The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason

This research paper discovers spectral phase transitions in large language models' hidden activation spaces during reasoning versus factual recall. A systematic spectral analysis across 11 models and 5 architecture families identifies seven core phenomena, including reasoning spectral compression and instruction tuning spectral reversal.