Related papers: New upper bound on block sensitivity and certifica…
We consider objective evaluation measures of saliency explanations for complex black-box machine learning models. We propose simple robust variants of two notions that have been considered in recent literature: (in)fidelity, and…
In assignment problems, decision makers are often interested in not only the optimal assignment, but also the sensitivity of the optimal assignment to perturbations in the assignment weights. Typically, only perturbations to individual…
This paper studies the hazard-free formula complexity of Boolean functions. Our first result shows that unate functions are the only Boolean functions for which the monotone formula complexity of the hazard-derivative equals the hazard-free…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the…
We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…
In the sensitive distance oracle problem, there are three phases. We first preprocess a given directed graph $G$ with $n$ nodes and integer weights from $[-W,W]$. Second, given a single batch of $f$ edge insertions and deletions, we update…
The $CONGEST$ model for distributed network computing is well suited for analyzing the impact of limiting the throughput of a network on its capacity to solve tasks efficiently. For many "global" problems there exists a lower bound of…
The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth…
Circuit lower bounds are important since it is believed that a super-polynomial circuit lower bound for a problem in NP implies that P!=NP. Razborov has proved superpolynomial lower bounds for monotone circuits by using method of…
We show that there exists a Boolean function $F$ which observes the following separations among deterministic query complexity $(D(F))$, randomized zero error query complexity $(R_0(F))$ and randomized one-sided error query complexity…
We study the problem of certifying the robustness of Bayesian neural networks (BNNs) to adversarial input perturbations. Given a compact set of input points $T \subseteq \mathbb{R}^m$ and a set of output points $S \subseteq \mathbb{R}^n$,…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
Bose proved the inequality $b\geq v+r-1$ for resolvable balanced incomplete block designs (RBIBDs) and Kageyama improved it for RBIBDs which are not affine resolvable. In this note we prove a new lower bound on the number of blocks $b$ that…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
Multi-distribution learning extends agnostic Probably Approximately Correct (PAC) learning to the setting in which a family of $k$ distributions, $\{D_i\}_{i\in[k]}$, is considered and a classifier's performance is measured by its error…
Polynomial representations of Boolean functions over various rings such as $\mathbb{Z}$ and $\mathbb{Z}_m$ have been studied since Minsky and Papert (1969). From then on, they have been employed in a large variety of fields including…
A seminal result of Nisan and Szegedy (STOC, 1992) shows that for any total Boolean function, the degree of the real polynomial that computes the function, and the minimal degree of a real polynomial that point-wise approximates the…
Detection of correlation in a pair of random graphs is a fundamental statistical and computational problem that has been extensively studied in recent years. In this work, we consider a pair of correlated (sparse) stochastic block models…
We give two approximation algorithms solving the Stochastic Boolean Function Evaluation (SBFE) problem for symmetric Boolean functions. The first is an $O(\log n)$-approximation algorithm, based on the submodular goal-value approach of…