# Loop Unrolled Shallow Equilibrium Regularizer (LUSER) -- A Memory-Efficient Inverse Problem Solver

arXiv: https://arxiv.org/abs/2210.04987 · HTML: https://mlsanity.com/paper/2210.04987/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 18 references that are in the map.
- First posted on arXiv 10 Oct 2022.

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

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Low-Memory Neural Network Training: A Technical Report](https://mlsanity.com/paper/1904.10631/) (2019)
- [HUMUS-Net: Hybrid unrolled multi-scale network architecture for accelerated MRI reconstruction](https://mlsanity.com/paper/2203.08213/) (2022)
- [Invert to Learn to Invert](https://mlsanity.com/paper/1911.10914/) (2019)
- [Conditional Injective Flows for Bayesian Imaging](https://mlsanity.com/paper/2204.07664/) (2022)

## Built on by (most cited first, 4 of 4)

- [Deep equilibrium models as estimators for continuous latent variables](https://mlsanity.com/paper/2211.05943/) (2022)
- [Refining Amortized Posterior Approximations using Gradient-Based Summary Statistics](https://mlsanity.com/paper/2305.08733/) (2023)
- [Solving Inverse Problems with Model Mismatch using Untrained Neural Networks within Model-based Architectures](https://mlsanity.com/paper/2403.04847/) (2024)
- [PETAL: Physics Emulation Through Averaged Linearizations for Solving Inverse Problems](https://mlsanity.com/paper/2305.11056/) (2023)

## Abstract (arXiv)

In inverse problems we aim to reconstruct some underlying signal of interest from potentially corrupted and often ill-posed measurements. Classical optimization-based techniques proceed by optimizing a data consistency metric together with a regularizer. Current state-of-the-art machine learning approaches draw inspiration from such techniques by unrolling the iterative updates for an optimization-based solver and then learning a regularizer from data. This loop unrolling (LU) method has shown tremendous success, but often requires a deep model for the best performance leading to high memory costs during training. Thus, to address the balance between computation cost and network expressiveness, we propose an LU algorithm with shallow equilibrium regularizers (LUSER). These implicit models are as expressive as deeper convolutional networks, but far more memory efficient during training. The proposed method is evaluated on image deblurring, computed tomography (CT), as well as single-coil Magnetic Resonance Imaging (MRI) tasks and shows similar, or even better, performance while requiring up to 8 times less computational resources during training when compared against a more typical LU architecture with feedforward convolutional regularizers.