 representative tools and show the potential of current foundation models in skillfully utilizing tools. Finally, we discuss several open problems that require further investigation for tool learning. In general, we hope this paper could inspire future research in integrating tools with foundation models.

The drive for predictable LLM reasoning in their integration with compound systems has popularized structured outputs, yet concerns remain about performance trade-offs compared to unconstrained natural language. At the same time, training on unconstrained Chain of Thought (CoT) traces has brought about a new class of strong reasoning models that nevertheless present novel compute budget and faithfulness challenges. This paper introduces iSelf-Discover, an instance-level adaptation of the Self-Discover framework, and using it compares dynamically generated structured JSON reasoning with its unstructured counterpart. Our empirical evaluation across diverse benchmarks using state-of-the-art open-source models supports a consistent advantage for unstructured reasoning. Notably, on the complex MATH benchmark, unstructured plans achieved relative performance improvements of up to 18.90\% over structured approaches. Zero-shot unstructured iSelf-Discover variants are also shown to outperform their five-shot structured counterparts, underscoring the significance of this gap, even when structured plans are dynamically generated to ensure reasoning precedes the final answer. We further demonstrate that the optimal granularity of plan generation (instance-level vs. task-level) is context-dependent. These findings invite re-evaluation of the reliance on structured formats for complex problem-solving and how compound systems should be organized.

This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture for road network design problems (NDPs). We train a graph neural network (GNN) to approximate the solution of the user equilibrium (UE) traffic assignment problem and use inferences made by the trained model to calculate fitness function evaluations of a genetic algorithm (GA) to approximate solutions for NDPs. Using three test networks, two NDP variants and an exact solver as benchmark, we show that on average, our proposed framework can provide solutions within 1.5% gap of the best results in less than 0.5% of the time used by the exact solution procedure. Our framework can be utilized within an expert system for infrastructure planning to determine the best infrastructure planning and management decisions under different scenarios. Given the flexibility of the framework, it can easily be adapted to many other decision problems that can be modeled as bi-level problems on graphs. Moreover, we foreseen interesting future research directions, thus we also put forward a brief research agenda for this topic. The key observation from our research that can shape future research is that the fitness function evaluation time using the inferences made by the GNN model was in the order of milliseconds, which points to an opportunity and a need for novel heuristics that 1) can cope well with noisy fitness function values provided by deep learning models, and 2) can use the significantly enlarged efficiency of the evaluation step to explore the search space effectively (rather than efficiently). This opens a new avenue for a modern class of metaheuristics that are crafted for use with AI-powered predictors.

We present Diversity-Aware Meta Visual Prompting~(DAM-VP), an efficient and effective prompting method for transferring pre-trained models to downstream tasks with frozen backbone. A challenging issue in visual prompting is that image datasets sometimes have a large data diversity whereas a per-dataset generic prompt can hardly handle the complex distribution shift toward the original pretraining data distribution properly. To address this issue, we propose a dataset Diversity-Aware prompting strategy whose initialization is realized by a Meta-prompt. Specifically, we cluster the downstream dataset into small homogeneity subsets in a diversity-adaptive way, with each subset has its own prompt optimized separately. Such a divide-and-conquer design reduces the optimization difficulty greatly and significantly boosts the prompting performance. Furthermore, all the prompts are initialized with a meta-prompt, which is learned across several datasets. It is a bootstrapped paradigm, with the key observation that the prompting knowledge learned from previous datasets could help the prompt to converge faster and perform better on a new dataset. During inference, we dynamically select a proper prompt for each input, based on the feature distance between the input and each subset. Through extensive experiments, our DAM-VP demonstrates superior efficiency and effectiveness, clearly surpassing previous prompting methods in a series of downstream datasets for different pretraining models. Our code is available at: https://github.com/shikiw/DAM-VP.

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In this paper, we introduce a fundamentally different strategy: We formulate the structure learning problem as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones, without imposing any structural assumptions on the graph such as bounded treewidth or in-degree. Code implementing the proposed algorithm is open-source and publicly available at https://github.com/xunzheng/notears.

