mlsanityData to 14 Oct 2026

Metric Space Magnitude for Evaluating the Diversity of Latent Representations

arXiv 2311.16054 ↗First posted 27 Nov 2023cs.LG math.GT stat.MLcited by 17

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Abstract (arXiv)

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.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Builds on 24 of its 49 references that are in the map. First posted on arXiv 27 Nov 2023.

Builds on

24 of 49 references.

References · 24

  1. 2019Sentence-BERT: Sentence Embeddings using Siamese BERT-Networkscited by 9,170
  2. 2015Rethinking the Inception Architecture for Computer Visioncited by 5,475
  3. 2018How Powerful are Graph Neural Networks?cited by 4,393
  4. 2019Improved Precision and Recall Metric for Assessing Generative Modelscited by 944
  5. 2020Reliable Fidelity and Diversity Metrics for Generative Modelscited by 434
  6. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 413
  7. 2018Assessing Generative Models via Precision and Recallcited by 406
  8. 2022The Vendi Score: A Diversity Evaluation Metric for Machine Learningcited by 311
  9. 2015A note on the evaluation of generative modelscited by 292
  10. 2020Evaluation of Text Generation: A Surveycited by 277
  11. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 234
  12. 2020Evaluating the Evaluation of Diversity in Natural Language Generationcited by 129
12 more
  1. 2020Scalable Deep Generative Modeling for Sparse Graphscited by 65
  2. 2014Geodesic Exponential Kernels: When Curvature and Linearity Conflictcited by 47
  3. 2022On Evaluation Metrics for Graph Generative Modelscited by 46
  4. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 39
  5. 2019Persistent homology detects curvaturecited by 26
  6. 2020Diversity, Density, and Homogeneity: Quantitative Characteristic Metrics for Text Collectionscited by 22
  7. 2022On the effectiveness of persistent homologycited by 20
  8. 2023Metric Space Magnitude and Generalisation in Neural Networkscited by 15
  9. 2021Weighting vectors for machine learning: numerical harmonic analysis applied to boundary detectioncited by 6
  10. 2021The magnitude vector of imagescited by 4
  11. 2022Diversity Enhancement via Magnitudecited by 2
  12. 2022Parallel black-box optimization of expensive high-dimensional multimodal functions via magnitudecited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 6; 2026: 10.

17 papers.

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  1. 2025No Metric to Rule Them All: Toward Principled Evaluations of Graph-Learning Datasetscited by 16
  2. 2025Geometry-Aware Edge Pooling for Graph Neural Networkscited by 5
  3. 2025From Topology to Retrieval: Decoding Embedding Spaces with Unified Signaturescited by 5
  4. 2024Approximating Metric Magnitude of Point Setscited by 4
  5. 2026Magnitude Distance: A Geometric Measure of Dataset Similaritycited by 2
  6. 2025Is magnitude 'generically continuous' for finite metric spaces?cited by 1
  7. 2026Cross-Fusion Distance: A Novel Metric for Measuring Fusion and Separability Between Data Groups in Representation Spacecited by 1
  8. 2025Predict Training Data Quality via Its Geometry in Metric Spacecited by 0
  9. 2025Persistent reachability homology in machine learning applicationscited by 0
  10. 2026Measuring Dataset Diversity from a Geometric Perspectivecited by 0
  11. 2026Local Message-Passing for Discrete Graph Generationcited by 0
  12. 2026Diversity Curves for Graph Representation Learningcited by 0
5 more
  1. 2026Magnitude-Based Features for Multispecies Spatial Datacited by 0
  2. 2026Measuring What Persists: Conditioning Mechanisms and a Geometric Framework for AI Agent Identitycited by 0
  3. 2026Evaluating the Diversity of AI-Generated Content with Diversity Profilescited by 0
  4. 2026Generalization in Neural Networks Through the Lens of Magnitude Potentialcited by 0
  5. 2026PLDiv: Measuring Dataset Diversity and Semantic Collapse via Persistence Landscapescited by 0