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Networks of spiking neurons and Winner-Take-All spiking circuits (WTA-SNNs)can detect information encoded in spatio-temporal multi-valued events. Theseare described by the timing of events of interest, e.g., clicks, as well as bycategorical numerical values assigned to each event, e.g., like or dislike.Other use cases include object recognition from data collected by neuromorphiccameras, which produce, for each pixel, signed bits at the times ofsufficiently large brightness variations. Existing schemes for trainingWTA-SNNs are limited to rate-encoding solutions, and are hence able to detectonly spatial patterns. Developing more general training algorithms forarbitrary WTA-SNNs inherits the challenges of training (binary) Spiking NeuralNetworks (SNNs). These amount, most notably, to the non-differentiability ofthreshold functions, to the recurrent behavior of spiking neural models, and tothe difficulty of implementing backpropagation in neuromorphic hardware. Inthis paper, we develop a variational online local training rule for WTA-SNNs,referred to as VOWEL, that leverages only local pre- and post-synapticinformation for visible circuits, and an additional common reward signal forhidden circuits. The method is based on probabilistic generalized linear neuralmodels, control variates, and variational regularization. Experimental resultson real-world neuromorphic datasets with multi-valued events demonstrate theadvantages of WTA-SNNs over conventional binary SNNs trained withstate-of-the-art methods, especially in the presence of limited computingresources.

VOWEL: A Local Online Learning Rule for Recurrent Networks of Probabilistic Spiking Winner-Take-All Circuits