Learning Neural Algebras

Pedro Zuidberg Dos Martires

Postdoctoral Researcher at Örebro University (Sweden)

Abstract algebra provides a formalism to study sets and how the elements of these sets relate to each other by defining relations between set elements. Abstract algebraic structures are abundantly present in artificial intelligence. For instance, Boolean algebra constitutes the bedrock of symbolic AI. Interestingly, the relations combining two set elements are usually predefined: two Boolean variables are ‘added’ using the logical or: 0 ∨ 1 = 1. But what about adding up a different kind of set elements, let’s say images? How do we define a relation that adds up two images? In order to answer this question we propose to formulate the question in an abstract algebra setting where relations between set elements are learned from data, while at the same time adhering to user-specified properties, such as commutativity (a+b=b+a).

Keywords: neuro-symbolic, learn to reason, neural networks, abstract algebra
Scientific area: neuro-symbolic artificial intelligence