9 papers
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…
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…
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 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…
Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
Isao Ishikawa, Yuka Hashimoto, Masahiro Ikeda +1
This paper presents a novel approach for estimating the Koopman operator defined on a reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method, what…