Discrete neural nets and polymorphic learning

TL;DR

This paper introduces a discrete analogue of neural networks using universal algebra, unifying classical approximation results and proposing a polymorphism-based learning algorithm for relational structures.

Contribution

It presents a novel discrete neural network framework grounded in universal algebra and develops a learning algorithm based on polymorphisms.

Findings

Unified algebraic framework for neural nets and universal algebra theorems

Development of a polymorphism-based learning algorithm

Application to classical learning tasks demonstrating effectiveness

Abstract

Theorems from universal algebra such as that of Murski\u{i} from the 1970s have a striking similarity to universal approximation results for neural nets along the lines of Cybenko's from the 1980s. We consider here a discrete analogue of the classical notion of a neural net which places these results in a unified setting. We introduce a learning algorithm based on polymorphisms of relational structures and show how to use it for a classical learning task.