Subgradient Descent Learns Orthogonal Dictionaries
Authors: Yu Bai, Qijia Jiang, Ju Sun
ICLR 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Preliminary synthetic and real experiments corroborate our analysis and show that our algorithm works well empirically in recovering orthogonal dictionaries. |
| Researcher Affiliation | Academia | Yu Bai, Qijia Jiang & Ju Sun Stanford University {yub,qjiang2,sunju}@stanford.edu |
| Pseudocode | No | The algorithm is described by a mathematical formula for the update rule: 'q(k+1) = q(k) η(k)v q(k) η(k)v , for k = 0, 1, 2, . . . . (3.16)' but is not presented in a formal pseudocode block or algorithm environment. |
| Open Source Code | No | The paper references 'GRANSO,6 Available online: http://www.timmitchell.com/software/GRANSO/' as a third-party tool used for additional experiments, but it does not provide source code for the methodology developed in this paper. |
| Open Datasets | No | The paper uses synthetic data generated internally and 'Two natural images are picked for this experiment', but no specific public dataset names, links, DOIs, or citations for dataset access are provided for either. |
| Dataset Splits | No | The paper does not explicitly describe training, validation, or test dataset splits. It mentions generating 'problem instances' for synthetic data and dividing images into 'blocks' but not traditional ML splits. |
| Hardware Specification | Yes | For a large dictionary of dimension n = 400 and sample complexity m = 10n2 (i.e., 1.6 106), GRANSO successfully identifies a basis after 1500 iterations with CPU time 4 hours on a two-socket Intel Xeon E5-2640v4 processor (10-core Broadwell, 2.40 GHz) |
| Software Dependencies | No | The paper mentions using 'GRANSO' as a 'quasi-Newton type method' in Appendix H, but it does not specify version numbers for GRANSO or any other software dependencies. |
| Experiment Setup | Yes | To recover the dictionary, we run the Riemannian subgradient descent algorithm Eq. (3.16) with decaying step size η(k) = 1/ k, corresponding to the boundary case α = 1/2 in Theorem 3.8 with a much better base size. ... we perform R = round (5n log n) runs on each instance. |