mlsanityData to 7 Oct 2026

Bispectral Neural Networks

arXiv 2209.03416 ↗First posted 7 Sep 2022cs.LGcited by 17

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Abstract (arXiv)

We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the space over which a signal is defined. The model incorporates the ansatz of the bispectrum, an analytically defined group invariant that is complete -- that is, it preserves all signal structure while removing only the variation due to group actions. Here, we demonstrate that BNNs are able to simultaneously learn groups, their irreducible representations, and corresponding equivariant and complete-invariant maps purely from the symmetries implicit in data. Further, we demonstrate that the completeness property endows these networks with strong invariance-based adversarial robustness. This work establishes Bispectral Neural Networks as a powerful computational primitive for robust invariant representation learning

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Builds on 21 of its 61 references that are in the map. First posted on arXiv 7 Sep 2022.

Builds on

21 of 61 references.

References · 21

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  4. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  5. 2016Group Equivariant Convolutional Networkscited by 1,154
  6. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
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  11. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  12. 2019Approximating CNNs with Bag-of-local-Features models works surprisingly well on ImageNetcited by 260
9 more
  1. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  2. 2017Deep Complex Networkscited by 215
  3. 2018Excessive Invariance Causes Adversarial Vulnerabilitycited by 66
  4. 2020PyTorch Metric Learningcited by 57
  5. 2018Covariant Compositional Networks For Learning Graphscited by 54
  6. 2014Learning the Irreducible Representations of Commutative Lie Groupscited by 41
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  8. 2020Disentangling images with Lie group transformations and sparse codingcited by 14
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 6; 2024: 4; 2025: 5; 2026: 2.

17 papers.

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  1. 2024Pre-trained Large Language Models Use Fourier Features to Compute Additioncited by 38
  2. 2023Harmonics of Learning: Universal Fourier Features Emerge in Invariant Networkscited by 23
  3. 2023On genuine invariance learning without weight-tyingcited by 13
  4. 2024On the Ability of Deep Networks to Learn Symmetries from Data: A Neural Kernel Theorycited by 10
  5. 2023A polar prediction model for learning to represent visual transformationscited by 6
  6. 2023Learning Lie Group Symmetry Transformations with Neural Networkscited by 6
  7. 2023A General Framework for Robust G-Invariance in G-Equivariant Networkscited by 5
  8. 2024The Selective G-Bispectrum and its Inversion: Applications to G-Invariant Networkscited by 5
  9. 2024Learning Symmetries via Weight-Sharing with Doubly Stochastic Tensorscited by 5
  10. 2025Learning Equivariant Functions via Quadratic Formscited by 2
  11. 2025Selective Disk Bispectrum: A Complete and Rotation Invariant Image Descriptorcited by 1
  12. 2025A Differentiable Measure of Algebraic Complexity: Provably Exact Discovery of Group Structurescited by 1
5 more
  1. 2023Learning Linear Groups in Neural Networkscited by 0
  2. 2025Bispectral OT: Dataset Comparison using Symmetry-Aware Optimal Transportcited by 0
  3. 2025Interpretable Discovery of One-parameter Subgroups: A Modular Framework for Elliptical, Hyperbolic, and Parabolic Symmetriescited by 0
  4. 2026Spectral Discovery of Continuous Symmetries via Generalized Fourier Transformscited by 0
  5. 2026bispectrum: Selective G-Bispectra Made Practicalcited by 0