Network architecture 1 underlying maximal separation of neuronal representations

Abstract

One of the most basic and general tasks faced by all nervous systems is extracting relevant information from the organism's surrounding world. While physical signals available to sensory systems are often continuous, variable, overlapping and noisy, high-level neuronal representations used for decision-making tend to be discrete, specific, invariant, and highly separable. This study addresses the question of how neuronal specificity is generated. Inspired by experimental findings on network architecture in the olfactory system of the locust, I construct a highly simplified theoretical framework which allows for analytic solution of its key properties. For generalized feed-forward systems, I show that an intermediate range of connectivity values between source- and target-populations leads to a combinatorial explosion of wiring possibilities, resulting in input spaces which are, by their very nature, exquisitely sparsely populated. In particular, connection probability 1/2, as found in the locust antennal-lobe-mushroom-body circuit, serves to maximize separation of neuronal representations across the target Kenyon-cells, and explains their specific and reliable responses. This analysis yields a function expressing response specificity in terms of lower network-parameters; thus leading to a simple neuronal algorithm for generating arbitrarily sparse and selective codes and linking network architecture and neural coding. I then suggest how ecologically meaningful representations are constructed from this code.