What Are Step-Level Reward Models Rewarding? Counterintuitive Findings from MCTS-Boosted Mathematical Reasoning

TL;DR

This paper investigates the mechanisms behind step-level reward models in mathematical reasoning, revealing that language descriptions are less critical than logical coherence, guiding more efficient SRM development.

Contribution

It uncovers the counterintuitive finding that natural language descriptions are less impactful, emphasizing the importance of logical coherence in SRMs for mathematical reasoning.

Findings

Removing natural language descriptions has minimal impact on SRM performance.

SRMs excel at assessing logical coherence in mathematical language.

SRMs struggle with natural language understanding.

Abstract

Step-level reward models (SRMs) can significantly enhance mathematical reasoning performance through process supervision or step-level preference alignment based on reinforcement learning. The performance of SRMs is pivotal, as they serve as critical guidelines, ensuring that each step in the reasoning process is aligned with desired outcomes. Recently, AlphaZero-like methods, where Monte Carlo Tree Search (MCTS) is employed for automatic step-level preference annotation, have proven particularly effective. However, the precise mechanisms behind the success of SRMs remain largely unexplored. To address this gap, this study delves into the counterintuitive aspects of SRMs, particularly focusing on MCTS-based approaches. Our findings reveal that the removal of natural language descriptions of thought processes has minimal impact on the efficacy of SRMs. Furthermore, we demonstrate that SRMs are adept at assessing the complex logical coherence present in mathematical language while having difficulty in natural language. These insights provide a nuanced understanding of the core elements that drive effective step-level reward modeling in mathematical reasoning. By shedding light on these mechanisms, this study offers valuable guidance for developing more efficient and streamlined SRMs, which can be achieved by focusing on the crucial parts of mathematical reasoning.