Efficiently escaping saddle points on manifolds
Authors: Christopher Criscitiello, Nicolas Boumal
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Generalizing Jin et al. s recent work on perturbed gradient descent (PGD) for optimization on linear spaces [...], we propose a version of perturbed Riemannian gradient descent (PRGD) to show that necessary optimality conditions can be met approximately with high probability, without evaluating the Hessian. ... This matches the complexity of PGD in the Euclidean case. Crucially, the dependence on dimension is low. ... The algorithm requires knowledge of the Lipschitz constants defined below, which makes this a mostly theoretical algorithm but see Appendix D for explicit constants in the case of PCA. |
| Researcher Affiliation | Academia | Chris Criscitiello Department of Mathematics Princeton University Princeton, NJ 08544 ccriscitiello6@gmail.com Nicolas Boumal Department of Mathematics Princeton University Princeton, NJ 08544 nboumal@math.princeton.edu |
| Pseudocode | Yes | Algorithm 1 PRGD(x0, , r, T , , T, b) ... procedure TANGENTSPACESTEPS(x, s0, , b, T ) |
| Open Source Code | No | No explicit statement or link providing access to the source code for the described methodology was found. The paper indicates its theoretical nature: 'The algorithm requires knowledge of the Lipschitz constants defined below, which makes this a mostly theoretical algorithm but see Appendix D for explicit constants in the case of PCA.' |
| Open Datasets | No | The paper is theoretical and does not conduct experiments, therefore no dataset information is provided. It mentions applications like 'PCA and low-rank matrix completion' but these are not datasets used in empirical evaluation. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments with data, therefore no information about dataset splits for training, validation, or testing is provided. |
| Hardware Specification | No | The paper is theoretical and does not describe empirical experiments, therefore no hardware specifications are provided. |
| Software Dependencies | No | The paper is theoretical and does not describe empirical experiments or specific implementations, therefore no software dependencies with version numbers are provided. |
| Experiment Setup | No | The paper is theoretical and does not describe empirical experiments, therefore no experimental setup details such as hyperparameters or training configurations are provided. |