# Variational Learning ISTA

arXiv: https://arxiv.org/abs/2407.06646 · HTML: https://mlsanity.com/paper/2407.06646/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 9 Jul 2024.

## Builds on (most cited first, 17 of 17)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Hierarchical Multiscale Recurrent Neural Networks](https://mlsanity.com/paper/1609.01704/) (2016)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Experimental design for MRI by greedy policy search](https://mlsanity.com/paper/2010.16262/) (2020)
- [Bayesian Recurrent Neural Networks](https://mlsanity.com/paper/1704.02798/) (2017)
- [Ada-LISTA: Learned Solvers Adaptive to Varying Models](https://mlsanity.com/paper/2001.08456/) (2020)
- [Hyperparameter Tuning is All You Need for LISTA](https://mlsanity.com/paper/2110.15900/) (2021)
- [Compressive Sensing and Neural Networks from a Statistical Learning Perspective](https://mlsanity.com/paper/2010.15658/) (2020)
- [Tradeoffs between Convergence Speed and Reconstruction Accuracy in Inverse Problems](https://mlsanity.com/paper/1605.09232/) (2016)
- [Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networks](https://mlsanity.com/paper/2112.04364/) (2021)
- [Neurally Augmented ALISTA](https://mlsanity.com/paper/2010.01930/) (2020)
- [Bayesian Compressive Sensing Using Normal Product Priors](https://mlsanity.com/paper/1708.07450/) (2017)
- [Beyond Codebook-Based Analog Beamforming at mmWave: Compressed Sensing and Machine Learning Methods](https://mlsanity.com/paper/2211.02102/) (2022)

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

- [AbsTopK: Rethinking Sparse Autoencoders For Bidirectional Features](https://mlsanity.com/paper/2510.00404/) (2025)

## Abstract (arXiv)

Compressed sensing combines the power of convex optimization techniques with a sparsity-inducing prior on the signal space to solve an underdetermined system of equations. For many problems, the sparsifying dictionary is not directly given, nor its existence can be assumed. Besides, the sensing matrix can change across different scenarios. Addressing these issues requires solving a sparse representation learning problem, namely dictionary learning, taking into account the epistemic uncertainty of the learned dictionaries and, finally, jointly learning sparse representations and reconstructions under varying sensing matrix conditions. We address both concerns by proposing a variant of the LISTA architecture. First, we introduce Augmented Dictionary Learning ISTA (A-DLISTA), which incorporates an augmentation module to adapt parameters to the current measurement setup. Then, we propose to learn a distribution over dictionaries via a variational approach, dubbed Variational Learning ISTA (VLISTA). VLISTA exploits A-DLISTA as the likelihood model and approximates a posterior distribution over the dictionaries as part of an unfolded LISTA-based recovery algorithm. As a result, VLISTA provides a probabilistic way to jointly learn the dictionary distribution and the reconstruction algorithm with varying sensing matrices. We provide theoretical and experimental support for our architecture and show that our model learns calibrated uncertainties.