# Statistical Consistency and Generalization of Contrastive Representation Learning

arXiv: https://arxiv.org/abs/2605.02116 · HTML: https://mlsanity.com/paper/2605.02116/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 62 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 10 of 10)

- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Microsoft COCO Captions: Data Collection and Evaluation Server](https://mlsanity.com/paper/1504.00325/) (2015)
- [Generalization bounds for deep convolutional neural networks](https://mlsanity.com/paper/1905.12600/) (2019)
- [Self-supervised Learning from a Multi-view Perspective](https://mlsanity.com/paper/2006.05576/) (2020)
- [InfoNCE Induces Gaussian Distribution](https://mlsanity.com/paper/2602.24012/) (2026)
- [A Statistical Theory of Contrastive Pre-training and Multimodal Generative AI](https://mlsanity.com/paper/2501.04641/) (2025)
- [FastCLIP: A Suite of Optimization Techniques to Accelerate CLIP Training with Limited Resources](https://mlsanity.com/paper/2407.01445/) (2024)
- [Generalization Analysis for Supervised Contrastive Representation Learning under Non-IID Settings](https://mlsanity.com/paper/2505.04937/) (2025)
- [Contrastive Predictive Coding Done Right for Mutual Information Estimation](https://mlsanity.com/paper/2510.25983/) (2025)
- [Sparse Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2311.03881/) (2023)

## Built on by (most cited first, 1 of 1)

- [Expressivity In Multimodal Contrastive Learning](https://mlsanity.com/paper/2608.17203/) (2026)

## Abstract (arXiv)

Contrastive representation learning (CRL) underpins many modern foundation models. Despite recent theoretical progress, existing analyses suffer from several key limitations: (i) the statistical consistency of CRL remains poorly understood; (ii) available generalization bounds deteriorate as the number of negative samples increases, contradicting the empirical benefits of large negative sets; and (iii) the retrieval performance of CRL has received limited theoretical attention. In this paper, we develop a unified statistical learning theory for CRL. For downstream tasks, we evaluate retrieval quality using an AUC-type population criterion and show that the contrastive loss is statistically consistent with optimal ranking. We further establish a calibration-style inequality that quantitatively relates excess contrastive risk to excess retrieval suboptimality. For upstream training, we study both supervised and self-supervised contrastive objectives and derive generalization bounds of order O(1/m + 1/√n) and O(1/√m + 1/√n), respectively, where m denotes the number of negative samples and n the number of anchor points. These bounds not only explain the empirical advantages of large negative sets but also reveal an explicit trade-off between m and n. Extensive experiments on large-scale vision--language models corroborate our theoretical predictions.