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Randomized smoothing has been shown to provide good certified-robustness guarantees for high-dimensional classification problems. It uses the probabilities of predicting the top two most-likely classes around an input point under a…
It is well-known that classifiers are vulnerable to adversarial perturbations. To defend against adversarial perturbations, various certified robustness results have been derived. However, existing certified robustnesses are limited to…
Uncertainty quantification is necessary for developers, physicians, and regulatory agencies to build trust in machine learning predictors and improve patient care. Beyond measuring uncertainty, it is crucial to express it in clinically…
In this article, we investigate the physical implications of the causality constraint via effective sound speed $c_s(\leq 1)$ on Quantum Circuit Complexity(QCC) in the framework of Cosmological Effective Field Theory (COSMOEFT) using the…
Safety is a critical property for control systems in medicine, transportation, manufacturing, and other applications, and can be defined as ensuring positive invariance of a predefined safe set. This paper investigates the problems of…
The classical Yao principle states that the complexity R_epsilon(f) of an optimal randomized algorithm for a function f with success probability 1-epsilon equals the complexity max_mu D_epsilon^mu(f) of an optimal deterministic algorithm…
The rapid growth of deep learning applications in real life is accompanied by severe safety concerns. To mitigate this uneasy phenomenon, much research has been done providing reliable evaluations of the fragility level in different deep…
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, i.e. one…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
A fundamental task in any physical theory is to quantify certain physical quantity in a meaningful way. In this paper we show that both fidelity distance and affinity distance satisfy the strong contractibility, and the corresponding…
The article studies edge coverage for control flow graphs extended with explicit constraints. Achieving a given level of white-box coverage for a given code is a classic problem in software testing. We focus on designing test sets that…
Aggregate object detection metrics inherently mask catastrophic and repeatable failures in operationally critical, long-tail minority classes. This paper formally defines this pervasive vulnerability as the Hard-Category Reliability Problem…
While significant progress has been made in specifying neural networks capable of representing uncertainty, deep networks still often suffer from overconfidence and misaligned predictive distributions. Existing approaches for measuring this…
We determine the exact freezing threshold, r^f, for a family of models of random boolean constraint satisfaction problems, including NAE-SAT and hypergraph 2-colouring, when the constraint size is sufficiently large. If the…
Clustering algorithms are widely used in many societal resource allocation applications, such as loan approvals and candidate recruitment, among others, and hence, biased or unfair model outputs can adversely impact individuals that rely on…
We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary $W$ that is implementable in the absence of error, we prove that the worst-case (and hence…
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$, $\bullet \quad \mathrm{deg}(f) = O(\widetilde{\mathrm{deg}}(f)^2)$: The degree of $f$ is at most quadratic in the approximate degree of $f$.…
Let $A$ be an $s$-sparse Hermitian matrix, $f(x)$ be a univariate function, and $i, j$ be two indices. In this work, we investigate the query complexity of approximating $\bra{i} f(A) \ket{j}$. We show that for any continuous function…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
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…