# On the Similarities of Embeddings in Contrastive Learning

arXiv: https://arxiv.org/abs/2506.09781 · HTML: https://mlsanity.com/paper/2506.09781/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 45 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (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)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [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)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Do Better ImageNet Models Transfer Better?](https://mlsanity.com/paper/1805.08974/) (2018)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Spatiotemporal Contrastive Video Representation Learning](https://mlsanity.com/paper/2008.03800/) (2020)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [InfoXLM: An Information-Theoretic Framework for Cross-Lingual Language Model Pre-Training](https://mlsanity.com/paper/2007.07834/) (2020)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Combined Scaling for Zero-shot Transfer Learning](https://mlsanity.com/paper/2111.10050/) (2021)
- [Decoupled Contrastive Learning](https://mlsanity.com/paper/2110.06848/) (2021)
- [Solo-learn: A Library of Self-supervised Methods for Visual Representation Learning](https://mlsanity.com/paper/2108.01775/) (2021)
- [Self-Supervised Learning with Kernel Dependence Maximization](https://mlsanity.com/paper/2106.08320/) (2021)
- [Improving Transferability of Representations via Augmentation-Aware Self-Supervision](https://mlsanity.com/paper/2111.09613/) (2021)
- [Provable Stochastic Optimization for Global Contrastive Learning: Small Batch Does Not Harm Performance](https://mlsanity.com/paper/2202.12387/) (2022)
- [Investigating the Benefits of Projection Head for Representation Learning](https://mlsanity.com/paper/2403.11391/) (2024)

## Built on by (most cited first, 2 of 2)

- [Autograder+: A Multi-Faceted AI Framework for Rich Pedagogical Feedback in Programming Education](https://mlsanity.com/paper/2510.26402/) (2025)
- [Distilling Formal Logic into Neural Spaces: A Kernel Alignment Approach for Signal Temporal Logic](https://mlsanity.com/paper/2603.05198/) (2026)

## Abstract (arXiv)

Contrastive learning operates on a simple yet effective principle: Embeddings of positive pairs are pulled together, while those of negative pairs are pushed apart. In this paper, we propose a unified framework for understanding contrastive learning through the lens of cosine similarity, and present two key theoretical insights derived from this framework. First, in full-batch settings, we show that perfect alignment of positive pairs is unattainable when negative-pair similarities fall below a threshold, and this misalignment can be mitigated by incorporating within-view negative pairs into the objective. Second, in mini-batch settings, smaller batch sizes induce stronger separation among negative pairs in the embedding space, i.e., higher variance in their similarities, which in turn degrades the quality of learned representations compared to full-batch settings. To address this, we propose an auxiliary loss that reduces the variance of negative-pair similarities in mini-batch settings. Empirical results show that incorporating the proposed loss improves performance in small-batch settings.