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 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. 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.

翻译：我们从算法的角度开始对生物神经网络进行调查。 我们开发了一个简化但生物上可信的模型, 用于在神经神经网络中进行分配计算, 并研究计算时间和网络复杂性之间的权衡。 我们的目标是抽象真实的神经网络, 在不捕捉所有有趣的特征的同时, 保存高层次的行为, 并允许我们得出与生物相关的结论。 在本文中, 我们关注一个重要的“ 赢取全” (WTA) 问题, 这类似于一个神经领导选举单位: 一个由输入的神经元和相应的输出值组成的网络, 一个由输入的美元组成的网络, 一个由输入的神经网络和计算的时间组合组成的网络。 我们显示, 一个与发射输入的“赢取” 匹配值($) 和“ 美元” 相应输出的神经网络的单一输出, 使用抑制性神经的神经电路, 将一个更低的输出量驱动器驱动着网络。 我们试图理解, 使用抑制剂的数值是如何影响网络的整合时间的。 我们显示, 可能大大超过天- WTA 值 的数值 值 值 值 值 的理论中, 使用一个更精确 的模型中, 使用一个精确 。