Related papers: A Direct Reduction from the Polynomial to the Adve…

We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove…

An adversary is essentially an algorithm intent on making a classification system perform in some particular way given an input, e.g., increase the probability of a false negative. Recent work builds adversaries for deep learning systems…

We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a…

We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new…

A dynamic algorithm against an adaptive adversary is required to be correct when the adversary chooses the next update after seeing the previous outputs of the algorithm. We obtain faster dynamic algorithms against an adaptive adversary and…

We give a general method for proving quantum lower bounds for problems with small range. Namely, we show that, for any symmetric problem defined on functions $f:\{1, ..., N\}\to\{1, ..., M\}$, its polynomial degree is the same for all…

Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number. The proof then follows by arguing the minimum value is…

Despite ongoing research on the topic of adversarial examples in deep learning for computer vision, some fundamentals of the nature of these attacks remain unclear. As the manifold hypothesis posits, high-dimensional data tends to be part…

We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…

Adversarial machine learning concerns situations in which learners face attacks from active adversaries. Such scenarios arise in applications such as spam email filtering, malware detection and fake image generation, where security methods…

In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…

Differentially private (DP) machine learning allows us to train models on private data while limiting data leakage. DP formalizes this data leakage through a cryptographic game, where an adversary must predict if a model was trained on a…

Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…

The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…

Powerful adversarial attack methods are vital for understanding how to construct robust deep neural networks (DNNs) and for thoroughly testing defense techniques. In this paper, we propose a black-box adversarial attack algorithm that can…

Low-degree polynomials have emerged as a powerful paradigm for providing evidence of statistical-computational gaps across a variety of high-dimensional statistical models [Wein25]. For detection problems -- where the goal is to test a…

Current neural-network-based classifiers are susceptible to adversarial examples. The most empirically successful approach to defending against such adversarial examples is adversarial training, which incorporates a strong self-attack…

Over recent years, devising classification algorithms that are robust to adversarial perturbations has emerged as a challenging problem. In particular, deep neural nets (DNNs) seem to be susceptible to small imperceptible changes over test…

Adversarial learning can learn fairer and less biased models of language than standard methods. However, current adversarial techniques only partially mitigate model bias, added to which their training procedures are often unstable. In this…

Despite the great achievements of the modern deep neural networks (DNNs), the vulnerability/robustness of state-of-the-art DNNs raises security concerns in many application domains requiring high reliability. Various adversarial attacks are…