Oral
Towards Fast Computation of Certified Robustness for ReLU Networks
Tsui-Wei Weng · Huan Zhang · Hongge Chen · Zhao Song · Cho-Jui Hsieh · Luca Daniel · Duane Boning · Inderjit Dhillon

Thu Jul 12th 04:40 -- 04:50 PM @ A7

Verifying the robustness property of a general Rectified Linear Unit (ReLU) network is an NP-complete problem. Although finding the exact minimum adversarial distortion is hard, giving a certified lower bound of the minimum distortion is possible. Current available methods of computing such a bound are either time-consuming or deliver low quality bounds that are too loose to be useful. In this paper, we exploit the special structure of ReLU networks and provide two computationally efficient algorithms (Fast-Lin, Fast-Lip) that are able to certify non-trivial lower bounds of minimum adversarial distortions. Experiments show that (1) our methods deliver bounds close to (the gap is 2-3X) exact minimum distortions found by Reluplex in small networks while our algorithms are more than 10,000 times faster; (2) our methods deliver similar quality of bounds (the gap is within 35\% and usually around 10\%; sometimes our bounds are even better) for larger networks compared to the methods based on solving linear programming problems but our algorithms are 33-14,000 times faster; (3) our method is capable of solving large MNIST and CIFAR networks up to 7 layers with more than 10,000 neurons within tens of seconds on a single CPU core. In addition, we show that there is no polynomial time algorithm that can approximately find the minimum $\ell_1$ adversarial distortion of a ReLU network with a $0.99\ln n$ approximation ratio unless NP=P, where $n$ is the number of neurons in the network.

#### Author Information

##### Inderjit Dhillon (UT Austin & Amazon)

Inderjit Dhillon is the Gottesman Family Centennial Professor of Computer Science and Mathematics at UT Austin, where he is also the Director of the ICES Center for Big Data Analytics. His main research interests are in big data, machine learning, network analysis, linear algebra and optimization. He received his B.Tech. degree from IIT Bombay, and Ph.D. from UC Berkeley. Inderjit has received several awards, including the ICES Distinguished Research Award, the SIAM Outstanding Paper Prize, the Moncrief Grand Challenge Award, the SIAM Linear Algebra Prize, the University Research Excellence Award, and the NSF Career Award. He has published over 160 journal and conference papers, and has served on the Editorial Board of the Journal of Machine Learning Research, the IEEE Transactions of Pattern Analysis and Machine Intelligence, Foundations and Trends in Machine Learning and the SIAM Journal for Matrix Analysis and Applications. Inderjit is an ACM Fellow, an IEEE Fellow, a SIAM Fellow and an AAAS Fellow.