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Metric Space Magnitude for Evaluating the Diversity of Latent Representations

组织者

马修·伯菲特 , 李京艳 , 吴杰 , 杨南君 , 周嘉伟

演讲者

Katharina Limbeck

时间

2024年11月21日 16:30 至 18:00

地点

A3-2a-201

线上

Zoom 482 240 1589 (BIMSA)

摘要

The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. During this talk we discuss the role of magnitude for machine learning applications, specifically for the evaluation of diversity. We present a family of magnitude-based measures of the intrinsic diversity of latent representations, formalising a novel notion of dissimilarity between magnitude functions of finite metric spaces. Our measures are provably stable under perturbations of the data, can be efficiently calculated, and enable a rigorous multi-scale characterisation and comparison of latent representations. We show their utility and superior performance across different domains and tasks, including (i) the automated estimation of diversity, (ii) the detection of mode collapse, and (iii) the evaluation of generative models for text, image, and graph data.