Geometry of Decision Making in Language Models

TL;DR

This paper investigates the internal geometric structure of large language models, revealing how their hidden representations evolve across layers and contribute to decision-making in multiple-choice tasks.

Contribution

It introduces a large-scale analysis of the intrinsic dimension of LLM representations, uncovering a layered geometric pattern linked to decision-making processes.

Findings

Early layers operate on low-dimensional manifolds

Middle layers expand the representation space

Later layers compress representations for decision-making

Abstract

Large Language Models (LLMs) show strong generalization across diverse tasks, yet the internal decision-making processes behind their predictions remain opaque. In this work, we study the geometry of hidden representations in LLMs through the lens of \textit{intrinsic dimension} (ID), focusing specifically on decision-making dynamics in a multiple-choice question answering (MCQA) setting. We perform a large-scale study, with 28 open-weight transformer models and estimate ID across layers using multiple estimators, while also quantifying per-layer performance on MCQA tasks. Our findings reveal a consistent ID pattern across models: early layers operate on low-dimensional manifolds, middle layers expand this space, and later layers compress it again, converging to decision-relevant representations. Together, these results suggest LLMs implicitly learn to project linguistic inputs onto structured, low-dimensional manifolds aligned with task-specific decisions, providing new geometric insights into how generalization and reasoning emerge in language models.