Related papers: Towards Large Certified Radius in Randomized Smoot…

Certified defenses such as randomized smoothing have shown promise towards building reliable machine learning systems against $\ell_p$-norm bounded attacks. However, existing methods are insufficient or unable to provably defend against…

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, which has the…

Providing formal guarantees of algorithmic fairness is of paramount importance to socially responsible deployment of machine learning algorithms. In this work, we study formal guarantees, i.e., certificates, for individual fairness (IF) of…

Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the…

As current computing capabilities increase, modern machine learning and computer vision system tend to increase in complexity, mostly by means of larger models and advanced optimization strategies. Although often neglected, in many problems…

This paper presents a novel Bayesian strategy for the estimation of smooth signals corrupted by Gaussian noise. The method assumes a smooth evolution of a succession of continuous signals that can have a numerical or an analytical…

We study finite-sum non-convex optimization $\min_{x\in\mathbb{R}^d} F(x) \;=\; \frac{1}{n}\sum_{i=1}^n f_i(x)$ and analyze a variance-reduced cubic Newton method based on EMA-smoothed SARAH estimators for both gradient and Hessian…

As ML models are increasingly deployed in critical applications, robustness against adversarial perturbations is crucial. While numerous defenses have been proposed to counter such attacks, they typically assume that all adversarial…

We introduce a clipping strategy for Stochastic Gradient Descent (SGD) which uses quantiles of the gradient norm as clipping thresholds. We prove that this new strategy provides a robust and efficient optimization algorithm for smooth…

This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

The growing reliance on artificial intelligence in safety- and security-critical applications is raising concerns about the robustness of neural networks to erroneous or adversarial input. Certification is a methodology for ensuring model…

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…

Backdoor attack is a severe security threat to deep neural networks (DNNs). We envision that, like adversarial examples, there will be a cat-and-mouse game for backdoor attacks, i.e., new empirical defenses are developed to defend against…

In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…

Surface roughness is an important quantity to many engineering and precision manufacturing disciplines. In this paper we investigate the problem of estimating the root-mean-square roughness of a sample by passive linear optical methods. By…

Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…

This work proposes a novel approach to reinforce localization security in wireless networks in the presence of malicious nodes that are able to manipulate (spoof) radio measurements. It substitutes the original measurement model by another…

In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…