Nearly-tight VC-dimension and Pseudodimension Bounds for Piecewise Linear Neural Networks
Authors: Peter L. Bartlett, Nick Harvey, Christopher Liaw, Abbas Mehrabian
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We prove new upper and lower bounds on the VC-dimension of deep neural networks with the Re LU activation function. These bounds are tight for almost the entire range of parameters. [...] The proof appears in Section 2. [...] The proofs of Theorem 7 and Remark 9 appear in Section 4. |
| Researcher Affiliation | Academia | Peter L. Bartlett EMAIL Department of Statistics and Computer Science Division University of California Berkeley, CA 94720-3860, USA Nick Harvey EMAIL Christopher Liaw EMAIL Abbas Mehrabian EMAIL Department of Computer Science University of British Columbia Vancouver, BC V6T 1Z4, Canada |
| Pseudocode | No | The paper describes mathematical proofs and theoretical constructs. It does not contain any clearly labeled pseudocode blocks or algorithms in a structured format. |
| Open Source Code | No | The paper does not contain any statements about releasing source code, nor does it provide links to any code repositories or supplementary materials. |
| Open Datasets | No | This paper is a theoretical work focused on mathematical proofs and bounds. It does not describe experiments that use datasets, and therefore, no information about publicly available or open datasets is provided. |
| Dataset Splits | No | This paper is theoretical and does not involve empirical experiments with datasets. Consequently, there is no mention of dataset splits (training, validation, test) in the text. |
| Hardware Specification | No | This is a theoretical research paper focused on mathematical proofs and bounds for neural networks. No empirical experiments were conducted that would require specific hardware, and thus no hardware specifications are mentioned. |
| Software Dependencies | No | This paper is purely theoretical, focusing on mathematical proofs rather than computational experiments. Therefore, it does not specify any software dependencies with version numbers. |
| Experiment Setup | No | This paper is purely theoretical, focusing on mathematical proofs and bounds. It does not include any experimental results, and therefore no experimental setup details, hyperparameters, or training configurations are provided. |