Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Escaping from saddle points on Riemannian manifolds
Authors: Yue Sun, Nicolas Flammarion, Maryam Fazel
NeurIPS 2019 | Venue PDF | 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 EMAIL Nicolas Flammarion EPFL Lausanne, Switzerland EMAIL Maryam Fazel University of Washington Seattle, WA 98105 EMAIL |
| 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 . |