# IdEst: Assessing Self-Supervised Learning Representations via Intrinsic Dimension

arXiv: https://arxiv.org/abs/2606.03338 · HTML: https://mlsanity.com/paper/2606.03338/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 66 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [iBOT: Image BERT Pre-Training with Online Tokenizer](https://mlsanity.com/paper/2111.07832/) (2021)
- [EVA-CLIP: Improved Training Techniques for CLIP at Scale](https://mlsanity.com/paper/2303.15389/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [Perception Encoder: The best visual embeddings are not at the output of the network](https://mlsanity.com/paper/2504.13181/) (2025)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [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)
- [Benchmarking Representation Learning for Natural World Image Collections](https://mlsanity.com/paper/2103.16483/) (2021)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [The geometry of hidden representations of large transformer models](https://mlsanity.com/paper/2302.00294/) (2023)
- [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023)
- [Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks](https://mlsanity.com/paper/2111.13171/) (2021)
- [Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks](https://mlsanity.com/paper/2006.09313/) (2020)
- [LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihood](https://mlsanity.com/paper/2206.14882/) (2022)
- [LiDAR: Sensing Linear Probing Performance in Joint Embedding SSL Architectures](https://mlsanity.com/paper/2312.04000/) (2023)
- [Around the World in 80 Timesteps: A Generative Approach to Global Visual Geolocation](https://mlsanity.com/paper/2412.06781/) (2024)

## Built on by (most cited first, 2 of 2)

- [The Cross-Architecture Substrate: A Domain-Transcendent, Calibration-Surviving Geometric Invariant of Modern Vision Encoders](https://mlsanity.com/paper/2606.07882/) (2026)
- [Geometry-Aware Graph Construction via Adaptive Spectral Bandwidth Control](https://mlsanity.com/paper/2609.03306/) (2026)

## Abstract (arXiv)

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning meaningful representations from unlabeled data. However, the standard protocol for evaluating these representations, linear probing, is computationally expensive, sensitive to hyperparameters, and provides limited insight into the geometric structure of the representation space. In this work, motivated by connections between neural network generalization and intrinsic dimension (ID) we propose IdEst, a method for estimating the ID of SSL representations via the Minimum Spanning Tree dimension estimator (dimMST). Across diverse datasets, architectures, and SSL pretraining objectives, we show that IdEst strongly correlates with downstream linear probe performances. Furthermore, we demonstrate that IdEst enables efficient hyperparameter selection, significantly reducing the computational cost compared to supervised alternatives. Our results highlight intrinsic dimensionality as a principled geometric proxy for assessing SSL representations, complementing standard supervised probing protocols.