MathBode: Frequency-Domain Fingerprints of LLM Mathematical Reasoning

Charles Wang

MathBode: Frequency-Domain Fingerprints of LLM Mathematical Reasoning: 5 upvotes on Hugging Face Daily Papers, #56 of 82 papers on 2025-09-30. Day-by-day upvote history.

This paper presents MathBode, a dynamic diagnostic for mathematical reasoning in large language models (LLMs). Instead of one-shot accuracy, MathBode treats each parametric problem as a system: we drive a single parameter sinusoidally and fit first-harmonic responses of model outputs and exact solutions. This yields interpretable, frequency-resolved metrics -- gain (amplitude tracking) and phase (lag) -- that form Bode-style fingerprints. Across five closed-form families (linear solve, ratio/saturation, compound interest, 2x2 linear systems, similar triangles), the diagnostic surfaces systematic low-pass behavior and growing phase lag that accuracy alone obscures. We compare several models against a symbolic baseline that calibrates the instrument (G approx 1, phi approx 0). Results separate frontier from mid-tier models on dynamics, providing a compact, reproducible protocol that complements standard benchmarks with actionable measurements of reasoning fidelity and consistency. We open-source the dataset and code to enable further research and adoption.

Paper page on Hugging Face · arXiv

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