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 Shift Toward Open and Reproducible AI Research," Under Review, 2026. doi: 10.48550/arXiv.2606.16974..
ReLU Network with Width $d+\mathcalO(1)$ Can Achieve Optimal Approximation Rate
Authors: Chenghao Liu, Minghua Chen
ICML 2024 | Venue PDF | LLM Run Details | Input Tokens: 41,669 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 3,878 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we address this gap by proving that Re LU networks with width d + 1 can achieve the optimal approximation rate for continuous functions over the domain [0, 1]d under Lp norm for p [1, ). We further show that for the uniform norm, a width of d + 11 is sufficient. We also extend the results to narrow feed-forward networks with various activations, confirming their capability to approximate at the optimal rate. This work adds to the understanding of universal approximation of narrow networks. |
| Researcher Affiliation | Academia | 1School of Data Science, City University of Hong Kong. Correspondence to: Minghua Chen <EMAIL>. |
| Pseudocode | No | The paper focuses on theoretical proofs and constructions but does not include any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide any information or links regarding the availability of open-source code for the described methodology. |
| Open Datasets | No | As a theoretical paper, it does not involve training on datasets or mention any public datasets, links, or citations for such use. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments involving validation dataset splits. |
| Hardware Specification | No | As a theoretical paper, no hardware specifications for running experiments are mentioned. |
| Software Dependencies | No | As a theoretical paper, no specific software dependencies with version numbers are mentioned. |
| Experiment Setup | No | As a theoretical paper, no experimental setup details like hyperparameter values or training configurations are provided. |