Alpha-Beta-CROWN verifier bridges neural networks and control theory

A new tutorial from researchers at UIUC and other institutions introduces alpha-beta-CROWN as a unified framework bridging control theory with state-of-the-art neural network verification. The verifier treats neural networks as computation graphs and produces certified output bounds along with explicit linear relaxations of the nonlinear functions. These bounds directly support reachability analysis and form the foundation for satisfiability checking and optimization routines. Crucially, the framework reduces many control problems—such as verifying Lyapunov conditions or stability inequalities—to bounding real-valued expressions over a state domain. By recursively partitioning and pruning subdomains based on computed bounds, alpha-beta-CROWN achieves scalable verification even for high-dimensional neural network controllers that traditional methods cannot handle.

The tutorial, accepted for ACC 2026, emphasizes GPU parallelization as the key enabler of this scalability. Unlike prior approaches tied to specific structural assumptions about the system or certificate format, alpha-beta-CROWN is general-purpose and can be applied to a wide range of control tasks (e.g., safety verification for autonomous driving, robotics, power systems). The authors provide step-by-step guidance on using the verifier’s bounding engine for control-specific problems, making formal verification more accessible to practitioners. This work directly addresses the growing need for rigorous guarantees in learning-based control, where empirical performance alone is insufficient for safety-critical deployments.