A Probabilistic Model for Non-Contrastive Learning
This provides a theoretical foundation for self-supervised learning, addressing a gap in understanding for researchers, though it is incremental as it builds on existing SSL frameworks.
The paper tackles the lack of theoretical insights in self-supervised learning by proposing a probabilistic model that relates to non-contrastive loss functions, showing that its maximum likelihood estimate can reduce to PCA or approach a simple non-contrastive loss depending on data augmentation informativeness.
Self-supervised learning (SSL) aims to find meaningful representations from unlabeled data by encoding semantic similarities through data augmentations. Despite its current popularity, theoretical insights about SSL are still scarce. For example, it is not yet known whether commonly used SSL loss functions can be related to a statistical model, much in the same as OLS, generalized linear models or PCA naturally emerge as maximum likelihood estimates of an underlying generative process. In this short paper, we consider a latent variable statistical model for SSL that exhibits an interesting property: Depending on the informativeness of the data augmentations, the MLE of the model either reduces to PCA, or approaches a simple non-contrastive loss. We analyze the model and also empirically illustrate our findings.