The discovery that synaptic plasticity is mediated by processes sensitive to the precise relative timing of pre- and post-synaptic events overturned models of synaptic change based on average activity levels (so-called rate-dependent models). This experimental discovery contradicted the conceptual framework that has dominated since the work of Donald Hebb (1949), and requires different theoretical and computational tools.
Individual synaptic events have inherent random variability, so computational synaptic dynamics in the new paradigm must be based in the theory of stochastic processes. Previous work modeling the stochastic dynamics of neural systems uses approximation tools -- the nonlinear Fokker-Planck equation (FPE) -- known to be deeply flawed and potentially misleading. The situation recalls the use of the FPE by machine learning theorists in the early to mid 1990s; indeed the dynamics of spike-timing-dependent plasticity in neural systems and those of stochastic approximation algorithms in the machine learning literature are very similar.
This project establishes rigorous tools for treating the stochastic dynamics of learning systems based on spike-timing-dependent synaptic plasticity. It develops well-grounded approximation techniques (and exact solutions where available) and applies them to synaptic dynamics in natural and artificial learning systems. The new methods are compared to those employed in the recent literature to provide insight into the accuracy and appropriateness of the various methods. The project is relevant to both computational neuroscience and machine learning, and will also provide interdisciplinary research training for graduate and undergraduate students.