# Contrastive Conformal Sets

arXiv: https://arxiv.org/abs/2603.26261 · HTML: https://mlsanity.com/paper/2603.26261/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 30 of 32)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [RepVGG: Making VGG-style ConvNets Great Again](https://mlsanity.com/paper/2101.03697/) (2021)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Debiased Contrastive Learning](https://mlsanity.com/paper/2007.00224/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Contrastive Training for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2007.05566/) (2020)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Modeling Uncertainty with Hedged Instance Embedding](https://mlsanity.com/paper/1810.00319/) (2018)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Conformal Prediction Bands for Multivariate Functional Data](https://mlsanity.com/paper/2106.01792/) (2021)
- [Neuron Activation Coverage: Rethinking Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2306.02879/) (2023)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Hybrid Discriminative-Generative Training via Contrastive Learning](https://mlsanity.com/paper/2007.09070/) (2020)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [A Simple Framework for Uncertainty in Contrastive Learning](https://mlsanity.com/paper/2010.02038/) (2020)
- [Data clustering: a fundamental method in data science and management](https://mlsanity.com/paper/2412.18760/) (2024)

## Abstract (arXiv)

Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack a principled construction of geometric sets in the semantic feature space with distribution-free guarantees at any user-specified coverage level. We extend conformal prediction to this setting by introducing covering sets equipped with learnable generalized hyper-ball constraints. We propose a method that constructs conformal sets guaranteeing user-specified coverage of positive samples while maximizing negative sample exclusion. We theoretically motivate volume minimization 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.