mlsanityData to 7 Oct 2026

Convolutional Neural Networks as 2-D systems

arXiv 2303.03042 ↗First posted 6 Mar 2023math.OC cs.LG cs.SYcited by 5

Not on the map. Why?

Abstract (arXiv)

This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of linear filters, is realized in state space as a linear time-invariant 2-D system. The overall convolutional Neural Network composed of convolutional layers and nonlinear activation functions is then viewed as a 2-D version of a Lur'e system, i.e., a linear dynamical system interconnected with static nonlinear components. One benefit of this 2-D Lur'e system perspective on CNNs is that we can use robust control theory much more efficiently for Lipschitz constant estimation than previously possible.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 31 of its 71 references that are in the map. First posted on arXiv 6 Mar 2023.

Builds on

31 of 71 references.

References · 31

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2016Layer Normalizationcited by 5,579
  3. 2013Intriguing properties of neural networkscited by 5,114
  4. 2014Fully Convolutional Networks for Semantic Segmentationcited by 4,845
  5. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  6. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  7. 2020Inductive Biases for Deep Learning of Higher-Level Cognitioncited by 273
  8. 2018Sorting out Lipschitz function approximationcited by 211
  9. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 178
  10. 2019On the Inductive Bias of Neural Tangent Kernelscited by 177
  11. 2019Orthogonal Convolutional Neural Networkscited by 122
  12. 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 100
19 more
  1. 2020Training robust neural networks using Lipschitz boundscited by 98
  2. 2020Pooling Methods in Deep Neural Networks, a Reviewcited by 52
  3. 2020Lipschitz Bounded Equilibrium Networkscited by 49
  4. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 43
  5. 2020Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllerscited by 42
  6. 2021Efficient-CapsNet: Capsule Network with Self-Attention Routingcited by 41
  7. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  8. 2020Imitation Learning with Stability and Safety Guaranteescited by 34
  9. 2021Pay attention to your loss: understanding misconceptions about 1-Lipschitz neural networkscited by 30
  10. 2019Deep neural networks, generic universal interpolation, and controlled ODEscited by 28
  11. 2020Approximating Lipschitz continuous functions with GroupSort neural networkscited by 27
  12. 2020Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimizationcited by 17
  13. 2021Semialgebraic Representation of Monotone Deep Equilibrium Models and Applications to Certificationcited by 16
  14. 2016Norm-preserving Orthogonal Permutation Linear Unit Activation Functions (OPLU)cited by 15
  15. 2022Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networkscited by 15
  16. 2022Lipschitz constant estimation for 1D convolutional neural networkscited by 13
  17. 2020Offset-free setpoint tracking using neural network controllerscited by 10
  18. 2020Large Norms of CNN Layers Do Not Hurt Adversarial Robustnesscited by 7
  19. 2021Linear systems with neural network nonlinearities: Improved stability analysis via acausal Zames-Falb multiplierscited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 0; 2026: 1.

5 papers.

  1. 2024Lipschitz constant estimation for general neural network architectures using control toolscited by 8
  2. 2024Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activationscited by 6
  3. 2024State space representations of the Roesser type for convolutional layerscited by 3
  4. 2024LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layerscited by 2
  5. 2026Convex training of Lipschitz-regularized shallow neural networkscited by 0