Symmetry and Geometry in Neural Representations (24w5269)


Sophia Sanborn (University of British Columbia)

(UC Santa Barbara)

Christian Shewmake (UC Berkeley)


The Banff International Research Station will host the “Symmetry and Geometry in Neural Representations” workshop in Banff from October 13 - 18, 2024.

In recent years, there has been a growing appreciation for the importance of modeling the geometric structure in data - a perspective that has developed in both the geometric deep learning and geometric statistics communities. In parallel, an emerging set of findings in neuroscience suggests that group-equivariance and the preservation of geometry and topology may be fundamental principles of neural coding in biology.

This workshop will bring together researchers from applied geometry and geometric machine learning with theoretical and empirical neuroscientists whose work reveals the elegant implementation of geometric structure in biological neural circuitry. Group theory and geometry were instrumental in unifying models of fundamental forces and elementary particles in 20th-century physics. Likewise, they have the potential to unify our understanding of how neural systems form useful representations of the world.

The goal of this workshop is to unify the emerging paradigm shifts towards structured representations in deep neural networks and the geometric modeling of neural data, while promoting a solid mathematical foundation in differential geometry and group theory.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta’s Advanced Education and Technology, and Mexico’s Consejo Nacional de Ciencia y Tecnología (CONACYT).