# Feature Learning in Image Hierarchies using Functional Maximal Correlation

arXiv: https://arxiv.org/abs/2305.20074 · HTML: https://mlsanity.com/paper/2305.20074/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [On Feature Decorrelation in Self-Supervised Learning](https://mlsanity.com/paper/2105.00470/) (2021)
- [VICRegL: Self-Supervised Learning of Local Visual Features](https://mlsanity.com/paper/2210.01571/) (2022)
- [Self-Supervised Learning with an Information Maximization Criterion](https://mlsanity.com/paper/2209.07999/) (2022)
- [An Information-Theoretic Perspective on Variance-Invariance-Covariance Regularization](https://mlsanity.com/paper/2303.00633/) (2023)
- [On Universal Features for High-Dimensional Learning and Inference](https://mlsanity.com/paper/1911.09105/) (2019)
- [EMP-SSL: Towards Self-Supervised Learning in One Training Epoch](https://mlsanity.com/paper/2304.03977/) (2023)
- [The Normalized Cross Density Functional: A Framework to Quantify Statistical Dependence for Random Processes](https://mlsanity.com/paper/2212.04631/) (2022)

## Built on by (most cited first, 1 of 1)

- [A Family of Kernelized Matrix Costs for Multiple-Output Mixture Neural Networks](https://mlsanity.com/paper/2509.24076/) (2025)

## Abstract (arXiv)

This paper proposes the Hierarchical Functional Maximal Correlation Algorithm (HFMCA), a hierarchical methodology that characterizes dependencies across two hierarchical levels in multiview systems. By framing view similarities as dependencies and ensuring contrastivity by imposing orthonormality, HFMCA achieves faster convergence and increased stability in self-supervised learning. HFMCA defines and measures dependencies within image hierarchies, from pixels and patches to full images. We find that the network topology for approximating orthonormal basis functions aligns with a vanilla CNN, enabling the decomposition of density ratios between neighboring layers of feature maps. This approach provides powerful interpretability, revealing the resemblance between supervision and self-supervision through the lens of internal representations.