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..
Quantitative convergence of trained neural networks to Gaussian processes
Authors: Andrea Agazzi, Eloy Mosig García, Dario Trevisan
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 4 Numerical Experiments We conduct some numerical experiments in Figure 1 to support our theoretical results. In both experiments, t is taken as the product of the learning rate and the number of iterations or epochs. |
| Researcher Affiliation | Academia | Eloy Mosig García Department of Mathematics University of Pisa Largo Bruno Pontecorvo, 5, 56127 Pisa PI, Italia EMAIL Andrea Agazzi Department of Mathematics and Statistics University of Bern Alpeneggstrasse 22, 3012 Bern EMAIL Dario Trevisan Department of Mathematics University of Pisa Largo Bruno Pontecorvo, 5, 56127 Pisa PI, Italia EMAIL |
| Pseudocode | No | The paper describes theoretical results and numerical experiments. There are no explicitly labeled 'Pseudocode' or 'Algorithm' blocks, nor are there structured steps formatted like code within the main text. |
| Open Source Code | Yes | The code is available at https://github.com/ emosig/quantitative_gaussian_trained NN. |
| Open Datasets | No | The training set and test set were drawn from a uniform distribution on a fixed interval, and the labels y of the training points correspond to a sine function with additive noise. |
| Dataset Splits | No | The training set and test set were drawn from a uniform distribution on a fixed interval, and the labels y of the training points correspond to a sine function with additive noise. |
| Hardware Specification | No | Our experiments were run on the author s personal computer and do not require any particular hardware specifications. |
| Software Dependencies | Yes | The networks were programmed with Py Torch 2.6.0 Paszke et al. [2019], and the Gaussian process Gt was constructed using the library neural tangents 0.6.5 Novak et al. [2020] for the kernels K and k , needed to construct µt and Σt in (2.5). The operator It(B) was programmed by solving the linear system of equations BX = 1n e Bt with the linalg package of Num Py Harris et al. [2020]. ... Python Optimal Transport 0.9.5 library Flamary et al. [2021]. |
| Experiment Setup | Yes | The leftmost and center plots in Figure 1 represent 100 trained shallow neural networks with sigmoid activation of width n1 = 700 on the leftmost plot and n1 = 1000 in the central plot. The networks have been trained for 2 104 epochs with learning rates of 1 700 and 7 1000 (hence t 28.571 on the leftmost plot and t = 140 in the central one) to fit two training points, corresponding to different random seeds on each case. ... trained indepently over a single training point, for 100 epochs and with a learning rate of 0.1 (hence t = 10), 104 neural networks for each width and then calculated the empirical Wasserstein distance for a variety of widths, ranging from 2 to 256. |