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.