The paper introduces T2T (Thickening-to-Thinning), a dynamic reward framework for large language models that mimics human learning by separating exploration and consolidation phases. During incorrect attempts, T2T encourages exploration to broaden the search space, while after correct solutions it applies length penalties to promote concise reasoning. Experiments on mathematical benchmarks across five mainstream LLMs show that T2T outperforms standard GRPO and recent baselines, improving overall reasoning performance.
arXiv:2606. 17024v1 Announce Type: new Abstract: Sparse reward reinforcement learning (RL) has become a standard tool for improving LLM reasoning, but its success depends critically on the coverage present in the base model.
arXiv:2607. 16205v1 Announce Type: new Abstract: Reinforcement learning with verifiable rewards has emerged as a standard approach for enhancing reasoning in large language models, which typically optimizes the policy by contrasting multiple self generated rollouts.
The paper introduces a method to enhance large language model (LLM) exploration in Reinforcement Learning with Verifiable Rewards (RLVR) by guiding the target model with partial reasoning trajectories from smaller, weaker language models. This weak-model guidance disrupts over‑confidence, preserves generative diversity, and mitigates entropy collapse without extra fine‑tuning or complex reward designs. Experiments on mathematical benchmarks show consistent improvements over vanilla RLVR, especially as the number of allowed attempts ($k$) increases, indicating broader reasoning coverage.
arXiv:2606.03021v4 Announce Type: replace Abstract: Recent developments in Large Language Models (LLMs) have showcased impressive reasoning capabilities, with Reinforcement Learning with Verifiable R...
arXiv:2509. 25004v2 Announce Type: replace Abstract: Online reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving the reasoning abilities of large language models, but most methods still optimize reasoning trajectories over the static problem set, wasting rollout budget on solved or overly difficult problems.
The paper reports that in on‑policy distillation for large language models, reasoning performance can be improved by supervising only a tiny fraction of generated tokens—sometimes just one or two tokens per reasoning trajectory, about 0.05% of all tokens. This sparse supervision consistently matches or exceeds full‑token training across nine teacher‑student setups on mathematical reasoning, and is also validated on coding reasoning, Llama models, and PPO‑based reinforcement learning with verifiable reward. The findings suggest that effective post‑training does not require token‑intensive supervision and may align more closely with natural learning processes that focus on critical reasoning steps.
The paper introduces EquivAug, a data augmentation framework that applies symbolic equivalence transformations to chain-of-thought (CoT) solutions, generating diverse yet provably correct reasoning paths for supervised fine-tuning (SFT). By converting CoT solutions into formal symbolic representations, applying equivalence transformations, and reconstructing natural-language explanations, EquivAug produces training data that varies in reasoning steps rather than surface-level lexical differences. Experiments on GSM8K and FOLIO show that EquivAug consistently achieves the highest reasoning path diversity after SFT and the strongest accuracy after GRPO, establishing a positive correlation between CoT diversity during SFT and downstream reinforcement learning with verifiable rewards (RLVR) performance.
arXiv:2607.28077v2 Announce Type: replace Abstract: Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models, but prompt groups with identica...
arXiv:2507.14843v5 Announce Type: replace Abstract: Recent advances highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising approach to enhancing LLM capabilities. However, it...
arXiv:2509. 04027v4 Announce Type: replace Abstract: Test-time scaling, primarily manifested through multi-step Chain-of-Thought (CoT) reasoning via Reinforcement Learning (RL), has emerged as a pivotal paradigm for enhancing the reasoning capabilities of Large Language Models (LLMs).
arXiv:2606. 24994v1 Announce Type: new Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) for language-model reasoning can fail at both extremes of task difficulty: easy prompts often produce all-correct, low-diversity rollout groups with little gradient signal, while hard prompts can produce all-incorrect groups with no positive reward.
arXiv:2605. 24396v2 Announce Type: replace Abstract: Long chains of thought (CoT) from current language models frequently contain logical gaps and unjustified leaps, limiting the gains from additional test-time compute.