Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification
Shiqi Wang, Huan Zhang, Kaidi Xu, Xue Lin, Suman Jana, Cho-Jui Hsieh, J. Zico Kolter
TL;DR
The paper tackles robust neural network verification by enabling complete BaB with efficient, GPU-friendly bound propagation. It introduces β-CROWN, which encodes neuron split constraints per neuron via optimizable β parameters, deriving bounds from both primal and dual perspectives and jointly optimizing intermediate-layer bounds. This yields substantially tighter relaxations than fixed LP relaxations and matches LP quality while maintaining the parallelism of bound propagation on GPUs; in complete verification, β-CROWN BaB achieves up to three orders of magnitude speedups over LP-based BaB, and in incomplete verification, it delivers higher verified accuracy with much lower runtimes compared to SDP and other strong verifiers. The approach also supports early stopping for efficient incomplete verification and secures strong performance on VNN-COMP 2021 benchmarks, backed by public code. Overall, β-CROWN offers a scalable, high-accuracy, GPU-accelerated path for both complete and incomplete robustness verification of neural networks.
Abstract
Bound propagation based incomplete neural network verifiers such as CROWN are very efficient and can significantly accelerate branch-and-bound (BaB) based complete verification of neural networks. However, bound propagation cannot fully handle the neuron split constraints introduced by BaB commonly handled by expensive linear programming (LP) solvers, leading to loose bounds and hurting verification efficiency. In this work, we develop $β$-CROWN, a new bound propagation based method that can fully encode neuron splits via optimizable parameters $β$ constructed from either primal or dual space. When jointly optimized in intermediate layers, $β$-CROWN generally produces better bounds than typical LP verifiers with neuron split constraints, while being as efficient and parallelizable as CROWN on GPUs. Applied to complete robustness verification benchmarks, $β$-CROWN with BaB is up to three orders of magnitude faster than LP-based BaB methods, and is notably faster than all existing approaches while producing lower timeout rates. By terminating BaB early, our method can also be used for efficient incomplete verification. We consistently achieve higher verified accuracy in many settings compared to powerful incomplete verifiers, including those based on convex barrier breaking techniques. Compared to the typically tightest but very costly semidefinite programming (SDP) based incomplete verifiers, we obtain higher verified accuracy with three orders of magnitudes less verification time. Our algorithm empowered the $α,\!β$-CROWN (alpha-beta-CROWN) verifier, the winning tool in VNN-COMP 2021. Our code is available at http://PaperCode.cc/BetaCROWN