5 papers
Winning Lottery Tickets in Neural Networks via a Quantum-Inspired Classical Algorithm
Natsuto Isogai, Hayata Yamasaki, Sho Sonoda +1
Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks f…
Generalization Error Bounds for Picard-Type Operator Learning in Nonlinear Parabolic PDEs
Koichi Taniguchi, Sho Sonoda
Operator learning for partial differential equations (PDEs) aims to learn solution operators on infinite-dimensional function spaces from finite-resolution data. In this setting, i…
Why and When Deep is Better than Shallow: Implementation-Agnostic State-Transition Model of Deep Learning
Sho Sonoda, Yuka Hashimoto, Isao Ishikawa +1
Why and when does depth improve generalization? We study this question in an implementation-agnostic state-transition model, where a depth- predictor is a readout class comp…
Why High-rank Neural Networks Generalize?: An Algebraic Framework with RKHSs
Yuka Hashimoto, Sho Sonoda, Isao Ishikawa +1
We derive a new Rademacher complexity bound for deep neural networks using Koopman operators, group representations, and reproducing kernel Hilbert spaces (RKHSs). The proposed bou…
Deep Ridgelet Transform and Unified Universality Theorem for Deep and Shallow Joint-Group-Equivariant Machines
Sho Sonoda, Yuka Hashimoto, Isao Ishikawa +1
We present a constructive universal approximation theorem for learning machines equipped with joint-group-equivariant feature maps, called the joint-equivariant machines, based on…