Winning Lottery Tickets in Neural Networks via a Quantum-Inspired Classical Algorithm

TL;DR

This paper presents a classical algorithm inspired by quantum computing that efficiently samples sparse neural network subnetworks, matching quantum performance and outperforming traditional classical methods in runtime.

Contribution

The authors develop a polynomial-time classical algorithm for subnetwork sampling that replicates quantum algorithm efficiency, removing exponential data dependence.

Findings

The classical algorithm achieves empirical risk comparable to quantum sampling.

It exhibits exponentially better runtime scaling than naive classical methods.

The approach provides a quantum-inspired classical alternative for neural network subnetwork selection.

Abstract

Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly solving an optimization problem over a large-scale network, this algorithm constructs a sparse subnetwork by sampling hidden nodes from an optimized probability distribution defined using the ridgelet transform. The quantum algorithm performs this sampling in time $O(D)$ in the data dimension $D$, whereas a naive classical implementation relies on handling exponentially many candidate nodes and hence takes $\exp[O(D)]$ time. In this work, we construct and analyze a quantum-inspired fully classical algorithm for the same sampling task. We show that our algorithm runs in time $O(\operatorname{poly}(D))$, thereby removing the exponential dependence on $D$ from the previous classical approach. Numerical simulations show that the proposed sampler achieves empirical risk comparable to exact sampling from the optimized distribution and substantially lower than sampling from the non-optimized uniform distribution, while also exhibiting exponentially improved runtime scaling compared with the conventional classical implementation. These successful dequantization results show that sparse subnetwork selection via optimized sampling can be achieved classically with polynomial data-dimension scaling on conventional computers without quantum hardware, providing an alternative to the existing quantum algorithm.