Rethinking Intrinsic Dimension Estimation in Neural Representations

TL;DR

This paper critically examines the limitations of current intrinsic dimension estimators in neural representations, revealing they often do not measure true underlying dimensions and proposing a new perspective.

Contribution

It identifies a key discrepancy between theory and practice in intrinsic dimension estimation and introduces a novel approach to address this issue.

Findings

Common ID estimators do not track the true intrinsic dimension.

Empirical and theoretical analysis shows limitations of existing methods.

Proposes a new perspective on ID estimation in neural representations.

Abstract

The analysis of neural representation has become an integral part of research aiming to better understand the inner workings of neural networks. While there are many different approaches to investigate neural representations, an important line of research has focused on doing so through the lens of intrinsic dimensions (IDs). Although this perspective has provided valuable insights and stimulated substantial follow-up research, important limitations of this approach have remained largely unaddressed. In this paper, we highlight a crucial discrepancy between theory and practice of IDs in neural representations, theoretically and empirically showing that common ID estimators are, in fact, not tracking the true underlying ID of the representation. We contrast this negative result with an investigation of the underlying factors that may drive commonly reported ID-related results on neural representation in the literature. Building on these insights, we offer a new perspective on ID estimation in neural representations.