# Bridging Mini-Batch and Asymptotic Analysis in Contrastive Learning: From InfoNCE to Kernel-Based Losses

arXiv: https://arxiv.org/abs/2405.18045 · HTML: https://mlsanity.com/paper/2405.18045/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 52 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 30 of 37)

- [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)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (2020)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (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)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [On Feature Decorrelation in Self-Supervised Learning](https://mlsanity.com/paper/2105.00470/) (2021)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods](https://mlsanity.com/paper/2205.11508/) (2022)
- [Decoupled Contrastive Learning](https://mlsanity.com/paper/2110.06848/) (2021)
- [On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features](https://mlsanity.com/paper/2203.01238/) (2022)
- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)
- [Imbalance Trouble: Revisiting Neural-Collapse Geometry](https://mlsanity.com/paper/2208.05512/) (2022)
- [Self-Supervised Learning with Kernel Dependence Maximization](https://mlsanity.com/paper/2106.08320/) (2021)
- [Learning towards Minimum Hyperspherical Energy](https://mlsanity.com/paper/1805.09298/) (2018)
- [How Does SimSiam Avoid Collapse Without Negative Samples? A Unified Understanding with Self-supervised Contrastive Learning](https://mlsanity.com/paper/2203.16262/) (2022)
- [Dissecting Supervised Contrastive Learning](https://mlsanity.com/paper/2102.08817/) (2021)
- [The Power of Contrast for Feature Learning: A Theoretical Analysis](https://mlsanity.com/paper/2110.02473/) (2021)
- [Dual Temperature Helps Contrastive Learning Without Many Negative Samples: Towards Understanding and Simplifying MoCo](https://mlsanity.com/paper/2203.17248/) (2022)
- [Unsupervised Feature Learning by Cross-Level Instance-Group Discrimination](https://mlsanity.com/paper/2008.03813/) (2020)
- [Learning with Hyperspherical Uniformity](https://mlsanity.com/paper/2103.01649/) (2021)
- [Contrastive Learning Can Find An Optimal Basis For Approximately View-Invariant Functions](https://mlsanity.com/paper/2210.01883/) (2022)
- [Regularizing Neural Networks via Minimizing Hyperspherical Energy](https://mlsanity.com/paper/1906.04892/) (2019)

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

- [Multimodal Reasoning Agent for Zero-Shot Composed Image Retrieval](https://mlsanity.com/paper/2505.19952/) (2025)
- [A Principled Framework for Multi-View Contrastive Learning](https://mlsanity.com/paper/2507.06979/) (2025)
- [SupCLAP: Controlling Optimization Trajectory Drift in Audio-Text Contrastive Learning with Support Vector Regularization](https://mlsanity.com/paper/2509.21033/) (2025)
- [On the Similarities of Embeddings in Contrastive Learning](https://mlsanity.com/paper/2506.09781/) (2025)
- [Understanding InfoNCE: Transition Probability Matrix Induced Feature Clustering](https://mlsanity.com/paper/2511.12180/) (2025)
- [Neural Collapse by Design: Learning Class Prototypes on the Hypersphere](https://mlsanity.com/paper/2605.20302/) (2026)
- [Differentiable Koopman Operator for Contrastive Learning on Dynamic Graphs](https://mlsanity.com/paper/2610.02990/) (2026)

## Abstract (arXiv)

What do different contrastive learning (CL) losses actually optimize for? Although multiple CL methods have demonstrated remarkable representation learning capabilities, the differences in their inner workings remain largely opaque. In this work, we analyse several CL families and prove that, under certain conditions, they admit the same minimisers when optimizing either their batch-level objectives or their expectations asymptotically. In both cases, an intimate connection with the hyperspherical energy minimisation (HEM) problem resurfaces. Drawing inspiration from this, we introduce a novel CL objective, coined Decoupled Hyperspherical Energy Loss (DHEL). DHEL simplifies the problem by decoupling the target hyperspherical energy from the alignment of positive examples while preserving the same theoretical guarantees. Going one step further, we show the same results hold for another relevant CL family, namely kernel contrastive learning (KCL), with the additional advantage of the expected loss being independent of batch size, thus identifying the minimisers in the non-asymptotic regime. Empirical results demonstrate improved downstream performance and robustness across combinations of different batch sizes and hyperparameters and reduced dimensionality collapse, on several computer vision datasets.