mlsanityData to 14 Oct 2026

On the Implicit Bias of Linear Equivariant Steerable Networks

arXiv 2303.04198 ↗First posted 7 Mar 2023cs.LG math.OCcited by 7

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Abstract (arXiv)

We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action. Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation. Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 28 of its 31 references that are in the map. First posted on arXiv 7 Mar 2023.

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28 of 31 references.

References · 28

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  2. 2016Group Equivariant Convolutional Networkscited by 1,165
  3. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 787
  4. 2017The Implicit Bias of Gradient Descent on Separable Datacited by 655
  5. 2018Gradient Descent Finds Global Minima of Deep Neural Networkscited by 574
  6. 2019General E(2)-Equivariant Steerable CNNscited by 446
  7. 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 426
  8. 2019Gradient Descent Maximizes the Margin of Homogeneous Neural Networkscited by 320
  9. 2016Steerable CNNscited by 305
  10. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 295
  11. 2018Characterizing Implicit Bias in Terms of Optimization Geometrycited by 266
  12. 2018Implicit Bias of Gradient Descent on Linear Convolutional Networkscited by 251
16 more
  1. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  2. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 194
  3. 2019Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limitcited by 187
  4. 2018Gradient descent aligns the layers of deep linear networkscited by 182
  5. 2020Directional convergence and alignment in deep learningcited by 178
  6. 2019Scale-Equivariant Steerable Networkscited by 110
  7. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 91
  8. 2022On the Implicit Bias in Deep-Learning Algorithmscited by 86
  9. 2020A Unifying View on Implicit Bias in Training Linear Neural Networkscited by 75
  10. 2018Stochastic Gradient Descent on Separable Data: Exact Convergence with a Fixed Learning Ratecited by 64
  11. 2016Generalization Error of Invariant Classifierscited by 42
  12. 2019Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature Spacescited by 34
  13. 2021Implicit Bias of Linear Equivariant Networkscited by 19
  14. 2019Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filterscited by 18
  15. 2018RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networkscited by 17
  16. 2013Learning Theory and Algorithms for Revenue Optimization in Second-Price Auctions with Reservecited by 16

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 2; 2026: 2.

7 papers.

  1. 2023Optimization Dynamics of Equivariant and Augmented Neural Networkscited by 18
  2. 2024On the hardness of learning under symmetriescited by 13
  3. 2024Ensembles provably learn equivariance through data augmentationcited by 8
  4. 2025Data Augmentation and Regularization for Learning Group Equivariancecited by 3
  5. 2025Statistical Learning Guarantees for Group-Invariant Barron Functionscited by 1
  6. 2026Conservation Laws from Data Symmetry in Neural Networkscited by 1
  7. 2026Equivariance and Augmentation for Bayesian Neural Networkscited by 0