In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the simplification that for each fixed upper-level variable, the lower-level solution must be a singleton (a.k.a., Lower-Level Singleton, LLS). In this work, we first design a counter-example to illustrate the invalidation of such LLS condition. Then by formulating BLPs from the view point of optimistic bi-level and aggregating hierarchical objective information, we establish Bi-level Descent Aggregation (BDA), a flexible and modularized algorithmic framework for generic bi-level optimization. Theoretically, we derive a new methodology to prove the convergence of BDA without the LLS condition. Our investigations also demonstrate that BDA is indeed compatible to a verify of particular first-order computation modules. Additionally, as an interesting byproduct, we also improve these conventional first-order bi-level schemes (under the LLS simplification). Particularly, we establish their convergences with weaker assumptions. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed BDA for different tasks, including hyper-parameter optimization and meta learning.

Model merging aims to cheaply combine individual task-specific models into a single multitask model. In this work, we view past merging methods as leveraging different notions of a ''task subspace'' in which models are matched before being merged. We connect the task subspace of a given model to its loss landscape and formalize how this approach to model merging can be seen as solving a linear system of equations. While past work has generally been limited to linear systems that have a closed-form solution, we consider using the conjugate gradient method to find a solution. We show that using the conjugate gradient method can outperform closed-form solutions, enables merging via linear systems that are otherwise intractable to solve, and flexibly allows choosing from a wide variety of initializations and estimates for the ''task subspace''. We ultimately demonstrate that our merging framework called ''Matching Models in their Task Subspace'' (MaTS) achieves state-of-the-art results in multitask and intermediate-task model merging. We release all of the code and checkpoints used in our work at https://github.com/r-three/mats.

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent these algorithmic decisions as discrete state transitions. Therefore, we propose a novel framework: GraphFSA (Graph Finite State Automaton). GraphFSA is designed to learn a finite state automaton that runs on each node of a given graph. We test GraphFSA on cellular automata problems, showcasing its abilities in a straightforward algorithmic setting. For a comprehensive empirical evaluation of our framework, we create a diverse range of synthetic problems. As our main application, we then focus on learning more elaborate graph algorithms. Our findings suggest that GraphFSA exhibits strong generalization and extrapolation abilities, presenting an alternative approach to represent these algorithms.

In this paper, we propose a framework for solving a single-agent task by using multiple agents, each focusing on different aspects of the task. This approach has two main advantages: 1) it allows for training specialized agents on different parts of the task, and 2) it provides a new way to transfer knowledge, by transferring trained agents. Our framework generalizes the traditional hierarchical decomposition, in which, at any moment in time, a single agent has control until it has solved its particular subtask. We illustrate our framework with empirical experiments on two domains.

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.

Large language models (LLMs) with chain-of-thought reasoning have demonstrated remarkable problem-solving capabilities, but controlling their computational effort remains a significant challenge for practical deployment. Recent proprietary systems like OpenAI's gpt-oss series have introduced discrete operational modes for intuitive reasoning control, but the open-source community has largely failed to achieve such capabilities. In this paper, we introduce ThinkDial, the first open-recipe end-to-end framework that successfully implements gpt-oss-style controllable reasoning through discrete operational modes. Our system enables seamless switching between three distinct reasoning regimes: High mode (full reasoning capability), Medium mode (50 percent token reduction with <10 percent performance degradation), and Low mode (75 percent token reduction with <15 percent performance degradation). We achieve this through an end-to-end training paradigm that integrates budget-mode control throughout the entire pipeline: budget-mode supervised fine-tuning that embeds controllable reasoning capabilities directly into the learning process, and two-phase budget-aware reinforcement learning with adaptive reward shaping. Extensive experiments demonstrate that ThinkDial achieves target compression-performance trade-offs with clear response length reductions while maintaining performance thresholds. The framework also exhibits strong generalization capabilities on out-of-distribution tasks.

We propose a new class of online learning algorithms, generalized implicit Follow-The-Regularized-Leader (FTRL), that expands the scope of FTRL framework. Generalized implicit FTRL can recover known algorithms, as FTRL with linearized losses and implicit FTRL, and it allows the design of new update rules, as extensions of aProx and Mirror-Prox to FTRL. Our theory is constructive in the sense that it provides a simple unifying framework to design updates that directly improve the worst-case upper bound on the regret. The key idea is substituting the linearization of the losses with a Fenchel-Young inequality. We show the flexibility of the framework by proving that some known algorithms, like the Mirror-Prox updates, are instantiations of the generalized implicit FTRL. Finally, the new framework allows us to recover the temporal variation bound of implicit OMD, with the same computational complexity.

