A Catalog of Elemental Neural Circuits

It is well-known that abstract neurons of the McCulloch-Pitts type compute input-output functions that are formally equivalent to suitably defined Boolean functions. Boolean functions, in turn, can be classified (up to isomorphism of underlying logical structure) into a limited number of basic types, each of which can be expressed by a canonic logical expression that is minimal in length. Translating this basic catalog of canonic formulae into their equivalent neural network representation leads to a catalog of basic, distinct neural circuits. Each such circuit computes a distinct Boolean function, and every Boolean function is computed by one such network, making this a kind of "periodic table" of elemental neural circuits. This brief article describes and details this catalog of circuits. Also discussed is the idea that learning in biological systems—e.g. adaptive reorganization of neural circuits— might correspond to something like logical minimization of the equivalent Boolean functions