EVALUATION OF THE EFFICIENCY OF NEURAL NETWORKS AGAINST CONVENTIONAL INTERPOLATION TECHNIQUES
DOI:
https://doi.org/10.28925/2663-4023.2026.35.1346Keywords:
neural networks, traditional interpolation methods, efficiency evaluation, gaussian processesAbstract
The specificity of neural network evaluation compared to traditional interpolation methods has been investigated. The research focuses on neural networks and traditional interpolation methods, covering a wide range of applications in various areas, including data processing, function approximation, and solving interpolation tasks with real and synthetic data. The problem addressed was a detailed analysis of the mathematical apparatus for both approaches.
During the study, aspects of the mathematical apparatus related to the evaluation of neural networks compared to traditional interpolation methods were considered. A comparative analysis of neural network evaluation and nine interpolation methods was conducted.
A common challenge for the comparative evaluation was identified, which lies in the absence of a unified and standardized methodology for comparing the effectiveness of neural networks with traditional interpolation methods, considering the diversity of conditions and requirements in different application areas.
It was also found that neural networks and traditional interpolation methods have their unique mathematical characteristics and evaluation methods. The mathematical models discussed serve to reproduce or approximate functions based on a priori information and known points. Within the experimental investigation, Gaussian Processes and neural networks showed the highest accuracy, considering hyperparameters. The choice of a specific method depends on the specific requirements of the task and data characteristics. Gaussian Processes demonstrated the highest accuracy (0.94) among all methods. This method is often used for modeling stochastic processes. The neural network showed very good accuracy on test data, reaching 0.92.
The obtained results provide important information for choosing the optimal application of neural networks or interpolation methods.
Downloads
References
Montanari, Y., & Zhong, Y. (2022). The interpolation phase transition in neural networks: Memorization and generalization under lazy training. Annals of Statistics, 50(5), 2816-2847. https://doi.org/10.1214/22-AOS2211
Y. Zhang, P. Tiňo, A. Leonardis and K. Tang, A Survey on Neural Network Interpretability. IEEE Transactions on Emerging Topics in Computational Intelligence vol. 5, no. 5, pp. 726-742, Oct. 2021, https://doi.org/10.1109/TETCI.2021.3100641
B. Ghorbani, T. Misiakiewicz (2021). When do neural networks outperform kernel methods? J. Stat. Mech. Theory Exp. 12 Paper No. 124009, 110 pp. https://doi.org/10.1088/1742-5468/ac3a81
E, W., MA, C. and WU, L. (2020). A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics. Sci. China Math. 63 1235-1258. https://doi.org/10.1007/s11425-019-1628-5
Hastie, T., Montanari, A., Rosset, S., & Tibshirani, R. J. (2022). Surprises in high-dimensional ridgeless least squares interpolation. Annals of Statistics, 50, 949-986. https://doi.org/10.1214/21-aos2133
Liang, T., & Rakhlin, A. (2020). Just interpolate: Kernel “Ridgeless” regression can generalize. Annals of Statistics, 48, 1329-1347. https://doi.org/10.1214/19-AOS1849
Mei, S., Misiakiewicz, T., & Montanari, A. (2022). Generalization error of random feature and kernel methods: Hypercontractivity and kernel matrix concentration. Applied and Computational Harmonic Analysis, 59, 3-84. https://doi.org/10.1016/j.acha.2021.12.003
Soltanolkotabi, M., Javanmard, A., & Lee, J. D. (2019). Theoretical insights into the optimization landscape of over-parameterized shallow neural networks. IEEE Transactions on Information Theory, 65, 742-769. https://doi.org/10.1109/TIT.2018.2854560
Vershynin, R. (2018). High-Dimensional Probability: An Introduction with Applications in Data Science. Cambridge Series in Statistical and Probabilistic Mathematics (No. 47). Cambridge University Press. https://doi.org/10.1017/9781108231596
Zou, D., Cao, Y., Zhou, D., & Gu, Q. (2020). Gradient descent optimizes over-parameterized deep ReLU networks. Machine Learning, 109, 467-492. https://doi.org/10.1007/s10994-019-05839-6
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Наталія Лащевська, Антон Шантир, Ольга Зінченко, Каміла Сторчак
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
