Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Discrete Reproducing Kernel Hilbert Spaces: Sampling and Distribution of Dirac-masses
Authors: Palle Jorgensen, Feng Tian
JMLR 2015 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) H over infinite, discrete and countable sets V. In this setting we analyze in detail the distributions of the corresponding Dirac point-masses of V. Illustrations include certain models from neural networks: An Extreme Learning Machine (ELM) is a neural networkconfiguration in which a hidden layer of weights are randomly sampled, and where the object is then to compute resulting output. For RKHSs H of functions defined on a prescribed countable infinite discrete set V , we characterize those which contain the Dirac masses δx for all points x in V. Further examples and applications where this question plays an important role are: (i) discrete Brownian motion-Hilbert spaces, i.e., discrete versions of the Cameron-Martin Hilbert space; (ii) energy-Hilbert spaces corresponding to graph-Laplacians where the set V of vertices is then equipped with a resistance metric; and finally (iii) the study of Gaussian free fields. |
| Researcher Affiliation | Academia | Palle Jorgensen EMAIL Department of Mathematics The University of Iowa Iowa City, IA 52242-1419, U.S.A. Feng Tian EMAIL Department of Mathematics, Informatics, and Cybersecurity Trine University Angola, IN 46703, U.S.A. |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. It is a theoretical mathematics paper focusing on definitions, theorems, lemmas, and proofs. |
| Open Source Code | No | The paper does not contain any concrete access information for source code. It is a theoretical mathematics paper without an implementation-focused methodology. |
| Open Datasets | No | The paper does not provide any concrete access information for publicly available datasets. It is a theoretical paper that does not conduct empirical studies requiring specific datasets. |
| Dataset Splits | No | The paper does not provide specific dataset split information as it is a theoretical work and does not involve experimental evaluation on datasets. |
| Hardware Specification | No | The paper does not provide specific hardware details as it is a theoretical work and does not describe any experimental setup requiring hardware. |
| Software Dependencies | No | The paper does not provide specific ancillary software details as it is a theoretical work and does not describe any computational implementation. |
| Experiment Setup | No | The paper does not contain specific experimental setup details or hyperparameters as it is a theoretical work and does not describe any experiments. |