Related papers: On (not) learning the M\"obius function
We improve bounds on the degree and sparsity of Boolean functions representing the Legendre symbol as well as on the $N$th linear complexity of the Legendre sequence. We also prove similar results for both the Liouville function for…
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on…
We find the number of compositions over finite abelian groups under two types of restrictions: (i) each part belongs to a given subset and (ii) small runs of consecutive parts must have given properties. Waring's problem over finite fields…
This article provides new asymptotic results for the summatory Mobius function $\sum_{p \leq x} \mu(p+a) =O \left (x(\log x)^{-c} \right )$ and the summatory Liouville function $\sum_{p \leq x} \lambda(p+a) =O \left (x(\log x)^{-c} \right…
Bayesian inference provides an attractive online-learning framework to analyze sequential data, and offers generalization guarantees which hold even with model mismatch and adversaries. Unfortunately, exact Bayesian inference is rarely…
We study the median slope selection problem in the oblivious RAM model. In this model memory accesses have to be independent of the data processed, i.e., an adversary cannot use observed access patterns to derive additional information…
We consider a query-based data acquisition problem for binary classification of unknown labels, which has diverse applications in communications, crowdsourcing, recommender systems and active learning. To ensure reliable recovery of unknown…
Following the success of Moore's predictions, we are approaching a limit in the miniaturization of semiconductors for computing materials. This has led to the exploration of various research paths to develop alternative computing paradigms,…
The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the…
Designing objective functions robust to label noise is crucial for real-world classification algorithms. In this paper, we investigate the robustness to label noise of an $f$-divergence-based class of objective functions recently proposed…
We consider the problem of reinforcing federated learning with formal privacy guarantees. We propose to employ Bayesian differential privacy, a relaxation of differential privacy for similarly distributed data, to provide sharper privacy…
We study the problem of transmission of information over classical and classical-quantum channels in the one-shot regime where the underlying codes are constrained to be group codes. In the achievability part, we introduce a new input…
A learning algorithm for multilayer neural networks based on biologically plausible mechanisms is studied. Motivated by findings in experimental neurobiology, we consider synaptic averaging in the induction of plasticity changes, which…
In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong…
We introduce a new model of membership query (MQ) learning, where the learning algorithm is restricted to query points that are \emph{close} to random examples drawn from the underlying distribution. The learning model is intermediate…
This paper concentrates on positive definite functions on finite abelian groups, which are central to harmonic analysis and related fields. By leveraging the group structure and employing Fourier analysis, we establish a lower bound for the…
We build a theoretical framework for designing and understanding practical meta-learning methods that integrates sophisticated formalizations of task-similarity with the extensive literature on online convex optimization and sequential…
In this paper, we provide lower bounds for Differentially Private (DP) Online Learning algorithms. Our result shows that, for a broad class of $(\varepsilon,\delta)$-DP online algorithms, for number of rounds $T$ such that $\log T\leq O(1 /…
We study the following problem: with the power of postselection (classically or quantumly), what is your ability to answer adaptive queries to certain languages? More specifically, for what kind of computational classes $\mathcal{C}$, we…
We consider the problem of designing an adaptive sequence of questions that optimally classify a candidate's ability into one of several categories or discriminative grades. A candidate's ability is modeled as an unknown parameter, which,…