  We introduce GEDI, a Bayesian framework that combines existing
self-supervised learning objectives with likelihood-based generative models.
This framework leverages the benefits of both GEnerative and DIscriminative
approaches, resulting in improved symbolic representations over standalone
solutions. Additionally, GEDI can be easily integrated and trained jointly with
existing neuro-symbolic frameworks without the need for additional supervision
or costly pre-training steps. We demonstrate through experiments on real-world
data, including SVHN, CIFAR10, and CIFAR100, that GEDI outperforms existing
self-supervised learning strategies in terms of clustering performance by a
significant margin. The symbolic component further allows it to leverage
knowledge in the form of logical constraints to improve performance in the
small data regime.
