Convexity Certificates for Symbolic Tensor Expressions

Authors: Paul G. Rump, Niklas Merk, Julien Klaus, Maurice Wenig, Joachim Giesen

IJCAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Finally, in Section 5, we evaluate our tensorial extension of the symbolic Hessian approach and show that it is provably more powerful than the approach restricted to vector input, that is, the extension can certify the convexity of a larger class of functions. An interactive implementation of our tensorial symbolic Hessian approach is available for testing at https://tenvexity.einsum.org.
Researcher Affiliation Academia Paul G. Rump , Niklas Merk , Julien Klaus , Maurice Wenig and Joachim Giesen Friedrich Schiller University Jena {paul.gerhardt.rump, niklas.merk, julien.klaus, maurice.wenig, joachim.giesen}@uni-jena.de
Pseudocode No The paper describes the symbolic Hessian approach and its steps but does not include formal pseudocode or an algorithm block.
Open Source Code Yes An interactive implementation of our tensorial symbolic Hessian approach is available for testing at https://tenvexity.einsum.org.
Open Datasets No The paper focuses on certifying the convexity of functions rather than training machine learning models on datasets. Therefore, it does not discuss or provide access to publicly available training datasets.
Dataset Splits No The paper focuses on certifying the convexity of functions, not on model training that typically requires validation splits. Therefore, it does not provide dataset split information for validation.
Hardware Specification Yes The reported computation times are the mean of ten singlethreaded executions, measured on a Windows 11 machine with an AMD Ryzen 9 7900X CPU.
Software Dependencies No The paper mentions "Windows 11" as the operating system, but does not provide specific version numbers for other software dependencies (e.g., programming languages, libraries, frameworks) used in their implementation.
Experiment Setup No The paper describes the steps of the convexity certifying algorithm and presents computation times for various functions, but it does not detail experimental setup parameters such as hyperparameters, learning rates, or batch sizes, as these are not relevant to the type of analysis performed.