# Ada-LISTA: Learned Solvers Adaptive to Varying Models

arXiv: https://arxiv.org/abs/2001.08456 · HTML: https://mlsanity.com/paper/2001.08456/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2020.

## Built on by (most cited first, 22 of 22)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem](https://mlsanity.com/paper/2101.08286/) (2021)
- [Hyperparameter Tuning is All You Need for LISTA](https://mlsanity.com/paper/2110.15900/) (2021)
- [Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration](https://mlsanity.com/paper/2312.15701/) (2023)
- [Towards Constituting Mathematical Structures for Learning to Optimize](https://mlsanity.com/paper/2305.18577/) (2023)
- [Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networks](https://mlsanity.com/paper/2112.04364/) (2021)
- [A Lightweight Deep Exclusion Unfolding Network for Single Image Reflection Removal](https://mlsanity.com/paper/2503.01938/) (2025)
- [Unveiling and Mitigating Adversarial Vulnerabilities in Iterative Optimizers](https://mlsanity.com/paper/2504.19000/) (2025)
- [Convolutional Sparse Coding Fast Approximation with Application to Seismic Reflectivity Estimation](https://mlsanity.com/paper/2106.15296/) (2021)
- [One-Shot Image Restoration](https://mlsanity.com/paper/2404.17426/) (2024)
- [Learned ISTA with Error-based Thresholding for Adaptive Sparse Coding](https://mlsanity.com/paper/2112.10985/) (2021)
- [Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning](https://mlsanity.com/paper/2407.13666/) (2024)
- [SINET: Sparsity-driven Interpretable Neural Network for Underwater Image Enhancement](https://mlsanity.com/paper/2409.01022/) (2024)
- [l0-Regularized Sparse Coding-based Interpretable Network for Multi-Modal Image Fusion](https://mlsanity.com/paper/2411.04519/) (2024)
- [A Design Space Study for LISTA and Beyond](https://mlsanity.com/paper/2104.04110/) (2021)
- [Variational Learning ISTA](https://mlsanity.com/paper/2407.06646/) (2024)
- [Physics-Inspired Binary Neural Networks: Interpretable Compression with Theoretical Guarantees](https://mlsanity.com/paper/2502.01908/) (2025)
- [Learned Interpretable Residual Extragradient ISTA for Sparse Coding](https://mlsanity.com/paper/2106.11970/) (2021)
- [Towards Robust Learning to Optimize with Theoretical Guarantees](https://mlsanity.com/paper/2506.14263/) (2025)
- [A Constrained Optimization Perspective of Unrolled Transformers](https://mlsanity.com/paper/2601.17257/) (2026)
- [Tunable Domain Adaptation Using Unfolding](https://mlsanity.com/paper/2603.26931/) (2026)
- [Sparse Koopman Autoencoders Identify Local Dynamical Regimes in Multibasin Systems](https://mlsanity.com/paper/2608.29057/) (2026)

## Abstract (arXiv)

Neural networks that are based on unfolding of an iterative solver, such as LISTA (learned iterative soft threshold algorithm), are widely used due to their accelerated performance. Nevertheless, as opposed to non-learned solvers, these networks are trained on a certain dictionary, and therefore they are inapplicable for varying model scenarios. This work introduces an adaptive learned solver, termed Ada-LISTA, which receives pairs of signals and their corresponding dictionaries as inputs, and learns a universal architecture to serve them all. We prove that this scheme is guaranteed to solve sparse coding in linear rate for varying models, including dictionary perturbations and permutations. We also provide an extensive numerical study demonstrating its practical adaptation capabilities. Finally, we deploy Ada-LISTA to natural image inpainting, where the patch-masks vary spatially, thus requiring such an adaptation.