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Found 22 papers, 10 papers with code
Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming
Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control.
Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks
The resulting SDP can be adapted to increase either the estimation accuracy (by capturing the interaction between activation functions of different layers) or scalability (by decomposition and parallel implementation).
Probabilistic Verification and Reachability Analysis of Neural Networks via Semidefinite Programming
In this context, we discuss two relevant problems: (i) probabilistic safety verification, in which the goal is to find an upper bound on the probability of violating a safety specification; and (ii) confidence ellipsoid estimation, in which given a confidence ellipsoid for the input of the neural network, our goal is to compute a confidence ellipsoid for the output.
Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation.
Robust Deep Learning as Optimal Control: Insights and Convergence Guarantees
By interpreting the min-max problem as an optimal control problem, it has recently been shown that one can exploit the compositional structure of neural networks in the optimization problem to improve the training time significantly.
Enforcing robust control guarantees within neural network policies
When designing controllers for safety-critical systems, practitioners often face a challenging tradeoff between robustness and performance.
Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimization
Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness of feedback systems involving neural networks.
Learning Lyapunov Functions for Hybrid Systems
By designing the learner and the verifier according to the analytic center cutting-plane method from convex optimization, we show that when the set of Lyapunov functions is full-dimensional in the parameter space, our method finds a Lyapunov function in a finite number of steps.
Optimization and Control
Performance Bounds for Neural Network Estimators: Applications in Fault Detection
We exploit recent results in quantifying the robustness of neural networks to input variations to construct and tune a model-based anomaly detector, where the data-driven estimator model is provided by an autoregressive neural network.
On Centralized and Distributed Mirror Descent: Convergence Analysis Using Quadratic Constraints
Our numerical experiments on strongly convex problems indicate that our framework certifies superior convergence rates compared to the existing rates for distributed GD.
DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splitting
Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising alternative.
Learning Region of Attraction for Nonlinear Systems
Estimating the region of attraction (ROA) of general nonlinear autonomous systems remains a challenging problem and requires a case-by-case analysis.
Towards Understanding The Semidefinite Relaxations of Truncated Least-Squares in Robust Rotation Search
To induce robustness against outliers for rotation search, prior work considers truncated least-squares (TLS), which is a non-convex optimization problem, and its semidefinite relaxation (SDR) as a tractable alternative.
One-Shot Reachability Analysis of Neural Network Dynamical Systems
The arising application of neural networks (NN) in robotic systems has driven the development of safety verification methods for neural network dynamical systems (NNDS).
ReachLipBnB: A branch-and-bound method for reachability analysis of neural autonomous systems using Lipschitz bounds
We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings.
Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis.
Certified Invertibility in Neural Networks via Mixed-Integer Programming
Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network's output.
Certified Robustness via Dynamic Margin Maximization and Improved Lipschitz Regularization
As a result, there has been an increasing interest in developing training procedures that can directly manipulate the decision boundary in the input space.
Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation
Control Barrier Functions (CBFs) provide an elegant framework for designing safety filters for nonlinear control systems by constraining their trajectories to an invariant subset of a prespecified safe set.
Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees
With a convex formulation of the barrier function synthesis, we propose to first learn an empirically well-behaved NN basis function and then apply a fine-tuning algorithm that exploits the convexity and counterexamples from the verification failure to find a valid barrier function with finite-step termination guarantees: if there exist valid barrier functions, the fine-tuning algorithm is guaranteed to find one in a finite number of iterations.
Actor-Critic Physics-informed Neural Lyapunov Control
Crucial to our approach is the use of Zubov's Partial Differential Equation (PDE), which precisely characterizes the true region of attraction of a given control policy.
Gradient-Regularized Out-of-Distribution Detection
In this work, we propose the idea of leveraging the information embedded in the gradient of the loss function during training to enable the network to not only learn a desired OOD score for each sample but also to exhibit similar behavior in a local neighborhood around each sample.
