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  1. Free, publicly-accessible full text available January 1, 2023
  2. Neural networks have become increasingly effective at many difficult machine learning tasks. However, the nonlinear and large-scale nature of neural networks makes them hard to analyze, and, therefore, they are mostly used as blackbox models without formal guarantees. This issue becomes even more complicated when neural networks are used in learning-enabled closed-loop systems, where a small perturbation can substantially impact the system being controlled. Therefore, it is of utmost importance to develop tools that can provide useful certificates of stability, safety, and robustness for neural network-driven systems.In this overview, we present a convex optimization framework for the analysis of neural networks. The main idea is to abstract hard-to-analyze components of a neural network (e.g., the nonlinear activation functions) with the formalism of quadratic constraints. This abstraction allows us to reason about various properties of neural networks (safety, robustness, generalization, stability in closed-loop settings, etc.) via semidefinite programming.
    Free, publicly-accessible full text available December 14, 2022
  3. Free, publicly-accessible full text available December 14, 2022
  4. 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. However, providing safety and stability guarantees for these systems is challenging due to the nonlinear and compositional structure of neural networks. In this paper, we propose a novel forward reachability analysis method for the safety verification of linear time-varying systems with neural networks in feedback interconnection. Our technical approach relies on abstracting the nonlinear activation functions by quadratic constraints, which leads to an outer-approximation of forward reachable sets of the closed-loop system. We show that we can compute these approximate reachable sets using semidefinite programming. We illustrate our method in a quadrotor example, in which we first approximate a nonlinear model predictive controller via a deep neural network and then apply our analysis tool to certify finite-time reachability and constraint satisfaction of the closed-loop system.
  5. This article addresses the problem of verifying the safety of autonomous systems with neural network (NN) controllers. We focus on NNs with sigmoid/tanh activations and use the fact that the sigmoid/tanh is the solution to a quadratic differential equation. This allows us to convert the NN into an equivalent hybrid system and cast the problem as a hybrid system verification problem, which can be solved by existing tools. Furthermore, we improve the scalability of the proposed method by approximating the sigmoid with a Taylor series with worst-case error bounds. Finally, we provide an evaluation over four benchmarks, including comparisons with alternative approaches based on mixed integer linear programming as well as on star sets.