Learning Precise Spike Train to Spike Train Transformations in Multilayer Feedforward Neuronal Networks

TL;DR

This paper introduces a novel synaptic weight update rule for training multilayer spiking neural networks to perform precise spike train transformations, based solely on spike timing and avoiding rate-based or probabilistic models.

Contribution

It presents a spike timing-based learning rule that generalizes error backpropagation to deterministic spiking neurons, with a new error functional and virtual spike assignment for gradient computation.

Findings

Effective learning demonstrated in simulations.

Highlights asymmetries between excitatory and inhibitory synapses.

Provides a closed-form solution for spike train error comparison.

Abstract

We derive a synaptic weight update rule for learning temporally precise spike train to spike train transformations in multilayer feedforward networks of spiking neurons. The framework, aimed at seamlessly generalizing error backpropagation to the deterministic spiking neuron setting, is based strictly on spike timing and avoids invoking concepts pertaining to spike rates or probabilistic models of spiking. The derivation is founded on two innovations. First, an error functional is proposed that compares the spike train emitted by the output neuron of the network to the desired spike train by way of their putative impact on a virtual postsynaptic neuron. This formulation sidesteps the need for spike alignment and leads to closed form solutions for all quantities of interest. Second, virtual assignment of weights to spikes rather than synapses enables a perturbation analysis of individual spike times and synaptic weights of the output as well as all intermediate neurons in the network, which yields the gradients of the error functional with respect to the said entities. Learning proceeds via a gradient descent mechanism that leverages these quantities. Simulation experiments demonstrate the efficacy of the proposed learning framework. The experiments also highlight asymmetries between synapses on excitatory and inhibitory neurons.