mlsanityData to 14 Oct 2026

Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems

arXiv 2309.12128 ↗First posted 21 Sep 2023cs.LGcited by 3

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Abstract (arXiv)

Neural networks have become a prominent approach to solve inverse problems in recent years. While a plethora of such methods was developed to solve inverse problems empirically, we are still lacking clear theoretical guarantees for these methods. On the other hand, many works proved convergence to optimal solutions of neural networks in a more general setting using overparametrization as a way to control the Neural Tangent Kernel. In this work we investigate how to bridge these two worlds and we provide deterministic convergence and recovery guarantees for the class of unsupervised feedforward multilayer neural networks trained to solve inverse problems. We also derive overparametrization bounds under which a two-layers Deep Inverse Prior network with smooth activation function will benefit from our guarantees.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 33 of its 61 references that are in the map. First posted on arXiv 21 Sep 2023.

Builds on

33 of 61 references.

References · 33

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  2. 2017Deep Image Priorcited by 1,098
  3. 2018On Lazy Training in Differentiable Programmingcited by 675
  4. 2018Gradient Descent Provably Optimizes Over-parameterized Neural Networkscited by 659
  5. 2019Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networkscited by 566
  6. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 421
  7. 2015An Introduction to Matrix Concentration Inequalitiescited by 397
  8. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 315
  9. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 291
  10. 2021Deep learning: a statistical viewpointcited by 240
  11. 2019On instabilities of deep learning in image reconstruction - Does AI come at a cost?cited by 212
  12. 2019Towards moderate overparameterization: global convergence guarantees for training shallow neural networkscited by 176
21 more
  1. 2018NETT: Solving Inverse Problems with Deep Neural Networkscited by 89
  2. 2018Overparameterized Nonlinear Learning: Gradient Descent Takes the Shortest Path?cited by 88
  3. 2019DeepRED: Deep Image Prior Powered by REDcited by 85
  4. 2017DeLiGAN : Generative Adversarial Networks for Diverse and Limited Datacited by 77
  5. 2018Image Restoration using Total Variation Regularized Deep Image Priorcited by 65
  6. 2020Learned convex regularizers for inverse problemscited by 55
  7. 2022Learned reconstruction methods with convergence guaranteescited by 46
  8. 2015From error bounds to the complexity of first-order descent methods for convex functionscited by 43
  9. 2022Can Push-forward Generative Models Fit Multimodal Distributions?cited by 41
  10. 2020The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problemscited by 40
  11. 2021On Measuring and Controlling the Spectral Bias of the Deep Image Priorcited by 36
  12. 2019Algorithmic Guarantees for Inverse Imaging with Untrained Network Priorscited by 32
  13. 2020Stabilizing Invertible Neural Networks Using Mixture Modelscited by 30
  14. 2018Disconnected Manifold Learning for Generative Adversarial Networkscited by 27
  15. 2020Learning disconnected manifolds: a no GANs landcited by 25
  16. 2021Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Conditioncited by 22
  17. 2021Learning local regularization for variational image restorationcited by 16
  18. 2020Mathematical Models of Overparameterized Neural Networkscited by 15
  19. 2020BP-DIP: A Backprojection based Deep Image Priorcited by 11
  20. 2022Unveiling the Latent Space Geometry of Push-Forward Generative Modelscited by 3
  21. 2023Convergence Guarantees of Overparametrized Wide Deep Inverse Priorcited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 1.

3 papers.

  1. 2024Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems trained with Gradient Descentcited by 1
  2. 2025Implicit Regularization of the Deep Inverse Prior Trained with Inertiacited by 0
  3. 2026CogGen: Cognitive-Load-Inspired Fully Unsupervised Deep Generative Modeling for Compressively Sampled MRI Reconstructioncited by 0