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..
Gradient Descent Meets Shift-and-Invert Preconditioning for Eigenvector Computation
Authors: Zhiqiang Xu
NeurIPS 2018 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We test our algorithm on both synthetic and real data. Throughout experiments, our SI-rg EIGS solver is warm-started by a few power iterations, and four iterations of Nesterov s AGD are run to approximately solve the least-squares subproblems. The same initial x0 is used for different solvers. All the algorithms are implemented in matlab and running single threaded. All the ground-truth information is obtained by matlab s eigs function for benchmarking purpose. |
| Researcher Affiliation | Industry | Zhiqiang Xu Cognitive Computing Lab (CCL), Baidu Research National Engineering Laboratory of Deep Learning Technology and Application, China EMAIL |
| Pseudocode | Yes | Algorithm 1 Shift-and-Inverted Riemannian Gradient Descent Eigensolver |
| Open Source Code | Yes | The implementation of our algorithm is available at https://github.com/zhiqiangxu2001/SI-rg EIGS. |
| Open Datasets | Yes | We follow Shamir [2015] to generate synthetic data. Note that A s full eigenvalue decomposition can be written as A = VnΣV n , where Σ is diagonal. Thus, it suffices to generate random orthogonal matrix Vn and set Σ = diag(1, 1 , 1 1.1 , , 1 1.4 , g1/n, , gn 6/n) with gi being standard normal samples, i.e., gi N(0, 1). Here we set n = 1000 and σ = 1.005 |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, or detailed splitting methodology) for training, validation, or testing. |
| Hardware Specification | No | The paper states that algorithms are implemented in MATLAB and run single-threaded, but it does not provide specific hardware details (e.g., CPU/GPU models, memory). |
| Software Dependencies | No | The paper states that algorithms are 'implemented in matlab' but does not specify the MATLAB version or any other software dependencies with version numbers. |
| Experiment Setup | Yes | Throughout experiments, our SI-rg EIGS solver is warm-started by a few power iterations, and four iterations of Nesterov s AGD are run to approximately solve the least-squares subproblems. The same initial x0 is used for different solvers. Constant step-sizes are hand-tuned. For real data, we explore an automatic step-size scheme, specifically, Barzilai-Borwein (BB) step-size, which is a non-monotone step-size scheme and performs well in practice [Wen and Yin, 2013]. In our context, it is set as follows: αt+1 = xt xt 1 2 2 /|(xt xt 1) (ˆgt ˆgt 1)|, or αt+1 = |(xt xt 1) (ˆgt ˆgt 1)| / ˆgt ˆgt 1 2 2 . |