text:   Robustness",4,"['Check out our new work on ""Curse of Dimensionality on Randomized Smoothing"". This is a joint work with\xa0@tomgoldsteincs and\xa0@umdcs students\xa0Aounon Kumar and Alex Levine. \nPaper: <LINK>\nWe have three main results (see the sub-tweets): <LINK>', '(1) We show that the robustness radius of almost any i.i.d. smoothing distribution to defend against L_p attacks decreases as 1/(d^(1/2-1/p)). Note that unlike the standard case of L_2, for p&gt;2, this decreases with the input dimension d. https://t.co/Ssdu366X0y', '(2) Using an isotropic Gaussian smoothing as in\xa0Cohen @deepcohen , Kolter \n@zicokolte et al.\xa0is almost as good as any other\xa0i.i.d. smoothing distributions for p&gt;2 within a constant factor of the robustness radius. The gap becomes tighter by using generalized Gaussian dists https://t.co/HwBsTyRL8c', '(3) We show that for smoothing over an L_{\\infty} ball, this dependency to the input dimension d becomes worst as 1/d^(1-1/p) https://t.co/ih2ipb4CMB']",20,02,902