# Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems trained with Gradient Descent

arXiv: https://arxiv.org/abs/2403.05395 · HTML: https://mlsanity.com/paper/2403.05395/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 8 Mar 2024.

## Builds on (most cited first, 13 of 13)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Towards moderate overparameterization: global convergence guarantees for training shallow neural networks](https://mlsanity.com/paper/1902.04674/) (2019)
- [Overparameterized Nonlinear Learning: Gradient Descent Takes the Shortest Path?](https://mlsanity.com/paper/1812.10004/) (2018)
- [From error bounds to the complexity of first-order descent methods for convex functions](https://mlsanity.com/paper/1510.08234/) (2015)
- [Mathematical Models of Overparameterized Neural Networks](https://mlsanity.com/paper/2012.13982/) (2020)
- [Convergence beyond the over-parameterized regime using Rayleigh quotients](https://mlsanity.com/paper/2301.08117/) (2023)
- [Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems](https://mlsanity.com/paper/2309.12128/) (2023)

## Built on by (most cited first, 1 of 1)

- [Implicit Regularization of the Deep Inverse Prior Trained with Inertia](https://mlsanity.com/paper/2506.02986/) (2025)

## Abstract (arXiv)

Advanced machine learning methods, and more prominently neural networks, have become standard to solve inverse problems over the last years. However, the theoretical recovery guarantees of such methods are still scarce and difficult to achieve. Only recently did unsupervised methods such as Deep Image Prior (DIP) get equipped with convergence and recovery guarantees for generic loss functions when trained through gradient flow with an appropriate initialization. In this paper, we extend these results by proving that these guarantees hold true when using gradient descent with an appropriately chosen step-size/learning rate. We also show that the discretization only affects the overparametrization bound for a two-layer DIP network by a constant and thus that the different guarantees found for the gradient flow will hold for gradient descent.