Given a matrix Min R^{mtimes n}, the low rank matrix completion problem asks us to find a rank-k approximation of M as UV^top for Uin R^{mtimes k} and Vin R^{ntimes k} by only observing a few entries specified by a set of entries Omegasubseteq [m]times [n]. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli and Sanghavi~jns13 showed that if M has incoherent rows and columns, then alternating minimization provably recovers the matrix M by observing a nearly linear in n number of entries. While the sample complexity has been subsequently improved~glz17, alternating minimization steps are required to be computed exactly. This hinders the development of more efficient algorithms and fails to depict the practical implementation of alternating minimization, where the updates are usually performed approximately in favor of efficiency. In this paper, we take a major step towards a more efficient and error-robust alternating minimization framework. To this end, we develop an analytical framework for alternating minimization that can tolerate moderate amount of errors caused by approximate updates. Moreover, our algorithm runs in time widetilde O(|Omega| k), which is nearly linear in the time to verify the solution while preserving the sample complexity. This improves upon all prior known alternating minimization approaches which require widetilde O(|Omega| k^2) time.

While knowledge distillation (transfer) has been attracting attentions from the research community, the recent development in the fields has heightened the need for reproducible studies and highly generalized frameworks to lower barriers to such high-quality, reproducible deep learning research. Several researchers voluntarily published frameworks used in their knowledge distillation studies to help other interested researchers reproduce their original work. Such frameworks, however, are usually neither well generalized nor maintained, thus researchers are still required to write a lot of code to refactor/build on the frameworks for introducing new methods, models, datasets and designing experiments. In this paper, we present our developed open-source framework built on PyTorch and dedicated for knowledge distillation studies. The framework is designed to enable users to design experiments by declarative PyYAML configuration files, and helps researchers complete the recently proposed ML Code Completeness Checklist. Using the developed framework, we demonstrate its various efficient training strategies, and implement a variety of knowledge distillation methods. We also reproduce some of their original experimental results on the ImageNet and COCO datasets presented at major machine learning conferences such as ICLR, NeurIPS, CVPR and ECCV, including recent state-of-the-art methods. All the source code, configurations, log files and trained model weights are publicly available at https://github.com/yoshitomo-matsubara/torchdistill .

Effective scheduling under tight resource, timing, and operational constraints underpins large-scale planning across sectors such as capital projects, manufacturing, logistics, and IT fleet transitions. However, the reliability of large language models (LLMs) when reasoning under high-constraint regimes is insufficiently characterized. To address this gap, we present R-ConstraintBench, a scalable framework that evaluates models on Resource-Constrained Project Scheduling Problems (RCPSP), an NP-Complete feasibility class, while difficulty increases via linear growth in constraints. R-ConstraintBench incrementally increases non-redundant precedence constraints in Directed Acyclic Graphs (DAGs) and then introduces downtime, temporal windows, and disjunctive constraints. As an illustrative example, we instantiate the benchmark in a data center migration setting and evaluate multiple LLMs using feasibility and error analysis, identifying degradation thresholds and constraint types most associated with failure. Empirically, strong models are near-ceiling on precedence-only DAGs, but feasibility performance collapses when downtime, temporal windows, and disjunctive constraints interact, implicating constraint interaction, not graph depth, as the principal bottleneck. Performance on clean synthetic ramps also does not guarantee transfer to domain-grounded scenarios, underscoring limited generalization.

We introduce the Series-Parallel Workflow Decomposition (SP\-WD) heuristic algorithm for the Workflow Scheduling Problem (WSP) decomposition. We demonstrate that the SPWD algorithm facilitates the scheduling of large WSP instances with the hybrid D-Wave Constrained Quadratic Model solver, enabling the scheduling of instances that would otherwise exceed its capacity limitations. We also describe the accompanying execution environment used to obtain the results of the experiments with real-life workflow instances available in the WfCommons standardization initiative repository.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning steps. In this work, we introduce Prove, a simple yet effective framework that leverages translated programs derived from natural language solutions as a verification mechanism to filter out potentially incorrect reasoning paths before aggregating final answers. Unlike vanilla majority voting, our approach filters out solutions whose corresponding program output is inconsistent with the generated solution, aggregating only those that pass verification. We conducted extensive experiments using 13 open-source LLMs from various model families and sizes, ranging from 0.5B to 13B parameters, across eight mathematical benchmarks. Our results show that Prove consistently outperforms vanilla majority voting as a heuristic for solving mathematical reasoning tasks across all model sizes and datasets, achieving improvements of up to 18% on GSM8K and 8% on MATH-500. Our codes are available at https://github.com/declare-lab/prove.

