A Dynamical System View of Langevin-Based Non-Convex Sampling
Authors: Mohammad Reza Karimi Jaghargh, Ya-Ping Hsieh, Andreas Krause
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | To address these issues, we develop a novel framework that lifts the above issues by harnessing several tools from the theory of dynamical systems. Our key result is that, for a large class of state-of-the-art sampling schemes, their last-iterate convergence in Wasserstein distances can be reduced to the study of their continuous-time counterparts, which is much better understood. Coupled with standard assumptions of MCMC sampling, our theory immediately yields the last-iterate Wasserstein convergence of many advanced sampling schemes such as mirror Langevin, proximal, randomized mid-point, and Runge-Kutta methods. |
| Researcher Affiliation | Academia | Mohammad Reza Karimi ETH Zürich mkarimi@inf.ethz.ch Ya-Ping Hsieh ETH Zürich yaping.hsieh@inf.ethz.ch Andreas Krause ETH Zürich krausea@ethz.ch |
| Pseudocode | No | The paper describes algorithms using mathematical equations and descriptions (e.g., (LRM), (RMM), (ORMM)), but it does not provide any explicitly labeled pseudocode blocks or algorithms. |
| Open Source Code | No | The paper does not provide any statement or link indicating that open-source code for the described methodology is available. |
| Open Datasets | No | This is a theoretical paper and does not involve training on datasets. Therefore, it does not mention public datasets for training. |
| Dataset Splits | No | This is a theoretical paper and does not involve empirical experiments with data splits. Therefore, it does not provide training/test/validation dataset splits. |
| Hardware Specification | No | This is a theoretical paper and does not report on empirical experiments. Therefore, it does not describe the hardware used to run experiments. |
| Software Dependencies | No | This is a theoretical paper and does not report on empirical experiments. Therefore, it does not provide specific version numbers for software dependencies. |
| Experiment Setup | No | This is a theoretical paper and does not report on empirical experiments. Therefore, it does not provide details about an experimental setup, such as hyperparameters or training settings. |