A Nash Equilibrium Framework For Training-Free Multimodal Step Verification

2026-05-19

AI Summary

This work addresses the challenge of subtle errors in reasoning chains generated by multimodal large language models, where existing verification approaches either rely heavily on annotated data or naively average scores from multiple sources while overlooking the critical signals embedded in inter-scorer disagreement. The paper introduces a novel framework that formulates step-level verification as a Nash equilibrium game among multiple evaluators: consensus indicates reliability, whereas disagreement reveals instability. By deriving a closed-form solution to compute equilibrium scores, the method enables training-free filtering and ranking of reasoning steps. Notably, it requires no task-specific adaptation and leverages scoring divergence—rather than average confidence—to capture cross-modal consistency. Evaluated across six benchmarks, the approach consistently outperforms baselines by 2.4%–5.2%, matching the performance of trainable critic models and demonstrating strong effectiveness and generalization.

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.

Problem

• multimodal reasoning
• step verification
• Nash equilibrium
• training-free verification
• reasoning errors

Innovation

• Nash equilibrium
• training-free verification
• multimodal reasoning
• disagreement-aware filtering
• step-wise validation