mlsanityData to 14 Oct 2026

The Shape of Data: Intrinsic Distance for Data Distributions

arXiv 1905.11141 ↗First posted 27 May 2019stat.ML cs.LGcited by 38

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Abstract (arXiv)

The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data distributions focus on global data properties such as mean and covariance; in that sense, they are extrinsic and uni-scale. We develop a first-of-its-kind intrinsic and multi-scale method for characterizing and comparing data manifolds, using a lower-bound of the spectral variant of the Gromov-Wasserstein inter-manifold distance, which compares all data moments. In a thorough experimental study, we demonstrate that our method effectively discerns the structure of data manifolds even on unaligned data of different dimensionalities; moreover, we showcase its efficacy in evaluating the quality of generative models.

Key facts. Cited by 38 papers in the map (data through 14 Oct 2026). First posted on arXiv 27 May 2019.

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Citing papers per year: 2021: 6; 2022: 4; 2023: 8; 2024: 11; 2025: 6; 2026: 3.

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  1. 2022Relative representations enable zero-shot latent space communicationcited by 191
  2. 2023Similarity of Neural Network Models: A Survey of Functional and Representational Measurescited by 131
  3. 2021Pros and Cons of GAN Evaluation Measures: New Developmentscited by 123
  4. 2021Unleashing Transformers: Parallel Token Prediction with Discrete Absorbing Diffusion for Fast High-Resolution Image Generation from Vector-Quantized Codescited by 71
  5. 2021Representation Topology Divergence: A Method for Comparing Neural Network Representationscited by 66
  6. 2023Latent Space Translation via Semantic Alignmentcited by 52
  7. 2024Do Vision and Language Encoders Represent the World Similarly?cited by 44
  8. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 39
  9. 2022PyTorch Image Quality: Metrics for Image Quality Assessmentcited by 34
  10. 2021Manifold Topology Divergence: a Framework for Comparing Data Manifoldscited by 31
  11. 2024ReSi: A Comprehensive Benchmark for Representational Similarity Measurescited by 19
  12. 2024SuperLoRA: Parameter-Efficient Unified Adaptation of Multi-Layer Attention Modulescited by 10
26 more
  1. 2024Latent Space Translation via Inverse Relative Projectioncited by 10
  2. 2024Neural Lineagecited by 9
  3. 2023Bootstrapping Parallel Anchors for Relative Representationscited by 8
  4. 2024TexTile: A Differentiable Metric for Texture Tileabilitycited by 7
  5. 2023Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processescited by 6
  6. 2022Log-Euclidean Signatures for Intrinsic Distances Between Unaligned Datasetscited by 5
  7. 2024Mapping the Multiverse of Latent Representationscited by 5
  8. 2025Approximating Latent Manifolds in Neural Networks via Vanishing Idealscited by 5
  9. 2025RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Taskscited by 4
  10. 2025Connecting Neural Models Latent Geometries with Relative Geodesic Representationscited by 4
  11. 2023Neural FIM for learning Fisher Information Metrics from point cloud datacited by 3
  12. 2023Understanding Deep Generative Models with Generalized Empirical Likelihoodscited by 3
  13. 2023Metrics to Quantify Global Consistency in Synthetic Medical Imagescited by 3
  14. 2026Mitigating the Contractivity Trap in Diffusion ODEs via Stein Stabilizationcited by 3
  15. 2021A Method for Evaluating Deep Generative Models of Images via Assessing the Reproduction of High-order Spatial Contextcited by 2
  16. 2022Image Quality Assessment for Magnetic Resonance Imagingcited by 2
  17. 2024FedAnchor: Enhancing Federated Semi-Supervised Learning with Label Contrastive Loss for Unlabeled Clientscited by 2
  18. 2025Manifold Approximation leads to Robust Kernel Alignmentcited by 2
  19. 2024Latent Functional Maps: a spectral framework for representation alignmentcited by 1
  20. 2025k-NN as a Simple and Effective Estimator of Transferabilitycited by 1
  21. 2023Using Skew to Assess the Quality of GAN-generated Image Featurescited by 0
  22. 2024Identifying Sub-networks in Neural Networks via Functionally Similar Representationscited by 0
  23. 2024Normalized Space Alignment: A Versatile Metric for Representation Analysiscited by 0
  24. 2025MAYA: Addressing Inconsistencies in Generative Password Guessing through a Unified Benchmarkcited by 0
  25. 2026From Layers to Networks: Comparing Neural Representations via Diffusion Geometrycited by 0
  26. 2026Symmetric Divergence and Normalized Similarity: A Unified Topological Framework for Representation Analysiscited by 0