  In this work, we propose time-integrated spike-timing-dependent plasticity
(TI-STDP), a mathematical model of synaptic plasticity that allows spiking
neural networks to continuously adapt to sensory input streams in an
unsupervised fashion. Notably, we theoretically establish and formally prove
key properties related to the synaptic adjustment mechanics that underwrite
TI-STDP. Empirically, we demonstrate the efficacy of TI-STDP in simulations of
jointly learning deeper spiking neural networks that process input digit pixel
patterns, at both full image and patch-levels, comparing to two powerful
historical instantations of STDP; trace-based STDP (TR-STDP) and event-based
post-synaptic STDP (EV-STDP). Usefully, we demonstrate that not only are all
forms of STDP capable of meaningfully adapting the synaptic efficacies of a
multi-layer biophysical architecture, but that TI-STDP is notably able to do so
without requiring the tracking of a large window of pre- and post-synaptic
spike timings, the maintenance of additional parameterized traces, or the
restriction of synaptic plasticity changes to occur within very narrow windows
of time. This means that our findings show that TI-STDP can efficiently embody
the benefits of models such as canonical STDP, TR-STDP, and EV-STDP without
their costs or drawbacks. Usefully, our results further demonstrate the promise
of using a spike-correlation scheme such as TI-STDP in conducting credit
assignment in discrete pulse-based neuromorphic models, particularly those than
acquire a lower-level distributed representation jointly with an upper-level,
more abstract representation that self-organizes to cluster based on inherent
cross-pattern similarities. We further demonstrate TI-STDP's effectiveness in
adapting a simple neuronal circuit that learns a simple bi-level, part-whole
hierarchy from sensory input patterns.
