Optimization without Retraction on the Random Generalized Stiefel Manifold
Authors: Simon Vary, Pierre Ablin, Bin Gao, Pierre-Antoine Absil
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments demonstrate its effectiveness in various machine learning applications involving generalized orthogonality constraints, including CCA, ICA, and the GEVP. |
| Researcher Affiliation | Collaboration | ICTEAM Institute, UCLouvain, Louvain-la-neuve, Belgium Department of Statistics, University of Oxford, Oxford, United Kingdom Apple Machine Learning Group, Paris, France Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China. |
| Pseudocode | No | The paper describes the iterative update rule as a mathematical formula (e.g., Xk+1 = Xk ηkΛξk,ζk,ζ k(Xk)) but does not provide a clearly labeled pseudocode block or algorithm section. |
| Open Source Code | Yes | The code is available at: https://github.com/simonvary/landing-generalized-stiefel. |
| Open Datasets | Yes | For stochastic CCA, we use the benchmark problem used by Ma et al. (2015); Wang et al. (2016), in which the MNIST dataset is split in half by taking left and right halves of each image, and compute the top-p canonical correlation components by solving (3). |
| Dataset Splits | No | The paper mentions using the MNIST dataset and its size (N=60,000), but it does not specify explicit training, validation, or test dataset splits (e.g., percentages or sample counts) needed for reproduction. |
| Hardware Specification | No | The paper mentions "CUDA implementation using cupy" in the context of computational time comparisons, implying the use of GPUs. However, it does not provide any specific hardware details such as GPU models (e.g., NVIDIA A100, RTX 3090), CPU models, memory specifications, or cloud computing instance types used for the experiments. |
| Software Dependencies | No | The paper mentions "CUDA implementation using cupy" but does not specify version numbers for either CUDA or the cupy library, nor does it list other software dependencies with their versions. |
| Experiment Setup | Yes | All methods use the fixed stepsize η = 0.1, and the landing methods have ω = 1. The normalizing parameter ω is chosen to be ω = 105 for the landing with ΨR B(X), ω = 0.1 for the landing with ΨB(X), and ω = 200 for PLAM. In our experiments, we have N = 60 000, n = 392, p = 5, and r = 512. |