mlsanityData to 13 Oct 2026

A Feedforward Unitary Equivariant Neural Network

arXiv 2208.12146 ↗First posted 25 Aug 2022cs.LGcited by 2

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Abstract (arXiv)

We devise a new type of feedforward neural network. It is equivariant with respect to the unitary group U(n). The input and output can be vectors in mathbbCn with arbitrary dimension n. No convolution layer is required in our implementation. We avoid errors due to truncated higher order terms in Fourier-like transformation. The implementation of each layer can be done efficiently using simple calculations. As a proof of concept, we have given empirical results on the prediction of the dynamics of atomic motion to demonstrate the practicality of our approach.

Key facts. Cited by 2 papers in the map (data through 13 Oct 2026). Builds on 17 of its 29 references that are in the map. First posted on arXiv 25 Aug 2022.

Builds on

17 of 29 references.

References · 17

  1. 2016Group Equivariant Convolutional Networkscited by 1,157
  2. 2021E(n) Equivariant Graph Neural Networkscited by 957
  3. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 739
  4. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  5. 2018Spherical CNNscited by 452
  6. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 350
  7. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 297
  8. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 246
  9. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 170
  10. 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 76
  11. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  12. 2015Neural Network with Unbounded Activation Functions is Universal Approximatorcited by 63
5 more
  1. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
  2. 2018N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentialscited by 42
  3. 20183D G-CNNs for Pulmonary Nodule Detectioncited by 36
  4. 2020Efficient Generalized Spherical CNNscited by 29
  5. 2021Rotation-Equivariant Deep Learning for Diffusion MRIcited by 20

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Precoder Learning by Leveraging Unitary Equivariance Propertycited by 0
  2. 2026On the Equivariant Learning of the Q-tensor Order Parametercited by 0