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:虽然深层神经网络在图像识别、语言翻译、数据挖掘和游戏游戏方面取得了重大进步,但这种范式存在众所周知的局限性,例如缺乏解释性、难以纳入先前的知识以及模块性。神经象征性混合系统最近通过纳入诸如计算逻辑等象征性推理中的想法而成为扩展深神经网络的一个直截了当的途径。我们在本文件中提出了神经象征系统可取的标准清单,并审查了某些现有方法如何解决这些标准。我们随后提议扩大一种普遍化的逻辑,允许建立一个由替代的神经象征性混合结构组成的等等同神经结构。然而,与以往依赖持续优化培训过程的方法不同,我们的框架被设计成一个使用离散优化的双轨神经网络。我们提供了正确性的证据,并讨论了在实施系统中实现这一框架必须克服的一些挑战。