# Learning unfolded networks with a cyclic group structure

arXiv: https://arxiv.org/abs/2211.09238 · HTML: https://mlsanity.com/paper/2211.09238/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 16 Nov 2022.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Coarse-to-Fine Volumetric Prediction for Single-Image 3D Human Pose](https://mlsanity.com/paper/1611.07828/) (2016)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [Exploiting Cyclic Symmetry in Convolutional Neural Networks](https://mlsanity.com/paper/1602.02660/) (2016)
- [Spin-Weighted Spherical CNNs](https://mlsanity.com/paper/2006.10731/) (2020)
- [Simple, Efficient, and Neural Algorithms for Sparse Coding](https://mlsanity.com/paper/1503.00778/) (2015)
- [On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural Networks](https://mlsanity.com/paper/1806.00701/) (2018)
- [Rethinking the CSC Model for Natural Images](https://mlsanity.com/paper/1909.05742/) (2019)

## Abstract (arXiv)

Deep neural networks lack straightforward ways to incorporate domain knowledge and are notoriously considered black boxes. Prior works attempted to inject domain knowledge into architectures implicitly through data augmentation. Building on recent advances on equivariant neural networks, we propose networks that explicitly encode domain knowledge, specifically equivariance with respect to rotations. By using unfolded architectures, a rich framework that originated from sparse coding and has theoretical guarantees, we present interpretable networks with sparse activations. The equivariant unfolded networks compete favorably with baselines, with only a fraction of their parameters, as showcased on (rotated) MNIST and CIFAR-10.