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Center for Nonlinear Studies |
Over the last decade neurophysiologists have found that learning-related synaptic changes in several systems are sensitive to the relative timing between pre- and post- synaptic spike events. The temporal resolution involved is on a scale of a few tens of milleseconds. This spike-timing-dependent plasticity (STDP) stands in contrast to earlier experimental results that lacked this time resolution, and hence described synaptic plasticity in terms of correlations between pre- and post-synaptic events estimated over many spikes.
Rate-based learning models, involving statistical averages, are conveniently described by deterministic differential or difference equations. STDP learning models, on the other hand, have intrinsic random components, and their dynamics are properly described in terms of stochastic dynamical systems. Synaptic strengths evolving under STDP and the iterative statistical estimators in stochastic approximation algorithms from machine learning share a common dynamical description in terms of a, usually intractable, master equation and it approximations.
I will discuss viable and non-viable approximate solution techniques for the ensemble dynamics, and an exact solution for a particular STDP learning rule observed in rat hippocampal neurons.
Host: Andy Fraser, Space & Remote Sensing, ISR-2