mlsanityData to 7 Oct 2026

Topological Autoencoders

arXiv 1906.00722 ↗First posted 3 Jun 2019cs.LG math.AT stat.MLcited by 124

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Abstract (arXiv)

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

Key facts. Cited by 124 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Jun 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 19; 2022: 11; 2023: 22; 2024: 23; 2025: 23; 2026: 26.

124 papers.

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  1. 2021Generalized Shape Metrics on Neural Representationscited by 109
  2. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  3. 2021Topological Graph Neural Networkscited by 86
  4. 2021Representation Topology Divergence: A Method for Comparing Neural Network Representationscited by 66
  5. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  6. 2022Attribution and Obfuscation of Neural Text Authorship: A Data Mining Perspectivecited by 40
  7. 2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
  8. 2021Manifold Topology Divergence: a Framework for Comparing Data Manifoldscited by 31
  9. 2023Learning Topology-Preserving Data Representationscited by 30
  10. 2025What are you sinking? A geometric approach on attention sinkcited by 26
  11. 2023Geometric Autoencoders -- What You See is What You Decodecited by 23
  12. 2021Topological Obstructions to Autoencodingcited by 20
38 more
  1. 2021Measuring and Explaining the Inter-Cluster Reliability of Multidimensional Projectionscited by 20
  2. 2023Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimizationcited by 18
  3. 2023Differentiable Euler Characteristic Transforms for Shape Classificationcited by 18
  4. 2023ZADU: A Python Library for Evaluating the Reliability of Dimensionality Reduction Embeddingscited by 15
  5. 2023Canonical normalizing flows for manifold learningcited by 15
  6. 2022Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstructioncited by 14
  7. 2024TopoFR: A Closer Look at Topology Alignment on Face Recognitioncited by 13
  8. 2022Uniform Manifold Approximation with Two-phase Optimizationcited by 12
  9. 2023Classes are not Clusters: Improving Label-based Evaluation of Dimensionality Reductioncited by 11
  10. 2021Improving Metric Dimensionality Reduction with Distributed Topologycited by 10
  11. 2021GeomCA: Geometric Evaluation of Data Representationscited by 9
  12. 2024Boosting Graph Pooling with Persistent Homologycited by 9
  13. 2021Data-Centric AI Requires Rethinking Data Notioncited by 8
  14. 2021Learning shared neural manifolds from multi-subject FMRI datacited by 8
  15. 2022EVNet: An Explainable Deep Network for Dimension Reductioncited by 8
  16. 2022FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundlescited by 7
  17. 2021GenURL: A General Framework for Unsupervised Representation Learningcited by 6
  18. 2024Diffeomorphic interpolation for efficient persistence-based topological optimizationcited by 6
  19. 2025Stop Misusing t-SNE and UMAP for Visual Analyticscited by 6
  20. 2021A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysiscited by 5
  21. 2021Topologically Regularized Data Embeddingscited by 5
  22. 2023Topological Node2vec: Enhanced Graph Embedding via Persistent Homologycited by 5
  23. 2025TopoCL: Topological Contrastive Learning for Time Seriescited by 5
  24. 2025The Flood Complex: Large-Scale Persistent Homology on Millions of Pointscited by 5
  25. 2022Rethinking Persistent Homology for Visual Recognitioncited by 4
  26. 2023Topological Obstructions and How to Avoid Themcited by 4
  27. 2024Point-Level Topological Representation Learning on Point Cloudscited by 4
  28. 2024Relative Representations: Topological and Geometric Perspectivescited by 4
  29. 2024Efficient Distribution Matching of Representations via Noise-Injected Deep InfoMaxcited by 4
  30. 2024Revisiting Point Cloud Completion: Are We Ready For The Real-World?cited by 4
  31. 2022Topology-Preserving Dimensionality Reduction via Interleaving Optimizationcited by 3
  32. 2022Homology-constrained vector quantization entropy regularizercited by 3
  33. 2023Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)cited by 3
  34. 2024Sampling-enabled scalable manifold learning unveils the discriminative cluster structure of high-dimensional datacited by 3
  35. 2024Pooling Image Datasets With Multiple Covariate Shift and Imbalancecited by 3
  36. 2024Inductive Global and Local Manifold Approximation and Projectioncited by 3
  37. 2024Disentangled Representation Learning with the Gromov-Monge Gapcited by 3
  38. 2024Achieving Domain-Independent Certified Robustness via Knowledge Continuitycited by 3

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