# Local Coherence or Global Validity? Investigating RLVR Traces in Math Domains

arXiv: https://arxiv.org/abs/2510.18176 · HTML: https://mlsanity.com/paper/2510.18176/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 17 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 17 of 17)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [DeepSeek-R1 Thoughtology: Let's think about LLM Reasoning](https://mlsanity.com/paper/2504.07128/) (2025)
- [Evaluating Mathematical Reasoning of Large Language Models: A Focus on Error Identification and Correction](https://mlsanity.com/paper/2406.00755/) (2024)
- [Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens](https://mlsanity.com/paper/2505.13775/) (2025)
- [Do Cognitively Interpretable Reasoning Traces Improve LLM Performance?](https://mlsanity.com/paper/2508.16695/) (2025)
- [Interpretable Traces, Unexpected Outcomes: Investigating the Disconnect in Trace-Based Knowledge Distillation](https://mlsanity.com/paper/2505.13792/) (2025)
- [RL in Name Only? Analyzing the Structural Assumptions in RL post-training for LLMs](https://mlsanity.com/paper/2505.13697/) (2025)

## Built on by (most cited first, 5 of 5)

- [Measuring Weak-to-Strong Legibility of Reasoning Models](https://mlsanity.com/paper/2603.20508/) (2026)
- [Teaching Language Models to Forecast Research Success Through Comparative Idea Evaluation](https://mlsanity.com/paper/2605.21491/) (2026)
- [BODHI: Do LLMs Branch Out and Discover Heterogeneous Inferences?](https://mlsanity.com/paper/2608.02867/) (2026)
- [Reward Granularity in RLVR: Comparing Process and Outcome Reward Structures for Mathematical Reasoning in Small Language Models](https://mlsanity.com/paper/2607.02869/) (2026)
- [Humans Disengage, Reasoning Models Persist: Separating Difficulty Registration from Deliberation Allocation](https://mlsanity.com/paper/2606.26502/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR)-based post-training of Large Language Models (LLMs) has been shown to improve accuracy on reasoning tasks and continues to attract significant attention. Existing RLVR methods, however, typically treat all tokens uniformly without accounting for token-level advantages. These methods primarily evaluate performance based on final answer correctness or Pass@K accuracy, and yet make claims about RL post-training leading to improved reasoning traces. This motivates our investigation into the effect of RL post-training on intermediate tokens which are not directly incentivized. To study this, we design an experimental setup using the GRPO algorithm with Qwen-2.5-0.5B model on the GSM8K dataset. We introduce trace coherence, a First-Order Logic (FOL)-based measure to capture the consistency of reasoning steps by identifying errors in the traces. We distinguish between trace validity and trace coherence, noting that the former implies logical soundness while the latter measures local coherence via lack of errors. Our results show that RL post-training overall improves trace coherence with the most significant gains on problems where the base model fails but the RL model succeeds. Surprisingly, RL enhances local coherence without necessarily producing valid or correct solutions. This highlights a crucial distinction: improved local coherence in reasoning steps does not guarantee final answer correctness. We argue that claims of improved reasoning via RL must be examined with care, as these may be based on improved trace coherence, which may not translate into fully valid mathematical proofs.