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We study distributed algorithms implemented in a simplified biologicallyinspired model for stochastic spiking neural networks. We focus on tradeoffsbetween computation time and network complexity, along with the role ofrandomness in efficient neural computation.  It is widely accepted that neural computation is inherently stochastic. Inrecent work, we explored how this stochasticity could be leveraged to solve the`winner-take-all' leader election task. Here, we focus on using randomness inneural algorithms for similarity testing and compression. In the most basicsetting, given two $n$-length patterns of firing neurons, we wish todistinguish if the patterns are equal or $\epsilon$-far from equal.  Randomization allows us to solve this task with a very compact network, using$O \left (\frac{\sqrt{n}\log n}{\epsilon}\right)$ auxiliary neurons, which issublinear in the input size. At the heart of our solution is the design of a$t$-round neural random access memory, or indexing network, which we call aneuro-RAM. This module can be implemented with $O(n/t)$ auxiliary neurons andis useful in many applications beyond similarity testing.  Using a VC dimension-based argument, we show that the tradeoff betweenruntime and network size in our neuro-RAM is nearly optimal. Our result hasseveral implications -- since our neuro-RAM can be implemented withdeterministic threshold gates, it shows that, in contrast to similaritytesting, randomness does not provide significant computational advantages forthis problem. It also establishes a separation between feedforward networkswhose gates spike with sigmoidal probability functions, and well-studieddeterministic sigmoidal networks, whose gates output real number sigmoidalvalues, and which can implement a neuro-RAM much more efficiently.

Neuro-RAM Unit with Applications to Similarity Testing and Compression in Spiking Neural Networks