Lookahead Branching for Neural Network Verification

Neural network verification relies on branch-and-bound (BaB) algorithms to prove properties about network behavior. A critical component of BaB is the branching heuristic, which determines the order in which neurons are split. Most existing heuristics rely on local, immediate information, which can lead to inefficient search paths. This paper investigates whether investing more computational effort into 'lookahead'—simulating potential future branching decisions—can improve the overall efficiency of the verification process.

The authors propose a unified lookahead branching template that can be integrated into any BaB-based verifier. The process involves three main steps: (1) pre-selecting a subset of promising unstable neurons to reduce computational cost, (2) simulating splits on these candidates up to a specified depth, and (3) aggregating the results using a scoring function to choose the best branch.

Crucially, the framework also identifies 'lemmas'—tightened variable bounds discovered during simulation—that can be used to prune the search space further. The authors demonstrate the flexibility of this approach by implementing it in two distinct, state-of-the-art verifiers: Marabou (a CPU-based SMT solver) and alpha-beta-CROWN (a GPU-accelerated bound-propagation solver).

Lookahead branching consistently improves verification performance across diverse benchmarks. By simulating the cascading effects of branching decisions, the solver avoids poor choices that would otherwise lead to duplicated effort. The authors report that their method leads to significant speedups and increases the number of solved instances by up to 57% compared to existing state-of-the-art heuristics like Filtered Smart Branching (FSB). The study also confirms that the benefits are most pronounced when lookahead is applied at the top of the search tree, where branching decisions have the greatest impact on the downstream search space.