  Self-supervised learning is a popular and powerful method for utilizing large
amounts of unlabeled data, for which a wide variety of training objectives have
been proposed in the literature. In this study, we perform a Bayesian analysis
of state-of-the-art self-supervised learning objectives, elucidating the
underlying probabilistic graphical models in each class and presenting a
standardized methodology for their derivation from first principles. The
analysis also indicates a natural means of integrating self-supervised learning
with likelihood-based generative models. We instantiate this concept within the
realm of cluster-based self-supervised learning and energy models, introducing
a novel lower bound which is proven to reliably penalize the most important
failure modes. Furthermore, this newly proposed lower bound enables the
training of a standard backbone architecture without the necessity for
asymmetric elements such as stop gradients, momentum encoders, or specialized
clustering layers - typically introduced to avoid learning trivial solutions.
Our theoretical findings are substantiated through experiments on synthetic and
real-world data, including SVHN, CIFAR10, and CIFAR100, thus showing that our
objective function allows to outperform existing self-supervised learning
strategies in terms of clustering, generation and out-of-distribution detection
performance by a wide margin. We also demonstrate that GEDI can be integrated
into a neuro-symbolic framework to mitigate the reasoning shortcut problem and
to learn higher quality symbolic representations thanks to the enhanced
classification performance.
