A Statistical Theory of Contrastive Learning via Approximate Sufficient Statistics

2025-03-21

AI Summary

This work addresses the theoretical question of how data augmentations guide contrastive learning (exemplified by SimCLR) toward learning effective representations. We propose a unified analytical framework grounded in *approximate sufficient statistics*. First, we generalize the notion of sufficiency to the broad class of *f*-divergences and rigorously prove that minimizing contrastive loss is equivalent to maximizing the encoder’s approximate sufficiency for downstream tasks. Furthermore, we quantify how augmentation-induced bias affects generalization performance. Our theory establishes that stronger approximate sufficiency implies better downstream performance—both in regression and classification—and yields an interpretable, tight upper bound on task error. Empirical validation on standard benchmarks confirms the theory: SimCLR encoders exhibit measurable approximate sufficiency, and downstream accuracy improves monotonically with this sufficiency metric.

Technology Category

• Machine Learning: Learning Theory
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Contrastive learning -- a modern approach to extract useful representations from unlabeled data by training models to distinguish similar samples from dissimilar ones -- has driven significant progress in foundation models. In this work, we develop a new theoretical framework for analyzing data augmentation-based contrastive learning, with a focus on SimCLR as a representative example. Our approach is based on the concept of emph{approximate sufficient statistics}, which we extend beyond its original definition in cite{oko2025statistical} for contrastive language-image pretraining (CLIP) using KL-divergence. We generalize it to equivalent forms and general f-divergences, and show that minimizing SimCLR and other contrastive losses yields encoders that are approximately sufficient. Furthermore, we demonstrate that these near-sufficient encoders can be effectively adapted to downstream regression and classification tasks, with performance depending on their sufficiency and the error induced by data augmentation in contrastive learning. Concrete examples in linear regression and topic classification are provided to illustrate the broad applicability of our results.

Problem

• Develops theory for contrastive learning via approximate sufficient statistics
• Analyzes SimCLR performance in downstream regression and classification
• Generalizes sufficient statistics to f-divergences for contrastive losses

Innovation

• Extends approximate sufficient statistics concept
• Generalizes to equivalent forms and f-divergences
• Demonstrates near-sufficient encoders for downstream tasks