Structural constraints on neural circuit computation

A connectome is the exact structure of the nervous system of an organism.

A number of efforts are currently underway to experimentally decipher the connectome or parts thereof in a variety of organisms. Ascertaining the detailed physiological properties of all the neurons in these connectomes, however, is out of the scope of such projects and indeed out of reach of current experimental technology. It is therefore unclear to what extent knowledge of the connectome alone will advance a mechanistic understanding of computation occurring in these neural circuits, especially when the high-level function(s) of the said circuit is unknown. While it is generally acknowledged that the structure of a neural circuit constrains what it can compute, the nature and scope of these "connectomic constraints" are not well understood. Theoretical work is therefore called for, in order to achieve a broad understanding of the issues involved and to build a framework within which neuroscientists can think about the connectomics data, formulate meaningful hypotheses and make testable predictions to advance an understanding of the neuronal circuit(s) in question.

I will talk about some work (with Arunava Banerjee) in which we have examined these issues in the context of feedforward neuronal networks.

Specifically, for feedforward networks equipped with neurons that obey a deterministic spiking neuron model, we asked if just by knowing the architecture of a network, we can rule out spike-timed computations that it could be doing, no matter what response properties each of its neurons may have. Our neurons obey an abstract model constrained by a small number of axioms. We showed results of this form for certain classes of architectures. We also showed that for certain other classes of network architectures, given the limited assumptions on the individual neurons, there are fundamental limits to constraints imposed by network structure alone. I will also briefly discuss some additional theoretical tools I've been building, towards these ends.

(The talk is self-contained; no Neuroscience background is assumed.)