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.
How to Escape Saddle Points Efficiently
Authors: Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M. Kakade, Michael I. Jordan
ICML 2017 | Venue PDF | LLM Run Details | Input Tokens: 17,083 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 5,270 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper shows that a perturbed form of gradient descent converges to a second-order stationary point in a number iterations which depends only poly-logarithmically on dimension (i.e., it is almost dimension-free ). The convergence rate of this procedure matches the well-known convergence rate of gradient descent to first-order stationary points, up to log factors. This paper presents the first sharp analysis that shows that (perturbed) gradient descent finds an approximate second-order stationary point in at most polylog(d) iterations, thus escaping all saddle points efficiently. |
| Researcher Affiliation | Collaboration | 1University of California, Berkeley 2Duke University 3Microsoft Research India 4University of Washington. |
| Pseudocode | Yes | Algorithm 1 Perturbed Gradient Descent (Meta-algorithm); Algorithm 2 Perturbed Gradient Descent: PGD(x0, ℓ, ρ, ϵ, c, δ, f); Algorithm 3 Perturbed Gradient Descent with Local Improvement: PGDli(x0, ℓ, ρ, ϵ, c, δ, f, β) |
| Open Source Code | No | The paper does not provide any statement about making its source code available or provide a link to a code repository. |
| Open Datasets | No | The paper is theoretical and does not conduct empirical experiments involving datasets or training. The example of Matrix Factorization is used for theoretical analysis, not empirical evaluation. |
| Dataset Splits | No | The paper is theoretical and does not describe empirical experiments with data splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe any empirical experiments, therefore no specific hardware specifications are mentioned. |
| Software Dependencies | No | The paper focuses on theoretical analysis and algorithm design, not on implementation details that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper focuses on theoretical analysis and does not describe an experimental setup with hyperparameters or system-level training settings. |