Closing the Loop: Branch-and-Bound for Scalable Verification of Nonlinear Neural Feedback Systems

Despite recent advances in the verification of nonlinear neural feedback systems, scalability remains the central obstacle, as state-of-the-art solvers do not yet handle the network sizes and nonlinear dynamics of autonomy applications. Combinatorial solvers do not scale to large networks, whereas propagative solvers excessively sacrifice precision. This work seeks to improve the scalability of combinatorial solvers by formulating verification as branch-and-bound on an abstraction of the closed-loop system. We introduce rail, an interface that exposes polyhedral enclosures of the dynamics to LiRPA-style bound propagation, and clipper, a branch-and-bound algorithm that jointly refines enclosures and splits controller activations. This framework enables joint reasoning on the computational graph of the closed-loop system, preserving symbolic correlations across time steps. We present our construction and show that it yields significant improvements over the state of the art.