Geometry of Decision Making in Language Models

Abhinav Joshi, Divyanshu Bhatt, Ashutosh Modi

Keywords: Large Language Models, Intrinsic Dimension, Interpretability, Decision-Making, Reasoning

TL;DR: Transformer-based language models learn low-dimensional task manifolds across layers, with similar patterns/trends in intrinsic dimensions revealing similar compression strategies despite varying architectures/sizes.

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 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.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 19358