A computational perspective on neural-symbolic integration

Neural-Symbolic Integration (NSI) aims to marry the principles of symbolic AI techniques, such as logical reasoning, with the learning capabilities of neural networks. In recent years, many systems have been proposed to address this integration in a seemingly efficient manner. However, from the computational perspective, this is in principle impossible to do. Specifically, some of the core symbolic problems are provably hard, hence a general NSI system necessarily needs to adopt this computational complexity, too. Many NSI methods try to circumvent this downside by inconspicuously dropping parts of the symbolic capabilities while mapping the problems into static tensor representations in exchange for efficient deep learning acceleration. In this paper, we argue that the aim for a general NSI system, properly covering both the neural and symbolic paradigms, has important computational implications on the learning representations, the structure of the resulting computation graphs, and the underlying hardware and software stacks. Particularly, we explain how the currently prominent, tensor-based deep learning with static computation graphs is conceptually insufficient as a foundation for such general NSI, which we discuss in a wider context of established (statistical) relational and structured deep learning methods. Finally, we delve into the underlying hardware acceleration aspects and outline some promising computational directions toward fully expressive and efficient NSI.