Discrete neural nets and polymorphic learning
This work provides a theoretical bridge between neural networks and algebra, potentially offering new insights for discrete learning problems, but it appears incremental as it adapts existing concepts to a discrete setting.
The paper tackles the problem of unifying universal approximation theorems from neural networks and universal algebra by introducing a discrete analogue of neural nets and a learning algorithm based on polymorphisms of relational structures, demonstrating its application to a classical learning task.
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.