Exploring Topological Properties of ANNs (AAAI UC '25)

This project was the result of watching Ratatouille right after completing the final for my cognitive psychology course. Many thanks to my professor, Prof. Adrian Rodriguez Contreras, for fielding my incoherent questions about neuralinked rats and the psychology of autonomous cars, and to Prof. Peer Herholz for directing me to many interesting and useful resources.

I am also grateful to Jason Grant, the AAAI UC chair, for his mentorship, and to the other UC students for sharing their research and perspectives with me during the conference.

I had a wonderful time presenting my poster at the conference and hearing about all the enthusiasm for topological data analysis from many of those who stopped by. Though I am not currently working on this project, TDA is an area that I am highly interested in, and I hope to use more of this flavor of analysis in the future.

Abstract

Biological neural systems often represent information on low-dimensional manifolds that reflect the topology of their encoded variables, as seen in rodent head direction cells forming circular manifolds. This proposal examines whether artificial neural networks trained on tasks with well-defined topologies—such as planar or spherical coordinates from autonomous driving datasets like Apolloscape, cyclic temporal variables, or graph-structured road networks—develop similar low-dimensional representations aligned with the variables' inherent topology.

We consider convolutional and vision transformer models for image data, graph neural networks for road network graphs, and 3D or point-based models for LIDAR point clouds, analyzing their internal activations with dimensionality reduction and topological data analysis.

If successful, this approach not only elucidates the nature of internal representations in ANNs but also offers insights into the computational principles that bridge artificial systems and biological cognition.