Low-Precision Arithmetic for Fast Gaussian Processes

• URL: http://arxiv.org/abs/2207.06856v1
• Date: Thu, 14 Jul 2022 12:20:46 GMT
• Title: Low-Precision Arithmetic for Fast Gaussian Processes
• Authors: Wesley J. Maddox, Andres Potapczynski, Andrew Gordon Wilson
• Abstract summary: Low-precision arithmetic has had a transformative effect on the training of neural networks. We propose a multi-faceted approach involving conjugate gradients with re-orthogonalization, mixed precision, and preconditioning. Our approach significantly improves the numerical stability and practical performance of conjugate gradients in low-precision over a wide range of settings.
• Score: 39.720581185327816
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Low-precision arithmetic has had a transformative effect on the training of neural networks, reducing computation, memory and energy requirements. However, despite its promise, low-precision arithmetic has received little attention for Gaussian processes (GPs), largely because GPs require sophisticated linear algebra routines that are unstable in low-precision. We study the different failure modes that can occur when training GPs in half precision. To circumvent these failure modes, we propose a multi-faceted approach involving conjugate gradients with re-orthogonalization, mixed precision, and preconditioning. Our approach significantly improves the numerical stability and practical performance of conjugate gradients in low-precision over a wide range of settings, enabling GPs to train on $1.8$ million data points in $10$ hours on a single GPU, without any sparse approximations.

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