# Invert to Learn to Invert

arXiv: https://arxiv.org/abs/1911.10914 · HTML: https://mlsanity.com/paper/1911.10914/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2019.

## Built on by (most cited first, 18 of 18)

- [ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer](https://mlsanity.com/paper/2201.09376/) (2022)
- [Reversible Vision Transformers](https://mlsanity.com/paper/2302.04869/) (2023)
- [Over-and-Under Complete Convolutional RNN for MRI Reconstruction](https://mlsanity.com/paper/2106.08886/) (2021)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)
- [Preconditioned training of normalizing flows for variational inference in inverse problems](https://mlsanity.com/paper/2101.03709/) (2021)
- [Data augmentation for deep learning based accelerated MRI reconstruction with limited data](https://mlsanity.com/paper/2106.14947/) (2021)
- [Deep Bayesian inference for seismic imaging with tasks](https://mlsanity.com/paper/2110.04825/) (2021)
- [Learning by example: fast reliability-aware seismic imaging with normalizing flows](https://mlsanity.com/paper/2104.06255/) (2021)
- [Dual-Domain Reconstruction Networks with V-Net and K-Net for fast MRI](https://mlsanity.com/paper/2203.05725/) (2022)
- [Loop Unrolled Shallow Equilibrium Regularizer (LUSER) -- A Memory-Efficient Inverse Problem Solver](https://mlsanity.com/paper/2210.04987/) (2022)
- [GLEAM: Greedy Learning for Large-Scale Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.08393/) (2022)
- [Refining Amortized Posterior Approximations using Gradient-Based Summary Statistics](https://mlsanity.com/paper/2305.08733/) (2023)
- [CAMP-Net: Consistency-Aware Multi-Prior Network for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2306.11238/) (2023)
- [Complexity of Injectivity and Verification of ReLU Neural Networks](https://mlsanity.com/paper/2405.19805/) (2024)
- [On Sensitivity and Robustness of Normalization Schemes to Input Distribution Shifts in Automatic MR Image Diagnosis](https://mlsanity.com/paper/2306.13276/) (2023)
- [On Instabilities of Unsupervised Denoising Diffusion Models in Magnetic Resonance Imaging Reconstruction](https://mlsanity.com/paper/2406.16983/) (2024)
- [A statistical perspective on algorithm unrolling models for inverse problems](https://mlsanity.com/paper/2311.06395/) (2023)
- [Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes](https://mlsanity.com/paper/2607.27188/) (2026)

## Abstract (arXiv)

Iterative learning to infer approaches have become popular solvers for inverse problems. However, their memory requirements during training grow linearly with model depth, limiting in practice model expressiveness. In this work, we propose an iterative inverse model with constant memory that relies on invertible networks to avoid storing intermediate activations. As a result, the proposed approach allows us to train models with 400 layers on 3D volumes in an MRI image reconstruction task. In experiments on a public data set, we demonstrate that these deeper, and thus more expressive, networks perform state-of-the-art image reconstruction.