# Improving Math Reasoning through Value-guided Informative Search

arXiv: https://arxiv.org/abs/2610.01080 · HTML: https://mlsanity.com/paper/2610.01080/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 16 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't](https://mlsanity.com/paper/2503.16219/) (2025)
- [Value-Guided Search for Efficient Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.17373/) (2025)
- [Lookahead Tree-Based Rollouts for Enhanced Trajectory-Level Exploration in Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2510.24302/) (2025)
- [Reinforced Efficient Reasoning via Semantically Diverse Exploration](https://mlsanity.com/paper/2601.05053/) (2026)
- [Nudging Beyond the Comfort Zone: Efficient Strategy-Guided Exploration for RLVR](https://mlsanity.com/paper/2605.15726/) (2026)
- [GAUGE: When Not to Trust LLM-as-a-Judge in User-Simulated Evaluation of Task-Oriented Agents](https://mlsanity.com/paper/2609.12191/) (2026)
- [Boosting LLM Exploration via Weak-Model Guidance in RLVR](https://mlsanity.com/paper/2608.27420/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the mathematical reasoning capabilities of large language models. Recent work introduces search into RLVR rollouts to increase trajectory diversity, but diversity alone does not ensure that the search-induced rollout policy improves upon the current policy. To address this gap, we propose APIVIS, a training-time framework that adapts finite-budget Gumbel search to chunk-level mathematical reasoning. APIVIS combines direct and searched responses within each rollout group, allowing improvements found by search to produce informative relative rewards. It further applies selective supervision to search-improved tokens, preserving a learning signal when uniform group rewards render GRPO ineffective. We show that exact value-guided selection improves the expected verifier reward at each searched state and that this guarantee extends to the complete rollout policy, with a corresponding approximate guarantee under bounded value-estimation error. Experiments on widely recognized mathematical reasoning benchmarks and different model scales demonstrate substantial improvements over competitive search-based methods, validating the effectiveness of APIVIS.