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

2026-05-13

AI Summary

This work addresses the exponential computational bottleneck faced by conventional methods in identifying “winning ticket” subnetworks within high-dimensional data. Inspired by quantum algorithms, the authors propose a fully classical approach for sparse subnetwork selection that leverages ridgelet transforms to construct an optimized probability distribution for efficient sampling of hidden nodes in shallow networks. This method achieves the first successful dequantization of the original quantum algorithm. Both theoretical analysis and empirical experiments demonstrate that the proposed algorithm attains empirical risk comparable to exact sampling while reducing runtime to polynomial dependence on data dimensionality, significantly outperforming uniform sampling and existing classical approaches.

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.

Problem

• sparse subnetwork selection
• quantum-inspired algorithm
• classical dequantization
• neural network pruning
• polynomial-time sampling

Innovation

• quantum-inspired algorithm
• sparse subnetwork selection
• polynomial-time sampling
• ridgelet transform
• dequantization