# Learning Trees of ℓ0-Minimization Problems

arXiv: https://arxiv.org/abs/2302.02548 · HTML: https://mlsanity.com/paper/2302.02548/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 60 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 27 of 27)

- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Complete Dictionary Recovery over the Sphere I: Overview and the Geometric Picture](https://mlsanity.com/paper/1511.03607/) (2015)
- [Compressed Sensing with Deep Image Prior and Learned Regularization](https://mlsanity.com/paper/1806.06438/) (2018)
- [Neural Proximal Gradient Descent for Compressive Imaging](https://mlsanity.com/paper/1806.03963/) (2018)
- [Deep Compressed Sensing](https://mlsanity.com/paper/1905.06723/) (2019)
- [Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation](https://mlsanity.com/paper/2005.03991/) (2020)
- [Simple, Efficient, and Neural Algorithms for Sparse Coding](https://mlsanity.com/paper/1503.00778/) (2015)
- [Global Guarantees for Enforcing Deep Generative Priors by Empirical Risk](https://mlsanity.com/paper/1705.07576/) (2017)
- [Modeling Sparse Deviations for Compressed Sensing using Generative Models](https://mlsanity.com/paper/1807.01442/) (2018)
- [Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors](https://mlsanity.com/paper/1906.08763/) (2019)
- [Complete Dictionary Recovery over the Sphere II: Recovery by Riemannian Trust-region Method](https://mlsanity.com/paper/1511.04777/) (2015)
- [Deep Networks for Compressed Image Sensing](https://mlsanity.com/paper/1707.07119/) (2017)
- [New Algorithms for Learning Incoherent and Overcomplete Dictionaries](https://mlsanity.com/paper/1308.6273/) (2013)
- [Dictionary Learning and Tensor Decomposition via the Sum-of-Squares Method](https://mlsanity.com/paper/1407.1543/) (2014)
- [Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling](https://mlsanity.com/paper/1806.10175/) (2018)
- [A Provably Convergent Scheme for Compressive Sensing under Random Generative Priors](https://mlsanity.com/paper/1812.04176/) (2018)
- [Local Identification of Overcomplete Dictionaries](https://mlsanity.com/paper/1401.6354/) (2014)
- [More Algorithms for Provable Dictionary Learning](https://mlsanity.com/paper/1401.0579/) (2014)
- [Restricted Isometry Property under High Correlations](https://mlsanity.com/paper/1904.05510/) (2019)
- [Sparse Recovery and Dictionary Learning from Nonlinear Compressive Measurements](https://mlsanity.com/paper/1809.09639/) (2018)
- [Sparse Matrix Factorization](https://mlsanity.com/paper/1311.3315/) (2013)
- [A Relaxation Argument for Optimization in Neural Networks and Non-Convex Compressed Sensing](https://mlsanity.com/paper/2002.00516/) (2020)
- [Non-Convex Compressed Sensing with Training Data](https://mlsanity.com/paper/2101.08310/) (2021)

## Abstract (arXiv)

The problem of computing minimally sparse solutions of under-determined linear systems is NP hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP) can be solved by convex ℓ1-minimization. While these classes have been very successful, they leave out many practical applications. In this paper, we consider adaptable classes that are tractable after training on a curriculum of increasingly difficult samples. The setup is intended as a candidate model for a human mathematician, who may not be able to tackle an arbitrary proof right away, but may be successful in relatively flexible subclasses, or areas of expertise, after training on a suitable curriculum.