Elliott presents a very insightful model of spike-timing-dependent plasticity (STDP), with a rigorous and thorough mathematical proof. The STDP learning rule is different from conventional Hebbian learning that can simply be stated as “cells that fire together wire together.” Instead, STDP includes spike timing as an essential condition in neural assembly. In other words, STDP says that if a post-synaptic neuron receives a spike (that is, a pulse) slightly before it fires, then the synapse is strengthened; if the spike is received after the neuron has fired, then the synapse is weakened.

In this model of STDP, the author shows a “non-Markovian random walk in synaptic strength.” He shows that STDP affects the probability of a fixed amplitude change in the synapse and not the amplitude itself. The model is based on a mechanism called “the tristate plasticity switch.”

The paper is organized in seven sections. Sections 1 and 2 introduce the stochastic model of STDP previously created [1], where synaptic updates are driven by probability density functions (PDFs). Section 3 presents a reformulation of the model, showing many important features such as unbounded weight updates, as well as non-Markovian random walks not restricting PDFs in synaptic changes. Further mathematical ingenuity follows, where a non-Markovian Fokker-Planck equation is derived, concluding the results. Section 4 takes a different perspective and investigates bounded processes, which is trivial, since unbounded random walks are already exhibited in the model. On the other hand, this is an important point to look into because, if boundaries are set, synaptic plasticity is highly dependent on the initial synaptic strength. This is due to the fact that “a synapse in an initial state of low strength can be potentiated more than it can be depressed,” and vice versa. Furthermore, if we understand such state dependence, then an explanation of synaptic metaplasticity could be revealed. Sections 5 and 6 put the methods provided in Sections 3 and 4 to work, and study fluctuations and the synaptic metaplasticity of the model. Section 7 discusses the work and offers direction for further studies and investigations.

It is interesting to note that the author places his work in the context of that of many others (such as Izhikevich’s [2]) that deal with the same questions and problems that arise when studying the nature of synaptic plasticity, in the field of cognitive neurocomputation. Some questions arise: What is the causality of synaptic plasticity? How can specific spike trains induce synaptic strength? This work gives accurate answers to such questions and achieves major advancements to build upon for future studies.