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].
Nonparametric Regression Using Over-parameterized Shallow ReLU Neural Networks
Authors: Yunfei Yang, Ding-Xuan Zhou
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | It is shown that over-parameterized neural networks can achieve minimax optimal rates of convergence (up to logarithmic factors) for learning functions from certain smooth function classes, if the weights are suitably constrained or regularized. Specifically, we consider the nonparametric regression of estimating an unknown d-variate function by using shallow Re LU neural networks. ... In this setting, we prove that least squares estimators based on shallow neural networks with certain norm constraints on the weights are minimax optimal, if the network width is sufficiently large. As a byproduct, we derive a new size-independent bound for the local Rademacher complexity of shallow Re LU neural networks, which may be of independent interest. |
| Researcher Affiliation | Academia | Yunfei Yang EMAIL Department of Mathematics, City University of Hong Kong Kowloon, Hong Kong, China. Ding-Xuan Zhou EMAIL School of Mathematics and Statistics, University of Sydney Sydney, NSW 2006, Australia. |
| Pseudocode | No | The paper does not contain any sections explicitly labeled as "Pseudocode" or "Algorithm", nor does it present any structured, code-like blocks describing a computational procedure. |
| Open Source Code | No | The paper does not provide any statements about releasing source code, a link to a code repository, or information about code included in supplementary materials. The paper is theoretical in nature. |
| Open Datasets | No | The paper discusses a conceptual "data set of n samples Dn = {(Xi, Yi)}n i=1" for theoretical analysis of nonparametric regression, but it does not specify or provide access information for any actual publicly available or open datasets used for experiments. |
| Dataset Splits | No | The paper is theoretical and focuses on mathematical analysis rather than empirical experimentation. Therefore, it does not provide details on training, validation, or test dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any computational experiments that would require specific hardware. Thus, there is no mention of GPU models, CPU specifications, or other hardware details. |
| Software Dependencies | No | The paper is theoretical and does not describe any implemented methods or computational experiments that would require specific software libraries or versions. |
| Experiment Setup | No | The paper is theoretical and focuses on mathematical proofs and convergence rates for neural networks. It does not describe any practical experiments, hyperparameters, model initialization, or training schedules. |