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math.FA2026
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…
math.FA2026
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…
math.FA2025
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…