IdEst: Assessing Self-Supervised Learning Representations via Intrinsic Dimension

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 ($\mathrm{dim}_\mathrm{MST}$). 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.

Large-scale AI models typically learn to understand images by training on vast amounts of unlabeled data, a technique called self-supervised learning (SSL). These models produce representations: compact descriptions of images that can subsequently be reused for practical applications such as object recognition. However, evaluating the quality of these representations typically requires labeled data and significant computational resources. This raises a natural question: can we assess representation quality without labels, by instead examining the geometric structure of the representations themselves? We propose IdEst, a method that assesses representation quality from a geometric perspective without requiring any labels. The core idea is that high-quality image representations compress information efficiently. Even though they live in a complex, high-dimensional space, they actually occupy a much simpler, low-dimensional structure. IdEst relies on intrinsic dimension estimation, a measure of the complexity of this underlying structure, to assess representation quality. We demonstrate that this geometric proxy correlates well with downstream performance across a wide range of SSL models. Beyond offering empirical insights, our work suggests that geometric descriptors can serve as a scalable, label-free complement to traditional evaluation methods.