Escaping from saddle points on Riemannian manifolds
Authors: Yue Sun, Nicolas Flammarion, Maryam Fazel
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In our numerical experiment, we choose H to be a diagonal matrix H = diag(0, 1, 2, 3, 4) and let k = 3. The Euclidean basis (ei) are an eigenbasis of H and the first order stationary points of the objective function are [ei1, ei2, ei3]G with distinct basis and G being unitary. The local minimizers are [e3, e4, e5]G. We start the iteration at X0 = [e2, e3, e4] and see in Fig. 3 the algorithm converges to a local minimum. |
| Researcher Affiliation | Academia | Yue Sun University of Washington Seattle, WA 98105 yuesun@uw.edu Nicolas Flammarion EPFL Lausanne, Switzerland nicolas.flammarion@epfl.ch Maryam Fazel University of Washington Seattle, WA 98105 mfazel@uw.edu |
| Pseudocode | Yes | Algorithm 1 Perturbed Riemannian gradient algorithm |
| Open Source Code | No | The paper mentions 'Manopt, a Matlab toolbox for optimization on manifolds' and other 'open-source packages' but does not provide a specific link or statement about the open-sourcing of the code implemented for this paper's methodology. |
| Open Datasets | No | The paper describes experiments on a 'k PCA problem' with a constructed matrix H = diag(0, 1, 2, 3, 4) and a 'Burer-Monteiro approach' with a constructed sparse matrix A R100 20. It does not mention using or providing access to any publicly available or open datasets. |
| Dataset Splits | No | The paper does not provide specific dataset split information (e.g., percentages, sample counts, or citations to predefined splits) for training, validation, or testing. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper mentions 'Manopt, a Matlab toolbox for optimization on manifolds' and 'geomstats: a python package' but does not provide specific version numbers for any ancillary software used in its experiments. |
| Experiment Setup | Yes | Set constants: ˆc 4, C := C(K, β, ρ) (defined in Lemma 2 and proof of Lemma 8) and cmax 1 56ˆc2 , r = cmax χ2 ϵ, χ = 3 max{log( dβ(f(x0) f ) ˆcϵ2δ ), 4}. Set threshold values: fthres = cmax ρ , gthres = cmax χ2 ϵ, tthres = χ cmax β ρϵ, tnoise = tthres 1. Set stepsize: η = cmax β . |