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

2026-05-08

AI Summary

This work addresses the overly pessimistic sample complexity bounds in supervised contrastive learning under extreme multi-class and long-tailed settings, where existing theoretical analyses fail to account for dependencies introduced by constructing contrastive tuples from limited labeled data. By refining U-statistic–based risk bound analyses and explicitly modeling such dependencies, the paper establishes a novel generalization error bound that, under mild assumptions on the class distribution, is independent of the probability of the rarest class. Leveraging tools from U-statistic theory and cross-class risk concentration, the derived bound scales linearly with the total number of classes \( R \) and exhibits an improved \( \mathcal{O}(k) \) dependence on the tuple size \( k \), significantly sharpening theoretical guarantees in long-tailed scenarios.

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 $ρ_{\min}^{-{1}/{2}}$ where $ρ_{\min}$ 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.

Problem

• Contrastive Representation Learning
• Extreme Multi-class Learning
• Sample Complexity
• Long-tailed Distribution
• U-Statistics

Innovation

• Supervised Contrastive Learning
• Extreme Multi-class Learning
• Generalization Bound
• U-Statistics
• Long-tailed Distribution