Conservation Laws and Spectral Structure in Neural Reasoning: A Geometric Analysis of Discrete Token Dynamics

NeurIPS 2025 Workshop NeurReps Submission146 Authors

Keywords: geometric interpretability, differential geometry, conservation laws, neural reasoning, discrete token systems

TL;DR: This paper develops geometric tools using Riemannian geometry and group theory to analyze reasoning trajectories in large language models, revealing complementary insights to information-theoretic methods.

Abstract: We investigate whether differential geometric tools can provide complementary insights to existing information-theoretic and complexity-based approaches for analyzing multi-hop reasoning in large language models. By applying mathematical frameworks from Riemannian geometry and group theory to reasoning trajectories in embedding spaces, we develop geometric measures that capture structural properties potentially missed by traditional complexity metrics. Our comparative analysis on OpenBookQA reveals that geometric measures including curvature, torsion, and symplectic invariants provide orthogonal information to entropy-based metrics, achieving improved reasoning quality assessment when combined with information-theoretic approaches. While geometric methods alone show modest improvements over complexity baselines, their integration with established frameworks yields statistically significant gains with 87.3% versus 78.5% accuracy in validity classification.

Submission Number: 146