# Fit-LRP

Neural network verifiers usually treat the input domain as an axis-aligned box, yet reachability, obstacle-avoidance and neural Lyapunov certificates in cyber-physical systems often live on oblique or non-convex polytopes, where box bounds become very loose. Fit-LRP optimizes the final affine bound from LiRPA or α-CROWN exactly over the true polyhedral constraints inside branch-and-bound, replacing the box approximation with a sequence of small linear programs. On the ARCH-COMP spacecraft rendezvous benchmark and two neural Lyapunov benchmarks, branching on the hardest region drops, and single-core CPU verification runs faster than α-CROWN on a GPU.

Neural network verifiers usually treat the input domain as an axis-aligned box, yet reachability, obstacle-avoidance and neural Lyapunov certificates in cyber-physical systems often live on oblique or non-convex polytopes, where box bounds become very loose. Fit-LRP optimizes the final affine bound from LiRPA or α-CROWN exactly over the true polyhedral constraints inside branch-and-bound, replacing the box approximation with a sequence of small linear programs. On the ARCH-COMP spacecraft rendezvous benchmark and two neural Lyapunov benchmarks, branching on the hardest region drops, and single-core CPU verification runs faster than α-CROWN on a GPU.