# A Message Passing Perspective on Learning Dynamics of Contrastive Learning

arXiv: https://arxiv.org/abs/2303.04435 · HTML: https://mlsanity.com/paper/2303.04435/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 46 references that are in the map.
- First posted on arXiv 8 Mar 2023.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [A Survey of Transformers](https://mlsanity.com/paper/2106.04554/) (2021)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Understanding self-supervised Learning Dynamics without Contrastive Pairs](https://mlsanity.com/paper/2102.06810/) (2021)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Contrastive Training for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2007.05566/) (2020)

## Built on by (most cited first, 22 of 22)

- [On the Generalization of Multi-modal Contrastive Learning](https://mlsanity.com/paper/2306.04272/) (2023)
- [Do Generated Data Always Help Contrastive Learning?](https://mlsanity.com/paper/2403.12448/) (2024)
- [Understanding Augmentation-based Self-Supervised Representation Learning via RKHS Approximation and Regression](https://mlsanity.com/paper/2306.00788/) (2023)
- [Rethinking Weak Supervision in Helping Contrastive Learning](https://mlsanity.com/paper/2306.04160/) (2023)
- [Adversarial Examples Are Not Real Features](https://mlsanity.com/paper/2310.18936/) (2023)
- [Identifiable Contrastive Learning with Automatic Feature Importance Discovery](https://mlsanity.com/paper/2310.18904/) (2023)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [Projection Head is Secretly an Information Bottleneck](https://mlsanity.com/paper/2503.00507/) (2025)
- [mathbbX-Sample Contrastive Loss: Improving Contrastive Learning with Sample Similarity Graphs](https://mlsanity.com/paper/2407.18134/) (2024)
- [Architecture Matters: Uncovering Implicit Mechanisms in Graph Contrastive Learning](https://mlsanity.com/paper/2311.02687/) (2023)
- [On the Role of Discrete Tokenization in Visual Representation Learning](https://mlsanity.com/paper/2407.09087/) (2024)
- [Idempotent Unsupervised Representation Learning for Skeleton-Based Action Recognition](https://mlsanity.com/paper/2410.20349/) (2024)
- [Understanding the Role of Equivariance in Self-supervised Learning](https://mlsanity.com/paper/2411.06508/) (2024)
- [An Augmentation Overlap Theory of Contrastive Learning](https://mlsanity.com/paper/2511.03114/) (2025)
- [An Augmentation-Aware Theory for Self-Supervised Contrastive Learning](https://mlsanity.com/paper/2505.22196/) (2025)
- [Difficult Examples Hurt Unsupervised Contrastive Learning: A Theoretical Perspective](https://mlsanity.com/paper/2501.01317/) (2025)
- [A Signed Graph Approach to Understanding and Mitigating Oversmoothing in GNNs](https://mlsanity.com/paper/2502.11394/) (2025)
- [SPA++: Generalized Graph Spectral Alignment for Versatile Domain Adaptation](https://mlsanity.com/paper/2508.05182/) (2025)
- [Node Embeddings via Neighbor Embeddings](https://mlsanity.com/paper/2503.23822/) (2025)
- [Learning Without Augmenting: Unsupervised Time Series Representation Learning via Frame Projections](https://mlsanity.com/paper/2510.22655/) (2025)
- [Eigenfunction Extraction for Ordered Representation Learning](https://mlsanity.com/paper/2510.24672/) (2025)
- [A Theoretical Framework for Masked Pretraining (MPT)](https://mlsanity.com/paper/2609.06460/) (2026)

## Abstract (arXiv)

In recent years, contrastive learning achieves impressive results on self-supervised visual representation learning, but there still lacks a rigorous understanding of its learning dynamics. In this paper, we show that if we cast a contrastive objective equivalently into the feature space, then its learning dynamics admits an interpretable form. Specifically, we show that its gradient descent corresponds to a specific message passing scheme on the corresponding augmentation graph. Based on this perspective, we theoretically characterize how contrastive learning gradually learns discriminative features with the alignment update and the uniformity update. Meanwhile, this perspective also establishes an intriguing connection between contrastive learning and Message Passing Graph Neural Networks (MP-GNNs). This connection not only provides a unified understanding of many techniques independently developed in each community, but also enables us to borrow techniques from MP-GNNs to design new contrastive learning variants, such as graph attention, graph rewiring, jumpy knowledge techniques, etc. We believe that our message passing perspective not only provides a new theoretical understanding of contrastive learning dynamics, but also bridges the two seemingly independent areas together, which could inspire more interleaving studies to benefit from each other. The code is available at https://github.com/PKU-ML/Message-Passing-Contrastive-Learning.