Geometric Signatures of Reasoning: A Spectral Perspective on Task Hardness
Chain-of-thought (CoT) reasoning enables large language models (LLMs) to solve complex problems by generating intermediate reasoning steps. While much attention has been paid to the length and content of these reasoning chains, far less is known about their internal geometry. We study the \emph{geometry} of CoT trajectories in the hidden state space of transformer models, formalizing each reasoning chain as a discrete curve in $\mathbb{R}^d$ and characterizing it through spectral, positional, and kinematic geometric functionals. We introduce the effective dimension $d_ρ$ as a measure of trajectory complexity and show theoretically that trajectories with flatter eigenvalue spectra correspo...
| Authors | Aria Masoomi, Mahsa Bazzaz, Adel Javanmard et al. |
|---|---|
| Primary category | cs.LG |
| Published | 2 July 2026 |
| Last updated at source | 2 July 2026 |
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