Maximizing Incremental Information Entropy for Contrastive Learning

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.

While Contrastive Learning (CL) has revolutionized self-supervised representation learning, its latent representations remain highly entangled and opaque, limiting their interpretability in safety-critical applications. We identify that a fundamental cause of this entanglement is the reliance on deterministic similarity measures, which treat all feature dimensions equally. In compositional scenes, this creates an Optimization Conflict: common background features, such as, "blue sky", are encouraged to align in positive pairs but simultaneously repelled in negative pairs, causing gradient oscillations that hinder precise semantic disentanglement. To address this, we propose BayesNCL (Bayesian Gated Non-Negative Contrastive Learning). Unlike standard approaches, BayesNCL introduces a probabilistic gating mechanism that dynamically filters out task-irrelevant, high-frequency common features while selectively retaining discriminative semantics. By formalizing feature selection as a variational inference problem with a sparse Bernoulli prior, our method effectively resolves the optimization conflict. Empirical experimental results on Imagenet-100 demonstrate that BayesNCL achieves a remarkable 142.1% improvement in semantic consistency compared to state-of-the-art baselines, yielding highly interpretable representations without compromising downstream task performance. Code is available at https://github.com/Cui-Peng-624/BayesNCL.

Contrastive learning has become a cornerstone of modern representation learning, allowing training with massive unlabeled data for both task-specific and general (foundation) models. A prototypical loss in contrastive training is InfoNCE and its variants. In this work, we show that the InfoNCE objective induces Gaussian structure in representations that emerge from contrastive training. We establish this result in two complementary regimes. First, we show that under certain alignment and concentration assumptions, projections of the high-dimensional representation asymptotically approach a multivariate Gaussian distribution. Next, under less strict assumptions, we show that adding a small asymptotically vanishing regularization term that promotes low feature norm and high feature entropy leads to similar asymptotic results. We support our analysis with experiments on synthetic and CIFAR-10 datasets across multiple encoder architectures and sizes, demonstrating consistent Gaussian behavior. This perspective provides a principled explanation for commonly observed Gaussianity in contrastive representations. The resulting Gaussian model enables principled analytical treatment of learned representations and is expected to support a wide range of applications in contrastive learning.