Time-Integrated Spike-Timing-Dependent-Plasticity

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.