Riemannian data-dependent randomized smoothing for neural networks certification
Certification of neural networks is an important and challenging problem that has been attracting the attention of the machine learning community since few years. In this paper, we focus on randomized smoothing (RS) which is considered as the state-of-the-art method to obtain certifiably robust neural networks. In particular, a new data-dependent RS technique called ANCER introduced recently can be used to certify ellipses with orthogonal axis near each input data of the neural network. In this work, we remark that ANCER is not invariant under rotation of input data and propose a new rotationally-invariant formulation of it which can certify ellipses without constraints on their axis. Our approach called Riemannian Data Dependant Randomized Smoothing (RDDRS) relies on information geometry techniques on the manifold of covariance matrices and can certify bigger regions than ANCER based on our experiments on the MNIST dataset.
Code (1)
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Data-Dependent Randomized Smoothing
Randomized smoothing is a recent technique that achieves state-of-art performance in training certifiably robust deep neural networks. While the smoothing family of distributions is often connected to the choice of the n…
Incremental Randomized Smoothing Certification
Randomized smoothing-based certification is an effective approach for obtaining robustness certificates of deep neural networks (DNNs) against adversarial attacks. This method constructs a smoothed DNN model and certifie…
Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework
Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning. However, most existing methods only leverage Gaussian smoothing nois…
ANCER: Anisotropic Certification via Sample-wise Volume Maximization
Randomized smoothing has recently emerged as an effective tool that enables certification of deep neural network classifiers at scale. All prior art on randomized smoothing has focused on isotropic $\ell_p$ certification…
Effects of Exponential Gaussian Distribution on (Double Sampling) Randomized Smoothing
Randomized Smoothing (RS) is currently a scalable certified defense method providing robustness certification against adversarial examples. Although significant progress has been achieved in providing defenses against $\…