How many samples are needed to leverage smoothness?

Authors: Vivien Cabannes, Stefano Vigogna

NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental All results are illustrated by numerical experiments, some of them to be found in Appendix C.
Researcher Affiliation Collaboration Vivien Cabannes Meta AI Stefano Vigogna University of Rome Tor Vergata
Pseudocode No The paper does not include a pseudocode block or an algorithm block. It presents mathematical derivations and theoretical analyses.
Open Source Code Yes All the code to run figures is available at https://github.com/facebookresearch/rates.
Open Datasets No The paper uses theoretical constructs like 'distribution ρ X Y', 'uniform on the torus Td', and 'Gaussian kernel' for its numerical experiments and theoretical analyses. It does not use or provide access to a specific, named publicly available dataset in the conventional machine learning sense.
Dataset Splits No The paper does not specify training, validation, or test dataset splits. Its numerical experiments focus on convergence rates with respect to the number of samples (n) in stylized or theoretical settings, rather than on specific data splits for model evaluation.
Hardware Specification No The paper does not explicitly describe the hardware used to run its numerical experiments. It focuses on theoretical bounds and stylized settings, and the computational resources are not specified.
Software Dependencies No The paper does not provide specific version numbers for any software dependencies. While it mentions code for figures is available, it does not list programming languages, libraries, or frameworks with their versions.
Experiment Setup Yes Figure 1 illustrates results with 'regularizer λ' and 'bandwidth σ' and explicitly notes 'Lambda: 3.04e-06' and 'Sigma: 0.46'. Appendix C.3 states, 'One hundred runs were launched and averaged to get a meaningful estimate of the expected excess risk. Convergence rates were computed for different hyperparameters, and the best set of hyperparameters (changing with respect to the number of samples but constant over run) was taken to show the best achievable convergence rate.'