相关论文: Quantum DNF Learnability Revisited

We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…

Since its introduction by Valiant in 1984, PAC learning of DNF expressions remains one of the central problems in learning theory. We consider this problem in the setting where the underlying distribution is uniform, or more generally, a…

We consider PAC learning of probability distributions (a.k.a. density estimation), where we are given an i.i.d. sample generated from an unknown target distribution, and want to output a distribution that is close to the target in total…

Several well-studied models of access to data samples, including statistical queries, local differential privacy and low-communication algorithms rely on queries that provide information about a function of a single sample. (For example, a…

In 1992 Mansour proved that every size-$s$ DNF formula is Fourier-concentrated on $s^{O(\log\log s)}$ coefficients. We improve this to $s^{O(\log\log k)}$ where $k$ is the read number of the DNF. Since $k$ is always at most $s$, our bound…

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…

We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…

Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown…

We study the problem of PAC learning $\gamma$-margin halfspaces with Random Classification Noise. We establish an information-computation tradeoff suggesting an inherent gap between the sample complexity of the problem and the sample…

Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size~$N$ and margin~$\gamma$ (how well the given data are separated), the query complexity of the best-known…

The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the $\textit{uniform convergence}$ of empirical error in $H$ to its mean, or equivalently, to the problem of $\textit{density…

In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with…

We explore potential quantum speedups for the fundamental problem of testing the properties of closeness and $k$-wise uniformity of probability distributions. Closeness testing is the problem of distinguishing whether two $n$-dimensional…

How quickly can a given class of concepts be learned from examples? It is common to measure the performance of a supervised machine learning algorithm by plotting its "learning curve", that is, the decay of the error rate as a function of…

In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…

The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth…

We study the problem of PAC learning one-hidden-layer ReLU networks with $k$ hidden units on $\mathbb{R}^d$ under Gaussian marginals in the presence of additive label noise. For the case of positive coefficients, we give the first…

Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…

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…

The problem of learning $t$-term DNF formulas (for $t = O(1)$) has been studied extensively in the PAC model since its introduction by Valiant (STOC 1984). A $t$-term DNF can be efficiently learnt using a $t$-term DNF only if $t = 1$ i.e.,…