Tensor-Train Networks for Learning Predictive Modeling of Multidimensional Data

2021/01/22 by da Costa, M. Nazareth, Attux, R., Cichocki, A. +1
#FOS: Computer and information sciences #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2101.09184

Abstract

In this work, we firstly apply the Train-Tensor (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 a 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.

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