AI & Applications

Geometry of neural networks with biological structure - Kameron Decker Harris, Assistant Professor, Western Washington University

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Abstract:

A theory of artificial neural networks has been developed using the language of reproducing kernel Hilbert spaces which have well-understood mathematical and statistical properties. However, theorists have typically studied networks with unstructured weights, whereas we know that the receptive fields of neurons in biological and end-to-end trained networks show interesting structures. I will present novel results that come from studying simple structures that occur in real neuronal networks using the kernel framework. Networks with sparse connections, which notably occur in cerebellum and the mushroom body, produce additive models. Networks of neurons with tuning properties, as studied ubiquitously in neuroscience, are found to induce a change of basis that allows the network to build Fourier, wavelet, or other representations. We will also see how such networks are related to the wavelet scattering transform, and I will close with some ideas for how kernels can be applied in the feature learning regime. This interplay between neuroscience, mathematics, and computer science promises many future discoveries.

Bio:

Kameron Decker Harris is an Assistant Professor of Computer Science at Western Washington University interested in research at the intersection of neuroscience, machine learning, and graph theory. He completed his PhD in Applied Mathematics at the University of Washington and was a Washington Research Foundation Postdoctoral Fellow and Fulbright scholar (Chile). Kameron grew up off-the-grid in Vermont and enjoys cooking and spending time outdoors.

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