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.

翻译：我们提出DeepPSL，一种概率软逻辑（PSL）的变体，用于构建一个融合推理与感知的端到端可训练系统。PSL通过凸图模型——铰链损失马尔可夫随机场（HL-MRF）表示一阶逻辑。PSL在概率逻辑框架中因可计算性脱颖而出，已应用于超过10亿条基础规则的系统中。我们方法的核心是利用深度神经网络表示一阶逻辑中的谓词，并通过近似反向传播通过HL-MRF，从而对所表示的一阶系统的每个方面进行训练。我们认为，该方法代表了深度学习与推理技术融合的有趣方向，可应用于知识库学习、多任务学习及可解释性。在三个不同任务上的评估表明，DeepPSL在可扩展性上显著优于最先进的神经符号方法，同时达到相当或更好的准确性。