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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.
Escape saddle points by a simple gradient-descent based algorithm
Authors: Chenyi Zhang, Tongyang Li
NeurIPS 2021 | Venue PDF | LLM Run Details | Input Tokens: 18,153 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 4,510 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 | Finally, we also perform numerical experiments that support our results. We perform our negative curvature ο¬nding algorithms using GD or SGD in various landscapes and general classes of nonconvex functions, and use comparative studies to show that our Algorithm 1 and Algorithm 3 achieve a higher probability of escaping saddle points using much fewer iterations than PGD and PSGD (typically less than 1/3 times of the iteration number of PGD and 1/2 times of the iteration number of PSGD, respectively). Moreover, we perform numerical experiments benchmarking the solution quality and iteration complexity of our algorithm against accelerated methods. |
| Researcher Affiliation | Academia | 1 Institute for Interdisciplinary Information Sciences, Tsinghua University, China 2 Center on Frontiers of Computing Studies, Peking University, China 3 School of Computer Science, Peking University, China 4 Center for Theoretical Physics, Massachusetts Institute of Technology, USA |
| Pseudocode | Yes | Algorithm 1: Negative Curvature Finding( x, r, T ). Algorithm 2: Perturbed Accelerated Gradient Descent with Accelerated Negative Curvature Finding(x0, , gamma, s, T 0, r0) Algorithm 3: Stochastic Negative Curvature Finding(x0, rs, Ts, m). |
| Open Source Code | Yes | All the experiments are performed on MATLAB R2019b on a computer with Six-Core Intel Core i7 processor and 16GB memory, and their codes are given in the supplementary material. |
| Open Datasets | No | The paper uses synthetic test functions (e.g., f(x1, x2) = 1/16 * x1^4 - 1/2 * x2^2) rather than publicly available datasets for its experiments. Therefore, there is no information about publicly available training data. |
| Dataset Splits | No | The paper focuses on theoretical convergence rates and numerical experiments on synthetic functions, and thus does not describe traditional training/validation/test dataset splits. |
| Hardware Specification | Yes | All the experiments are performed on MATLAB R2019b on a computer with Six-Core Intel Core i7 processor and 16GB memory |
| Software Dependencies | Yes | All the experiments are performed on MATLAB R2019b |
| Experiment Setup | Yes | Parameters: = 0.05 (step length), r = 0.1 (ball radius in PGD and parameter r in Algorithm 1), M = 300 (number of samplings). Parameters: = 0.02 (step length), r = 0.01 (variance in PSGD and rs in Algorithm 3), M = 300 (number of samplings). |