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of 684
pro vyhledávání: '"P. Nadimpalli"'
We consider the problem of testing whether an unknown and arbitrary set $S \subseteq \mathbb{R}^n$ (given as a black-box membership oracle) is convex, versus $\varepsilon$-far from every convex set, under the standard Gaussian distribution. The curre
Externí odkaz:
http://arxiv.org/abs/2410.17958
Autor:
Chen, Xi, De, Anindya, Huang, Yizhi, Li, Yuhao, Nadimpalli, Shivam, Servedio, Rocco A., Yang, Tianqi
The standard model of Boolean function property testing is not well suited for testing $\textit{sparse}$ functions which have few satisfying assignments, since every such function is close (in the usual Hamming distance metric) to the constant-0 func
Externí odkaz:
http://arxiv.org/abs/2410.09235
With the significant advances in deep generative models for image and video synthesis, Deepfakes and manipulated media have raised severe societal concerns. Conventional machine learning classifiers for deepfake detection often fail to cope with evol
Externí odkaz:
http://arxiv.org/abs/2410.01906
Autor:
Nadimpalli, Shivam, Patel, Shyamal
We give a non-adaptive algorithm that makes $2^{\tilde{O}(\sqrt{k\log(1/\varepsilon_2 - \varepsilon_1)})}$ queries to a Boolean function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$ and distinguishes between $f$ being $\varepsilon_1$-close to some $k$-junta
Externí odkaz:
http://arxiv.org/abs/2404.13502
We consider the following basic, and very broad, statistical problem: Given a known high-dimensional distribution ${\cal D}$ over $\mathbb{R}^n$ and a collection of data points in $\mathbb{R}^n$, distinguish between the two possibilities that (i) the
Externí odkaz:
http://arxiv.org/abs/2402.08133
Autor:
Dhar, Sabyasachi, Nadimpalli, Santosh
Let $p$ and $l$ be distinct odd primes, and let $F$ be a $p$-adic field. Let $\pi$ be a generic smooth integral representation of ${\rm GL}_n(F)$ over an $\overline{\mathbb{Q}}_l$-vector space. Let $E$ be a finite Galois extension of $F$ with $[E:F]=
Externí odkaz:
http://arxiv.org/abs/2401.13295
A subset $S$ of the Boolean hypercube $\mathbb{F}_2^n$ is a sumset if $S = \{a + b : a, b\in A\}$ for some $A \subseteq \mathbb{F}_2^n$. Sumsets are central objects of study in additive combinatorics, featuring in several influential results. We prov
Externí odkaz:
http://arxiv.org/abs/2401.07242
Inspired by the classic problem of Boolean function monotonicity testing, we investigate the testability of other well-studied properties of combinatorial finite set systems, specifically \emph{intersecting} families and \emph{union-closed} families.
Externí odkaz:
http://arxiv.org/abs/2311.11119
Publikováno v:
STOC 2024: Proceedings of the 56th Annual ACM Symposium on Theory of Computing, 1498-1506
The circuit class $\mathsf{QAC}^0$ was introduced by Moore (1999) as a model for constant depth quantum circuits where the gate set includes many-qubit Toffoli gates. Proving lower bounds against such circuits is a longstanding challenge in quantum c
Externí odkaz:
http://arxiv.org/abs/2311.09631
We study the approximability of general convex sets in $\mathbb{R}^n$ by intersections of halfspaces, where the approximation quality is measured with respect to the standard Gaussian distribution $N(0,I_n)$ and the complexity of an approximation is
Externí odkaz:
http://arxiv.org/abs/2311.08575