# Positive Pair Geometry Matters: Optimal Transport for Contrastive Learning of Visual Representations

arXiv: https://arxiv.org/abs/2609.24125 · HTML: https://mlsanity.com/paper/2609.24125/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Self-supervised Visual Feature Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/1902.06162/) (2019)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Softmax Splatting for Video Frame Interpolation](https://mlsanity.com/paper/2003.05534/) (2020)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Optimal Transport-Based Displacement Interpolation with Data Augmentation for Reduced Order Modeling of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2411.08750/) (2024)

## Abstract (arXiv)

Contrastive self-supervised learning has achieved strong performance by learning representations from multiple augmented views of the same image. However, most existing methods construct positive pairs using independently sampled stochastic augmentations, which may alter semantic content and ignore the intrinsic geometry of the data distribution. In this work, we propose OTCLR, an optimal transport-aware framework for contrastive learning representations that generates geometry-consistent positive samples. Instead of directly contrasting two randomly augmented views, we construct intermediate views between the original image and its augmented variants through entropic optimal-transport displacement interpolation. These transport-interpolated samples serve as positive views that better preserve image structure while explicitly modeling spatial distributional geometry. To further promote smooth representation learning, we evaluate auxiliary Sinkhorn regularization terms that encourage transport-interpolated views to remain consistent with their endpoint images. The proposed method can be incorporated into standard contrastive learning pipelines without modifying the encoder architecture. Experiments on multiple benchmark datasets show that our approach improves representation quality and transfer learning performance compared with conventional augmentation-based contrastive learning baselines.