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We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…

Machine Learning · Computer Science 2025-04-29 Stanislav Semenov

Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…

Probability · Mathematics 2024-02-15 A. D. Barbour , Nathan Ross , Guangqu Zheng

Heavy-tailed noise is pervasive in modern machine learning applications, arising from data heterogeneity, outliers, and non-stationary stochastic environments. While second-order methods can significantly accelerate convergence in…

Optimization and Control · Mathematics 2025-10-14 Abdurakhmon Sadiev , Peter Richtárik , Ilyas Fatkhullin

Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…

Machine Learning · Computer Science 2012-03-19 Kaizhu Huang , Rong Jin , Zenglin Xu , Cheng-Lin Liu

We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…

Optimization and Control · Mathematics 2024-03-27 Shuyao Li , Stephen J. Wright

We derive an online learning algorithm with improved regret guarantees for `easy' loss sequences. We consider two types of `easiness': (a) stochastic loss sequences and (b) adversarial loss sequences with small effective range of the…

Machine Learning · Computer Science 2019-08-28 Tobias Sommer Thune , Yevgeny Seldin

We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…

Optimization and Control · Mathematics 2026-02-03 Ruyu Wang , Chao Zhang

Several recent results provide theoretical insights into the phenomena of adversarial examples. Existing results, however, are often limited due to a gap between the simplicity of the models studied and the complexity of those deployed in…

Machine Learning · Computer Science 2021-01-05 Jeremias Sulam , Ramchandran Muthukumar , Raman Arora

A new, fast second-order method is proposed that achieves the optimal $\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-3/2}\right)$ complexity to obtain first-order $\epsilon$-stationary points. Crucially, this is deduced without assuming the…

Optimization and Control · Mathematics 2026-02-18 Serge Gratton , Sadok Jerad , Philippe L. Toint

We address the problem of Gaussian Process (GP) optimization in the presence of unknown and potentially varying adversarial perturbations. Unlike traditional robust optimization approaches that focus on maximizing performance under…

Machine Learning · Computer Science 2025-12-12 Artun Saday , Yaşar Cahit Yıldırım , Cem Tekin

Post-hoc attribution methods aim to explain deep learning predictions by highlighting influential input pixels. However, these explanations are highly non-robust: small, imperceptible input perturbations can drastically alter the…

Machine Learning · Computer Science 2025-06-19 Alaa Anani , Tobias Lorenz , Mario Fritz , Bernt Schiele

We derive upper bounds on the Wasserstein distance ($W_1$), with respect to $\sup$-norm, between any continuous $\mathbb{R}^d$ valued random field indexed by the $n$-sphere and the Gaussian, based on Stein's method. We develop a novel…

Probability · Mathematics 2024-05-02 Krishnakumar Balasubramanian , Larry Goldstein , Nathan Ross , Adil Salim

Predictions of certifiably robust classifiers remain constant in a neighborhood of a point, making them resilient to test-time attacks with a guarantee. In this work, we present a previously unrecognized threat to robust machine learning…

Machine Learning · Computer Science 2021-03-31 Akshay Mehra , Bhavya Kailkhura , Pin-Yu Chen , Jihun Hamm

Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown, in applications such as domain adaptation, to provide performances…

Machine Learning · Computer Science 2021-10-22 Alain Rakotomamonjy , Mokhtar Z. Alaya , Maxime Berar , Gilles Gasso

The threat of adversarial examples has motivated work on training certifiably robust neural networks to facilitate efficient verification of local robustness at inference time. We formalize a notion of global robustness, which captures the…

Machine Learning · Computer Science 2021-06-15 Klas Leino , Zifan Wang , Matt Fredrikson

We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…

Data Structures and Algorithms · Computer Science 2025-09-29 Aditya Bhaskara , Eric Evert , Vaidehi Srinivas , Aravindan Vijayaraghavan

Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog"…

Data Structures and Algorithms · Computer Science 2018-08-13 Oren Mangoubi , Nisheeth K. Vishnoi

Recent works have shown the effectiveness of randomized smoothing as a scalable technique for building neural network-based classifiers that are provably robust to $\ell_2$-norm adversarial perturbations. In this paper, we employ…

Machine Learning · Computer Science 2020-01-13 Hadi Salman , Greg Yang , Jerry Li , Pengchuan Zhang , Huan Zhang , Ilya Razenshteyn , Sebastien Bubeck

Recently, few certified defense methods have been developed to provably guarantee the robustness of a text classifier to adversarial synonym substitutions. However, all existing certified defense methods assume that the defenders are…

Computation and Language · Computer Science 2021-07-27 Jiehang Zeng , Xiaoqing Zheng , Jianhan Xu , Linyang Li , Liping Yuan , Xuanjing Huang

Reachability analysis of neural networks, which seeks to compute or bound the set of outputs attainable over a given input domain, is central to certifying safety and robustness in learning-enabled physical systems. Since exact reachable…

Machine Learning · Computer Science 2026-05-12 Taha Entesari , Mahyar Fazlyab