On Information Maximisation in Multi-View Self-Supervised Learning

The strong performance of multi-view self-supervised learning (SSL) prompted the development of many different approaches (e.g. SimCLR, BYOL, and DINO). A unified understanding of how each of these methods achieves its performance has been limited by apparent differences across objectives and algorithmic details. Through the lens of information theory, we show that many of these approaches are maximising an approximate lower bound on the mutual information between the representations of multiple views of the same datum. Further, we show that this bound decomposes into a ``reconstruction" term, treated identically by all SSL methods, and an ``entropy" term, where existing SSL methods differ in their treatment. We prove that an exact optimisation of both terms of this lower bound encompasses and unifies current theoretical properties such as recovering the true latent variables of the underlying generative process (Zimmermann et al., 2021) or or isolating content from style in such true latent variables (Von Kügelgen et al., 2021). This theoretical analysis motivates a naive but principled objective (EntRec), that exactly optimises both the reconstruction and entropy terms, thus benefiting from said theoretical properties unlike other SSL frameworks. Finally, we show EntRec achieves a downstream performance on-par with existing SSL methods on ImageNet (69.7% after 400 epochs) and on an array of transfer tasks when pre-trained on ImageNet. Furthermore, EntRec is more robust to modifying the batch size, a sensitive hyperparameter in other SSL methods.