# Rethinking Intrinsic Dimension Estimation in Neural Representations

arXiv: https://arxiv.org/abs/2604.20276 · HTML: https://mlsanity.com/paper/2604.20276/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 86 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Visual Transformers: Token-based Image Representation and Processing for Computer Vision](https://mlsanity.com/paper/2006.03677/) (2020)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [The Lipschitz Constant of Self-Attention](https://mlsanity.com/paper/2006.04710/) (2020)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [The geometry of hidden representations of large transformer models](https://mlsanity.com/paper/2302.00294/) (2023)
- [On the Origins of Linear Representations in Large Language Models](https://mlsanity.com/paper/2403.03867/) (2024)
- [Deep ReLU network approximation of functions on a manifold](https://mlsanity.com/paper/1908.00695/) (2019)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [On the Intrinsic Dimensionality of Image Representations](https://mlsanity.com/paper/1803.09672/) (2018)
- [Emergence of a High-Dimensional Abstraction Phase in Language Transformers](https://mlsanity.com/paper/2405.15471/) (2024)
- [Pay attention to your loss: understanding misconceptions about 1-Lipschitz neural networks](https://mlsanity.com/paper/2104.05097/) (2021)
- [DADApy: Distance-based Analysis of DAta-manifolds in Python](https://mlsanity.com/paper/2205.03373/) (2022)
- [Residual Stream Analysis with Multi-Layer SAEs](https://mlsanity.com/paper/2409.04185/) (2024)
- [The Intrinsic Dimension of Prompts in Internal Representations of Large Language Models](https://mlsanity.com/paper/2501.10573/) (2025)
- [Token embeddings violate the manifold hypothesis](https://mlsanity.com/paper/2504.01002/) (2025)
- [The representation landscape of few-shot learning and fine-tuning in large language models](https://mlsanity.com/paper/2409.03662/) (2024)
- [The Effect of Intrinsic Dataset Properties on Generalization: Unraveling Learning Differences Between Natural and Medical Images](https://mlsanity.com/paper/2401.08865/) (2024)

## Abstract (arXiv)

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.