Strong Allee Effect Synaptic Plasticity Rule in an Unsupervised Learning Environment

Synaptic plasticity, or the ability of a brain to change one or more of its functions or structures at the synaptic level, has generated and is still generating a lot of interest from the scientific community especially from neuroscientists. These interests went into high gear after empirical evidence was collected that challenged the established paradigm that human brain structures and functions are set from childhood and only modest changes were expected beyond. Early synaptic plasticity rules or laws to that regard include the basic Hebbian rule that proposed a mechanism for strengthening or weakening of synapses (weights) during learning and memory. This rule, however, did not account for the fact that weights must have bounded growth over time. Thereafter, many other rules that possess other desirable properties were proposed to complement the basic Hebbian rule. In particular, a desirable property in a synaptic plasticity rule is that the ambient system must account for inhibition, which is often achieved if the rule used allows for a lower bound in synaptic weights. To that regard, in this letter, we propose such a synaptic plasticity rule that is inspired by the Allee effect, a phenomenon often observed in population dynamics. We show that properties such as synaptic normalization, competition between weights, decorrelation potential, and dynamic stability are satisfied. We show that in fact, an Allee effect in synaptic plasticity can be construed as an absence of plasticity.