Any optimization algorithm programming interface can be seen as a black-box function with additional free parameters. In this spirit, simulated annealing (SA) can be implemented in pseudo-code within the dimensions of a single slide with free parameters relating to the annealing schedule. Such an implementation, however, necessarily neglects much of the structure necessary to take advantage of advances in computing resources and algorithmic breakthroughs. Simulated annealing is often introduced in myriad disciplines, from discrete examples like the Traveling Salesman Problem (TSP) to molecular cluster potential energy exploration or even explorations of a protein's configurational space. Theoretical guarantees also demand a stricter structure in terms of statistical quantities, which cannot simply be left to the user. We will introduce several standard paradigms and demonstrate how these can be "lifted" into a unified framework using object-oriented programming in Python. We demonstrate how clean, interoperable, reproducible programming libraries can be used to access and rapidly iterate on variants of Simulated Annealing in a manner which can be extended to serve as a best practices blueprint or design pattern for a data-driven optimization library.

We present a novel application of evolutionary algorithms to automate the creation of powerful foundation models. While model merging has emerged as a promising approach for LLM development due to its cost-effectiveness, it currently relies on human intuition and domain knowledge, limiting its potential. Here, we propose an evolutionary approach that overcomes this limitation by automatically discovering effective combinations of diverse open-source models, harnessing their collective intelligence without requiring extensive additional training data or compute. Our approach operates in both parameter space and data flow space, allowing for optimization beyond just the weights of the individual models. This approach even facilitates cross-domain merging, generating models like a Japanese LLM with Math reasoning capabilities. Surprisingly, our Japanese Math LLM achieved state-of-the-art performance on a variety of established Japanese LLM benchmarks, even surpassing models with significantly more parameters, despite not being explicitly trained for such tasks. Furthermore, a culturally-aware Japanese VLM generated through our approach demonstrates its effectiveness in describing Japanese culture-specific content, outperforming previous Japanese VLMs. This work not only contributes new state-of-the-art models back to the open-source community, but also introduces a new paradigm for automated model composition, paving the way for exploring alternative, efficient approaches to foundation model development.

Formal methods is pivotal for verifying the reliability of critical systems through rigorous mathematical proofs. However, its adoption is hindered by labor-intensive manual proofs and the expertise required to use theorem provers. Recent advancements in large language models (LLMs) offer new opportunities for automated theorem proving. Two promising approaches are generating tactics step by step and generating a whole proof directly with an LLM. However, existing work makes no attempt to combine the two approaches. In this work, we introduce HybridProver, a dual-model proof synthesis framework that combines tactic-based generation and whole-proof synthesis to harness the benefits of both approaches. HybridProver generates whole proof candidates for evaluation directly, then extracts proof sketches from those candidates. It then uses a tactic-based generation model that integrates automated tools to complete the sketches via stepwise refinement. We implement HybridProver for the Isabelle theorem prover and fine-tune LLMs on our optimized Isabelle datasets. Evaluation on the miniF2F dataset illustrates HybridProver's effectiveness. We achieve a 59.4% success rate on miniF2F, where the previous SOTA is 56.1%. Our ablation studies show that this SOTA result is attributable to combining whole-proof and tactic-based generation. Additionally, we show how the dataset quality, training parameters, and sampling diversity affect the final result during automated theorem proving with LLMs. All of our code, datasets, and LLMs are open source.

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction remains challenging. This is especially true in distributed memory systems, where each host manages only a subset of the input points. This process requires redistributing points across hosts and accurately computing the corresponding Voronoi cells. In this paper, we introduce a new distributed construction algorithm, which is implemented in our open-source C++ 3-dimensional Voronoi construction framework. Our approach leverages Delaunay triangulation as an intermediate step, which is then transformed into a Voronoi diagram. We introduce the algorithms we implemented for the precise construction and our load-balancing approach and compare the running time with other state-of-the-art frameworks. MadVoro is a versatile tool that can be applied in various scientific domains, such as mesh decomposition, computational physics, chemistry, and machine learning.

