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Nov 14

Adaptive Guidance Accelerates Reinforcement Learning of Reasoning Models

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

  • 6 authors
·
Jun 16

PassTSL: Modeling Human-Created Passwords through Two-Stage Learning

Textual passwords are still the most widely used user authentication mechanism. Due to the close connections between textual passwords and natural languages, advanced technologies in natural language processing (NLP) and machine learning (ML) could be used to model passwords for different purposes such as studying human password-creation behaviors and developing more advanced password cracking methods for informing better defence mechanisms. In this paper, we propose PassTSL (modeling human-created Passwords through Two-Stage Learning), inspired by the popular pretraining-finetuning framework in NLP and deep learning (DL). We report how different pretraining settings affected PassTSL and proved its effectiveness by applying it to six large leaked password databases. Experimental results showed that it outperforms five state-of-the-art (SOTA) password cracking methods on password guessing by a significant margin ranging from 4.11% to 64.69% at the maximum point. Based on PassTSL, we also implemented a password strength meter (PSM), and our experiments showed that it was able to estimate password strength more accurately, causing fewer unsafe errors (overestimating the password strength) than two other SOTA PSMs when they produce the same rate of safe errors (underestimating the password strength): a neural-network based method and zxcvbn. Furthermore, we explored multiple finetuning settings, and our evaluations showed that, even a small amount of additional training data, e.g., only 0.1% of the pretrained data, can lead to over 3% improvement in password guessing on average. We also proposed a heuristic approach to selecting finetuning passwords based on JS (Jensen-Shannon) divergence and experimental results validated its usefulness. In summary, our contributions demonstrate the potential and feasibility of applying advanced NLP and ML methods to password modeling and cracking.

  • 5 authors
·
Jul 19, 2024

The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning

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

  • 6 authors
·
Jun 2