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..
Approximation theory for 1-Lipschitz ResNets
Authors: Davide Murari, Takashi Furuya, Carola-Bibiane Schönlieb
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | This paper focuses on the theoretical analysis of 1-Lipschitz Res Nets. We have commented in Section 5 on the implementability of the considered models, and we now demonstrate that they do not have any intrinsic issues with trainability. To do so, we consider two classification problems. First, we train models to classify the two-moon dataset with additive Gaussian noise of standard deviation σ = 0.1. Then, we train networks to classify the MNIST dataset. We inspect how the performance varies as we consider models coming from the two families of architectures presented in this paper, and as we vary the network depth and width. |
| Researcher Affiliation | Academia | Davide Murari Department of Applied Mathematics and Theoretical Physics University of Cambridge EMAIL; Takashi Furuya Faculty of Life and Medical Sciences, Department of Biomedical Engineering Doshisha University RIKEN AIP EMAIL; Carola-Bibiane Schönlieb Department of Applied Mathematics and Theoretical Physics University of Cambridge EMAIL |
| Pseudocode | No | The paper describes mathematical proofs and theoretical concepts, but it does not include any structured pseudocode or algorithm blocks. The methods are described textually and through mathematical equations and theorems. |
| Open Source Code | Yes | The code is written in Py Torch and it is available at the repository https://github.com/davidemurari/1Lipschitz Res Nets. |
| Open Datasets | Yes | For the two-moon dataset, we generate 4,000 points, 20% of which are set as training points. For MNIST, we adopt the standard training/test split and preprocess the inputs by normalising them. |
| Dataset Splits | Yes | For the two-moon dataset, we generate 4,000 points, 20% of which are set as training points. For MNIST, we adopt the standard training/test split and preprocess the inputs by normalising them. |
| Hardware Specification | Yes | The experiments are run on a Quadro RTX 6000 GPU. |
| Software Dependencies | No | The code is written in Py Torch and it is available at the repository https://github.com/davidemurari/1Lipschitz Res Nets. No specific version numbers for PyTorch or other libraries are provided. |
| Experiment Setup | Yes | The batch size we consider for both tasks is 256. We optimise the weights for both tasks using Adam and a cosine annealing learning rate scheduler. The network weights can be initialised to satisfy the dynamical isometry property [22, 39], to avoid possible trainability problems when considering deep networks. |