# HEX: Hierarchical Emergence Exploitation in Self-Supervised Algorithms

arXiv: https://arxiv.org/abs/2410.23200 · HTML: https://mlsanity.com/paper/2410.23200/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 55 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [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)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (2020)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [With a Little Help from My Friends: Nearest-Neighbor Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2104.14548/) (2021)
- [Contrastive learning of global and local features for medical image segmentation with limited annotations](https://mlsanity.com/paper/2006.10511/) (2020)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods](https://mlsanity.com/paper/2205.11508/) (2022)
- [Boosting Contrastive Self-Supervised Learning with False Negative Cancellation](https://mlsanity.com/paper/2011.11765/) (2020)
- [Solo-learn: A Library of Self-supervised Methods for Visual Representation Learning](https://mlsanity.com/paper/2108.01775/) (2021)
- [On the duality between contrastive and non-contrastive self-supervised learning](https://mlsanity.com/paper/2206.02574/) (2022)
- [Use All The Labels: A Hierarchical Multi-Label Contrastive Learning Framework](https://mlsanity.com/paper/2204.13207/) (2022)
- [LoCo: Local Contrastive Representation Learning](https://mlsanity.com/paper/2008.01342/) (2020)
- [Rethinking the Augmentation Module in Contrastive Learning: Learning Hierarchical Augmentation Invariance with Expanded Views](https://mlsanity.com/paper/2206.00227/) (2022)
- [Reverse Engineering Self-Supervised Learning](https://mlsanity.com/paper/2305.15614/) (2023)
- [HiURE: Hierarchical Exemplar Contrastive Learning for Unsupervised Relation Extraction](https://mlsanity.com/paper/2205.02225/) (2022)
- [Hierarchical Contrast for Unsupervised Skeleton-based Action Representation Learning](https://mlsanity.com/paper/2212.02082/) (2022)
- [Contrastive Explanations in Neural Networks](https://mlsanity.com/paper/2008.00178/) (2020)
- [MaskCon: Masked Contrastive Learning for Coarse-Labelled Dataset](https://mlsanity.com/paper/2303.12756/) (2023)

## Built on by (most cited first, 7 of 7)

- [Hierarchical and Multimodal Data for Daily Activity Understanding](https://mlsanity.com/paper/2504.17696/) (2025)
- [AdaDim: Dimensionality Adaptation for SSL Representational Dynamics](https://mlsanity.com/paper/2505.12576/) (2025)
- [Subject Invariant Contrastive Learning for Human Activity Recognition](https://mlsanity.com/paper/2507.03250/) (2025)
- [Multi-level and Multi-modal Action Anticipation](https://mlsanity.com/paper/2506.02382/) (2025)
- [Countering Multi-modal Representation Collapse through Rank-targeted Fusion](https://mlsanity.com/paper/2511.06450/) (2025)
- [Information Router for Mitigating Modality Dominance in Vision-Language Models](https://mlsanity.com/paper/2604.16264/) (2026)
- [ModAn-MulSupCon: Modality-and Anatomy-Aware Multi-Label Supervised Contrastive Pretraining for Medical Imaging](https://mlsanity.com/paper/2508.18613/) (2025)

## Abstract (arXiv)

In this paper, we propose an algorithm that can be used on top of a wide variety of self-supervised (SSL) approaches to take advantage of hierarchical structures that emerge during training. SSL approaches typically work through some invariance term to ensure consistency between similar samples and a regularization term to prevent global dimensional collapse. Dimensional collapse refers to data representations spanning a lower-dimensional subspace. Recent work has demonstrated that the representation space of these algorithms gradually reflects a semantic hierarchical structure as training progresses. Data samples of the same hierarchical grouping tend to exhibit greater dimensional collapse locally compared to the dataset as a whole due to sharing features in common with each other. Ideally, SSL algorithms would take advantage of this hierarchical emergence to have an additional regularization term to account for this local dimensional collapse effect. However, the construction of existing SSL algorithms does not account for this property. To address this, we propose an adaptive algorithm that performs a weighted decomposition of the denominator of the InfoNCE loss into two terms: local hierarchical and global collapse regularization respectively. This decomposition is based on an adaptive threshold that gradually lowers to reflect the emerging hierarchical structure of the representation space throughout training. It is based on an analysis of the cosine similarity distribution of samples in a batch. We demonstrate that this hierarchical emergence exploitation (HEX) approach can be integrated across a wide variety of SSL algorithms. Empirically, we show performance improvements of up to 5.6% relative improvement over baseline SSL approaches on classification accuracy on Imagenet with 100 epochs of training.