The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason
We discover that large language models exhibit \emph{spectral phase transitions} in their hidden activation spaces when engaging in reasoning versus factual recall. Through systematic spectral analysis across \textbf{11 models} spanning \textbf{5 architecture families} (Qwen, Pythia, Phi, Llama, DeepSeek-R1), we identify \textbf{seven} core phenomena: (1)~\textbf{Reasoning Spectral Compression} -- 9/11 models show significantly lower $α$ for reasoning ($p < 0.05$), with larger effects in stronger models; (2)~\textbf{Instruction Tuning Spectral Reversal} -- base models show reasoning $α< $ factual $α$, while instruction-tuned models reverse this relationship; (3)~\textbf{Architecture-Depen...
| Authors | Yi Liu |
|---|---|
| Primary category | cs.LG |
| Published | 3 April 2026 |
| Last updated at source | 3 April 2026 |
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