mlsanityData to 14 Oct 2026

Geometric Autoencoders -- What You See is What You Decode

arXiv 2306.17638 ↗First posted 30 Jun 2023cs.LGcited by 23

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Abstract (arXiv)

Visualization is a crucial step in exploratory data analysis. One possible approach is to train an autoencoder with low-dimensional latent space. Large network depth and width can help unfolding the data. However, such expressive networks can achieve low reconstruction error even when the latent representation is distorted. To avoid such misleading visualizations, we propose first a differential geometric perspective on the decoder, leading to insightful diagnostics for an embedding's distortion, and second a new regularizer mitigating such distortion. Our ``Geometric Autoencoder'' avoids stretching the embedding spuriously, so that the visualization captures the data structure more faithfully. It also flags areas where little distortion could not be achieved, thus guarding against misinterpretation.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 20 of its 56 references that are in the map. First posted on arXiv 30 Jun 2023.

Builds on

20 of 56 references.

References · 20

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  3. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
  4. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  5. 2019An Introduction to Variational Autoencoderscited by 1,000
  6. 2013k-Sparse Autoencoderscited by 215
  7. 2019From Variational to Deterministic Autoencoderscited by 133
  8. 2019Topological Autoencoderscited by 127
  9. 2020Parametric UMAP embeddings for representation and semi-supervised learningcited by 104
  10. 2018geomstats: a Python Package for Riemannian Geometry in Machine Learningcited by 71
  11. 2017Metrics for Deep Generative Modelscited by 53
  12. 2021von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learningcited by 42
8 more
  1. 2018From Principal Subspaces to Principal Components with Linear Autoencoderscited by 39
  2. 2020Learning Flat Latent Manifolds with VAEscited by 33
  3. 2021On UMAP's true loss functioncited by 32
  4. 2023Learning Topology-Preserving Data Representationscited by 31
  5. 2019Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisationscited by 22
  6. 2020Isometric Autoencoderscited by 18
  7. 2022Unsupervised visualization of image datasets using contrastive learningcited by 16
  8. 2020Markov-Lipschitz Deep Learningcited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 11; 2026: 7.

23 papers.

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  1. 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 77
  2. 2025Temporal Distance-aware Transition Augmentation for Offline Model-based Reinforcement Learningcited by 6
  3. 2023MMP++: Motion Manifold Primitives with Parametric Curve Modelscited by 5
  4. 2025Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolationcited by 5
  5. 2025Random Forest Autoencoders for Guided Representation Learningcited by 4
  6. 2025DREAMS: Preserving both Local and Global Structure in Dimensionality Reductioncited by 4
  7. 2024Navigating the Effect of Parametrization for Dimensionality Reductioncited by 3
  8. 2026Improving Feasibility via Fast Autoencoder-Based Projectionscited by 3
  9. 2025Structure-preserving contrastive learning for spatial time seriescited by 1
  10. 2025Latent Manifold Reconstruction and Representation with Topological and Geometrical Regularizationcited by 1
  11. 2025Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Latercited by 1
  12. 2025Multi-Scale Geometric Autoencodercited by 1
11 more
  1. 2026On Geometry Regularization in Autoencoder Reduced-Order Models with Latent Neural ODE Dynamicscited by 1
  2. 2026Bi-Lipschitz Autoencoder With Injectivity Guaranteecited by 1
  3. 2024Integrative Variational Autoencoders for Generative Modeling of an Image Outcome with Multiple Input Imagescited by 0
  4. 2024Proper Latent Decompositioncited by 0
  5. 2025Investigating Image Manifolds of 3D Objects: Learning, Shape Analysis, and Comparisonscited by 0
  6. 2025Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparisoncited by 0
  7. 2025Multivariate Time Series Forecasting with Hybrid Euclidean-SPD Manifold Graph Neural Networkscited by 0
  8. 2026Manifold-Matching Autoencoderscited by 0
  9. 2026The Rashomon Effect for Visualizing High-Dimensional Datacited by 0
  10. 2026Sharp Reconstruction Bounds for Autoencoders Using the Same Forward Mapcited by 0
  11. 2026Federated Deep Clustering Networks for High-Dimensional and Heterogeneous Datacited by 0