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; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1]
Convexity Certificates from Hessians
Authors: Julien Klaus, Niklas Merk, Konstantin Wiedom, Sören Laue, Joachim Giesen
NeurIPS 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Here, we implement this approach for a class of functions that is rich enough to support classical machine learning. For this class of functions it was recently shown how to compute computational graphs of their Hessians. We show how to check these graphs for positive semidefiniteness. We compare our implementation of the Hessian approach with the well-established disciplined convex programming (DCP) approach and prove that the Hessian approach is at least as powerful as the DCP approach for differentiable functions. |
| Researcher Affiliation | Collaboration | Julien Klaus Friedrich Schiller University Jena EMAIL Niklas Merk Friedrich Schiller University Jena EMAIL Konstantin Wiedom Friedrich Schiller University Jena EMAIL Sören Laue Technical University of Kaiserslautern Data Assessment Solutions Gmb H EMAIL Joachim Giesen Friedrich Schiller University Jena EMAIL |
| Pseudocode | Yes | Algorithm 1 Certify convexity of a Hessian; Algorithm 2 Compute the positivity interval for a node v |
| Open Source Code | No | The paper states '[N/A]' for the question 'Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?' in its ethics checklist, and no explicit link or statement of code availability is found elsewhere. |
| Open Datasets | No | The paper focuses on theoretical development and algorithmic implementation for certifying convexity, not on empirical evaluation involving training on datasets. Therefore, no dataset access information is provided. |
| Dataset Splits | No | The paper does not report empirical experiments with dataset splits, as its focus is on theoretical and algorithmic contributions. |
| Hardware Specification | No | The paper indicates '[N/A]' for hardware specifications in its ethics checklist (3d: 'Did you include the total amount of compute and the type of resources used...'), consistent with its theoretical focus. |
| Software Dependencies | No | The paper discusses various software frameworks (e.g., CVX, GENO) in the context of related work or comparison, but it does not specify any particular software dependencies with version numbers required to reproduce its own implementation. |
| Experiment Setup | No | The paper describes a theoretical framework and algorithmic implementation but does not provide specific experimental setup details such as hyperparameters or training configurations, as it does not report empirical experiments. |