Revisiting linear machine learning through the perspective of inverse problems

Revisiting linear machine learning through the perspective of inverse problems Full article

Journal

Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945

Output data

Year: 2025, Volume: 33, Number: 2, Pages: 281-303 Pages count : 23 DOI: 10.1515/jiip-2025-0010

Tags

Machine learning; linear neural network; linear inverse and ill-posed problems; regularization

Authors

Liu Shuang ¹ , Kabanikhin Sergey ² , Strijhak Sergei ³ , Wang Ying-Ao ⁴ , Zhang Ye ⁵

Affiliations

1	Novosibirsk State University , Novosibirsk , Russian Federation
2	Sobolev Institute of Mathematics, Siberian Branch , Russian Academy of Sciences , Novosibirsk , Russian Federation
3	Ivannikov Institute for System Programming of the Russian Academy of Sciences , Moscow , Russian Federation
4	School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , P. R. China
5	MSU-BIT-SMBU Joint Research Center of Applied Mathematics , Shenzhen MSU-BIT University , Shenzhen 518172 , P. R. China

Funding (1)

Sobolev Institute of Mathematics

FWNF-2024-0001

In this paper, we revisit Linear Neural Networks (LNNs) with single-output neurons performing linear operations. The study focuses on constructing an optimal regularized weight matrix Q from training pairs { G , H } , reformulating the LNNs framework as matrix equations, and addressing it as a linear inverse problem. The ill-posedness of linear machine learning problems is analyzed through the lens of inverse problems. Furthermore, classical and modern regularization techniques from both the machine learning and inverse problems communities are reviewed. The effectiveness of LNNs is demonstrated through a real-world application in blood test classification, highlighting their practical value in solving real-life problems.

Liu S. , Kabanikhin S. , Strijhak S. , Wang Y-A. , Zhang Y.
Revisiting linear machine learning through the perspective of inverse problems
Journal of Inverse and Ill-Posed Problems. 2025. V.33. N2. P.281-303. DOI: 10.1515/jiip-2025-0010 OpenAlex

Submitted:	Feb 2, 2025
Accepted:	Feb 14, 2025
Published online:	Mar 28, 2025
Published print:	Apr 1, 2025

OpenAlex:

W4408919045

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