Related papers: The Cost of Compression: Tight Quadratic Black-Box…
CountSketch is a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering $\ell_2$-heavy hitters of a vector (entries with $v[i]^2 \geq…
We introduce a novel technique for ``lifting'' dimension lower bounds for linear sketches in the real-valued setting to dimension lower bounds for linear sketches with polynomially-bounded integer entries when the input is a…
The majority of streaming problems are defined and analyzed in a static setting, where the data stream is any worst-case sequence of insertions and deletions that is fixed in advance. However, many real-world applications require a more…
CountSketch and Feature Hashing (the "hashing trick") are popular randomized dimensionality reduction methods that support recovery of $\ell_2$-heavy hitters (keys $i$ where $v_i^2 > \epsilon \|\boldsymbol{v}\|_2^2$) and approximate inner…
Cardinality sketches are compact data structures for representing sets or vectors. These sketches are space-efficient, typically requiring only logarithmic storage in the input size, and enable approximation of cardinality (or the number of…
Traditional decision-based black-box adversarial attacks on image classifiers aim to generate adversarial examples by slightly modifying input images while keeping the number of queries low, where each query involves sending an input to the…
Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…
Linear sketches are powerful algorithmic tools that turn an n-dimensional input into a concise lower-dimensional representation via a linear transformation. Such sketches have seen a wide range of applications including norm estimation over…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
Deep neural networks are susceptible to adversarial inputs and various methods have been proposed to defend these models against adversarial attacks under different perturbation models. The robustness of models to adversarial attacks has…
Cardinality sketches are popular data structures that enhance the efficiency of working with large data sets. The sketches are randomized representations of sets that are only of logarithmic size but can support set merges and approximate…
Neural networks have been shown to be vulnerable against minor adversarial perturbations of their inputs, especially for high dimensional data under $\ell_\infty$ attacks. To combat this problem, techniques like adversarial training have…
Linear algebraic operations are ubiquitous in engineering applications, and arise often in a variety of fields including statistical signal processing and machine learning. With contemporary large datasets, to perform linear algebraic…
Adversarial examples are known as carefully perturbed images fooling image classifiers. We propose a geometric framework to generate adversarial examples in one of the most challenging black-box settings where the adversary can only…
In the subspace sketch problem one is given an $n\times d$ matrix $A$ with $O(\log(nd))$ bit entries, and would like to compress it in an arbitrary way to build a small space data structure $Q_p$, so that for any given $x \in \mathbb{R}^d$,…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
Deep neural networks are vulnerable to adversarial attacks. White-box adversarial attacks can fool neural networks with small adversarial perturbations, especially for large size images. However, keeping successful adversarial perturbations…
It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even…
Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in machine learning applications. However, sketching large…
We present a new approach for computing compact sketches that can be used to approximate the inner product between pairs of high-dimensional vectors. Based on the Weighted MinHash algorithm, our approach admits strong accuracy guarantees…