Spectral analysis of transformer hidden states reveals phase transitions distinguishing reasoning from recall, with the spectral exponent alpha predicting answer correctness at AUC up to 1.000 before output generation.
The spectral trajectory shows clear α gradient spikes at calculation boundaries (e.g., after “=”), with Layer 9 showing the most pronounced punctuation effect
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The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason
Spectral analysis of transformer hidden states reveals phase transitions distinguishing reasoning from recall, with the spectral exponent alpha predicting answer correctness at AUC up to 1.000 before output generation.