1 code implementation • 20 Oct 2020 • Alexander Levine, Aounon Kumar, Thomas Goldstein, Soheil Feizi
In this work, we show that there also exists a universal curvature-like bound for Gaussian random smoothing: given the exact value and gradient of a smoothed function, we compute a lower bound on the distance of a point to its closest adversarial example, called the Second-order Smoothing (SoS) robustness certificate.
no code implementations • 7 Aug 2016 • Thomas Goldstein, Paul Hand, Choongbum Lee, Vladislav Voroninski, Stefano Soatto
We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers.
no code implementations • 15 Oct 2015 • Bharat Singh, Soham De, Yangmuzi Zhang, Thomas Goldstein, Gavin Taylor
In this paper, we attempt to overcome the two above problems by proposing an optimization method for training deep neural networks which uses learning rates which are both specific to each layer in the network and adaptive to the curvature of the function, increasing the learning rate at low curvature points.
no code implementations • 1 Dec 2014 • Ali Ayremlou, Thomas Goldstein, Ashok Veeraraghavan, Richard Baraniuk
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition.