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We initiate the study of biological neural networks from the perspective ofstreaming algorithms. Like computers, human brains suffer from memorylimitations which pose a significant obstacle when processing large scale anddynamically changing data. In computer science, these challenges are capturedby the well-known streaming model, which can be traced back to Munro andPaterson `78 and has had significant impact in theory and beyond. In theclassical streaming setting, one must compute some function $f$ of a stream ofupdates $\mathcal{S} = \{u_1,\ldots,u_m\}$, given restricted single-pass accessto the stream. The primary complexity measure is the space used by thealgorithm.  We take the first steps towards understanding the connection betweenstreaming and neural algorithms. On the upper bound side, we design neuralalgorithms based on known streaming algorithms for fundamental tasks, includingdistinct elements, approximate median, heavy hitters, and more. The number ofneurons in our neural solutions almost matches the space bounds of thecorresponding streaming algorithms. As a general algorithmic primitive, we showhow to implement the important streaming technique of linear sketchingefficient in spiking neural networks. On the lower bound side, we give ageneric reduction, showing that any space-efficient spiking neural network canbe simulated by a space-efficiently streaming algorithm. This reduction lets ustranslate streaming-space lower bounds into nearly matching neural-space lowerbounds, establishing a close connection between these two models.

Spiking Neural Networks Through the Lens of Streaming Algorithms