7 papers
Unified generalization analysis for physics informed neural networks
Yuka Hashimoto, Tomoharu Iwata
Physics-Informed Neural Networks (PINNs) and their variational counterparts (VPINNs) are neural networks that incorporate physical laws, making them useful for scientific problems.…
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…
Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potential
Hachem Kadri, Joachim Tomasi, Yuka Hashimoto +1
Quantum kernel functions built using quantum-mechanical principles and have emerged as a centerpiece of quantum machine learning. The initial enthusiasm for quantum kernel machines…
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…
A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems
Yuanchao Xu, Kaidi Shao, Isao Ishikawa +3
We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing meth…
Spectral Truncation Kernels: Noncommutativity in -algebraic Kernel Machines
Yuka Hashimoto, Ayoub Hafid, Masahiro Ikeda +1
A central question in vector- and function-valued learning is how to design kernels that capture both local and non-local interactions while remaining computationally tractable. Ex…