Spectral Collapse Precedes CoT Drift: Degradation in the spectral integrity of attention graphs occurs several steps before visible logical errors in Chain-of-Thought (CoT) rollouts.

Motivation

Long-context reasoning often suffers from 'drift' where early minor errors compound. If spectral signatures degrade continuously rather than discretely, monitoring the 'spectral entropy' of the attention graph could serve as an early warning system for backtracking, making CoT more efficient.

Proposed Method

Generate long CoT solutions for complex problems. Have human annotators or strong models label the exact step where reasoning fails. Correlate this failure point with a time-series analysis of the attention graph's spectral gap and eigenvalue distribution. Check if a statistically significant 'spectral dip' occurs at steps $t-k$ before the error at step $t$.

Expected Contribution

A heuristic for 'Tree of Thoughts' search strategies that allows models to prune bad reasoning paths early based on internal topology rather than waiting for output evaluation.

Required Resources

Long-context reasoning datasets, automated evaluation pipelines (e.g., GPT-4 as judge), and visualization tools for spectral dynamics.

Source Paper

Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning

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