Contrastive Learning Inverts the Data Generating Process
It provides a theoretical foundation for understanding and improving contrastive learning in self-supervised learning, addressing a fundamental gap in the field.
The paper proves that contrastive learning with InfoNCE objectives implicitly inverts the data generating process, explaining why learned representations generalize well to downstream tasks, with empirical validation even under violated assumptions.
Contrastive learning has recently seen tremendous success in self-supervised learning. So far, however, it is largely unclear why the learned representations generalize so effectively to a large variety of downstream tasks. We here prove that feedforward models trained with objectives belonging to the commonly used InfoNCE family learn to implicitly invert the underlying generative model of the observed data. While the proofs make certain statistical assumptions about the generative model, we observe empirically that our findings hold even if these assumptions are severely violated. Our theory highlights a fundamental connection between contrastive learning, generative modeling, and nonlinear independent component analysis, thereby furthering our understanding of the learned representations as well as providing a theoretical foundation to derive more effective contrastive losses.