Contrastive Conformal Sets

TL;DR

This paper extends conformal prediction to contrastive learning, creating sets that guarantee positive sample coverage while excluding negatives, with theoretical and empirical validation.

Contribution

It introduces a novel conformal set construction with learnable constraints that balances positive coverage and negative exclusion in contrastive learning.

Findings

Improved positive coverage guarantees in contrastive embeddings.

Enhanced negative exclusion through learned set geometry.

Better inclusion-exclusion trade-offs than standard conformal methods.

Abstract

Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack principled guarantees on coverage within the semantic feature space. We extend conformal prediction to this setting by introducing minimum-volume covering sets equipped with learnable generalized multi-norm constraints. We propose a method that constructs conformal sets guaranteeing user-specified coverage of positive samples while maximizing negative sample exclusion. We establish theoretically that volume minimization serves as a proxy for negative exclusion, enabling our approach to operate effectively even when negative pairs are unavailable. The positive inclusion guarantee inherits the distribution-free coverage property of conformal prediction, while negative exclusion is maximized through learned set geometry optimized on a held-out training split. Experiments on simulated and real-world image datasets demonstrate improved inclusion-exclusion trade-offs compared to standard distance-based conformal baselines.