Exploring Geometric Representational Alignment through Ollivier Ricci curvature and Ricci Flow

The representational analysis explores the encoding of input data in high-dimensional spaces within distributed neural activations and facilitates the comparison of different systems, such as artificial neural networks and brains. Although existing methods offer relevant information, they typically do not account for local intrinsic geometrical properties within high-dimensional representation spaces. To overcome these limitations, we explore Ollivier Ricci curvature and Ricci flow as tools to study the similarity and alignment of representations between humans and artificial neural systems on a geometric basis. We used both simulations and a proof-of-principle study, in which we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and the corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify global and local structural similarities and differences by examining distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.