arXiv:2607.01571v1 Announce Type: new Abstract: 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
The increasing complexity and opacity of LLM reasoning necessitate novel analytical methods to understand and improve their performance, moving beyond superficial metrics.
Understanding the 'geometric signatures' of LLM reasoning could unlock new pathways for interpretability, efficiency, and robustness in AI systems, fundamentally altering how we train and deploy them.
The focus on LLM reasoning shifts from purely linguistic content to the underlying geometric dynamics in their hidden state spaces, potentially leading to more sophisticated control and optimization.
- · AI researchers
- · LLM developers
- · High-performance computing sector
- · LLM black box proponents
New metrics and diagnostic tools for LLM performance and reasoning capabilities.
Improved efficiency and reliability of LLMs, accelerating their adoption in critical applications.
A deeper theoretical understanding of intelligence, bridging AI and cognitive science through geometric principles.
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Read at arXiv cs.LG