Robust Convolution Neural ODEs via Contractivity-promoting regularization
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Abstract (arXiv)
Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems, and propose to use contraction theory to improve their robustness. For a contractive dynamical system two trajectories starting from different initial conditions converge to each other exponentially fast. Contractive Convolutional NODEs can enjoy increased robustness as slight perturbations of the features do not cause a significant change in the output. Contractivity can be induced during training by using a regularization term involving the Jacobian of the system dynamics. To reduce the computational burden, we show that it can also be promoted using carefully selected weight regularization terms for a class of NODEs with slope-restricted activation functions. The performance of the proposed regularizers is illustrated through benchmark image classification tasks on MNIST and FashionMNIST datasets, where images are corrupted by different kinds of noise and attacks.
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References · 29
- 2014Explaining and Harnessing Adversarial Examplescited by 7,364
- 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
- 2013Intriguing properties of neural networkscited by 5,155
- 2018Neural Ordinary Differential Equationscited by 3,779
- 2018Robustness May Be at Odds with Accuracycited by 880
- 2019Hamiltonian Neural Networkscited by 712
- 2015Distillation as a Defense to Adversarial Perturbations against Deep Neural Networkscited by 678
- 2017Stable Architectures for Deep Neural Networkscited by 341
- 2019Adversarial Attacks and Defenses in Images, Graphs and Text: A Reviewcited by 237
- 2020Feature Purification: How Adversarial Training Performs Robust Deep Learningcited by 107
- 2018Towards the first adversarially robust neural network model on MNISTcited by 104
- 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 101
17 more
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- 2021Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attackscited by 91
- 2019On Robustness of Neural Ordinary Differential Equationscited by 83
- 2021Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overviewcited by 45
- 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 44
- 2019Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularizationcited by 32
- 2020Stable Neural Flowscited by 25
- 2021Towards Robust Neural Networks via Close-loop Controlcited by 23
- 2020Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradientscited by 22
- 2021Robust Implicit Networks via Non-Euclidean Contractionscited by 20
- 2021Hamiltonian Deep Neural Networks Guaranteeing Non-vanishing Gradients by Designcited by 18
- 2019Contracting Implicit Recurrent Neural Networks: Stable Models with Improved Trainabilitycited by 17
- 2022Robust Classification using Contractive Hamiltonian Neural ODEscited by 13
- 2021Robustness Certificates for Implicit Neural Networks: A Mixed Monotone Contractive Approachcited by 8
- 2018NAIS-Net: Stable Deep Networks from Non-Autonomous Differential Equationscited by 7
- 2021Robustness against Adversarial Attacks in Neural Networks using Incremental Dissipativitycited by 7
- 2024Neural Exponential Stabilization of Control-affine Nonlinear Systemscited by 4
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