Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds
Authors: Clément Bonet, Lucas Drumetz, Nicolas Courty
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Then, we propose different applications such as classification of documents with a suitably learned ground cost on a manifold, and data set comparison on a product manifold. Additionally, we derive non-parametric schemes to minimize these new distances by approximating their Wasserstein gradient flows. |
| Researcher Affiliation | Academia | Cl ement Bonet EMAIL ENSAE, CREST, Institut Polytechnique de Paris Lucas Drumetz EMAIL IMT Atlantique, Lab-STICC Nicolas Courty EMAIL Universit e Bretagne Sud, IRISA |
| Pseudocode | Yes | Algorithm 1 Wasserstein gradient flows of CHSW |
| Open Source Code | Yes | 1. Code available at https://github.com/clbonet/Sliced-Wasserstein_Distances_and_Flows_on_ Cartan-Hadamard_Manifolds |
| Open Datasets | Yes | On Table 1, we report the results for the BBCSport data set (Kusner et al., 2015), the Movies reviews data set (Pang et al., 2002) and the Goodread data set (Maharjan et al., 2017). ... We focus here on *NIST data sets, which include MNIST (Le Cun and Cortes, 2010), EMNIST (Cohen et al., 2017), Fashion MNIST (Xiao et al., 2017), KMNIST (Clanuwat et al., 2018), and USPS (Hull, 1994). |
| Dataset Splits | Yes | All the data sets are split in 5 different train/test sets. |
| Hardware Specification | Yes | We used as CPU an Intel Xeon 4214 and as GPU a Titan RTX. |
| Software Dependencies | No | We use the pytorch-metric-learning library (Musgrave et al., 2020) to learn A. ... The Wasserstein distance is computed using the Python Optimal Transport (POT) library (Flamary et al., 2021). The paper mentions these libraries but does not provide specific version numbers for them or other key software components like Python or PyTorch. |
| Experiment Setup | Yes | SW is approximated with L = 500 projections. ... As hyperparameters, we chose n = 500 particles, a learning rate of τ = 0.1 with N = 200 epochs for centered targets, and τ = 0.5 with N = 300 epochs for bordered targets. |