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 [1].
Ridges, Neural Networks, and the Radon Transform
Authors: Michael Unser
JMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we investigate properties of the Radon transform in relation to ridges and to the characterization of neural networks. We introduce a broad category of hyper-spherical Banach subspaces (including the relevant subspace of measures) over which the back-projection operator is invertible. We also give conditions under which the back-projection operator is extendable to the full parent space with its null space being identifiable as a Banach complement. Starting from first principles, we then characterize the sampling functionals that are in the range of the filtered Radon transform. Next, we extend the definition of ridges for any distributional profile and determine their (filtered) Radon transform in full generality. Finally, we apply our formalism to clarify and simplify some of the results and proofs on the optimality of Re LU networks that have appeared in the literature. |
| Researcher Affiliation | Academia | Michael Unser EMAIL Biomedical Imaging Group Ecole polytechnique f ed erale de Lausanne (EPFL) CH-1015 Lausanne, Switzerland |
| Pseudocode | No | The paper focuses on theoretical mathematical analysis, definitions, theorems, and proofs. It does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to code repositories or mention code in supplementary materials. |
| Open Datasets | No | This paper is theoretical and does not conduct experiments using any datasets. Therefore, it does not provide access information for datasets. |
| Dataset Splits | No | This paper is theoretical and does not conduct experiments using any datasets. Therefore, there is no information about dataset splits. |
| Hardware Specification | No | This paper is theoretical and does not describe any experimental setup or computational results that would require specific hardware. No hardware specifications are mentioned. |
| Software Dependencies | No | This paper is theoretical and does not describe any experimental setup or computational results that would require specific software dependencies with version numbers. No software dependencies are mentioned. |
| Experiment Setup | No | This paper is theoretical and does not describe any experiments. Therefore, there are no details about an experimental setup, hyperparameters, or training configurations. |