Linearity Grafting: Relaxed Neuron Pruning Helps Certifiable Robustness

Certifiable robustness is a highly desirable property for adopting deep neural networks (DNNs) in safety-critical scenarios, but often demands tedious computations to establish. The main hurdle lies in the massive amount of non-linearity in large DNNs. To trade off the DNN expressiveness (which calls for more non-linearity) and robustness certification scalability (which prefers more linearity), we propose a novel solution to strategically manipulate neurons, by "grafting" appropriate levels of linearity. The core of our proposal is to first linearize insignificant ReLU neurons, to eliminate the non-linear components that are both redundant for DNN performance and harmful to its certification. We then optimize the associated slopes and intercepts of the replaced linear activations for restoring model performance while maintaining certifiability. Hence, typical neuron pruning could be viewed as a special case of grafting a linear function of the fixed zero slopes and intercept, that might overly restrict the network flexibility and sacrifice its performance. Extensive experiments on multiple datasets and network backbones show that our linearity grafting can (1) effectively tighten certified bounds; (2) achieve competitive certifiable robustness without certified robust training (i.e., over 30% improvements on CIFAR-10 models); and (3) scale up complete verification to large adversarially trained models with 17M parameters. Codes are available at https://github.com/VITA-Group/Linearity-Grafting.