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 [1].
The Sparse-Plus-Low-Rank Quasi-Newton Method for Entropic-Regularized Optimal Transport
Authors: Chenrui Wang, Yixuan Qiu
ICML 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, the convergence properties of the proposed algorithm are rigorously analyzed, and various numerical experiments are conducted to demonstrate its improved performance in solving large-scale OT problems. |
| Researcher Affiliation | Academia | 1School of Statistics and Data Science, Shanghai University of Finance and Economics, Shanghai, China. Correspondence to: Yixuan Qiu <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 The Sparse-plus-low-rank quasi-Newton method for entropic-regularized OT Algorithm 2 Sparsification scheme with a given density |
| Open Source Code | Yes | An efficient implementation of the method is included in the Reg OT Python package1. 1https://github.com/yixuan/regot-python The experiments in this section can be reproduced using the code on our Github repository2. 2https://github.com/Aoblex/numerical-experiments |
| Open Datasets | Yes | Specifically, we randomly select two images from the MNIST (Lecun et al., 1998) or Fashion-MNIST (Xiao et al., 2017) dataset... Finally, we reproduce the Image Net experiment in Tang & Qiu (2024) that uses OT to characterize the difference between two data distributions. |
| Dataset Splits | No | The paper describes synthetic datasets by their generation mechanism and image datasets by random selection of images, but it does not specify explicit training/test/validation splits for models, nor does it provide sample counts or percentages for partitioning data in a reproducible manner for typical machine learning experiments. |
| Hardware Specification | Yes | All experiments in this article are conducted on a personal computer with an Intel i9-13900K CPU, 32 GB memory, and a Ubuntu 25.04 operating system. |
| Software Dependencies | Yes | All experiments in this article are conducted on a personal computer with an Intel i9-13900K CPU, 32 GB memory, and a Ubuntu 25.04 operating system. |
| Experiment Setup | Yes | We consider both synthetic and realistic OT settings, and fix the regularization parameter to be η = 0.001. To make η comparable for different problems, we normalize all cost matrices to have a unit infinity norm, i.e., M M/ M . Line search method Finally, we use the Mor e Thuente line search algorithm (Mor e & Thuente, 1994) to compute the step size αk > 0 that satisfies the Wolfe conditions: f(xk + αkdk) f(xk) + c1αk(g T k dk), [g(xk + αkdk)]T dk c2(g T k dk), where 0 < c1 < 1/2 and c1 < c2 < 1 are pre-specified constants. To avoid introducing a large approximation error, we dynamically set τk to be the current gradient norm gk , so that the τk I term in (5) is negligible when xk is close to the optimum. An additional safeguard is to set a maximum shift τmax, in case gk is too large at the beginning. So overall, we take τk = min{τmax, gk } in each iteration. Based on this idea, the update rule for ρk is: ( max{ρmin, 0.99ρk 1}, if gk < gk 1 min{ρmax, 1.1ρk 1}, otherwise . |