1 citations · 2 across the 10 of their papers we have counts for
10 papers
The role of parameter Jacobians in the stability of network outputs
Halyun Jeong, Palle E. T. Jorgensen, Hyun-Kyoung Kwon +2
In the framework of network dynamics, learning models, and neural tangent kernels (NTK), we show that the corresponding linearized dynamics leads naturally to a semigroup formulati…
Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learning
Palle E. T. Jorgensen, Myung-Sin Song, James F. Tian
We present a new operator theoretic framework for analysis of complex systems with intrinsic subdivisions into components, taking the form of "residuals" in general, and "telescopi…
Factorization of positive definite kernels. Correspondences: -algebraic and operator valued context vs scalar valued kernels
Palle E. T. Jorgensen, James Tian
We introduce and study a class of generalized positive definite kernels of the form , where is a unital $C^{…
New duality in choices of feature spaces via kernel analysis
Palle E. T. Jorgensen, James Tian
We present a systematic study of the family of positive definite (p.d.) kernels with the use of their associated feature maps and feature spaces. For a fixed set , generalizing…
Gaussian processes in Non-commutative probability
Palle E. T. Jorgensen, James Tian
Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear o…
From Classical to Quantum: Polymorphisms in Non-Commutative Probability
Palle E. T. Jorgensen, James Tian
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classic…
Operator-Valued Kernels, Machine Learning, and Dynamical Systems
Palle E. T. Jorgensen, James Tian
In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. W…
Hilbert space-valued Gaussian processes, and quantum states
Palle E. T. Jorgensen, James Tian
We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as…
Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure
Palle E. T. Jorgensen, James Tian
Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stoch…
Operator theory, kernels, and Feedforward Neural Networks
Palle E. T. Jorgensen, Myung-Sin Song, James Tian
In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network m…