While deep neural networks have led to major advances in image recognition, language translation, data mining, and game playing, there are well-known limits to the paradigm such as lack of explainability, difficulty of incorporating prior knowledge, and modularity. Neuro symbolic hybrid systems have recently emerged as a straightforward way to extend deep neural networks by incorporating ideas from symbolic reasoning such as computational logic. In this paper, we propose a list desirable criteria for neuro symbolic systems and examine how some of the existing approaches address these criteria. We then propose an extension to generalized annotated logic that allows for the creation of an equivalent neural architecture comprising an alternate neuro symbolic hybrid. However, unlike previous approaches that rely on continuous optimization for the training process, our framework is designed as a binarized neural network that uses discrete optimization. We provide proofs of correctness and discuss several of the challenges that must be overcome to realize this framework in an implemented system.

翻译：虽然深度神经网络在图像识别、语言翻译、数据挖掘和游戏博弈等领域取得了重大进展，但该范式存在众所周知的局限性，例如缺乏可解释性、难以融入先验知识以及模块化程度不足。神经符号混合系统作为扩展深度神经网络的一种直接方式，通过引入计算逻辑等符号推理思想而近年来崭露头角。本文首先提出神经符号系统的理想标准清单，并考察现有方法对这些标准的满足程度。随后，我们对广义注释逻辑进行扩展，使其能够构建一种包含替代性神经符号混合体系的等效神经架构。然而，与依赖连续优化进行训练的既有方法不同，我们的框架被设计为采用离散优化的二值化神经网络。我们提供了正确性证明，并讨论了在实现系统中落实该框架所必须克服的若干挑战。