mlsanityData to 14 Oct 2026

Lipschitz-bounded 1D convolutional neural networks using the Cayley transform and the controllability Gramian

arXiv 2303.11835 ↗First posted 20 Mar 2023cs.LG cs.SY eess.SYcited by 9

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Abstract (arXiv)

We establish a layer-wise parameterization for 1D convolutional neural networks (CNNs) with built-in end-to-end robustness guarantees. In doing so, we use the Lipschitz constant of the input-output mapping characterized by a CNN as a robustness measure. We base our parameterization on the Cayley transform that parameterizes orthogonal matrices and the controllability Gramian of the state space representation of the convolutional layers. The proposed parameterization by design fulfills linear matrix inequalities that are sufficient for Lipschitz continuity of the CNN, which further enables unconstrained training of Lipschitz-bounded 1D CNNs. Finally, we train Lipschitz-bounded 1D CNNs for the classification of heart arrythmia data and show their improved robustness.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 20 of its 26 references that are in the map. First posted on arXiv 20 Mar 2023.

Builds on

20 of 26 references.

References · 20

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8 more
  1. 2023A Unified Algebraic Perspective on Lipschitz Neural Networkscited by 60
  2. 2023Direct Parameterization of Lipschitz-Bounded Deep Networkscited by 51
  3. 2020Lipschitz Bounded Equilibrium Networkscited by 49
  4. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 45
  5. 2021Pay attention to your loss: understanding misconceptions about 1-Lipschitz neural networkscited by 30
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 2; 2026: 2.

9 papers.

  1. 2024Lipschitz constant estimation for general neural network architectures using control toolscited by 8
  2. 2025An Adaptive Orthogonal Convolution Scheme for Efficient and Flexible CNN Architecturescited by 8
  3. 2024Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activationscited by 7
  4. 2024State space representations of the Roesser type for convolutional layerscited by 3
  5. 2025LipShiFT: A Certifiably Robust Shift-based Vision Transformercited by 3
  6. 2024LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layerscited by 2
  7. 2023Learning Stable and Robust Linear Parameter-Varying State-Space Modelscited by 1
  8. 2026Orthogonium : A Unified, Efficient Library of Orthogonal and 1-Lipschitz Building Blockscited by 0
  9. 2026LipSSM: Structurally Lipschitz-Bounded Cascaded State-Space Model via Metric Transfer between Consecutive SSM Layerscited by 0