# Symmetry Structured Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2203.02056 · HTML: https://mlsanity.com/paper/2203.02056/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Session-based Recommendations with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06939/) (2015)
- [Personalized Top-N Sequential Recommendation via Convolutional Sequence Embedding](https://mlsanity.com/paper/1809.07426/) (2018)
- [CosRec: 2D Convolutional Neural Networks for Sequential Recommendation](https://mlsanity.com/paper/1908.09972/) (2019)
- [Structured Receptive Fields in CNNs](https://mlsanity.com/paper/1605.02971/) (2016)
- [Accurate De Novo Prediction of Protein Contact Map by Ultra-Deep Learning Model](https://mlsanity.com/paper/1609.00680/) (2016)
- [Learning rotation invariant convolutional filters for texture classification](https://mlsanity.com/paper/1604.06720/) (2016)
- [Rotation Equivariance and Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/1805.12301/) (2018)
- [Use of symmetric kernels for convolutional neural networks](https://mlsanity.com/paper/1805.09421/) (2018)
- [Transformationally Identical and Invariant Convolutional Neural Networks through Symmetric Element Operators](https://mlsanity.com/paper/1806.03636/) (2018)

## Built on by (most cited first, 2 of 2)

- [Physics-Informed Neural Networks and Sequence Encoder: Application to heating and early cooling of thermo-stamping process](https://mlsanity.com/paper/2603.26245/) (2026)
- [Leveraging Kernel Symmetry for Joint Compression and Error Mitigation in Edge Model Transfer](https://mlsanity.com/paper/2604.17371/) (2026)

## Abstract (arXiv)

We consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for a sequential recommendation problem, as well as secondary structure inference problems of RNA and protein sequences. We develop a CNN architecture that generates and preserves the symmetry structure in the network's convolutional layers. We present parameterizations for the convolutional kernels that produce update rules to maintain symmetry throughout the training. We apply this architecture to the sequential recommendation problem, the RNA secondary structure inference problem, and the protein contact map prediction problem, showing that the symmetric structured networks produce improved results using fewer numbers of machine parameters.