A Catalog of Elemental Neural Circuits

It is well-known that abstract neurons of the McCulloch-Pitts type com-pute input-output functions that are formally equivalent to suitably defined Boolean functions. Boolean functions, in turn, can be classified (up to iso-morphism of underlying logical structure) into a limited number of basic types, each of which is non-isomorphic to each other type. These basic types are conveniently expressed by means of a canonic logical formula involving a minimal number of constituent operations. Each such canonic formula can be translated into an equivalent representation as a neural circuit, re-sulting in a catalog of basic, distinct neural circuits. Each circuit in this catalog 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 presents and discusses this catalog of circuits. An intriguing possibility raised by this analysis is that neural circuits in biological networks might, like the circuits in this catalog