Efficient Neural Network Robustness Certification with General Activation Functions

Finding minimum distortion of adversarial examples and thus certifying robustness in neural network classifiers for given data points is known to be a challenging problem. Nevertheless, recently it has been shown to be possible to give a non-trivial certified lower bound of minimum adversarial distortion, and some recent progress has been made towards this direction by exploiting the piece-wise linear nature of ReLU activations. However, a generic robustness certification for general activation functions still remains largely unexplored. To address this issue, in this paper we introduce CROWN, a general framework to certify robustness of neural networks with general activation functions for given input data points. The novelty in our algorithm consists of bounding a given activation function with linear and quadratic functions, hence allowing it to tackle general activation functions including but not limited to four popular choices: ReLU, tanh, sigmoid and arctan. In addition, we facilitate the search for a tighter certified lower bound by adaptively selecting appropriate surrogates for each neuron activation. Experimental results show that CROWN on ReLU networks can notably improve the certified lower bounds compared to the current state-of-the-art algorithm Fast-Lin, while having comparable computational efficiency. Furthermore, CROWN also demonstrates its effectiveness and flexibility on networks with general activation functions, including tanh, sigmoid and arctan.Comment: Accepted by NIPS 2018. Huan Zhang and Tsui-Wei Weng contributed equall

CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networks

Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial distortion of neural networks (with ReLU activations) has been shown to be an NP-complete problem, obtaining a non-trivial lower bound of minimum distortion as a provable robustness guarantee is possible. However, most previous works only focused on simple fully-connected layers (multilayer perceptrons) and were limited to ReLU activations. This motivates us to propose a general and efficient framework, CNN-Cert, that is capable of certifying robustness on general convolutional neural networks. Our framework is general -- we can handle various architectures including convolutional layers, max-pooling layers, batch normalization layer, residual blocks, as well as general activation functions; our approach is efficient -- by exploiting the special structure of convolutional layers, we achieve up to 17 and 11 times of speed-up compared to the state-of-the-art certification algorithms (e.g. Fast-Lin, CROWN) and 366 times of speed-up compared to the dual-LP approach while our algorithm obtains similar or even better verification bounds. In addition, CNN-Cert generalizes state-of-the-art algorithms e.g. Fast-Lin and CROWN. We demonstrate by extensive experiments that our method outperforms state-of-the-art lower-bound-based certification algorithms in terms of both bound quality and speed.Comment: Accepted by AAAI 201