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.

翻译：来自泛代数的定理，如1970年代Murskiĭ的定理，与1980年代沿Cybenko路线发展的神经网络通用逼近结果具有显著相似性。本文考虑经典神经网络概念的离散模拟，将这些结果置于统一框架中。我们提出一种基于关系结构多态性（polymorphism）的学习算法，并展示如何将其用于经典学习任务。