Foundations for a Circuit Complexity Theory of Sensory Processing

We introduce total wire length as salient complexity measure for an analysis of the circuit complexity of sensory processing in biological neural systems and neuromorphic engineering. This new complexity measure is applied to a set of basic computational problems that apparently need to be solved by circuits for translation-and scale-invariant sensory processing. We exhibit new circuit design strategies for these new benchmark functions that can be implemented within realistic complexity bounds, in particular with linear or almost linear total wire length. 1 Introduction Circuit complexity theory is a classical area of theoretical computer science, that provides estimates for the complexity of circuits for computing specific benchmark functions, such as binary addition, multiplication and sorting (see, e.g.