27 citations · 49 across the 9 of their papers we have counts for
8 papers · 1 filter
Mathematical Analysis of Adversarial Attacks
Zehao Dou, Stanley J. Osher, Bao Wang
In this paper, we analyze efficacy of the fast gradient sign method (FGSM) and the Carlini-Wagner's L2 (CW-L2) attack. We prove that, within a certain regime, the untargeted FGSM c…
Adversarial Defense via Data Dependent Activation Function and Total Variation Minimization
Bao Wang, Alex T. Lin, Wei Zhu +3
We improve the robustness of Deep Neural Net (DNN) to adversarial attacks by using an interpolating function as the output activation. This data-dependent activation remarkably imp…
Blended Coarse Gradient Descent for Full Quantization of Deep Neural Networks
Penghang Yin, Shuai Zhang, Jiancheng Lyu +3
Quantized deep neural networks (QDNNs) are attractive due to their much lower memory storage and faster inference speed than their regular full precision counterparts. To maintain…
Constrained dynamical optimal transport and its Lagrangian formulation
Wuchen Li, Stanley Osher
We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution…
Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach
Christian Parkinson, David Arnold, Andrea L. Bertozzi +2
We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a cont…
Generalized Proximal Smoothing for Phase Retrieval
Minh Pham, Penghang Yin, Arjun Rana +2
In this paper, we report the development of the generalized proximal smoothing (GPS) algorithm for phase retrieval of noisy data. GPS is a optimization-based algorithm, in which we…