Exploration-Lab/dim-discovery-archive

Geometry of Decision Making in Language Models

Abhinav Joshi · Divyanshu Bhatt · Ashutosh Modi
NeurIPS 2025

This repository contains the official implementation/release for the NeurIPS 2025 paper Geometry of Decision Making in Language Models. We study the internal decision-making processes of large language models through the lens of intrinsic dimension (ID), analyzing how hidden representations evolve across layers in a multiple-choice question answering (MCQA) setting. This repository provides additional experimental results, intrinsic-dimension estimations, and layer-wise performance analysis, that we believe will be a valuable resource for researchers for further exploration in this area.

Picture: In the transformer-based architectures, a vector (latent features) of the same hidden dimensions $d$, is transformed by transformer blocks $f_l$. Though the extrinsic dimension remains the same, we find that the feature space lies on low-dimensional manifolds of different intrinsic dimensions. Intrinsically, there exists a mapping $\phi_l$ corresponding to each $f_l$. We study how these compressed manifolds align with the decision-making process in middle layers. We project the internal representations back to the vocabulary space to inspect the decisiveness. There is a sudden shift in performance that is aligned with the follow-up of a sharp peak observed in the residual-post ID estimates.

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.

Structure

results/
  ├── dataset_name/
  │   ├── fewshot_xx/
  │   │   ├── model_id/
  │   │       ├── last_token_relative_depth_xx/
  │   │           ├── intrinsic/
  │   │               ├── results.csv (global intrinsic estimates)
  │   │               ├── mle_local_dims
  │   │                   ├── layer_name.csv (local intrinsic estimates)
  │   │           ├── llm_hook_args.json (arguments used for activation collection)
  │   │           ├── llm_intrinsic_args.json (arguments used for ID estimation)
  │   │           ├── accuracy_layer_name.json (accuracy per layer using logit lens)    
  │   │           ├── accuracy_output.json (overall accuracy on the dataset)
  │   │           ├── predictions.csv (predictions and corresponding ground truths)

Citation

@inproceedings{
joshi2025geometry,
title={Geometry of Decision Making in Language Models},
author={Abhinav Joshi and Divyanshu Bhatt and Ashutosh Modi},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=Jj4NdJtXwp}
}