Computing Higher Order Derivatives of Matrix and Tensor Expressions

Authors: Soeren Laue, Matthias Mitterreiter, Joachim Giesen

NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Experiments show a speedup of up to two orders of magnitude over state-of-the-art frameworks when evaluating higher order derivatives on CPUs and a speedup of about three orders of magnitude on GPUs.
Researcher Affiliation Academia Sören Laue Friedrich-Schiller-Universität Jena Germany soeren.laue@uni-jena.de Matthias Mitterreiter Friedrich-Schiller-Universität Jena Germany matthias.mitterreiter@uni-jena.de Joachim Giesen Friedrich-Schiller-Universität Jena Germany joachim.giesen@uni-jena.de
Pseudocode No The paper includes figures illustrating expression DAGs and tables detailing steps, but not formally labeled pseudocode or algorithm blocks.
Open Source Code Yes An interface to our framework for computing vector and matrix derivatives is available online at www.MatrixCalculus.org.
Open Datasets No The paper mentions problem types (quadratic functions, logistic regression, matrix factorization) and sets parameters (m=2n, k=5) but does not provide details on specific publicly available datasets or their access information.
Dataset Splits No The paper does not explicitly provide information about training/test/validation dataset splits.
Hardware Specification Yes The experiments were run in a pure CPU setting (Intel Xeon E5-2686, four cores) as well as in a pure GPU setting (NVIDIA Tesla V100), except for autograd, that does not provide GPU support.
Software Dependencies Yes We compare our framework to the state-of-the-art automatic differentiation frameworks Tensor Flow 1.10, Py Torch 0.4, Theano 1.0, and HIPS autograd 1.2 used with Python 3.6, that were all linked against Intel MKL.
Experiment Setup Yes We set m = 2n in the experiments. For the experiments, we set k = 5 and compute the gradient and Hessian with respect to U.