mlsanityData to 7 Oct 2026

The Sparse Manifold Transform

arXiv 1806.08887 ↗First posted 23 Jun 2018stat.ML cs.LG eess.IVcited by 36

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Abstract (arXiv)

We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal space into linear interpolations in a representational embedding space while maintaining approximate invertibility. The sparse manifold transform is an unsupervised and generative framework that explicitly and simultaneously models the sparse discreteness and low-dimensional manifold structure found in natural scenes. When stacked, it also models hierarchical composition. We provide a theoretical description of the transform and demonstrate properties of the learned representation on both synthetic data and natural videos.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Jun 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 8; 2023: 9; 2024: 4; 2025: 5; 2026: 5.

36 papers.

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  1. 2023White-Box Transformers via Sparse Rate Reductioncited by 77
  2. 2022Neural Manifold Clustering and Embeddingcited by 44
  3. 2024Where Do We Stand with Implicit Neural Representations? A Technical and Performance Surveycited by 41
  4. 2021Attention Approximates Sparse Distributed Memorycited by 29
  5. 2026Do Sparse Autoencoders Capture Concept Manifolds?cited by 25
  6. 2023Emergence of Segmentation with Minimalistic White-Box Transformerscited by 23
  7. 2023EMP-SSL: Towards Self-Supervised Learning in One Training Epochcited by 18
  8. 2021Two Sparsities Are Better Than One: Unlocking the Performance Benefits of Sparse-Sparse Networkscited by 15
  9. 2023BeMap: Balanced Message Passing for Fair Graph Neural Networkcited by 11
  10. 2022Bag of Image Patch Embedding Behind the Success of Self-Supervised Learningcited by 9
  11. 2023Identifying Interpretable Visual Features in Artificial and Biological Neural Systemscited by 9
  12. 2024Pose-Aware Self-Supervised Learning with Viewpoint Trajectory Regularizationcited by 7
24 more
  1. 2026SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Datacited by 7
  2. 2022Minimalistic Unsupervised Learning with the Sparse Manifold Transformcited by 6
  3. 2022Simple Emergent Action Representations from Multi-Task Policy Trainingcited by 6
  4. 2023A polar prediction model for learning to represent visual transformationscited by 6
  5. 2022Context-sensitive neocortical neurons transform the effectiveness and efficiency of neural information processingcited by 5
  6. 2022Unlocking the potential of two-point cells for energy-efficient and resilient training of deep netscited by 5
  7. 2024A Non-negative VAE:the Generalized Gamma Belief Networkcited by 4
  8. 2021Sparse Coding with Multi-Layer Decoders using Variance Regularizationcited by 3
  9. 2025Cloning Deterministic Worlds: The Critical Role of Latent Geometry in Long-Horizon World Modelscited by 3
  10. 2021Improved Training of Sparse Coding Variational Autoencoder via Weight Normalizationcited by 2
  11. 2024Block Sparse Bayesian Learning: A Diversified Schemecited by 2
  12. 2021SL-CycleGAN: Blind Motion Deblurring in Cycles using Sparse Learningcited by 1
  13. 2023Manifold Contrastive Learning with Variational Lie Group Operatorscited by 1
  14. 2023URLOST: Unsupervised Representation Learning without Stationarity or Topologycited by 1
  15. 2025Weaver: Kronecker Product Approximations of Spatiotemporal Attention for Traffic Network Forecastingcited by 1
  16. 2022Sensitivity of sparse codes to image distortionscited by 0
  17. 2022Commutativity and Disentanglement from the Manifold Perspectivecited by 0
  18. 2023Predictive Sparse Manifold Transformcited by 0
  19. 2025Measuring the Datacited by 0
  20. 2025Unsupervised Sparse Coding-based Spiking Neural Network for Real-time Spike Sortingcited by 0
  21. 2025Scaling Non-Parametric Sampling with Representationcited by 0
  22. 2026MotionPyramid: Hierarchical Motion Representation and Residual Interfacescited by 0
  23. 2026Toward a mechanistic understanding of inference in visual cortex and diffusion modelscited by 0
  24. 2026Subzero matrix completion for sparse data analysis: large-scale learning of latent low-rank structurecited by 0