Gianluca Peri — University of Florence #
Spectral Higher-Order Neural Networks #
Neural networks are the fundamental tools of modern machine learning. They process information by loading it in the activations of the so-called input neurons: the information flows along the architecture of nested layers until the output is reached, where the decision takes place. This latter information processing can be interpreted as a discrete mapping that is ultimately shaped by the underlying network's topology. For this reason, studying neural networks from the fundamental standpoint is of interest to statistical physicists and for the complex systems' community at large. One obvious extension of the usual neural models amounts to consider hypergraphs as the backbone for the interactions. Working in this generalized setting, we will show that neural hypergraphs, if properly parameterized, have performances which are at least comparable to those reported for standard neural networks, but crucially without the need of deploying a neural activation function (usually indispensable for modern neural models). Furthermore, we will prove that, in some learning contexts, hypergraph models perform better than their network counterparts, achieving better accuracies despite having access to the same training samples.