# Recursions Are All You Need: Towards Efficient Deep Unfolding Networks

arXiv: https://arxiv.org/abs/2305.05505 · HTML: https://mlsanity.com/paper/2305.05505/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Survey of Model Compression and Acceleration for Deep Neural Networks](https://mlsanity.com/paper/1710.09282/) (2017)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [A Deep Learning Approach to Structured Signal Recovery](https://mlsanity.com/paper/1508.04065/) (2015)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [Deep Networks for Compressed Image Sensing](https://mlsanity.com/paper/1707.07119/) (2017)
- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)

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

- [A TRPCA-Inspired Deep Unfolding Network for Hyperspectral Image Denoising via Thresholded t-SVD and Top-K Sparse Transformer](https://mlsanity.com/paper/2506.02364/) (2025)

## Abstract (arXiv)

The use of deep unfolding networks in compressive sensing (CS) has seen wide success as they provide both simplicity and interpretability. However, since most deep unfolding networks are iterative, this incurs significant redundancies in the network. In this work, we propose a novel recursion-based framework to enhance the efficiency of deep unfolding models. First, recursions are used to effectively eliminate the redundancies in deep unfolding networks. Secondly, we randomize the number of recursions during training to decrease the overall training time. Finally, to effectively utilize the power of recursions, we introduce a learnable unit to modulate the features of the model based on both the total number of iterations and the current iteration index. To evaluate the proposed framework, we apply it to both ISTA-Net+ and COAST. Extensive testing shows that our proposed framework allows the network to cut down as much as 75% of its learnable parameters while mostly maintaining its performance, and at the same time, it cuts around 21% and 42% from the training time for ISTA-Net+ and COAST respectively. Moreover, when presented with a limited training dataset, the recursive models match or even outperform their respective non-recursive baseline. Codes and pretrained models are available at https://github.com/Rawwad-Alhejaili/Recursions-Are-All-You-Need .