# On the Intrinsic Dimensionality of Image Representations

arXiv: https://arxiv.org/abs/1803.09672 · HTML: https://mlsanity.com/paper/1803.09672/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2018.

## Built on by (most cited first, 30 of 57)

- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Assessing the State of Self-Supervised Human Activity Recognition using Wearables](https://mlsanity.com/paper/2202.12938/) (2022)
- [Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributions](https://mlsanity.com/paper/2409.02426/) (2024)
- [Reward-Directed Conditional Diffusion: Provable Distribution Estimation and Reward Improvement](https://mlsanity.com/paper/2307.07055/) (2023)
- [Detecting Images Generated by Deep Diffusion Models using their Local Intrinsic Dimensionality](https://mlsanity.com/paper/2307.02347/) (2023)
- [When do GANs replicate? On the choice of dataset size](https://mlsanity.com/paper/2202.11765/) (2022)
- [Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks](https://mlsanity.com/paper/2109.02832/) (2021)
- [Diffusion Model for Data-Driven Black-Box Optimization](https://mlsanity.com/paper/2403.13219/) (2024)
- [Why Robust Generalization in Deep Learning is Difficult: Perspective of Expressive Power](https://mlsanity.com/paper/2205.13863/) (2022)
- [Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modeling](https://mlsanity.com/paper/2502.05743/) (2025)
- [50 Years of Automated Face Recognition](https://mlsanity.com/paper/2505.24247/) (2025)
- [The Effect of Intrinsic Dataset Properties on Generalization: Unraveling Learning Differences Between Natural and Medical Images](https://mlsanity.com/paper/2401.08865/) (2024)
- [Topology and geometry of data manifold in deep learning](https://mlsanity.com/paper/2204.08624/) (2022)
- [Sample Complexity of Nonparametric Off-Policy Evaluation on Low-Dimensional Manifolds using Deep Networks](https://mlsanity.com/paper/2206.02887/) (2022)
- [Biometric Template Protection for Neural-Network-based Face Recognition Systems: A Survey of Methods and Evaluation Techniques](https://mlsanity.com/paper/2110.05044/) (2021)
- [Data Representations' Study of Latent Image Manifolds](https://mlsanity.com/paper/2305.19730/) (2023)
- [LDReg: Local Dimensionality Regularized Self-Supervised Learning](https://mlsanity.com/paper/2401.10474/) (2024)
- [Measuring the Intrinsic Dimension of Earth Representations](https://mlsanity.com/paper/2511.02101/) (2025)
- [Geometry of Decision Making in Language Models](https://mlsanity.com/paper/2511.20315/) (2025)
- [Benchmarking fixed-length Fingerprint Representations across different Embedding Sizes and Sensor Types](https://mlsanity.com/paper/2307.08615/) (2023)
- [Unsupervised Embedding Adaptation via Early-Stage Feature Reconstruction for Few-Shot Classification](https://mlsanity.com/paper/2106.11486/) (2021)
- [Exploring the Representation Manifolds of Stable Diffusion Through the Lens of Intrinsic Dimension](https://mlsanity.com/paper/2302.09301/) (2023)
- [A Latent Fingerprint in the Wild Database](https://mlsanity.com/paper/2304.00979/) (2023)
- [Feature Fusion Methods for Indexing and Retrieval of Biometric Data: Application to Face Recognition with Privacy Protection](https://mlsanity.com/paper/2107.12675/) (2021)
- [A Manifold Two-Sample Test Study: Integral Probability Metric with Neural Networks](https://mlsanity.com/paper/2205.02043/) (2022)
- [FONDUE: an algorithm to find the optimal dimensionality of the latent representations of variational autoencoders](https://mlsanity.com/paper/2209.12806/) (2022)
- [Deep neural networks architectures from the perspective of manifold learning](https://mlsanity.com/paper/2306.03406/) (2023)
- [Mobile Contactless Palmprint Recognition: Use of Multiscale, Multimodel Embeddings](https://mlsanity.com/paper/2401.08111/) (2024)
- [Overparameterization Improves StyleGAN Inversion](https://mlsanity.com/paper/2205.06304/) (2022)

## Abstract (arXiv)

This paper addresses the following questions pertaining to the intrinsic dimensionality of any given image representation: (i) estimate its intrinsic dimensionality, (ii) develop a deep neural network based non-linear mapping, dubbed DeepMDS, that transforms the ambient representation to the minimal intrinsic space, and (iii) validate the veracity of the mapping through image matching in the intrinsic space. Experiments on benchmark image datasets (LFW, IJB-C and ImageNet-100) reveal that the intrinsic dimensionality of deep neural network representations is significantly lower than the dimensionality of the ambient features. For instance, SphereFace's 512-dim face representation and ResNet's 512-dim image representation have an intrinsic dimensionality of 16 and 19 respectively. Further, the DeepMDS mapping is able to obtain a representation of significantly lower dimensionality while maintaining discriminative ability to a large extent, 59.75% TAR @ 0.1% FAR in 16-dim vs 71.26% TAR in 512-dim on IJB-C and a Top-1 accuracy of 77.0% at 19-dim vs 83.4% at 512-dim on ImageNet-100.