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arXiv · 2305.00604

ISAAC Newton: Input-based Approximate Curvature for Newton's Method

Felix Petersen·Tobias Sutter·Christian Borgelt·Dongsung Huh·Hilde Kuehne·Yuekai Sun·Oliver Deussen
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Abstract

We present ISAAC (Input-baSed ApproximAte Curvature), a novel method that conditions the gradient using selected second-order information and has an asymptotically vanishing computational overhead, assuming a batch size smaller than the number of neurons. We show that it is possible to compute a good conditioner based on only the input to a respective layer without a substantial computational overhead. The proposed method allows effective training even in small-batch stochastic regimes, which makes it competitive to first-order as well as second-order methods.

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Felix Petersen, Tobias Sutter, Christian Borgelt, Dongsung Huh, Hilde Kuehne, Yuekai Sun, Oliver Deussen. 2023-05-01. ISAAC Newton: Input-based Approximate Curvature for Newton's Method. https://arxiv.org/abs/2305.00604

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