ReachNN: Reachability Analysis of Neural-Network Controlled Systems

TL;DR

ReachNN introduces a Bernstein polynomial-based reachability analysis method that verifies neural-network controlled systems with diverse activation functions, ensuring safety in dynamical systems.

Contribution

It presents a novel Bernstein polynomial approach for reachability analysis that handles a broader class of neural networks with multiple activation functions.

Findings

Effective verification on various benchmarks

Handles neural networks with heterogeneous activation functions

Provides theoretical and sampling-based error bounds

Abstract

Applying neural networks as controllers in dynamical systems has shown great promises. However, it is critical yet challenging to verify the safety of such control systems with neural-network controllers in the loop. Previous methods for verifying neural network controlled systems are limited to a few specific activation functions. In this work, we propose a new reachability analysis approach based on Bernstein polynomials that can verify neural-network controlled systems with a more general form of activation functions, i.e., as long as they ensure that the neural networks are Lipschitz continuous. Specifically, we consider abstracting feedforward neural networks with Bernstein polynomials for a small subset of inputs. To quantify the error introduced by abstraction, we provide both theoretical error bound estimation based on the theory of Bernstein polynomials and more practical sampling based error bound estimation, following a tight Lipschitz constant estimation approach based on forward reachability analysis. Compared with previous methods, our approach addresses a much broader set of neural networks, including heterogeneous neural networks that contain multiple types of activation functions. Experiment results on a variety of benchmarks show the effectiveness of our approach.