# A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning

Source: [A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning](<https://www.sota2.com/research/paper/6a0162b4dbc836b87d8232a3>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-30T05:00:11.986Z

Authors: Nong Minh Hieu, Antoine Ledent

Published: 2026-05-08T11:12:43.000Z

## Abstract

Contrastive Representation Learning (CRL) has achieved strong empirical success in multiple machine learning disciplines, yet its theoretical sample complexity remains poorly understood. Existing analyses usually assume that input tuples are identically and independently distributed, an assumption violated in most practical settings where contrastive tuples are constructed from a finite pool of labeled data, inducing dependencies among tuples. While one recent work analyzed this learning setting using U-Statistics to estimate the population risk, the techniques used therein require the risk of each class to concentrate uniformly, making excess risk bounds scale in the order of $\\rho\_{\\min}^{-{1}/{2}}$ where $\\rho\_{\\min}$ denotes the probability of the rarest class. Such a dependency can be overly pessimistic in the extreme multiclass settings where there are many tail classes which contribute minimally to the overall population risk. Our contributions are two-fold. Firstly, we improve upon the previous work and prove a bound with a sample complexity of the same order as the number of classes $R$, regardless of the distribution over classes. Furthermore, we formulate a different estimator that captures the concentration of the risk \\textit{across classes}, enabling sharper bounds in extreme multi-class learning scenarios, especially where class distributions are long-tailed. Under mild assumptions on the class distributions, the resulting sample complexity is $\\mathcal{{O}}(k)$ where $k$ is the number of samples per tuple.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on MNIST imbl](<https://www.sota2.com/research/sota/image-classification-on-mnist-imbl.md>): Image Classification; MNIST imbl; Macro Precision: 99.03.

- [Image Classification on CIFAR10 imbl](<https://www.sota2.com/research/sota/image-classification-on-cifar10-imbl.md>): Image Classification; CIFAR10 imbl; Macro Precision: 81.28.

- [Image Classification on CIFAR100 (Macro F1, Precision, Recall)](<https://www.sota2.com/research/sota/image-classification-on-cifar100-macro-f1-precision-recall.md>): Image Classification; CIFAR100; Macro Precision: 34.9.

- [Image Classification on MNIST imbalanced](<https://www.sota2.com/research/sota/image-classification-on-mnist-imbalanced.md>): Image Classification; MNIST imbalanced; Macro Precision: 99.03.

- [Image Classification on CIFAR10 imbalanced](<https://www.sota2.com/research/sota/image-classification-on-cifar10-imbalanced.md>): Image Classification; CIFAR10 imbalanced; Macro Precision: 81.28.

- [Image Classification on CIFAR100 (Macro Precision/Recall/F1)](<https://www.sota2.com/research/sota/image-classification-on-cifar100-macro-precision-recall-f1.md>): Image Classification; CIFAR100; Macro Precision: 34.9.

- [Image Classification on FashionMNIST imbl](<https://www.sota2.com/research/sota/image-classification-on-fashionmnist-imbl.md>): Image Classification; FashionMNIST imbl; Macro Precision: 92.53.

- [Image Classification on FashionMNIST imbalanced](<https://www.sota2.com/research/sota/image-classification-on-fashionmnist-imbalanced.md>): Image Classification; FashionMNIST imbalanced; Macro Precision: 92.53.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2605.07596>)

[PDF](<https://arxiv.org/pdf/2605.07596.pdf>)