A Nash Equilibrium Framework For Training-Free Multimodal Step Verification

TL;DR

This paper introduces a training-free, Nash equilibrium-based verification method for multimodal reasoning that leverages disagreement among specialized judges to improve step validation without task-specific training.

Contribution

It formalizes step verification as a Nash equilibrium game, enabling disagreement-aware filtering and ranking, and demonstrates its effectiveness across multiple benchmarks.

Findings

Achieves 2.4% to 5.2% improvements over baselines.

Outperforms some learned critics without training.

Provides a robust, task-agnostic verification method.

Abstract

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Learned critics need extensive labeled data and show inconsistent performance across different tasks. Meanwhile, existing training-free methods simply average scores from different sources, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We propose a training-free verification approach that treats step-wise verification as a coordination problem among specialized judges. We formalize these judges' interaction as a Nash equilibrium game where agreement signals valid steps while disagreement reveals instability. Our method computes equilibrium scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, our approach achieves consistent improvements of 2.4% to 5.2% over baseline models and shows competitive performance against learned critics, demonstrating that cross-modal agreement (not just average confidence) provides robust verification signals without task-specific adaptation.