Exploring Geometric Representational Alignment through Ollivier-Ricci Curvature and Ricci Flow
Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Efficient Curvature-aware Graph Network
Graph curvature provides geometric priors for Graph Neural Networks (GNNs), enhancing their ability to model complex graph structures, particularly in terms of structural awareness, robustness, and theoretical interpreta…
Computational EfficiencyOllivier-Ricci Curvature for Hypergraphs: A Unified Framework
Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization…
Recovering Manifold Structure Using Ollivier-Ricci Curvature
We introduce ORC-ManL, a new algorithm to prune spurious edges from nearest neighbor graphs using a criterion based on Ollivier-Ricci curvature and estimated metric distortion. Our motivation comes from manifold learning…
Accelerated Evaluation of Ollivier-Ricci Curvature Lower Bounds: Bridging Theory and Computation
Curvature serves as a potent and descriptive invariant, with its efficacy validated both theoretically and practically within graph theory. We employ a definition of generalized Ricci curvature proposed by Ollivier, whic…
DescriptiveTraining-Driven Representational Geometry Modularization Predicts Brain Alignment in Language Models
How large language models (LLMs) align with the neural representation and computation of human language is a central question in cognitive science. Using representational geometry as a mechanistic lens, we addressed this…