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arXiv · 1902.01813

Modular Block-diagonal Curvature Approximations for Feedforward Architectures

Felix Dangel·Stefan Harmeling·Philipp Hennig
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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.

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Felix Dangel, Stefan Harmeling, Philipp Hennig. 2019-02-05. Modular Block-diagonal Curvature Approximations for Feedforward Architectures. https://arxiv.org/abs/1902.01813

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