mlsanityData to 14 Oct 2026

Representation Learning via Manifold Flattening and Reconstruction

arXiv 2305.01777 ↗First posted 2 May 2023cs.LG math.DGcited by 11

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Abstract (arXiv)

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening Networks (FlatNet), are theoretically interpretable, computationally feasible at scale, and generalize well to test data, a balance not typically found in manifold-based learning methods. We present empirical results and comparisons to other models on synthetic high-dimensional manifold data and 2D image data. Our code is publicly available.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 23 of its 91 references that are in the map. First posted on arXiv 2 May 2023.

Builds on

23 of 91 references.

References · 23

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
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  10. 2019Dream to Control: Learning Behaviors by Latent Imaginationcited by 1,653
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  12. 2018Disentangling by Factorisingcited by 616
11 more
  1. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  2. 2022The Forward-Forward Algorithm: Some Preliminary Investigationscited by 266
  3. 2018Estimating the intrinsic dimension of datasets by a minimal neighborhood informationcited by 250
  4. 2020Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reductioncited by 142
  5. 2018Taming VAEscited by 85
  6. 2021ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reductioncited by 84
  7. 2020Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transformcited by 80
  8. 2022On the Principles of Parsimony and Self-Consistency for the Emergence of Intelligencecited by 50
  9. 2018Intrinsic Isometric Manifold Learning with Application to Localizationcited by 11
  10. 2015Scalable Out-of-Sample Extension of Graph Embeddings Using Deep Neural Networkscited by 5
  11. 2016Random projections of random manifoldscited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 6; 2025: 3; 2026: 2.

11 papers.

  1. 2024Emergence of a High-Dimensional Abstraction Phase in Language Transformerscited by 56
  2. 2025Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functionalcited by 20
  3. 2024Geometric Signatures of Compositionality Across a Language Model's Lifetimecited by 16
  4. 2024Masked Completion via Structured Diffusion with White-Box Transformerscited by 9
  5. 2024Words in Motion: Extracting Interpretable Control Vectors for Motion Transformerscited by 9
  6. 2024LightFF: Lightweight Inference for Forward-Forward Algorithmcited by 3
  7. 2025Who Said Neural Networks Aren't Linear?cited by 2
  8. 2025Latent Manifold Reconstruction and Representation with Topological and Geometrical Regularizationcited by 1
  9. 2026Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributionscited by 1
  10. 2024Normalized Space Alignment: A Versatile Metric for Representation Analysiscited by 0
  11. 2026Superposed Latent Autoencodercited by 0