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Pré-Publication, Document De Travail Année : 2023

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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Dates et versions

hal-03968630 , version 1 (01-02-2023)
hal-03968630 , version 2 (10-03-2023)

Identifiants

  • HAL Id : hal-03968630 , version 1

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Konstantin Usevich, Yassine Zniyed, Mariya Ishteva, Philippe Dreesen, André L F de Almeida. Two-layer decoupling of multivariate polynomials with coupled ParaTuck and CP decompositions. 2023. ⟨hal-03968630v1⟩
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