Related papers: Testing Unateness of Real-Valued Functions
The pointer function of G{\"{o}}{\"{o}}s, Pitassi and Watson \cite{DBLP:journals/eccc/GoosP015a} and its variants have recently been used to prove separation results among various measures of complexity such as deterministic, randomized and…
We revisit the relation between two fundamental property testing models for bounded-degree directed graphs: the bidirectional model in which the algorithms are allowed to query both the outgoing edges and incoming edges of a vertex, and the…
The sensitivity of a Boolean function f is the maximum over all inputs x, of the number of sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan and Szegedy) states that every sensitivity-s Boolean…
The {\em Total Influence} ({\em Average Sensitivity) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influence of a monotone Boolean function \ifnum\plusminus=1 $f: \{\pm1\}^n…
The randomized query complexity $R(f)$ of a boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is famously characterized (via Yao's minimax) by the least number of queries needed to distinguish a distribution $D_0$ over $0$-inputs from a…
We show examples of total Boolean functions that depend on $n$ variables and have spectral sensitivity $\Theta(\sqrt{\log n})$, which is asymptotically minimal. Our main new function combines the Hamming code with the Boolean address…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
In this paper we analyse the complexity of boolean functions takes value 0 on a sufficiently small number of points. For many functions this leads to the analysis of a single function attains 0 only on unsigned representation of numbers…
Test functions are important to validate new optimization algorithms and to compare the performance of various algorithms. There are many test functions in the literature, but there is no standard list or set of test functions one has to…
We show that, for almost all N-variable Boolean functions f, at least N/4-O(\sqrt{N} log N) queries are required to compute f in quantum black-box model with bounded error.
In the setup of i.i.d.~observations and a real valued differentiable functional~$T$, locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of~$T$)and for the confidence probability of…
We investigate the width complexity of nondeterministic unitary OBDDs (NUOBDDs). Firstly, we present a generic lower bound on their widths based on the size of strong 1-fooling sets. Then, we present classically cheap functions that are…
We present two new results about exact learning by quantum computers. First, we show how to exactly learn a $k$-Fourier-sparse $n$-bit Boolean function from $O(k^{1.5}(\log k)^2)$ uniform quantum examples for that function. This improves…
A key element of understanding the efficacy of overparameterized neural networks is characterizing how they represent functions as the number of weights in the network approaches infinity. In this paper, we characterize the norm required to…
Let $f:\{0,1\}^n \rightarrow \{0,1\}$ be a Boolean function. The certificate complexity $C(f)$ is a complexity measure that is quadratically tight for the zero-error randomized query complexity $R_0(f)$: $C(f) \leq R_0(f) \leq C(f)^2$. In…
Given a non-negative $n \times n$ matrix viewed as a set of distances between $n$ points, we consider the property testing problem of deciding if it is a metric. We also consider the same problem for two special classes of metrics, tree…
We prove that the most natural low-degree test for polynomials over finite fields is ``robust'' in the high-error regime for linear-sized fields. Specifically we consider the ``local'' agreement of a function $f: \mathbb{F}_q^m \to…
We investigate the randomized decision tree complexity of a specific class of read-once threshold functions. A read-once threshold formula can be defined by a rooted tree, every internal node of which is labeled by a threshold function…
We prove that for certain positive operators $T$, such as the Hardy-Littlewood maximal function and fractional integrals, there is a constant $D>1$, depending only on the dimension $n$, such that the two weight norm inequality…
Deep neural networks have significantly contributed to the success in predictive accuracy for classification tasks. However, they tend to make over-confident predictions in real-world settings, where domain shifting and out-of-distribution…