fluctuations of synaptic-weights, among many other physical, biological and ecological quantities, are driven by coincident events originating from two 'parent' processes. we propose a multiplicative shot-noise model that can capture the behavior of a broad range of such natural phenomena, and analytically derive an approximation that accurately predicts its statistics. we apply our results to study the effects of a multiplicative synaptic plasticity rule that was recently extracted from measurements in physiological conditions. using mean-field theory analysis and network simulations we investigate how this rule shapes the connectivity and dynamics of recurrent spiking neural networks. we show that the multiplicative plasticity rule, without fine-tuning, gives a stable, unimodal synaptic-weight distribution with a large fraction of strong synapses. the strong synapses remain stable over long times but do not `run away'. our results suggest that the multiplicative plasticity rule offers a new route to understand the tradeoff between flexibility and stability in neural circuits and other dynamic networks. joint work with bin wang.

https://mathweb.ucsd.edu/~bli/research/mathbiosci/mbbseminar/