Researcher(s)
- Nathan Manning, Computer Science, University of Delaware
- Lauren Rosica, Mathematics, University of Delaware
Faculty Mentor(s)
- Nikolas Schonsheck, Mathematics, University of Delaware
Abstract
Cyclic features of neural code are specific firing patterns of neurons in response to a
circular stimulus. Identifying and tracking cyclic features through neural networks can help
further our understanding of complex systems within the brain and how information is processed.
Our research simulates the activity of hippocampal place cells of an animal (such as a mouse or
rat) as it walks along a circular path. We summarize this data as a time series of neural firing
rates and then feed this information through a multi-layered feed-forward neural network.
Because this data lives in a high ambient dimension, we employ techniques from the
mathematical field of algebraic topology to understand the geometry of both the stimulus and
stimulus space. In particular, by using persistent cohomology and the circular coordinates
algorithm of de Silva et al. and Perea, we are able to extract circular parameterizations of this
high-dimensional encoding. Additionally, we implement a Hebbian learning rule to update
network connections in response to the simulated stimulus. Once the neural activity data has
been processed through the simulated multi-layered feed-forward network, we show that it is
possible to recover the cyclic feature that is illustrative of the path’s shape. That is, we
demonstrate how to track a faithful representation of stimulus space geometry through multiple
layers of a feed-forward network.