Modern LLM deployments confront a widening cost-performance spectrum: premium models deliver strong reasoning but are expensive, while lightweight models are economical yet brittle on complex tasks. Static escalation rules and keyword heuristics under-utilize this spectrum and fail to adapt across task types. We present xRouter, a tool-calling-based routing system in which a learned router can either answer directly or invoke one or more external models. The router is trained end-to-end with reinforcement learning using an explicit, cost-aware reward that encodes cost-performance trade-offs, eliminating the need for hand-engineered routing rules. Our implementation encompasses the full reinforcement learning framework, including reward and cost accounting, as well as the deployment and evaluation pipelines. Across diverse benchmarks, xRouter achieves strong cost-performance trade-offs (e.g., substantial cost reductions at comparable task completion rates), and provides empirical insights into what reliably helps learned routing and what does not, ranging from model trainability to the difficulty of eliciting sophisticated orchestration behaviors in small open models. We hope these findings and our open implementation will serve as a practical substrate for advancing learned, cost-aware LLM orchestration.

Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring the reasoning ability of LLMs but still face important challenges. Previous studies such as Chain-of-Thought (CoT) have revealed the effectiveness of intermediate steps guidance. However, such step-wise annotation requires heavy labor, leading to insufficient training steps for current benchmarks. To fill this gap, this work introduces MUSTARD, a data generation framework that masters uniform synthesis of theorem and proof data of high quality and diversity. MUSTARD synthesizes data in three stages: (1) It samples a few mathematical concept seeds as the problem category. (2) Then, it prompts a generative language model with the sampled concepts to obtain both the problems and their step-wise formal solutions. (3) Lastly, the framework utilizes a proof assistant (e.g., Lean Prover) to filter the valid proofs. With the proposed MUSTARD, we present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. Each data point contains an informal statement, an informal proof, and a translated formal proof that passes the prover validation. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data. We further apply the MUSTARDSAUCE for fine-tuning smaller language models. The fine-tuned Llama 2-7B achieves a 15.41% average relative performance gain in automated theorem proving, and 8.18% in math word problems. Codes and data are available at https://github.com/Eleanor-H/MUSTARD.

Designing effective agentic systems requires the seamless composition and integration of agents, tools, and models within dynamic and uncertain environments. Most existing methods rely on static, semantic retrieval approaches for tool or agent discovery. However, effective reuse and composition of existing components remain challenging due to incomplete capability descriptions and the limitations of retrieval methods. Component selection suffers because the decisions are not based on capability, cost, and real-time utility. To address these challenges, we introduce a structured, automated framework for agentic system composition that is inspired by the knapsack problem. Our framework enables a composer agent to systematically identify, select, and assemble an optimal set of agentic components by jointly considering performance, budget constraints, and compatibility. By dynamically testing candidate components and modeling their utility in real-time, our approach streamlines the assembly of agentic systems and facilitates scalable reuse of resources. Empirical evaluation with Claude 3.5 Sonnet across five benchmarking datasets shows that our online-knapsack-based composer consistently lies on the Pareto frontier, achieving higher success rates at significantly lower component costs compared to our baselines. In the single-agent setup, the online knapsack composer shows a success rate improvement of up to 31.6% in comparison to the retrieval baselines. In multi-agent systems, the online knapsack composer increases success rate from 37% to 87% when agents are selected from an agent inventory of 100+ agents. The substantial performance gap confirms the robust adaptability of our method across diverse domains and budget constraints.

The bandits with knapsack (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio alpha when B=Omega(T) or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent O(T^{1/2}) regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

Training large language models requires distributing computation across many accelerators, yet practitioners select parallelism strategies (data, tensor, pipeline, ZeRO) through trial and error because no unified systematic framework predicts their behavior. We introduce placement semantics: each strategy is specified by how it places four training states (parameters, optimizer, gradients, activations) across devices using five modes (replicated, sharded, sharded-with-gather, materialized, offloaded). From placement alone, without implementation details, we derive memory consumption and communication volume. Our predictions match published results exactly: ZeRO-3 uses 8x less memory than data parallelism at 1.5x communication cost, as reported in the original paper. We prove two conditions (gradient integrity, state consistency) are necessary and sufficient for distributed training to match single-device results, and provide composition rules for combining strategies safely. The framework unifies ZeRO Stages 1-3, Fully Sharded Data Parallel (FSDP), tensor parallelism, and pipeline parallelism as instances with different placement choices.

