Recognizable series on graphs and hypergraphs

Abstract We introduce the notion of Hypergraph Weighted Model (HWM), a computational model that generically associates a tensor network to a graph or a hypergraph and then computes a value by generalized tensor contractions directed by its hyperedges. A series r defined on a hypergraph family is said to be recognizable if there exists a HWM that computes it. This model generalizes the notion of recognizable series on strings and trees. We present some examples on non classical graphs families such as circular strings and pictures and we study properties of the model such as closure properties and recognizability of finite support series. We conclude by a section exploring the learnability of HWMs defined over the family of circular strings.

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