Christian Shewmake

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Researcher

Olshausen Lab

Current Research

How do neural circuits represent and transform information? Is there a framework which can lift us out of binary strings and logic gates and into the domain of stochastic dynamics in neural networks? I’m curious to explore this maneuver via specific problems in perception and memory through connections to differential geometry, information theory, dynamical systems, and optimization. Alongside these theoretical questions, I’m interested in new methods for geometric deep learning, neuromorphic computing, and brain-computer interfaces.

Currently, I’m working from a couple of angles to understand Lie groups and their connection to problems in perception and object understanding. One approach involves the construction of learning algorithms which can directly utilize machinery from Lie theory to improve object classification performance. Another direction blends ideas from sparse coding/the sparse manifold transform with dynamics on manifolds to represent signals from natural scenes. On the side, I’m tinkering with a model for persistent memory in analog dynamical systems. Aside from research, I organize the Lie theory and differential geometry working group here in the Center. I’m also a contributor to Geomstats—a python library for geometric computation and learning on manifolds.

Background

In 2017, I graduated from Washington University in St. Louis with a B.S. in Biomedical Engineering and a second major in Applied Mathematics. Afterward, I worked in R&D at Koniku blending synthetic biology, machine learning, and hardware design to create neuronal wetware chips for olfactory sensing. Motivated to understand the mathematics of neural representations and population coding, I returned to WashU for my M.S. in Systems Science and Mathematics in 2018. There, I explored a notion of memory in networked nonlinear systems and conserved quantities using manifold learning. During this process, I discovered the field of theoretical neuroscience and, in the summer of 2020, was fortunate to join Bruno Olshausen’s lab in the Redwood Center to explore geometric properties of neural representations in vision. This fall I’m applying to PhD programs bridging math, theoretical neuroscience, and machine learning. I look forward to contributing to these areas during my time at the Redwood Center and throughout my academic career.

Aside from exploring mathematics and brains, I enjoy connecting with people, places, their stories, and our collective journey toward understanding. I like unearthing sounds from unexpected patterns and learning place through long-distance cycling. I was fortunate to grow up in a big, supportive family in “The Natural State” of Arkansas.