Private linear equation solving: An application to federated learning and extreme learning machines

Daniel Heinlein, Anton Akusok, Kaj-Mikael Björk, Leonardo Espinosa-Leal,
Private linear equation solving: An application to federated learning and extreme learning machines,
Journal of Computational Science,
Volume 92,
2025,
102693,
ISSN 1877-7503,
https://doi.org/10.1016/j.jocs.2025.102693.
(https://www.sciencedirect.com/science/article/pii/S187775032500170X)
Abstract: In federated learning, multiple devices compute each a part of a common machine learning model using their own private data. These partial models (or their parameters) are then exchanged in a central server that builds an aggregated model. This sharing process may leak information about the data used to train them. This problem intensifies as the machine learning model becomes simpler, indicating a higher risk for single-hidden-layer feedforward neural networks, such as extreme learning machines. In this paper, we establish a mechanism to disguise the input data to a system of linear equations while guaranteeing that the modifications do not alter the solutions, and propose two possible approaches to apply these techniques to federated learning. Our findings show that extreme learning machines can be used in federated learning with an extra security layer, making them attractive in learning schemes with limited computational resources.
Keywords: Linear equation solving; Private computation; Extreme learning machines; Private federated learning