Counterexample Guided Branching via Directional Relaxation Analysis in Complete Neural Network Verification
This work addresses the problem of efficient neural network verification for safety-critical applications, representing an incremental improvement over existing dataflow methods.
The paper tackled the computational complexity of verifying deep neural networks against adversarial perturbations by proposing DRG-BaB, a framework that uses directional relaxation gaps to prioritize branching, resulting in significant reductions in search tree size and verification time compared to baselines.
Deep Neural Networks demonstrate exceptional performance but remain vulnerable to adversarial perturbations, necessitating formal verification for safety-critical deployment. To address the computational complexity of this task, researchers often employ abstraction-refinement techniques that iteratively tighten an over-approximated model. While structural methods utilize Counterexample-Guided Abstraction Refine- ment, state-of-the-art dataflow verifiers typically rely on Branch-and-Bound to refine numerical convex relaxations. However, current dataflow approaches operate with blind refinement processes that rely on static heuristics and fail to leverage specific diagnostic information from verification failures. In this work, we argue that Branch-and-Bound should be reformulated as a Dataflow CEGAR loop where the spurious counterexample serves as a precise witness to local abstraction errors. We propose DRG-BaB, a framework that introduces the Directional Relaxation Gap heuristic to prioritize branching on neurons actively contributing to falsification in the abstract domain. By deriving a closed-form spurious counterexample directly from linear bounds, our method transforms generic search into targeted refinement. Experiments on high-dimensional benchmarks demonstrate that this approach significantly reduces search tree size and verification time compared to established baselines.