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In this work we study the quantitative relation between the recursive teaching dimension (RTD) and the VC dimension (VCD) of concept classes of finite sizes. The RTD of a concept class $mathcal C subseteq {0, 1}^n$, introduced by Zilles et al. (2011), is a combinatorial complexity measure characterized by the worst-case number of examples necessary to identify a concept in $mathcal C$ according to the recursive teaching model. For any finite concept class $mathcal C subseteq {0,1}^n$ with $mathrm{VCD}(mathcal C)=d$, Simon & Zilles (2015) posed an open problem $mathrm{RTD}(mathcal C) = O(d)$, i.e., is RTD linearly upper bounded by VCD? Previously, the best known result is an exponential upper bound $mathrm{RTD}(mathcal C) = O(d cdot 2^d)$, due to Chen et al. (2016). In this paper, we show a quadratic upper bound: $mathrm{RTD}(mathcal C) = O(d^2)$, much closer to an answer to the open problem. We also discuss the challenges in fully solving the problem.
Adversarial attacks during the testing phase of neural networks pose a challenge for the deployment of neural networks in security critical settings. These attacks can be performed by adding noise that is imperceptible to humans on top of the origina
This note sharpens the standard upper bound of the least quadratic nonresidue from $n_pll p^{1/4sqrt{e}+varepsilon}$ to $n_pll p^{1/4e+varepsilon}$, where $varepsilon>0$, unconditionally.
We provide a negative resolution to a conjecture of Steinke and Zakynthinou (2020a), by showing that their bound on the conditional mutual information (CMI) of proper learners of Vapnik--Chervonenkis (VC) classes cannot be improved from $d log n +2$
Contextual Bandits find important use cases in various real-life scenarios such as online advertising, recommendation systems, healthcare, etc. However, most of the algorithms use flat feature vectors to represent context whereas, in the real world,
Let $G$ be a finite (not necessarily abelian) group and let $p=p(G)$ be the smallest prime number dividing $|G|$. We prove that $d(G)leq frac{|G|}{p}+9p^2-10p$, where $d(G)$ denotes the small Davenport constant of $G$ which is defined as the maximal