Neural Wasserstein Gradient Flows for Discrepancies with Riesz Kernels
Authors: Fabian Altekrüger, Johannes Hertrich, Gabriele Steidl
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In the following, we evaluate our results based on numerical examples. In Subsection 6.1, we benchmark the different numerical schemes based on the interaction energy flow starting at δ0. Here, we can evaluate the quality of the outcome based on the analytic results in Sect. 5. In Subsection 6.2, we apply the different schemes for MMD Wasserstein flows. Since no ground truth is available, we can only compare the visual impression. The implementation details and advantages of the both neural schemes are given in Appendix E1. |
| Researcher Affiliation | Academia | 1Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany 2Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany. |
| Pseudocode | Yes | Algorithm 1 Neural backward scheme; Algorithm 2 Neural forward scheme |
| Open Source Code | Yes | The code is available at https://github.com/Fabian Altekrueger/Neural Wasserstein Gradient Flows |
| Open Datasets | Yes | In order to show the scalability of the methods, we can use the proposed methods to sample from the MNIST dataset (Le Cun et al., 1998). |
| Dataset Splits | No | No specific dataset split information (percentages, sample counts, or predefined splits) is provided. The paper mentions: 'In Sect. 6.2 we use a full batch size for 5000 iterations in the first two time steps and then 1000 iterations for the neural forward scheme and for the neural backward scheme 20000 and 10000 iterations, respectively.' |
| Hardware Specification | No | No specific hardware details (e.g., exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) are provided. The paper discusses network sizes and batch sizes used for experiments. |
| Software Dependencies | No | No specific version numbers are provided for software dependencies. The paper mentions: 'Our code is written in Py Torch (Paszke et al., 2019).' |
| Experiment Setup | Yes | In Sect. 6.1 we use a batch size of 6000 in two and three dimensions... and a time step size of τ = 0.05 for all methods... train the networks with Adam optimizer... with a learning rate of 1e 3... train the neural forward scheme for 25000 iterations... and the neural backward scheme for 20000 iterations using a learning rate of 5e 4. |