Extrapolating from Regularised Solutions for Solving Ill-Conditioned Linear Systems in Machine Learning
arXiv:2606.30328v1 Announce Type: cross Abstract: 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 diffe
The increasing complexity and scale of machine learning models necessitate more robust and efficient numerical methods for solving linear systems, particularly in ill-conditioned scenarios.
Improving the speed and reliability of fundamental linear algebra operations directly impacts the efficiency of prototyping and deployment of new AI algorithms across various applications.
Machine learning engineers will have improved methods for handling ill-conditioned linear systems, potentially leading to faster model development and more stable AI applications.
- · Machine Learning Engineers
- · AI algorithm developers
- · Companies relying on rapid AI prototyping
- · Developers relying solely on brute-force or suboptimal numerical methods
Faster and more stable development cycles for advanced AI models are enabled by improved numerical methods.
This could accelerate the adoption of more complex AI architectures that previously faced numerical stability challenges.
The development of highly robust and rapidly deployable AI systems could expand the domains where AI is practically applicable, beyond current computational limitations.
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Read at arXiv cs.LG