Papers › Construction of the Kolmogorov-Arnold representation using the Newton-Kaczmarz method
Construction of the Kolmogorov-Arnold representation using the Newton-Kaczmarz method
Michael Poluektov, Andrew Polar
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
It is known that any continuous multivariate function can be represented exactly by a composition functions of a single variable - the so-called Kolmogorov-Arnold representation. It can be a convenient tool for tasks where it is required to obtain a predictive model that maps some vector input of a black box system into a scalar output. In this case, the representation may not be exact, and it is more correct to refer to such structure as the Kolmogorov-Arnold model (or, as more recently popularised, 'network'). Construction of such model based on the recorded input-output data is a challenging task. In the present paper, it is suggested to decompose the underlying functions of the representation into continuous basis functions and parameters. It is then proposed to find the parameters using the Newton-Kaczmarz method for solving systems of non-linear equations. The algorithm is then modified to support parallelisation. The paper demonstrates that such approach is also an excellent tool for data-driven solution of partial differential equations. Numerical examples show that for the considered model, the Newton-Kaczmarz method for parameter estimation is efficient and more robust with respect to the section of the initial guess than the straightforward application of the Gauss-Newton method. Finally, the Kolmogorov-Arnold model is compared to the MATLAB's built-in neural networks on a relatively large-scale problem (25 inputs, datasets of 10 million records), significantly outperforming the multilayer perceptrons (MLPs) in this particular problem (4-10 minutes vs. 4-8 hours of training time, as well as higher accuracy, lower CPU usage, and smaller memory footprint).
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections