FI-ODE: Certifiably Robust Forward Invariance in Neural ODEs
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Abstract (arXiv)
Forward invariance is a long-studied property in control theory that is used to certify that a dynamical system stays within some pre-specified set of states for all time, and also admits robustness guarantees (e.g., the certificate holds under perturbations). We propose a general framework for training and provably certifying robust forward invariance in Neural ODEs. We apply this framework to provide certified safety in robust continuous control. To our knowledge, this is the first instance of training Neural ODE policies with such non-vacuous certified guarantees. In addition, we explore the generality of our framework by using it to certify adversarial robustness for image classification.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 44 of its 63 references that are in the map. First posted on arXiv 30 Oct 2022.
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44 of 63 references.
References · 44
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,442
- 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
- 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
- 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
- 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
- 2019Differentiable Convex Optimization Layerscited by 458
- 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
- 2017Stable Architectures for Deep Neural Networkscited by 340
- 2019Control Barrier Functions: Theory and Applicationscited by 332
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- 2018Certified Defenses against Adversarial Examplescited by 305
- 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 261
- 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
- 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 224
- 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 193
- 2018Efficient Formal Safety Analysis of Neural Networkscited by 165
- 2022Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methodscited by 148
- 2020Neural Lyapunov Controlcited by 142
- 2019Branch and Bound for Piecewise Linear Neural Network Verificationcited by 138
- 2018A Dual Approach to Scalable Verification of Deep Networkscited by 125
- 2019A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networkscited by 124
- 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
- 2020Monotone operator equilibrium networkscited by 100
- 2021Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attackscited by 91
- 2019On Robustness of Neural Ordinary Differential Equationscited by 83
- 2019Robust Reinforcement Learning for Continuous Control with Model Misspecificationcited by 76
- 2021Lyapunov-stable neural-network controlcited by 66
- 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
- 2021CROP: Certifying Robust Policies for Reinforcement Learning through Functional Smoothingcited by 41
- 2020Enforcing robust control guarantees within neural network policiescited by 40
- 2019Policy Optimization for H2 Linear Control with H_∞ Robustness Guarantee: Implicit Regularization and Global Convergencecited by 39
- 2020Neural Certificates for Safe Control Policiescited by 35
- 2016Robustness of Control Barrier Functions for Safety Critical Controlcited by 29
- 2020On The Verification of Neural ODEs with Stochastic Guaranteescited by 24
- 2020Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradientscited by 22
- 2021Semialgebraic Representation of Monotone Deep Equilibrium Models and Applications to Certificationcited by 16
- 2022Reachability Analysis of a General Class of Neural Ordinary Differential Equationscited by 13
- 2022On the Forward Invariance of Neural ODEscited by 10
- 2022Near-optimal control of dynamical systems with neural ordinary differential equationscited by 9
- 2019H_∞ Model-free Reinforcement Learning with Robust Stability Guaranteecited by 7
- 2021No Need for Interactions: Robust Model-Based Imitation Learning using Neural ODEcited by 5
- 2022Neural Gaits: Learning Bipedal Locomotion via Control Barrier Functions and Zero Dynamics Policiescited by 2
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