Metric Space Magnitude for Evaluating the Diversity of Latent Representations
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916566421995520 |
|---|---|
| author | Limbeck, Katharina Andreeva, Rayna Sarkar, Rik Rieck, Bastian |
| author_facet | Limbeck, Katharina Andreeva, Rayna Sarkar, Rik Rieck, Bastian |
| contents | 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. We develop 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16054 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Metric Space Magnitude for Evaluating the Diversity of Latent Representations Limbeck, Katharina Andreeva, Rayna Sarkar, Rik Rieck, Bastian Machine Learning Geometric Topology 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. We develop 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. |
| title | Metric Space Magnitude for Evaluating the Diversity of Latent Representations |
| topic | Machine Learning Geometric Topology |
| url | https://arxiv.org/abs/2311.16054 |