On the Sample Complexity of Learning under Geometric Stability
Authors: Alberto Bietti, Luca Venturi, Joan Bruna
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we provide simple numerical experiments on synthetic data which illustrate our theoretical results. In Figure 1, we consider KRR on 5 000 training samples with inputs uniformly distributed on Sd 1, and outputs generated according to a target non-smooth function f = SGg , with g (x) = {w x 0.7}, where the averaging operator SG is over different groups in each plot. The regularization parameter λ is optimized on 5 000 test samples. We use the dot-product kernel function κ(u) = (u + 1)κ1(u), where κ1 is the arc-cosine kernel of degree 1, which corresponds to an infinite-width shallow Re LU network [9]. |
| Researcher Affiliation | Academia | Alberto Bietti NYU alberto.bietti@nyu.edu Luca Venturi NYU lv800@nyu.edu Joan Bruna NYU bruna@cims.nyu.edu Center for Data Science, New York University. Courant Institute for Mathematical Sciences, New York University. Center for Data Science and Courant Institute for Mathematical Sciences, New York University. |
| Pseudocode | No | The paper does not contain any clearly labeled 'Pseudocode' or 'Algorithm' sections, nor does it present any structured steps formatted like code or an algorithm. |
| Open Source Code | No | The paper does not include any explicit statements about releasing source code for the described methodology, nor does it provide a direct link to a code repository. |
| Open Datasets | No | The paper states, 'We consider KRR on 5 000 training samples with inputs uniformly distributed on Sd 1', indicating the use of synthetic data generated by the authors, for which no concrete access information (link, DOI, repository, or citation to an established public dataset) is provided. |
| Dataset Splits | No | The paper mentions '5 000 training samples' and '5 000 test samples', with the regularization parameter optimized on the test samples. However, it does not explicitly state a separate 'validation' split or percentage. |
| Hardware Specification | No | The paper describes its numerical experiments in Section 6 but does not provide any specific details regarding the hardware used, such as GPU models, CPU types, or memory. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, such as library names with version numbers, needed to replicate the experiment setup. |
| Experiment Setup | Yes | In this section, we provide simple numerical experiments on synthetic data which illustrate our theoretical results. In Figure 1, we consider KRR on 5 000 training samples with inputs uniformly distributed on Sd 1, and outputs generated according to a target non-smooth function f = SGg , with g (x) = {w x 0.7}, where the averaging operator SG is over different groups in each plot. The regularization parameter λ is optimized on 5 000 test samples. We use the dot-product kernel function κ(u) = (u + 1)κ1(u), where κ1 is the arc-cosine kernel of degree 1, which corresponds to an infinite-width shallow Re LU network [9]. |