DeepPSL: End-to-end perception and reasoning

We introduce DeepPSL a variant of probabilistic soft logic (PSL) to produce an end-to-end trainable system that integrates reasoning and perception. PSL represents first-order logic in terms of a convex graphical model -- hinge-loss Markov random fields (HL-MRFs). PSL stands out among probabilistic logic frameworks due to its tractability having been applied to systems of more than 1 billion ground rules. The key to our approach is to represent predicates in first-order logic using deep neural networks and then to approximately back-propagate through the HL-MRF and thus train every aspect of the first-order system being represented. We believe that this approach represents an interesting direction for the integration of deep learning and reasoning techniques with applications to knowledge base learning, multi-task learning, and explainability. Evaluation on three different tasks demonstrates that DeepPSL significantly outperforms state-of-the-art neuro-symbolic methods on scalability while achieving comparable or better accuracy.