# ERank in Latent Space as an Image-Complexity and Richness Measure

arXiv: https://arxiv.org/abs/2607.19315 · HTML: https://mlsanity.com/paper/2607.19315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 55 references that are in the map.
- First posted on arXiv 21 Jul 2026.

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

- [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)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [An End-to-End Trainable Neural Network for Image-based Sequence Recognition and Its Application to Scene Text Recognition](https://mlsanity.com/paper/1507.05717/) (2015)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Dynamic Neural Networks: A Survey](https://mlsanity.com/paper/2102.04906/) (2021)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [Implicit Regularization in Matrix Factorization](https://mlsanity.com/paper/1705.09280/) (2017)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [SemDeDup: Data-efficient learning at web-scale through semantic deduplication](https://mlsanity.com/paper/2303.09540/) (2023)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [DeepCore: A Comprehensive Library for Coreset Selection in Deep Learning](https://mlsanity.com/paper/2204.08499/) (2022)
- [Not All Images are Worth 16x16 Words: Dynamic Transformers for Efficient Image Recognition](https://mlsanity.com/paper/2105.15075/) (2021)
- [A Coreset Selection of Coreset Selection Literature: Introduction and Recent Advances](https://mlsanity.com/paper/2505.17799/) (2025)
- [Repeated Random Sampling for Minimizing the Time-to-Accuracy of Learning](https://mlsanity.com/paper/2305.18424/) (2023)
- [Data pruning and neural scaling laws: fundamental limitations of score-based algorithms](https://mlsanity.com/paper/2302.06960/) (2023)
- [Image Complexity-Aware Adaptive Retrieval for Efficient Vision-Language Models](https://mlsanity.com/paper/2512.15372/) (2025)

## Abstract (arXiv)

We propose the effective rank (ERank) of the channel covariance of an image's deep feature map as a per-sample, label-free measure of visual richness, computed from a single forward pass through a frozen pretrained encoder. ERank counts how many decorrelated channel directions an image activates, and we characterize its properties, including its behavior under noise. Empirically, ERank orders images from plain to visually rich, correlates with codec bitrate, sharpness, and edge density, and correlates with human complexity annotations on IC9600 with r = 0.72. As a data-selection criterion, removing low-ERank samples improves super-resolution and removing high-ERank samples improves OCR, in both pretraining and finetuning, while selection does not help classification, segmentation, or denoising. ERank is thus a cheap richness signal, useful exactly when task difficulty is governed by input richness.