Quantum Alphatron: quantum advantage for learning with kernels and noise

TL;DR

This paper introduces quantum versions of the Alphatron algorithm, achieving polynomial speedups in kernel evaluation and gradient computation, advancing quantum learning with kernels and neural networks.

Contribution

It presents the first fault-tolerant quantum algorithms for Alphatron, providing provable speedups in kernel and gradient evaluations for learning models.

Findings

Quantum Alphatron achieves polynomial speedup in kernel matrix evaluation.

Quantum Alphatron accelerates gradient computation in stochastic gradient descent.

Demonstrates quantum advantage in learning two-layer neural networks.

Abstract

At the interface of machine learning and quantum computing, an important question is what distributions can be learned provably with optimal sample complexities and with quantum-accelerated time complexities. In the classical case, Klivans and Goel discussed the \textit{Alphatron}, an algorithm to learn distributions related to kernelized regression, which they also applied to the learning of two-layer neural networks. In this work, we provide quantum versions of the Alphatron in the fault-tolerant setting. In a well-defined learning model, this quantum algorithm is able to provide a polynomial speedup for a large range of parameters of the underlying concept class. We discuss two types of speedups, one for evaluating the kernel matrix and one for evaluating the gradient in the stochastic gradient descent procedure. We also discuss the quantum advantage in the context of learning of two-layer neural networks. Our work contributes to the study of quantum learning with kernels and from samples.