Extrapolating from Regularised Solutions for Solving Ill-Conditioned Linear Systems in Machine Learning
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 th...
| Authors | Disha Hegde, Jon Cockayne, Chris. J. Oates |
|---|---|
| Primary category | stat.ML |
| Published | 29 June 2026 |
| Last updated at source | 29 June 2026 |
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