In this paper, we introduce Neural Probabilistic Soft Logic (NeuPSL), a novel neuro-symbolic (NeSy) framework that unites state-of-the-art symbolic reasoning with the low-level perception of deep neural networks. To model the boundary between neural and symbolic representations, we propose a family of energy-based models, NeSy Energy-Based Models, and show that they are general enough to include NeuPSL and many other NeSy approaches. Using this framework, we show how to seamlessly integrate neural and symbolic parameter learning and inference in NeuPSL. Through an extensive empirical evaluation, we demonstrate the benefits of using NeSy methods, achieving upwards of 30% improvement over independent neural network models. On a well-established NeSy task, MNIST-Addition, NeuPSL demonstrates its joint reasoning capabilities by outperforming existing NeSy approaches by up to 10% in low-data settings. Furthermore, NeuPSL achieves a 5% boost in performance over state-of-the-art NeSy methods in a canonical citation network task with up to a 40 times speed up.

翻译：本文提出神经概率软逻辑（NeuPSL），一种新颖的神经符号（NeSy）框架，它将最先进的符号推理与深度神经网络的底层感知能力相统一。为了建模神经表示与符号表示之间的界限，我们提出了一类基于能量的模型——NeSy能量模型，并证明其通用性足以涵盖NeuPSL及许多其他NeSy方法。利用这一框架，我们展示了如何在NeuPSL中无缝整合神经与符号的参数学习与推理。通过广泛的实证评估，我们证明了使用NeSy方法的优势，在独立神经网络模型基础上实现了高达30%的性能提升。在公认的NeSy任务MNIST-加法中，NeuPSL在低数据场景下以优于现有NeSy方法最高10%的表现证明了其联合推理能力。此外，在规范引用网络任务中，NeuPSL相较于最先进的NeSy方法实现了5%的性能提升，并获得了高达40倍的加速效果。