Geometry of Decision Making in Language Models
This work provides geometric insights into how generalization and reasoning emerge in LLMs, addressing the opacity of their decision-making for researchers and practitioners in AI.
The study investigated the internal decision-making processes in large language models (LLMs) by analyzing the geometry of hidden representations using intrinsic dimension (ID) across 28 transformer models in a multiple-choice question answering setting, revealing consistent patterns where early layers use low-dimensional manifolds, middle layers expand, and later layers compress to align with task-specific decisions.
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.