# Formal Models of Active Learning from Contrastive Examples

arXiv: https://arxiv.org/abs/2506.15893 · HTML: https://mlsanity.com/paper/2506.15893/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 18 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Investigating the Role of Negatives in Contrastive Representation Learning](https://mlsanity.com/paper/2106.09943/) (2021)
- [Counterfactual State Explanations for Reinforcement Learning Agents via Generative Deep Learning](https://mlsanity.com/paper/2101.12446/) (2021)
- [ALICE: Active Learning with Contrastive Natural Language Explanations](https://mlsanity.com/paper/2009.10259/) (2020)
- [Teaching Categories to Human Learners with Visual Explanations](https://mlsanity.com/paper/1802.06924/) (2018)
- [GANterfactual-RL: Understanding Reinforcement Learning Agents' Strategies through Visual Counterfactual Explanations](https://mlsanity.com/paper/2302.12689/) (2023)
- [Optimal Sample Complexity of Contrastive Learning](https://mlsanity.com/paper/2312.00379/) (2023)
- [Teaching an Active Learner with Contrastive Examples](https://mlsanity.com/paper/2110.14888/) (2021)
- [Robust Learning from Discriminative Feature Feedback](https://mlsanity.com/paper/2003.03946/) (2020)
- [On Exact Learning Monotone DNF from Membership Queries](https://mlsanity.com/paper/1405.0792/) (2014)
- [The Dimension of Self-Directed Learning](https://mlsanity.com/paper/2402.13400/) (2024)

## Built on by (most cited first, 2 of 2)

- [Learning Half-Spaces from Perturbed Contrastive Examples](https://mlsanity.com/paper/2602.02080/) (2026)
- [Learning Shuffle Ideals with Membership Queries and Contrastive Examples](https://mlsanity.com/paper/2609.32820/) (2026)

## Abstract (arXiv)

Machine learning can greatly benefit from providing learning algorithms with pairs of contrastive training examples -- typically pairs of instances that differ only slightly, yet have different class labels. Intuitively, the difference in the instances helps explain the difference in the class labels. This paper proposes a theoretical framework in which the effect of various types of contrastive examples on active learners is studied formally. The focus is on the sample complexity of learning concept classes and how it is influenced by the choice of contrastive examples. We illustrate our results with geometric concept classes and classes of Boolean functions. Interestingly, we reveal a connection between learning from contrastive examples and the classical model of self-directed learning.