Dynamics of driven networks: computation in recurrent neural circuits

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The long-term goal of my research is to advance a theory of driven recurrent network computation using mathematical tools from dynamical systems and information theory. ***In this proposal, my goal is to investigate the relationship between network architecture and the variability that emerges within networks driven by external signals.******Networks of neurons —either biological or artificial— are called recurrent if their connections are distributed and contain feedback loops. Such networks can perform remarkably complex computations, as evidenced by their ubiquity throughout the brain and ever-increasing use in machine learning. They are, however, notoriously hard to control and their dynamics are generally poorly understood, especially in the presence of external forcing. This is because recurrent networks are typically chaotic systems, meaning they have rich and sensitive dynamics leading to variable responses to inputs. How do the arrangement and strength of connections affect how severe and distributed chaos is in a network? What is the influence on the way connections are modulated to shape network function? I investigate these questions in three specific research aims directed at both the brain, and artificial networks. Aim 1 investigates how spatially structured connectivity shapes chaotic attractors in both rate and spiking models, and connects theoretical results to the study of cortical circuits. Aim 2 probes how chaos and synaptic plasticity interact to shape recurrent networks, and seeks to predict how artificial inputs from brain-computer interfaces steer motor cortex connectivity in ongoing experiments. Aim 3 develops schemes to take advantage of chaos and chaotic attractors to alter connection weights of artificial networks during training. ******My research program has two complementary objectives: (i) a mathematically rigorous understanding of driven recurrent network dynamics and (ii) the development of an analysis and modelling framework to interpret and guide neuroscience experiments. Both have tangible multidisciplinary applications ranging from the development of implants that can directly communicate with neural circuits in the brain, to the design of artificial neural networks. **