Product of tensors and description of networks

We study the characterization of the signal distribution in a network under the lens of tensor algebra. More specifically, we describe every activation function as tensor distributions with respect to the nodes, called activation tensors. The distribution of the signal is encoded in the total tensor of the network. We formally prove that the total tensor can be obtained by computing the Bhattacharya-Mesner Product, an n-ary operation for tensors of order n, on the set of activation tensors properly ordered and processed via two basic operations, that we call blow and forget. Our theoretical framework can be validated through the related code developed in Python.