Rethinking Intrinsic Dimension Estimation in Neural Representations

Rickmer Schulte, David Rügamer
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:10-18, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-schulte26a, title = { Rethinking Intrinsic Dimension Estimation in Neural Representations }, author = {Schulte, Rickmer and R{\"u}gamer, David}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {10--18}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/schulte26a/schulte26a.pdf}, url = {https://proceedings.mlr.press/v300/schulte26a.html}, 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. } }
Endnote
%0 Conference Paper %T Rethinking Intrinsic Dimension Estimation in Neural Representations %A Rickmer Schulte %A David Rügamer %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-schulte26a %I PMLR %P 10--18 %U https://proceedings.mlr.press/v300/schulte26a.html %V 300 %X 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.
APA
Schulte, R. & Rügamer, D.. (2026). Rethinking Intrinsic Dimension Estimation in Neural Representations . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:10-18 Available from https://proceedings.mlr.press/v300/schulte26a.html.

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