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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Continuous-time Riemannian SGD and SVRG Flows on Wasserstein Probabilistic Space
Authors: Mingyang Yi, Bohan Wang
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we empirically evaluate the proposed sampling algorithms on two examples. Gaussian. In this case, we set N = 100, d = 2, µξi (ξi, I) with each ξi N (0, I). Then, we get the target distribution µ N( ξ, I). Within this framework, we report the KL divergence DKL(πηT µ) and the Fisher divergence grad DKL(πηT µ) 2 (first order criteria), where the πηT is obtained by Riemannian GD flow, Riemannian SGD flow or SVRG flow. In this case, due to Example 1, the two criteria can be explicitly estimated. The results are summarized in Figure 3. Mixture Gaussian. In this case, we set N = 5, d = 2 with µξi 1/2N(ξi,1, I) + 1/2N(ξi,2, I), where ξi,k N(0, I). Unfortunately, the proposed flows can not be explicitly computed. Therefore, we implement their discrete versions as in Algorithms 1, 2. Then we report the KL divergence DKL(πηT µ) and Fisher divergence grad DKL(πηT µ) 2 with πηT are approximated by the discrete Riemannian GD, SGD, and SVRG Algorithms. Here, the KL divergence and Riemannian gradient are estimated by density estimation as in [], with 1000 independent samples. The results are summarized in Figure 3. |
| Researcher Affiliation | Collaboration | 1 Renmin University of China 2 Alibaba Group EMAIL EMAIL |
| Pseudocode | Yes | Algorithm 1 Discrete Riemannian SGD Input: Exponential map Exp, initialized π0, learning rate η, steps M. 1: for n = 0, , M 1 do 2: Sample ξn ξ independent with πn; 3: Update πn+1 = Expπn [ ηgrad DKL(π µξn)]; 4: end for 5: Return: πM. Algorithm 2 Discrete Riemannian SVRG Input: Exponential map Expπ, initialized π0, learning rate η, epoch I, steps M of each epoch. 1: Take π0 0 = π0; 2: for i = 0, , I 1 do 3: Compute grad F(πi 0) = 1/N PN j=1 gradfξj(πi 0) 4: for n = 0, , M 1 do 5: Uniformly sample ξi n {ξ1, , ξN} independent with πi n; 6: Update πi n+1 = Expπin[ η(gradfξin(πi n) Γπi n πi 0 (gradfξin(πi 0) grad F(πi 0)))]; 7: end for 8: πi+1 0 = πi M; 9: end for 10: Return: πN. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide any links to a code repository. The NeurIPS checklist sections for code access are marked as 'NA'. |
| Open Datasets | Yes | Gaussian. In this case, we set N = 100, d = 2, µξi (ξi, I) with each ξi N (0, I). Then, we get the target distribution µ N( ξ, I). Mixture Gaussian. In this case, we set N = 5, d = 2 with µξi 1/2N(ξi,1, I) + 1/2N(ξi,2, I), where ξi,k N(0, I). |
| Dataset Splits | No | The paper uses synthetically generated Gaussian and Mixture Gaussian data for its experiments. It describes how these datasets are constructed but does not mention any explicit training/test/validation splits, as the experiments involve direct simulation or approximation of flows rather than a standard machine learning task with data partitioning. |
| Hardware Specification | No | The paper does not specify any particular hardware used for running the experiments. The NeurIPS checklist question regarding 'Experiments Compute Resources' is marked as 'NA'. |
| Software Dependencies | No | The paper does not mention any specific software dependencies (e.g., programming languages, libraries, frameworks) or their version numbers used to conduct the experiments. The NeurIPS checklist question regarding 'Experimental Setting/Details' is marked as 'NA'. |
| Experiment Setup | Yes | Algorithm 1 Discrete Riemannian SGD Input: Exponential map Exp, initialized π0, learning rate η, steps M. ... Algorithm 2 Discrete Riemannian SVRG Input: Exponential map Expπ, initialized π0, learning rate η, epoch I, steps M of each epoch. ... In this case, we set N = 100, d = 2, µξi (ξi, I) with each ξi N (0, I). ... In this case, we set N = 5, d = 2 with µξi 1/2N(ξi,1, I) + 1/2N(ξi,2, I), where ξi,k N(0, I). ... Here, the KL divergence and Riemannian gradient are estimated by density estimation as in [], with 1000 independent samples. |