Reasoning emerges from constrained inference manifolds in large language models

TL;DR

This paper investigates the internal reasoning processes of large language models, revealing that effective reasoning depends on specific geometric and informational constraints within their internal representations.

Contribution

It introduces a new, label-free diagnostic based on internal dynamics and identifies key conditions for stable reasoning in large language models.

Findings

Inference dynamics form low-dimensional manifolds within high-dimensional spaces.

Stable reasoning requires representational expressivity, manifold compression, and information preservation.

Models outside this regime show pathological inference behaviors.

Abstract

Reasoning in large language models is predominantly evaluated through labeled benchmarks, conflating task performance with the quality of internal inference. Here we study reasoning as an intrinsic dynamical process by examining the evolution of internal representations during inference. We find that inference-time dynamics consistently self-organize into low-dimensional manifolds embedded within high-dimensional representation spaces. we find that such geometric compression, although pervasive, is not sufficient for stable or reliable reasoning. Instead, effective reasoning dynamics emerge within a constrained structural regime characterized by three conditions: adequate representational expressivity, spontaneous manifold compression, and preservation of non-degenerate information volume within the compressed subspace. Models outside this regime exhibit characteristic pathological inference dynamics. Based on these insights, we introduce a unified, label-free diagnostic computed solely from internal dynamics. These findings suggest that reasoning in LLMs is fundamentally governed by geometric and informational constraints, offering a complementary framework to benchmark-centric assessment.