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The relationships between the structural topology of artificial neural networks, their computational flow, and their performance is not well understood. Consequently, a unifying mathematical framework that describes computational performance in terms of their underlying structure does not exist. This paper makes a modest contribution to understanding the structure-computational flow relationship in artificial neural networks from the perspective of the dicliques that cover the structure of an artificial neural network and the Forman-Ricci curvature of an artificial neural network’s connections. Special diclique cover digraph representations of artificial neural networks useful for network analysis are introduced and it is shown that such covers generate semigroups that provide algebraic representations of neural network connectivity.

Characterizing Computation in Artificial Neural Networks by their Diclique Covers and Forman-Ricci Curvatures