  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.
