Notice: This website is continuously updated as new conference proceedings and journal volumes are published. Consequently, the figures presented here may differ from those reported in our publications.
A brief overview of our methodology is provided on the Methods page, along with references to publications documenting our approach and links to the code and data used in each study.
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.
Convergence Analysis of Gradient Descent for Eigenvector Computation
Authors: Zhiqiang Xu, Xin Cao, Xin Gao
IJCAI 2018 | Venue PDF | LLM Run Details | Input Tokens: 16,349 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 2,829 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Theoretical properties are verified in experiments. |
| Researcher Affiliation | Academia | 1 KAUST, Saudi Arabia 2 UNSW, Australia EMAIL, EMAIL, EMAIL |
| Pseudocode | No | The paper contains mathematical equations and derivations but does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any specific links to open-source code or explicitly state that the code for the described methodology is publicly available. |
| Open Datasets | No | For synthetic data, the paper describes how it is generated (e.g., "follow [Shamir, 2015] to generate data") but does not provide a direct link to a publicly available dataset or a citation with author names and year for the specific dataset used. For real data, it mentions "Schenk1" and provides a URL "www.cise.ufl.edu/research/sparse/matrices/" but this is a general collection and not a direct link/citation to a specific dataset or file used within the context of this paper. |
| Dataset Splits | No | The paper does not provide specific details on training, validation, or test dataset splits (e.g., percentages or sample counts). |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., CPU, GPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions 'matlab s eigs function' but does not specify any software dependencies with version numbers. |
| Experiment Setup | Yes | If the initial x0 = y y 2 where entries of y are i.i.d. standard normal samples, i.e., yi N(0, 1)... The solver with constant step-sizes α < p 2λ2 1(1+α p) will converge... the solver with diminishing step-sizes αt = c τ+t for sufficiently large constants c, τ > 0 will converge... We set n = 1000 and follow [Shamir, 2015] to generate data using the full eigenvalue decomposition A = UΣU . Σ = diag(Σ1, Σ2), where Σ2 = diag( |g1| / n , ..., |gn r| / n ) with gi N(0, 1) and r being the order of Σ1. In addition, the following two settings are considered: p = 1: Σ1 = diag(1, 1 η, 1 1.1η, 1 1.2η, 1 1.3η, 1 1.4η), and then p / λ1 = η > 0, where η {0.2, 0.5, 0.8}. p = 3: Σ1 = diag(1, 1, 1), and then p / λ1 = 1 |g1| / n . (Figure 1 labels: c=12.87, τ=10; c=14.48, τ=10; c=16.09, τ=10). |