Two-layer decoupling of multivariate polynomials with coupled ParaTuck and CP decompositions
Résumé
In this paper, we propose a new method for multivariate function approximation that generalized the classical decoupling problem. In the context of neural network, this can be seen as a two-layer feedforward network learning problem. In this work, we make use of both first and second-order information of the original function, modeled through paratuck and canonical polyadic (CP) decompositions, respectively. However, it is currently a challenge in the literature to handle the paratuck decomposition effectively. Our approach is a methodological work that demonstrates how the paratuck and CP decompositions can be combined in a coupled manner to achieve function decoupling according to the new model. Numerical simulations show the effectiveness of the proposed method on a simple synthetic example, demonstrating its ability to approximate multivariate functions accurately.
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