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Lookup NU author(s): Disha Hegde, Professor Chris OatesORCiD
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
© 2026, Transactions on Machine Learning Research. All rights reserved. Rapid prototyping of algorithms is a critical step in modern machine learning. Most algorithms exploit linear algebra, creating a need for lightweight numerical routines which – while potentially sub-optimal for the task at hand – can be rapidly implemented. For the numerical solution of ill-conditioned linear systems of equations, the standard solution for prototyping is Tikhonov-regularised inversion using a nugget. However, selection of the size of nugget is often difficult, and the use of data-adaptive procedures precludes automatic differentiation, introducing instabilities into end-to-end training. Further, while data-adaptive procedures perform multiple linear solves to select the size of nugget, only the result of one such solve is returned, which we argue is wasteful. This paper aims to circumvent the above difficulties, presenting autonugget; a Python package for automatic and stable numerical solution of linear systems suitable for rapid prototyping, and fully compatible with automatic differentiation using JAX. autonugget combines multiple linear solves using Richardson extrapolation to determine the solution of the ill-conditioned system, improving in accuracy over approximations based on a single nugget.
Author(s): Hegde D, Cockayne J, Oates CJ
Publication type: Article
Publication status: Published
Journal: Transactions on Machine Learning Research
Year: 2026
Volume: 2026-June
Pages: 1-26
Print publication date: 01/06/2026
Online publication date: 01/06/2026
Acceptance date: 02/04/2018
Date deposited: 15/07/2026
ISSN (electronic): 2835-8856
Publisher: Transactions on Machine Learning Research
URL: https://openreview.net/pdf?id=fqbkenUpRa
