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. ParaTuck decomposition alone is not sufficient due to lack of reliable algorithms for ParaTuck decomposition. 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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