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Found 17 papers, 7 papers with code
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.
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.
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.
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).
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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).
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.
