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].
Optimal Convergence Rates of Deep Convolutional Neural Networks: Additive Ridge Functions
Authors: Zhiying Fang, Guang Cheng
TMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we consider the mean squared error analysis for deep convolutional neural networks. We show that, for additive ridge functions, convolutional neural networks followed by one fully connected layer with Re LU activation functions can reach optimal mini-max rates (up to a log factor). The input dimension only appears in the constant of convergence rates. This work shows the statistical optimality of convolutional neural networks and may shed light on why convolutional neural networks are able to behave well for high dimensional input. Compared with significant achievements and developments in practical applications, theoretical insurances are left behind. |
| Researcher Affiliation | Academia | Zhiying Fang EMAIL Institute of Applied Mathematics Shenzhen Polytechnic1 School of Data Science The Chinese University of Hong Kong, Shenzhen2 Guang Cheng EMAIL Department of Statistics University of California, Los Angeles |
| Pseudocode | No | The paper focuses on mathematical proofs, theorems, and definitions related to convolutional neural networks and convergence rates. It does not contain any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about providing source code, nor does it include links to code repositories or mention code in supplementary materials for the methodology described. |
| Open Datasets | No | This paper is a theoretical work that analyzes the convergence rates of deep convolutional neural networks for additive ridge functions. It does not conduct empirical studies or use specific datasets, thus no information on publicly available datasets is provided. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical experiments with datasets. Therefore, there is no mention of dataset splits (e.g., training, validation, test) required for reproducibility. |
| Hardware Specification | No | This paper presents a theoretical analysis of deep convolutional neural networks. It does not describe any experimental setup or report on empirical results that would necessitate the use or specification of particular hardware. |
| Software Dependencies | No | The paper is theoretical and focuses on mathematical derivations and proofs. It does not describe an implementation or experimental work, and therefore does not list any specific software dependencies with version numbers. |
| Experiment Setup | No | This paper is purely theoretical, focusing on mathematical analysis and proofs of convergence rates. It does not include an experimental section, and consequently, there are no details provided regarding hyperparameters, training configurations, or other experimental setup parameters. |