Committee: 

Dr. Dyer, Advisor

Dr. Davenport, Chair

Dr. Batra

Abstract: The objective of the proposed research is to develop a framework that studies neural representations from a geometric perspective, with an eye towards rendering both artificial and biological neural networks more interpretable and discovering their governing principles. Specifically, the aims of my work are: i) Studying structure-function relationships in neural networks via multi-scale, multi-manifold models of representational geometry, ii) Leveraging the structure in tasks and data for the interpretability, transfer, and adaptation of representations, and iii) Exploiting structure and symmetry for the disentanglement of representational manifolds. In each of the three aims, I also discuss potential applications of the proposed work to open problems in computational neuroscience and artificial intelligence.