# HOME: High-Order Mixed-Moment-based Embedding for Representation Learning

arXiv: https://arxiv.org/abs/2207.07743 · HTML: https://mlsanity.com/paper/2207.07743/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 15 Jul 2022.

## Builds on (most cited first, 23 of 23)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [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)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Self-Supervised Learning of Pretext-Invariant Representations](https://mlsanity.com/paper/1912.01991/) (2019)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Self-Supervised Pre-Training of Swin Transformers for 3D Medical Image Analysis](https://mlsanity.com/paper/2111.14791/) (2021)
- [Discriminative Unsupervised Feature Learning with Exemplar Convolutional Neural Networks](https://mlsanity.com/paper/1406.6909/) (2014)
- [Whitening for Self-Supervised Representation Learning](https://mlsanity.com/paper/2007.06346/) (2020)
- [Split-Brain Autoencoders: Unsupervised Learning by Cross-Channel Prediction](https://mlsanity.com/paper/1611.09842/) (2016)
- [SPICE: Semantic Pseudo-labeling for Image Clustering](https://mlsanity.com/paper/2103.09382/) (2021)
- [Jigsaw Clustering for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/2104.00323/) (2021)
- [Unsupervised Contrastive Learning based Transformer for Lung Nodule Detection](https://mlsanity.com/paper/2205.00122/) (2022)

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

- [PointJEM: Self-supervised Point Cloud Understanding for Reducing Feature Redundancy via Joint Entropy Maximization](https://mlsanity.com/paper/2312.03339/) (2023)

## Abstract (arXiv)

Minimum redundancy among different elements of an embedding in a latent space is a fundamental requirement or major preference in representation learning to capture intrinsic informational structures. Current self-supervised learning methods minimize a pair-wise covariance matrix to reduce the feature redundancy and produce promising results. However, such representation features of multiple variables may contain the redundancy among more than two feature variables that cannot be minimized via the pairwise regularization. Here we propose the High-Order Mixed-Moment-based Embedding (HOME) strategy to reduce the redundancy between any sets of feature variables, which is to our best knowledge the first attempt to utilize high-order statistics/information in this context. Multivariate mutual information is minimum if and only if multiple variables are mutually independent, which suggests the necessary conditions of factorized mixed moments among multiple variables. Based on these statistical and information theoretic principles, our general HOME framework is presented for self-supervised representation learning. Our initial experiments show that a simple version in the form of a three-order HOME scheme already significantly outperforms the current two-order baseline method (i.e., Barlow Twins) in terms of the linear evaluation on representation features.