Riemannian Convex Potential Maps
Authors: Samuel Cohen, Brandon Amos, Yaron Lipman
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate that these flows can model standard distributions on spheres, and tori, on synthetic and geological data. Our experimental demonstrations show that RCPMs are competitive and model standard distributions on spheres and tori. We further show a case study in modeling continental drift where we transport Earth s land mass on the sphere. This section empirically demonstrates the practicality and flexibility of RCPMs. We consider synthetic manifold learning tasks similar to Rezende et al. (2020); Lou et al. (2020) on both spheres and tori, and a real-life application over the sphere. |
| Researcher Affiliation | Collaboration | 1University College London 2Facebook AI Research 3Weizmann Institute of Science. |
| Pseudocode | No | The paper describes mathematical formulations and derivations, but it does not include any explicitly labeled pseudocode blocks or algorithms. |
| Open Source Code | Yes | Our source code is freely available online at github.com/facebookresearch/rcpm. |
| Open Datasets | No | The paper mentions using 'synthetic' data for spheres and tori and 'geological data' for continental drift, attributing the source maps to '2020 Colorado Plateau Geosystems Inc.'. While these sources might allow for data reconstruction or access, the paper does not provide concrete access information such as specific URLs, DOIs, repository names, or formal citations with authors and years for publicly available datasets. |
| Dataset Splits | No | The paper describes training and evaluating models, and refers to metrics like KL and ESS, but it does not explicitly specify the proportion or number of samples used for training, validation, or test sets, nor does it mention cross-validation setups. |
| Hardware Specification | No | The paper compares runtime with other models but does not provide any specific details about the hardware used for its experiments, such as GPU models, CPU types, or cloud computing specifications. |
| Software Dependencies | No | The paper acknowledges the use of several software libraries (JAX, Hydra, Jupyter, Matplotlib, numpy, pandas, SciPy) and cites their respective original publication years. However, it does not provide specific version numbers for these software dependencies, which are required for precise replication. |
| Experiment Setup | Yes | More implementation details are provided in app. C. |