Advancements in LLMs have recently unveiled challenges tied to computational efficiency and continual scalability due to their requirements of huge parameters, making the applications and evolution of these models on devices with limited computation resources and scenarios requiring various abilities increasingly cumbersome. Inspired by modularity within the human brain, there is a growing tendency to decompose LLMs into numerous functional modules, allowing for inference with part of modules and dynamic assembly of modules to tackle complex tasks, such as mixture-of-experts. To highlight the inherent efficiency and composability of the modular approach, we coin the term brick to represent each functional module, designating the modularized structure as configurable foundation models. In this paper, we offer a comprehensive overview and investigation of the construction, utilization, and limitation of configurable foundation models. We first formalize modules into emergent bricks - functional neuron partitions that emerge during the pre-training phase, and customized bricks - bricks constructed via additional post-training to improve the capabilities and knowledge of LLMs. Based on diverse functional bricks, we further present four brick-oriented operations: retrieval and routing, merging, updating, and growing. These operations allow for dynamic configuration of LLMs based on instructions to handle complex tasks. To verify our perspective, we conduct an empirical analysis on widely-used LLMs. We find that the FFN layers follow modular patterns with functional specialization of neurons and functional neuron partitions. Finally, we highlight several open issues and directions for future research. Overall, this paper aims to offer a fresh modular perspective on existing LLM research and inspire the future creation of more efficient and scalable foundational models.

Recent studies have highlighted their proficiency in some simple tasks like writing and coding through various reasoning strategies. However, LLM agents still struggle with tasks that require comprehensive planning, a process that challenges current models and remains a critical research issue. In this study, we concentrate on travel planning, a Multi-Phases planning problem, that involves multiple interconnected stages, such as outlining, information gathering, and planning, often characterized by the need to manage various constraints and uncertainties. Existing reasoning approaches have struggled to effectively address this complex task. Our research aims to address this challenge by developing a human-like planning framework for LLM agents, i.e., guiding the LLM agent to simulate various steps that humans take when solving Multi-Phases problems. Specifically, we implement several strategies to enable LLM agents to generate a coherent outline for each travel query, mirroring human planning patterns. Additionally, we integrate Strategy Block and Knowledge Block into our framework: Strategy Block facilitates information collection, while Knowledge Block provides essential information for detailed planning. Through our extensive experiments, we demonstrate that our framework significantly improves the planning capabilities of LLM agents, enabling them to tackle the travel planning task with improved efficiency and effectiveness. Our experimental results showcase the exceptional performance of the proposed framework; when combined with GPT-4-Turbo, it attains 10times the performance gains in comparison to the baseline framework deployed on GPT-4-Turbo.

Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by limited datasets due to the high cost of manual curation and the scarcity of challenging problems with verified formal-informal correspondences. We propose leveraging theoretical computer science (TCS) as a scalable source of rigorous proof problems, where algorithmic definitions enable automated generation of arbitrarily many challenging theorem-proof pairs. We demonstrate this approach on two TCS domains: Busy Beaver problems, which involve proving bounds on Turing machine halting behavior, and Mixed Boolean Arithmetic problems, which combine logical and arithmetic reasoning. Our framework automatically synthesizes problems with parallel formal (Lean4) and informal (Markdown) specifications, creating a scalable pipeline for generating verified proof challenges. Evaluation on frontier models reveals substantial gaps in automated theorem proving: while DeepSeekProver-V2-671B achieves 57.5\% success on Busy Beaver problems, it manages only 12\% on Mixed Boolean Arithmetic problems. These results highlight the difficulty of long-form proof generation even for problems that are computationally easy to verify, demonstrating the value of TCS domains for advancing automated reasoning research.

CLAX is a JAX-based library that implements classic click models using modern gradient-based optimization. While neural click models have emerged over the past decade, complex click models based on probabilistic graphical models (PGMs) have not systematically adopted gradient-based optimization, preventing practitioners from leveraging modern deep learning frameworks while preserving the interpretability of classic models. CLAX addresses this gap by replacing EM-based optimization with direct gradient-based optimization in a numerically stable manner. The framework's modular design enables the integration of any component, from embeddings and deep networks to custom modules, into classic click models for end-to-end optimization. We demonstrate CLAX's efficiency by running experiments on the full Baidu-ULTR dataset comprising over a billion user sessions in approx 2 hours on a single GPU, orders of magnitude faster than traditional EM approaches. CLAX implements ten classic click models, serving both industry practitioners seeking to understand user behavior and improve ranking performance at scale and researchers developing new click models. CLAX is available at: https://github.com/philipphager/clax

