Universal Logic Topology: The spectral signatures of valid reasoning are isomorphic across different formal languages (Mathematics, Code, and Formal Logic), but distinct from Natural Language.

Motivation

The paper demonstrates this phenomenon in mathematics. Testing if this spectral geometry is a universal property of 'rigid' reasoning versus 'associative' generation would determine if this metric can generalize to code generation (detecting bugs) or legal reasoning (detecting contradictions), addressing the 'Transferability' limitation.

Proposed Method

Collect datasets for three domains: Mathematics (MATH), Code Generation (HumanEval), and Formal Logic (Folio). Extract attention graph spectra for correct vs. incorrect outputs in all domains. Perform Manifold Alignment or Canonical Correlation Analysis (CCA) to determine if the 'validity' clusters in spectral space share a common topological structure across domains.

Expected Contribution

Evidence of a domain-agnostic 'geometry of truth' in Transformer latent spaces, enabling a universal validity verifier for high-stakes AI applications.

Required Resources

Standard NLP research compute, diverse datasets (code, logic, math), and statistical analysis expertise.

Source Paper

Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning

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