Tensor-Train networks for learning predictive modeling of multidimensional data

Author(s)

da Costa, Nazareth ; Attux, Romis ; Cichocki, Andrzej ; Romano, Joao M. T.

• Document type: Journal article
• Source: Neurocomputing; v. 637, p. 22-pg., 2025-07-07.

Abstract

In this work, we firstly apply Tensor-Train (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor model and standard multilayer neural networks is also carried out in the context of prediction of the Mackey-Glass noisy chaotic time series and NASDAQ index. We show that the weights of a multidimensional regression model can be learned by means of TT network and the optimization of TT weights is more robust to the impact of coefficient initialization and hyper-parameter setting. Furthermore, an efficient algorithm based on alternating least squares has been proposed for approximating the weights in TT format with a reduction of computational calculus, providing a much faster convergence than the well-known adaptive learning-method algorithms, widely applied for optimizing neural networks. (AU)

• FAPESP's process: 14/23936-4 - Applications of multidimensional data processing using tensor methods
• Grantee: Michele Nazareth da Costa
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 20/09838-0 - BI0S - Brazilian Institute of Data Science
• Grantee: João Marcos Travassos Romano
• Support Opportunities: Research Grants - Research Centers in Engineering Program