# Contrastive Self-Supervised Learning As Neural Manifold Packing

arXiv: https://arxiv.org/abs/2506.13717 · HTML: https://mlsanity.com/paper/2506.13717/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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)
- [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)
- [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)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (2020)
- [Albumentations: fast and flexible image augmentations](https://mlsanity.com/paper/1809.06839/) (2018)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [Solo-learn: A Library of Self-supervised Methods for Visual Representation Learning](https://mlsanity.com/paper/2108.01775/) (2021)
- [Spherical Latent Spaces for Stable Variational Autoencoders](https://mlsanity.com/paper/1808.10805/) (2018)
- [Pushing the limits of self-supervised ResNets: Can we outperform supervised learning without labels on ImageNet?](https://mlsanity.com/paper/2201.05119/) (2022)
- [Classification and Geometry of General Perceptual Manifolds](https://mlsanity.com/paper/1710.06487/) (2017)
- [Self-Supervised Learning with an Information Maximization Criterion](https://mlsanity.com/paper/2209.07999/) (2022)
- [Neural tuning and representational geometry](https://mlsanity.com/paper/2104.09743/) (2021)
- [Learning Efficient Coding of Natural Images with Maximum Manifold Capacity Representations](https://mlsanity.com/paper/2303.03307/) (2023)
- [Interpreting neural computations by examining intrinsic and embedding dimensionality of neural activity](https://mlsanity.com/paper/2107.04084/) (2021)
- [Linear Readout of Object Manifolds](https://mlsanity.com/paper/1512.01834/) (2015)
- [Towards an Improved Understanding and Utilization of Maximum Manifold Capacity Representations](https://mlsanity.com/paper/2406.09366/) (2024)
- [Collapse-Proof Non-Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2410.04959/) (2024)
- [Classifying minimum energy states for interacting particles: Regular simplices](https://mlsanity.com/paper/2109.07091/) (2021)

## Built on by (most cited first, 3 of 3)

- [Hypersolid: Emergent Vision Representations via Short-Range Repulsion](https://mlsanity.com/paper/2601.21255/) (2026)
- [Amorphous Solid Model of Vectorial Hopfield Neural Networks](https://mlsanity.com/paper/2507.22787/) (2025)
- [Geometric origin of adversarial vulnerability in deep learning](https://mlsanity.com/paper/2509.01235/) (2025)

## Abstract (arXiv)

Contrastive self-supervised learning based on point-wise comparisons has been widely studied for vision tasks. In the visual cortex of the brain, neuronal responses to distinct stimulus classes are organized into geometric structures known as neural manifolds. Accurate classification of stimuli can be achieved by effectively separating these manifolds, akin to solving a packing problem. We introduce Contrastive Learning As Manifold Packing (CLAMP), a self-supervised framework that recasts representation learning as a manifold packing problem. CLAMP introduces a loss function inspired by the potential energy of short-range repulsive particle systems, such as those encountered in the physics of simple liquids and jammed packings. In this framework, each class consists of sub-manifolds embedding multiple augmented views of a single image. The sizes and positions of the sub-manifolds are dynamically optimized by following the gradient of a packing loss. This approach yields interpretable dynamics in the embedding space that parallel jamming physics, and introduces geometrically meaningful hyperparameters within the loss function. Under the standard linear evaluation protocol, which freezes the backbone and trains only a linear classifier, CLAMP achieves competitive performance with state-of-the-art self-supervised models. Furthermore, our analysis reveals that neural manifolds corresponding to different categories emerge naturally and are effectively separated in the learned representation space, highlighting the potential of CLAMP to bridge insights from physics, neural science, and machine learning.