Shrink & Cert: Bi-level Optimization for Certified Robustness

In this paper, we advance the concept of shrinking weights to train certifiably robust models from the fresh perspective of gradient-based bi-level optimization. Lack of robustness against adversarial attacks remains a challenge in safety-critical applications. Many attempts have been made in literature which only provide empirical verification of the defenses to certain attacks and can be easily broken. Methods in other lines of work can only develop certified guarantees of the model robustness in limited scenarios and are computationally expensive. We present a weight shrinkage formulation that is computationally inexpensive and can be solved as a simple first-order optimization problem. We show that model trained with our method has lower Lipschitz bounds in each layer, which directly provides formal guarantees on the certified robustness. We demonstrate that our approach, Shrink \& Cert (SaC) achieves provably robust networks which simultaneously give excellent standard and robust accuracy. We demonstrate the success of our approach on CIFAR-10 and ImageNet datasets and compare them with existing robust training techniques. Code : \url{https://github.com/sagarverma/BiC}