AISTATS 2020poster20 citations
Modular Block-diagonal Curvature Approximations for Feedforward Architectures
Felix Dangel, Stefan Harmeling, Philipp Hennig
Abstract
We propose a modular extension of backpropagation for the computation of block-diagonal approximations to various curvature matrices of the training objective (in particular, the Hessian, generalized Gauss-Newton, and positive-curvature Hessian). The approach reduces the otherwise tedious manual derivation of these matrices into local modules, and is easy to integrate into existing machine learning libraries. Moreover, we develop a compact notation derived from matrix differential calculus. We outline different strategies applicable to our method. They subsume recently-proposed block-diagonal approximations as special cases, and are extended to convolutional neural networks in this work.
BibTeX
@InProceedings{pmlr-v108-dangel20a,
title = { Modular Block-diagonal Curvature Approximations for Feedforward Architectures},
author = {Dangel, Felix and Harmeling, Stefan and Hennig, Philipp},
booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
pages = {799--808},
year = {2020},
editor = {Chiappa, Silvia and Calandra, Roberto},
volume = {108},
series = {Proceedings of Machine Learning Research},
month = {26--28 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v108/dangel20a/dangel20a.pdf},
url = {https://proceedings.mlr.press/v108/dangel20a.html},
abstract = {We propose a modular extension of backpropagation for the computation of block-diagonal approximations to various curvature matrices of the training objective (in particular, the Hessian, generalized Gauss-Newton, and positive-curvature Hessian). The approach reduces the otherwise tedious manual derivation of these matrices into local modules, and is easy to integrate into existing machine learning libraries. Moreover, we develop a compact notation derived from matrix differential calculus. We outline different strategies applicable to our method. They subsume recently-proposed block-diagonal approximations as special cases, and are extended to convolutional neural networks in this work.}
}