Quantum Ridgelet Transform: Winning Lottery Ticket of Neural Networks with Quantum Computation

Hayata Yamasaki, Sathyawageeswar Subramanian, Satoshi Hayakawa, Sho Sonoda
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:39008-39034, 2023.

Abstract

A significant challenge in the field of quantum machine learning (QML) is to establish applications of quantum computation to accelerate common tasks in machine learning such as those for neural networks. Ridgelet transform has been a fundamental mathematical tool in the theoretical studies of neural networks, but the practical applicability of ridgelet transform to conducting learning tasks was limited since its numerical implementation by conventional classical computation requires an exponential runtime $\exp(O(D))$ as data dimension $D$ increases. To address this problem, we develop a quantum ridgelet transform (QRT), which implements the ridgelet transform of a quantum state within a linear runtime $O(D)$ of quantum computation. As an application, we also show that one can use QRT as a fundamental subroutine for QML to efficiently find a sparse trainable subnetwork of large shallow wide neural networks without conducting large-scale optimization of the original network. This application discovers an efficient way in this regime to demonstrate the lottery ticket hypothesis on finding such a sparse trainable neural network. These results open an avenue of QML for accelerating learning tasks with commonly used classical neural networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-yamasaki23a, title = {Quantum Ridgelet Transform: Winning Lottery Ticket of Neural Networks with Quantum Computation}, author = {Yamasaki, Hayata and Subramanian, Sathyawageeswar and Hayakawa, Satoshi and Sonoda, Sho}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {39008--39034}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/yamasaki23a/yamasaki23a.pdf}, url = {https://proceedings.mlr.press/v202/yamasaki23a.html}, abstract = {A significant challenge in the field of quantum machine learning (QML) is to establish applications of quantum computation to accelerate common tasks in machine learning such as those for neural networks. Ridgelet transform has been a fundamental mathematical tool in the theoretical studies of neural networks, but the practical applicability of ridgelet transform to conducting learning tasks was limited since its numerical implementation by conventional classical computation requires an exponential runtime $\exp(O(D))$ as data dimension $D$ increases. To address this problem, we develop a quantum ridgelet transform (QRT), which implements the ridgelet transform of a quantum state within a linear runtime $O(D)$ of quantum computation. As an application, we also show that one can use QRT as a fundamental subroutine for QML to efficiently find a sparse trainable subnetwork of large shallow wide neural networks without conducting large-scale optimization of the original network. This application discovers an efficient way in this regime to demonstrate the lottery ticket hypothesis on finding such a sparse trainable neural network. These results open an avenue of QML for accelerating learning tasks with commonly used classical neural networks.} }
Endnote
%0 Conference Paper %T Quantum Ridgelet Transform: Winning Lottery Ticket of Neural Networks with Quantum Computation %A Hayata Yamasaki %A Sathyawageeswar Subramanian %A Satoshi Hayakawa %A Sho Sonoda %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-yamasaki23a %I PMLR %P 39008--39034 %U https://proceedings.mlr.press/v202/yamasaki23a.html %V 202 %X A significant challenge in the field of quantum machine learning (QML) is to establish applications of quantum computation to accelerate common tasks in machine learning such as those for neural networks. Ridgelet transform has been a fundamental mathematical tool in the theoretical studies of neural networks, but the practical applicability of ridgelet transform to conducting learning tasks was limited since its numerical implementation by conventional classical computation requires an exponential runtime $\exp(O(D))$ as data dimension $D$ increases. To address this problem, we develop a quantum ridgelet transform (QRT), which implements the ridgelet transform of a quantum state within a linear runtime $O(D)$ of quantum computation. As an application, we also show that one can use QRT as a fundamental subroutine for QML to efficiently find a sparse trainable subnetwork of large shallow wide neural networks without conducting large-scale optimization of the original network. This application discovers an efficient way in this regime to demonstrate the lottery ticket hypothesis on finding such a sparse trainable neural network. These results open an avenue of QML for accelerating learning tasks with commonly used classical neural networks.
APA
Yamasaki, H., Subramanian, S., Hayakawa, S. & Sonoda, S.. (2023). Quantum Ridgelet Transform: Winning Lottery Ticket of Neural Networks with Quantum Computation. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:39008-39034 Available from https://proceedings.mlr.press/v202/yamasaki23a.html.

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