Recent advances in few-step diffusion models have demonstrated their efficiency and effectiveness by shortcutting the probabilistic paths of diffusion models, especially in training one-step diffusion models from scratch (a.k.a. shortcut models). However, their theoretical derivation and practical implementation are often closely coupled, which obscures the design space. To address this, we propose a common design framework for representative shortcut models. This framework provides theoretical justification for their validity and disentangles concrete component-level choices, thereby enabling systematic identification of improvements. With our proposed improvements, the resulting one-step model achieves a new state-of-the-art FID50k of 2.85 on ImageNet-256x256 under the classifier-free guidance setting with one step generation, and further reaches FID50k of 2.53 with 2x training steps. Remarkably, the model requires no pre-training, distillation, or curriculum learning. We believe our work lowers the barrier to component-level innovation in shortcut models and facilitates principled exploration of their design space.

Recently, test-time scaling has garnered significant attention from the research community, largely due to the substantial advancements of the o1 model released by OpenAI. By allocating more computational resources during the inference phase, large language models~(LLMs) can extensively explore the solution space by generating more thought tokens or diverse solutions, thereby producing more accurate responses. However, developing an o1-like reasoning approach is challenging, and researchers have been making various attempts to advance this open area of research. In this paper, we present a preliminary exploration into enhancing the reasoning abilities of LLMs through reward-guided tree search algorithms. This framework is implemented by integrating the policy model, reward model, and search algorithm. It is primarily constructed around a tree search algorithm, where the policy model navigates a dynamically expanding tree guided by a specially trained reward model. We thoroughly explore various design considerations necessary for implementing this framework and provide a detailed report of the technical aspects. To assess the effectiveness of our approach, we focus on mathematical reasoning tasks and conduct extensive evaluations on four challenging datasets, significantly enhancing the reasoning abilities of LLMs.

Automatic differentiation (autodiff) has revolutionized machine learning. It allows to express complex computations by composing elementary ones in creative ways and removes the burden of computing their derivatives by hand. More recently, differentiation of optimization problem solutions has attracted widespread attention with applications such as optimization layers, and in bi-level problems such as hyper-parameter optimization and meta-learning. However, so far, implicit differentiation remained difficult to use for practitioners, as it often required case-by-case tedious mathematical derivations and implementations. In this paper, we propose automatic implicit differentiation, an efficient and modular approach for implicit differentiation of optimization problems. In our approach, the user defines directly in Python a function F capturing the optimality conditions of the problem to be differentiated. Once this is done, we leverage autodiff of F and the implicit function theorem to automatically differentiate the optimization problem. Our approach thus combines the benefits of implicit differentiation and autodiff. It is efficient as it can be added on top of any state-of-the-art solver and modular as the optimality condition specification is decoupled from the implicit differentiation mechanism. We show that seemingly simple principles allow to recover many existing implicit differentiation methods and create new ones easily. We demonstrate the ease of formulating and solving bi-level optimization problems using our framework. We also showcase an application to the sensitivity analysis of molecular dynamics.

The CASH problem has been widely studied in the context of automated configurations of machine learning (ML) pipelines and various solvers and toolkits are available. However, CASH solvers do not directly handle black-box constraints such as fairness, robustness or other domain-specific custom constraints. We present our recent approach [Liu, et al., 2020] that leverages the ADMM optimization framework to decompose CASH into multiple small problems and demonstrate how ADMM facilitates incorporation of black-box constraints.

Large Language Models (LLMs) have demonstrated the ability to tackle increasingly complex tasks through advanced reasoning, long-form content generation, and tool use. Solving these tasks often involves long inference-time computations. In human problem solving, a common strategy to expedite work is collaboration: by dividing the problem into sub-tasks, exploring different strategies concurrently, etc. Recent research has shown that LLMs can also operate in parallel by implementing explicit cooperation frameworks, such as voting mechanisms or the explicit creation of independent sub-tasks that can be executed in parallel. However, each of these frameworks may not be suitable for all types of tasks, which can hinder their applicability. In this work, we propose a different design approach: we run LLM "workers" in parallel , allowing them to synchronize via a concurrently-updated attention cache and prompt these workers to decide how best to collaborate. Our approach allows the instances to come up with their own collaboration strategy for the problem at hand, all the while "seeing" each other's partial progress in the concurrent cache. We implement this approach via Hogwild! Inference: a parallel LLM inference engine where multiple instances of the same LLM run in parallel with the same attention cache, with "instant" access to each other's generated tokens. Hogwild! inference takes advantage of Rotary Position Embeddings (RoPE) to avoid recomputation while improving parallel hardware utilization. We find that modern reasoning-capable LLMs can perform inference with shared Key-Value cache out of the box, without additional fine-tuning.

