Search Results for author:
Found 13 papers, 2 papers with code
Quantum Circuit $C^*$-algebra Net
This interaction enables the circuits to share information among them, which contributes to improved generalization performance in machine learning tasks.
Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
This paper presents a novel approach for estimating the Koopman operator defined on a reproducing kernel Hilbert space (RKHS) and its spectra.
$C^*$-Algebraic Machine Learning: Moving in a New Direction
Machine learning has a long collaborative tradition with several fields of mathematics, such as statistics, probability and linear algebra.
Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks
We identify hidden layers inside a deep neural network (DNN) with group actions on the data domain, and formulate a formal deep network as a dual voice transform with respect to the Koopman operator, a linear representation of the group action.
Koopman-based generalization bound: New aspect for full-rank weights
Our bound is tighter than existing norm-based bounds when the condition numbers of weight matrices are small.
Noncommutative $C^*$-algebra Net: Learning Neural Networks with Powerful Product Structure in $C^*$-algebra
We propose a new generalization of neural networks with noncommutative $C^*$-algebra.
Learning in RKHM: a $C^*$-Algebraic Twist for Kernel Machines
Supervised learning in reproducing kernel Hilbert space (RKHS) and vector-valued RKHS (vvRKHS) has been investigated for more than 30 years.
$C^*$-algebra Net: A New Approach Generalizing Neural Network Parameters to $C^*$-algebra
We apply our framework to practical problems such as density estimation and few-shot learning and show that our framework enables us to learn features of data even with a limited number of samples.
Reproducing kernel Hilbert C*-module and kernel mean embeddings
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS).
Kernel Mean Embeddings of Von Neumann-Algebra-Valued Measures
Kernel mean embedding (KME) is a powerful tool to analyze probability measures for data, where the measures are conventionally embedded into a reproducing kernel Hilbert space (RKHS).
Analysis via Orthonormal Systems in Reproducing Kernel Hilbert $C^*$-Modules and Applications
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS).
Krylov Subspace Method for Nonlinear Dynamical Systems with Random Noise
In this paper, we address a lifted representation of nonlinear dynamical systems with random noise based on transfer operators, and develop a novel Krylov subspace method for estimating the operators using finite data, with consideration of the unboundedness of operators.
Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators
The development of a metric for structural data is a long-term problem in pattern recognition and machine learning.
