In this note, hyperseparoids are introduced; hyperseparoids are to separoids as Tverberg’s theorem is to Radon’s theorem. Also, a geometric representation theorem for acyclic kseparoids is presented which generalises that for separoids exhibited in [2].

Abstract There is a longstanding debate whether the Kolmogorov–Arnold representation theorem can explain use of more than one hidden layer in neural networks. The decomposes multivariate function into an interior and outer therefore has indeed similar structure as network with two layers. But there are distinctive differences. One main obstacles that depends on represented be wildly varying eve...