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..
Hessian-guided Perturbed Wasserstein Gradient Flows for Escaping Saddle Points
Authors: Naoya Yamamoto, Juno Kim, Taiji Suzuki
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this study, we propose a perturbative modification to WGF that efficiently avoids saddle points. ... We theoretically derive the computational complexity for PWGF to achieve a second-order stationary point. Furthermore, we prove that PWGF converges to a global optimum in polynomial time for strictly benign objectives. |
| Researcher Affiliation | Academia | Naoya Yamamoto The University of Tokyo EMAIL Juno Kim UC Berkeley EMAIL Taiji Suzuki The University of Tokyo, RIKEN AIP EMAIL |
| Pseudocode | Yes | Algorithm 1 PWGF (continuous-time) ... Algorithm 2 PWGF (discrete-time) |
| Open Source Code | No | Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [NA] Justification: The conducted experiments are toy simulations. |
| Open Datasets | No | Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [NA] Justification: The conducted experiments are toy simulations. |
| Dataset Splits | No | The paper describes synthetic data generation for numerical experiments, such as 'generated 800 i.i.d. input data points z from the standard normal distribution N(0, 1) for each coordinate'. This is data generation, not dataset splitting in the conventional sense of training, validation, and test sets from a pre-existing dataset. |
| Hardware Specification | No | The paper does not provide specific hardware details. Appendix F, which covers Experimental details, mentions input/output dimensions and number of neurons but no information on GPUs, CPUs, or memory. |
| Software Dependencies | No | The paper mentions 'SGD was used in the optimization process' but does not specify its version or any other software dependencies with version numbers. |
| Experiment Setup | Yes | Experimental details. ... We used parameters as ηp = 0.015, kthres = 100. In addition, SGD was used in the optimization process with the learning rate η = 10 7. ... We set kthres = 100, ηp = 3 10 3, Fthres = 10 2. |