Improved Particle Approximation Error for Mean Field Neural Networks
Authors: Atsushi Nitanda
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we improve the dependence on logarithmic Sobolev inequality (LSI) constants in their particle approximation errors which can exponentially deteriorate with the regularization coefficient. Specifically, we establish an LSI-constant-free particle approximation error concerning the objective gap by leveraging the problem structure in risk minimization. As the application, we demonstrate improved convergence of MFLD, sampling guarantee for the mean-field stationary distribution, and uniform-in-time Wasserstein propagation of chaos in terms of particle complexity. |
| Researcher Affiliation | Collaboration | Atsushi Nitanda CFAR and IHPC, Agency for Science, Technology and Research (A STAR), Singapore College of Computing and Data Science, Nanyang Technological University, Singapore atsushi_nitanda@cfar.a-star.edu.sg |
| Pseudocode | No | The paper describes mathematical derivations and proofs but does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper is theoretical and does not mention releasing any source code or provide links to a code repository. The NeurIPS checklist confirms that the paper does not include experiments, implying no code release for such. |
| Open Datasets | No | This paper is theoretical and does not involve experiments or the use of datasets. |
| Dataset Splits | No | This paper is theoretical and does not involve experiments or specify dataset splits for training, validation, or testing. |
| Hardware Specification | No | This paper is theoretical and does not include experiments that would require hardware specifications. The NeurIPS checklist (Question 8, Answer NA) confirms this. |
| Software Dependencies | No | This paper is theoretical and does not include experiments that would require specific software dependencies with version numbers. The NeurIPS checklist (Question 6, Answer NA) confirms this. |
| Experiment Setup | No | This paper is theoretical and does not include experiments or describe an experimental setup. The NeurIPS checklist (Question 6, Answer NA) confirms this. |