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