Riemannian coordinate descent algorithms on matrix manifolds
Authors: Andi Han, Pratik Jawanpuria, Bamdev Mishra
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5. Experiments. We now benchmark the performance of the proposed RCD and RCDlin algorithms in terms of computational efficiency (flop counts and/or runtime) and convergence quality (distance to optimality). |
| Researcher Affiliation | Collaboration | 1Riken AIP, Japan 2Microsoft India. Correspondence to: Andi Han <andi.han@riken.jp>. |
| Pseudocode | Yes | Algorithm 1 Riemannian coordinate descent (RCD/RCDlin) |
| Open Source Code | Yes | Our codes are implemented using the Manopt toolbox (Boumal et al., 2014) and run on a laptop with an i5-10500 3.1GHz CPU processor. The codes are available at https://github.com/andyjm3. |
| Open Datasets | Yes | For experiment settings, we train 5-dimensional embeddings (n = 5) for Word Net mammals subtree (Miller, 1998). |
| Dataset Splits | No | The paper describes generating synthetic data for some experiments and using WordNet, but no explicit train/validation/test dataset splits (e.g., percentages, sample counts, or specific predefined splits) are provided for reproducibility of data partitioning. |
| Hardware Specification | Yes | Our codes are implemented using the Manopt toolbox (Boumal et al., 2014) and run on a laptop with an i5-10500 3.1GHz CPU processor. |
| Software Dependencies | No | Our codes are implemented using the Manopt toolbox (Boumal et al., 2014). However, no specific version numbers for Manopt or other software dependencies are provided. |
| Experiment Setup | Yes | For all the methods, we tune the stepsize. ... For RCDlin-c and RCDlin-tc, we use a linearly-decaying stepsize, i.e., η/(1 + 0.1 epoch). For RGD we use a fixed stepsize η which generally leads to better convergence. We tune and set η = 1.0 for RCDlin and 0.5 for RGD. ... We set S = np/5 and select the coordinates randomly without replacement. |