Category Theory for Artificial General Intelligence

Category theory has been successfully applied beyond pure mathematics and applications to artificial intelligence (AI) and machine learning (ML) have been developed. Here we first give an overview of the current development of category theory for AI and ML, and we then compare and elucidate the essential features of various category-theoretical approaches to AI and ML. Broadly, there are three types of category theory for AI and ML, namely category theory for data representation learning, category theory for learning (optimisation) algorithms and category theory for compositional architecture design and analysis. There are various approaches even within each type of category theory for AI and ML; among other things, we shed new light on the relationships between the two types of category theory for neural network architectures as have been developed by the authors recently (i.e., neural string diagrams and neural circuit diagrams). The three types of category theory can be integrated together and to that end we focus upon a categorical deep learning framework, which integrates categorical structures with a universal probabilistic programming language. We also discuss the significance of categorical approaches in relation with the ultimate goal of development of artificial general intelligence.