Merav Parter and Cameron Musco: Computational Tradeoffs in Biological Neural Networks: Self-Stabilizing Winner-Take-All Networks

Friday, October 21, 2016 - 1:00pm to 2:30pm
Merav Parter and Cameron Musco

We initiate a line of investigation into biological neural networks from an algorithmic perspective. We develop a simplified but biologically plausible model for distributed computation in \emph{stochastic spiking neural networks} and study tradeoffs between computation time and network complexity in this model. Our aim is to abstract real neural networks in a way that, while not capturing all interesting features, preserves high-level behavior and allows us to make biologically relevant conclusions.

In this paper, we focus on the important `winner-take-all' (WTA) problem, which is analogous to a neural leader election unit: a network consisting of $n$ input neurons and $n$ corresponding output neurons must converge to a state in which a single output corresponding to a firing input (the `winner') fires, while all other outputs remain silent.
Neural circuits for WTA rely on inhibitory neurons, which suppress the activity of competing outputs and drive the network towards a converged state with a single firing winner. We attempt to understand how the number of inhibitors used affects network convergence time.
We show that it is possible to significantly outperform naive WTA constructions through a more refined use of inhibition, solving the problem in $O(\theta)$ rounds in expectation with just $O(\log^{1/\theta} n)$ inhibitors for any $\theta$. An alternative construction gives convergence in $O(\log^{1/\theta} n)$ rounds with $O(\theta)$ inhibitors.
We compliment these upper bounds with our main technical contribution, a nearly matching lower bound for networks using $\ge \log \log n$ inhibitors. Our lower bound uses familiar indistinguishability and locality arguments from distributed computing theory applied to the neural setting. It lets us derive a number of interesting conclusions about the structure of any network solving WTA with good probability, and the use of randomness and inhibition within such a network.