Title: Pre-Synaptic Pool Modification (PSPM): A Supervised Learning Procedure for Spiking Neural Networks,
Abstract: A central question in neuroscience is how to develop realistic models that
predict output firing behavior based on provided external stimulus. Given a set
of external inputs and a set of output spike trains, the objective is to
discover a network structure which can accomplish the transformation as
accurately as possible. Due to the difficulty of this problem in its most
general form, approximations have been made in previous work. Past
approximations have sacrificed network size, recurrence, allowed spiked count,
or have imposed layered network structure. Here we present a learning rule
without these sacrifices, which produces a weight matrix of a leaky
integrate-and-fire (LIF) network to match the output activity of both
deterministic LIF networks as well as probabilistic integrate-and-fire (PIF)
networks. Inspired by synaptic scaling, our pre-synaptic pool modification
(PSPM) algorithm outputs deterministic, fully recurrent spiking neural networks
that can provide a novel generative model for given spike trains. Similarity in
output spike trains is evaluated with a variety of metrics including a
van-Rossum like measure and a numerical comparison of inter-spike interval
distributions. Application of our algorithm to randomly generated networks
improves similarity to the reference spike trains on both of these stated
measures. In addition, we generated LIF networks that operate near criticality
when trained on critical PIF outputs. Our results establish that learning rules
based on synaptic homeostasis can be used to represent input-output
relationships in fully recurrent spiking neural networks.