The paper introduces Function-Structured Graph Reinforcement Learning (FSG‑RL), a framework that links subproblem graphs to Python code and uses multiple verifiers for feedback. It first trains a policy via supervised fine‑tuning to generate code from function graphs, then refines it with Group Relative Policy Optimization (GRPO) that employs answer‑gated rewards and span‑level credit assignment. On a benchmark combining GSM8K, MathQA, MATH, and Omni‑MATH, GRPO raises final‑answer accuracy from 43.25 % to 67.50 % and full‑solution success from 32.25 % to 52.25 %, with further improvements when teacher supervision is added.
arXiv:2609.38409v1 Announce Type: new Abstract: Recent progress in large language model reasoning has been driven by benchmarks and reinforcement learning environments with automatically verifiable r...
arXiv:2606. 20008v1 Announce Type: new Abstract: Reinforcement learning with verifiable rewards has become a central tool for improving the reasoning ability of large language models, but current methods face a trade-off between simplicity and credit assignment.
The paper introduces Proof‑R1, a reinforcement‑learning framework that trains large language models to generate verifiable proofs for natural‑language logical reasoning tasks. Proof‑R1 only accepts a generated conclusion into the proof state when it satisfies formal verification constraints, ensuring each reasoning step is machine‑checkable. The method also reconstructs the dependency closure that supports the final answer, aligning credit with valid proof steps, and shows improved answer accuracy and verifiability across multiple benchmarks and models.
The paper investigates the reliability of rule- and model-based verifiers used in reinforcement learning with verifiable reward (RLVR) for mathematical reasoning. It finds that rule-based verifiers often miss equivalent answers in different formats, causing false negatives that degrade RL performance as models improve. Model-based verifiers achieve higher static accuracy but become vulnerable to reward hacking during RL, misclassifying certain response patterns as correct after fine-tuning.
The paper introduces APIVIS, a training-time framework that integrates finite-budget Gumbel search into reinforcement learning with verifiable rewards (RLVR) for mathematical reasoning. APIVIS combines direct and searched responses within each rollout group, uses selective supervision on search-improved tokens, and applies value-guided selection to improve verifier rewards at each searched state. Experiments on standard mathematical reasoning benchmarks and various model scales show significant performance gains over existing search-based methods.
arXiv:2608. 03119v1 Announce Type: new Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) improves LLM reasoning but typically relies on ground-truth (GT) answers, limiting scalability.
Achieving strong optimization generalization across diverse optimization problems while requiring limited training resources remains a challenging problem for optimization-oriented large language models (LLMs). Existing approaches typically rely on large-scale supervised datasets, costly reasoning annotations, and expensive intermediate step verification, resulting in substantial training overhead.
Post-training of reasoning language models is commonly driven by supervised distillation and reinforcement learning with verifiable rewards. Distillation often relies on chain-of-thought annotations that are expensive to obtain and may themselves be noisy, incomplete, or partially incorrect; even when the final solution is correct, an imperfect rationale can interfere with learning.
arXiv:2606. 20068v1 Announce Type: new Abstract: While reinforcement learning from verifiable rewards (RLVR) typically has relied on a single binary verification signal, symbolic proof assistants in formal reasoning offer rich, fine-grained structured feedback.
ConsensusBench is a new dataset that supplies rule‑based process‑level signals for large language model reasoning. It identifies key intermediate conclusions—called Consensus Nodes—by filtering correct trajectories and clustering semantically equivalent statements. By incorporating a process reward derived from these nodes into GRPO‑style reinforcement learning, the authors create ConsensusPR, which reduces reward sparsity and improves performance on benchmarks such as AIME, GSM8K, and MATH‑500.
arXiv:2602. 07832v3 Announce Type: replace-cross Abstract: Process rewards have been widely used in deep reinforcement learning to improve training efficiency, reduce variance, and prevent reward hacking.
arXiv:2504. 18587v2 Announce Type: replace-cross Abstract: Reinforcement learning has emerged as a powerful approach for improving the reasoning capabilities of large language models, as demonstrated by systems such as OpenAI's O1~\cite{o1} and DeepSeek-R1~\cite{r1}.