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Counting to Ten with Two Fingers: Compressed Counting with Spiking Neurons

Authors Yael Hitron, Merav Parter

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Yael Hitron
  • Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Merav Parter
  • Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel


We are grateful to Cameron Musco, Renan Gross and Eylon Yogev for various useful discussions.

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Yael Hitron and Merav Parter. Counting to Ten with Two Fingers: Compressed Counting with Spiking Neurons. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 57:1-57:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


We consider the task of measuring time with probabilistic threshold gates implemented by bio-inspired spiking neurons. In the model of spiking neural networks, network evolves in discrete rounds, where in each round, neurons fire in pulses in response to a sufficiently high membrane potential. This potential is induced by spikes from neighboring neurons that fired in the previous round, which can have either an excitatory or inhibitory effect. Discovering the underlying mechanisms by which the brain perceives the duration of time is one of the largest open enigma in computational neuro-science. To gain a better algorithmic understanding onto these processes, we introduce the neural timer problem. In this problem, one is given a time parameter t, an input neuron x, and an output neuron y. It is then required to design a minimum sized neural network (measured by the number of auxiliary neurons) in which every spike from x in a given round i, makes the output y fire for the subsequent t consecutive rounds. We first consider a deterministic implementation of a neural timer and show that Theta(log t) (deterministic) threshold gates are both sufficient and necessary. This raised the question of whether randomness can be leveraged to reduce the number of neurons. We answer this question in the affirmative by considering neural timers with spiking neurons where the neuron y is required to fire for t consecutive rounds with probability at least 1-delta, and should stop firing after at most 2t rounds with probability 1-delta for some input parameter delta in (0,1). Our key result is a construction of a neural timer with O(log log 1/delta) spiking neurons. Interestingly, this construction uses only one spiking neuron, while the remaining neurons can be deterministic threshold gates. We complement this construction with a matching lower bound of Omega(min{log log 1/delta, log t}) neurons. This provides the first separation between deterministic and randomized constructions in the setting of spiking neural networks. Finally, we demonstrate the usefulness of compressed counting networks for synchronizing neural networks. In the spirit of distributed synchronizers [Awerbuch-Peleg, FOCS'90], we provide a general transformation (or simulation) that can take any synchronized network solution and simulate it in an asynchronous setting (where edges have arbitrary response latencies) while incurring a small overhead w.r.t the number of neurons and computation time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • stochastic neural networks
  • approximate counting
  • synchronizer


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