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..
ResNet with one-neuron hidden layers is a Universal Approximator
Authors: Hongzhou Lin, Stefanie Jegelka
NeurIPS 2018 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We begin by empirically exploring the difference between narrow fully connected networks, with d neurons per hidden layer, and Res Net via a simple example: classifying the unit ball in the plane. Figure 2 shows the results. |
| Researcher Affiliation | Academia | Hongzhou Lin MIT Cambridge, MA 02139 EMAIL Stefanie Jegelka MIT Cambridge, MA 02139 EMAIL |
| Pseudocode | No | The paper describes mathematical constructions and proof steps but does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code or provide a link to a code repository for the described methodology. |
| Open Datasets | No | The training set consists of randomly generated samples (zi, yi)i=1 n R2 { 1, 1} with yi = 1 if zi 2 1; 1 if 2 zi 2 3. |
| Dataset Splits | No | The paper describes a 'training set' for its motivating example but does not provide specific details on training/validation/test dataset splits. |
| Hardware Specification | No | The paper describes empirical observations in Section 2 but does not provide any specific hardware details (e.g., GPU/CPU models, memory) used for the experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers (e.g., Python, PyTorch, TensorFlow versions) that would be needed to replicate the experiments. |
| Experiment Setup | Yes | As loss, we use the logistic loss 1 n P log(1 + e yi ˆ yi), where ˆyi = f N (zi) is the output of the network on the i-th sample. Decision boundaries obtained by training fully connected networks with width d = 2 per hidden layer (top row) and Res Net (bottom row) with one neuron in the hidden layers on the unit ball classification problem. |