Previous theoretical work on contrastive learning (CL) with InfoNCE showed that, under certain assumptions, the learned representations uncover the ground-truth latent factors. We argue these theories overlook crucial aspects of how CL is deployed in practice. Specifically, they assume that within a positive pair, all latent factors either vary to a similar extent, or that some do not vary at all. However, in practice, positive pairs are often generated using augmentations such as strong cropping to just a few pixels. Hence, a more realistic assumption is that all latent factors change, with a continuum of variability across these factors. We introduce AnInfoNCE, a generalization of InfoNCE that can provably uncover the latent factors in this anisotropic setting, broadly generalizing previous identifiability results in CL. We validate our identifiability results in controlled experiments and show that AnInfoNCE increases the recovery of previously collapsed information in CIFAR10 and ImageNet, albeit at the cost of downstream accuracy. Additionally, we explore and discuss further mismatches between theoretical assumptions and practical implementations, including extensions to hard negative mining and loss ensembles.

在对比学习中，我们提出了AnInfoNCE，它能够在现实场景中揭示潜在因素，并广义上推广了以往的可识别性结果。我们的控制实验验证了我们的可识别性结果，并展示了在CIFAR10和ImageNet中恢复先前已经损失的信息的能力，但同时降低了下游任务的准确度。此外，我们还探讨了理论假设与实际实现之间的进一步不匹配，包括对硬性负样本挖掘和损失集合的扩展。

InfoNCE: 理论与实践之间的差距辨识