相关论文: Quantum DNF Learnability Revisited

Multi-distribution learning is a natural generalization of PAC learning to settings with multiple data distributions. There remains a significant gap between the known upper and lower bounds for PAC-learnable classes. In particular, though…

The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…

Without large quantum computers to empirically evaluate performance, theoretical frameworks such as the quantum statistical query (QSQ) are a primary tool to study quantum algorithms for learning classical functions and search for quantum…

In 1992 Blum and Rudich [BR92] gave an algorithm that uses membership and equivalence queries to learn $k$-term DNF formulas over $\{0,1\}^n$ in time $\textsf{poly}(n,2^k)$, improving on the naive $O(n^k)$ running time that can be achieved…

Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…

We study a recent model of collaborative PAC learning where $k$ players with $k$ different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small…

Given a DNF formula on n variables, the two natural size measures are the number of terms or size s(f), and the maximum width of a term w(f). It is folklore that short DNF formulas can be made narrow. We prove a converse, showing that…

We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…

We give the first almost optimal polynomial-time proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. For $s$-sparse polynomial over $n$ variables and $\epsilon=1/s^\beta$, $\beta>1$, our…

We present the first nearly optimal differentially private PAC learner for any concept class with VC dimension 1 and Littlestone dimension $d$. Our algorithm achieves the sample complexity of…

$ \newcommand{\eps}{\varepsilon} $In learning theory, the VC dimension of a concept class $C$ is the most common way to measure its "richness." In the PAC model $$ \Theta\Big(\frac{d}{\eps} + \frac{\log(1/\delta)}{\eps}\Big) $$ examples are…

The stochastic nature of renewable energy and load demand requires efficient and accurate solutions for probabilistic optimal power flow (OPF). Quantum neural networks (QNNs), which combine quantum computing and machine learning, offer…

Using the recently developed framework of [Daniely et al, 2014], we show that under a natural assumption on the complexity of refuting random K-SAT formulas, learning DNF formulas is hard. Furthermore, the same assumption implies the…

It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…

Kearns' statistical query (SQ) oracle (STOC'93) lends a unifying perspective for most classical machine learning algorithms. This ceases to be true in quantum learning, where many settings do not admit, neither an SQ analog nor a quantum…

Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…

Machine learning algorithms often encounter different or "out-of-distribution" (OOD) data at deployment time, and OOD detection is frequently employed to detect these examples. While it works reasonably well in practice, existing…

We consider the problem of learning low-degree quantum objects up to $\varepsilon$-error in $\ell_2$-distance. We show the following results: $(i)$ unknown $n$-qubit degree-$d$ (in the Pauli basis) quantum channels and unitaries can be…

The model of learning with \emph{local membership queries} interpolates between the PAC model and the membership queries model by allowing the learner to query the label of any example that is similar to an example in the training set. This…

Using quantum algorithms, we obtain, for accuracy $\epsilon>0$ and confidence $1-\delta,0<\delta<1,$ a new sample complexity upper bound of $O((\mbox{log}(\frac{1}{\delta}))/\epsilon)$ as $\epsilon,\delta\rightarrow 0$ for a general…