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

Friday, July 26, 2019 - 1:00pm to 2:30pm
Yael Hitron
Weizmann Institute

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 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 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 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{loglog 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 adversarial response latency) while incurring a small overhead w.r.t the number of neurons and computation time.