A Theory of Contrastive Learning with Natural Images

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.

Contrastive learning relies on informative negatives to shape the representation space, yet obtaining hard negatives is costly, often requiring large batch sizes or extensive memory banks. We propose SynCo (Synthetic negatives in Contrastive learning), an approach that synthesizes hard negatives directly in the representation space from cached queue embeddings, with no additional forward passes or input-space processing. We find that six lightweight synthesis strategies, exhaustively covering the geometric, stochastic, and adversarial perturbation families, consistently improve learned representations at negligible computational cost. Although applicable to any InfoNCE-based contrastive objective, we demonstrate SynCo within the MoCo framework. On ImageNet ILSVRC-2012 linear evaluation at 200 epochs, SynCo yields improvements of +0.4% over MoCo-v2 and +1.0% over MoCHi. Unlike MoCHi, which degrades at extended pretraining schedules (underperforming MoCo-v2 by 2.4% at 800 epochs), SynCo does not: with a simple synthetic negative schedule, performance improves by +0.5% over MoCo-v2 at 800 epochs. SynCo also transfers well to a range of downstream tasks.

Contrastive learning has become a leading paradigm for self-supervised representation learning, yet the conditions under which it recovers meaningful latent geometry remain incompletely understood. We develop a measure-theoretic framework formalizing the diversity condition, a support requirement on positive-pair sampling that is necessary for isometric latent recovery. We show that the standard full-support von Mises-Fisher setting implies the satisfaction of the diversity condition and as a consequence global contrastive loss minimizers recover latent geometry up to orthogonal transformation, while restricted conditionals can make non-orthogonal maps attain strictly lower asymptotic contrastive loss. We introduce a support-corrected Information Noise Contrastive Estimation (InfoNCE) variant as a theoretical fix: this correction makes orthogonal latent space recovery achievable but does not uniquely select it. Experiments on synthetic benchmarks validate the identifiability predictions, and CIFAR-10 experiments are consistent with the qualitative prediction that architectural inductive bias becomes more important when sampling diversity is limited. Together, our results clarify how sampling mechanisms and encoder inductive bias interact in contrastive representation learning.