Discrete neural nets and polymorphic learning

07/29/2023

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by   Charlotte Aten, et al.

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Theorems from universal algebra such as that of Murskiĭ 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.