Exploring Geometric Representational Alignment through Ollivier-Ricci Curvature and Ricci Flow

2025-01-01

AI Summary

Existing methods for comparing facial representations between human brains and artificial neural networks (ANNs) predominantly rely on global statistical measures, neglecting fine-grained local geometric structure. Method: This study introduces Ollivier–Ricci curvature and discrete Ricci flow—concepts from differential geometry—into representational alignment analysis for the first time. We construct representation graphs from neural and behavioral responses, then integrate community detection to enable localized, geometry-aware comparison. Contribution/Results: Applied to face recognition, our approach reveals systematic differences in local curvature distributions among VGG-Face, human-aligned ANN variants, and human behavioral data, while uncovering cross-system correspondences in community structure. These findings validate a local, differential-geometric alignment paradigm for neuro-computational model comparison, offering a novel geometric framework for investigating shared and divergent principles of information processing in biological and artificial intelligence systems.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Representation Learning for Vision
• Humans and AI: Brain-Sensing and Analysis

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Computational social science

Abstract

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.

Problem

• High-Dimensional Space
• Information Alignment
• Brain-Computer Comparison

Innovation

• Olivier's Simplified Bending and Streaming
• High-Dimensional Information Alignment
• Graph Representation Analysis