State-of-the-art neural network (NN) verifiers demonstrate that applying the branch-and-bound (BaB) procedure with fast bounding techniques plays a key role in tackling many challenging verification properties. In this work, we introduce the linear constraint-driven clipping framework, a class of scalable and efficient methods designed to enhance the efficacy of NN verifiers. Under this framework, we develop two novel algorithms that efficiently utilize linear constraints to 1) reduce portions of the input space that are either verified or irrelevant to a subproblem in the context of branch-and-bound, and 2) directly improve intermediate bounds throughout the network. The process novelly leverages linear constraints that often arise from bound propagation methods and is general enough to also incorporate constraints from other sources. It efficiently handles linear constraints using a specialized GPU procedure that can scale to large neural networks without the use of expensive external solvers. Our verification procedure, Clip-and-Verify, consistently tightens bounds across multiple benchmarks and can significantly reduce the number of subproblems handled during BaB. We show that our clipping algorithms can be integrated with BaB-based verifiers such as α,β-CROWN, utilizing either the split constraints in activation-space BaB or the output constraints that denote the unverified input space. We demonstrate the effectiveness of our procedure on a broad range of benchmarks where, in some instances, we witness a 96% reduction in the number of subproblems during branch-and-bound, and also achieve state-of-the-art verified accuracy across multiple benchmarks. Clip-and-Verify is part of the α,β-CROWN verifier (http://abcrown.org), the VNN-COMP 2025 winner. Code available at https://github.com/Verified-Intelligence/Clip_and_Verify.

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT li2024chain,merrill2023expresssive.

Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted mathematical and computer science communities. State-of-the-art methods utilize single Large Language Models (LLMs) as agents or provers to either generate complete proof or perform tree searches. However, single-agent methods inherently lack a structured way to combine high-level reasoning in Natural Language (NL) with Formal Language (FL) verification feedback. To solve these issues, we propose MA-LoT: Multi-Agent Lean-based Long Chain-of-Thought framework, (to the best of our knowledge), the first multi-agent framework for Lean4 theorem proving that balance high-level NL reasoning and FL verification in Long CoT. Using this structured interaction, our approach enables deeper insights and long-term coherence in proof generation, with which past methods struggle. We do this by leveraging emergent formal reasoning ability in Long CoT using our novel LoT-Transfer Learning training-inference pipeline. Extensive experiments show that our framework achieves 54.51% accuracy rate on the Lean4 version of MiniF2F-Test dataset, largely outperforming GPT-4 (22.95%), single-agent tree search (InternLM-Step-Prover, 50.70%), and whole-proof generation (DeepSeek-Prover-v1.5, 48.36%) baselines. Furthermore, our findings highlight the potential of combining Long CoT with formal verification for a more insightful generation in a broader perspective.

Mathematical reasoning remains a significant challenge for Large Language Models (LLMs) due to hallucinations. When combined with formal proof assistants like Lean, these hallucinations can be eliminated through rigorous verification, making theorem proving reliable. However, even with formal verification, LLMs still struggle with long proofs and complex mathematical formalizations. While Lean with LLMs offers valuable assistance with retrieving lemmas, generating tactics, or even complete proofs, it lacks a crucial capability: providing a sense of proof progress. This limitation particularly impacts the overall development efficiency in large formalization projects. We introduce LeanProgress, a method that predicts the progress in the proof. Training and evaluating our models made on a large corpus of Lean proofs from Lean Workbook Plus and Mathlib4 and how many steps remain to complete it, we employ data preprocessing and balancing techniques to handle the skewed distribution of proof lengths. Our experiments show that LeanProgress achieves an overall prediction accuracy of 75.1\% in predicting the amount of progress and, hence, the remaining number of steps. When integrated into a best-first search framework using Reprover, our method shows a 3.8\% improvement on Mathlib4 compared to baseline performances of 41.2\%, particularly for longer proofs. These results demonstrate how proof progress prediction can enhance both automated and interactive theorem proving, enabling users to make more informed decisions about proof strategies.