# 6DCNN with roto-translational convolution filters for volumetric data processing

arXiv: https://arxiv.org/abs/2107.12078 · HTML: https://mlsanity.com/paper/2107.12078/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 54 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 26 of 26)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [LieTransformer: Equivariant self-attention for Lie Groups](https://mlsanity.com/paper/2012.10885/) (2020)
- [Attentive Group Equivariant Convolutional Networks](https://mlsanity.com/paper/2002.03830/) (2020)
- [Group Equivariant Stand-Alone Self-Attention For Vision](https://mlsanity.com/paper/2010.00977/) (2020)
- [Effective Rotation-invariant Point CNN with Spherical Harmonics kernels](https://mlsanity.com/paper/1906.11555/) (2019)
- [Equivariant Graph Neural Networks for 3D Macromolecular Structure](https://mlsanity.com/paper/2106.03843/) (2021)
- [N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials](https://mlsanity.com/paper/1803.01588/) (2018)
- [Geometric Prediction: Moving Beyond Scalars](https://mlsanity.com/paper/2006.14163/) (2020)
- [Protein model quality assessment using rotation-equivariant, hierarchical neural networks](https://mlsanity.com/paper/2011.13557/) (2020)
- [Spherical convolutions on molecular graphs for protein model quality assessment](https://mlsanity.com/paper/2011.07980/) (2020)
- [Protein sequence-to-structure learning: Is this the end(-to-end revolution)?](https://mlsanity.com/paper/2105.07407/) (2021)

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

- [ILPO-NET: Network for the invariant recognition of arbitrary volumetric patterns in 3D](https://mlsanity.com/paper/2403.19612/) (2024)
- [On the Fourier analysis in the SO(3) space : EquiLoPO Network](https://mlsanity.com/paper/2404.15979/) (2024)

## Abstract (arXiv)

In this work, we introduce 6D Convolutional Neural Network (6DCNN) designed to tackle the problem of detecting relative positions and orientations of local patterns when processing three-dimensional volumetric data. 6DCNN also includes SE(3)-equivariant message-passing and nonlinear activation operations constructed in the Fourier space. Working in the Fourier space allows significantly reducing the computational complexity of our operations. We demonstrate the properties of the 6D convolution and its efficiency in the recognition of spatial patterns. We also assess the 6DCNN model on several datasets from the recent CASP protein structure prediction challenges. Here, 6DCNN improves over the baseline architecture and also outperforms the state of the art.