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 embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Gradient Dynamics of Shallow Univariate ReLU Networks
Authors: Francis Williams, Matthew Trager, Daniele Panozzo, Claudio Silva, Denis Zorin, Joan Bruna
NeurIPS 2019 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present a theoretical and empirical study of the gradient dynamics of overparameterized shallow Re LU networks with one-dimensional input, solving least-squares interpolation. For our numerical experiments, we use gradient descent with the parameterization (1) and α(m) = m, appropriately scaling the weights a, b, c to achieve different dynamical behaviors. We also refer to Section D in the Appendix for additional experiments. |
| Researcher Affiliation | Academia | Francis Williams Matthew Trager Claudio Silva Daniele Panozzo Denis Zorin Joan Bruna New York University |
| Pseudocode | No | The paper describes methods through mathematical formulations and textual descriptions, but it does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain an explicit statement or link indicating that the source code for their methodology is publicly available. |
| Open Datasets | No | The paper mentions using "10 points sampled from a square wave" and fitting to a "sinusoid" for numerical experiments. These are either custom or synthetic datasets, and no concrete access information (link, DOI, formal citation) for a publicly available dataset is provided. |
| Dataset Splits | No | The paper mentions using "10 points sampled from a square wave" and fitting to a "sinusoid", but it does not specify any training, validation, or test dataset splits. The only numerical detail given for training is "10000 epochs" for some experiments. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU models, CPU models, or memory specifications used for running the experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers (e.g., specific libraries or frameworks like PyTorch or TensorFlow with their versions). |
| Experiment Setup | Yes | For our numerical experiments, we use gradient descent with the parameterization (1) and α(m) = m, appropriately scaling the weights a, b, c to achieve different dynamical behaviors. We show in Figure 4 that as we vary δ, the network function goes from being smooth and non-adaptive in the kernel regime (δ = , i.e.training only the parameter c) to very adaptive (δ = , i.e.training only the parameters a, b). Note that as δ increases, clusters of knots emerge at the sample positions (collinear points in the uv diagrams). The caption of Figure 4 states "(10000 epochs)". |