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arXiv · 2604.10858

Tensor-based Multi-layer Decoupling

Joppe De Jonghe·Konstantin Usevich·Philippe Dreesen·Mariya Ishteva
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Abstract

The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained largely unexplored. This work introduces a tensor-based framework for multi-layer decoupling, which is based on ParaTuck-type tensor decompositions and constrained optimization. We provide theoretical justification behind the considered tensor decompositions and parameterizations. Furthermore, we formulate a structured coupled matrix-tensor factorization that incorporates both Jacobian and function evaluations, together with a bilevel optimization approach for adaptively balancing first- and zeroth-order information. The feasibility of the proposed methodology is illustrated on synthetic systems, a nonlinear system identification benchmark and neural network compression.

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Joppe De Jonghe, Konstantin Usevich, Philippe Dreesen, Mariya Ishteva. 2026-04-12. Tensor-based Multi-layer Decoupling. https://arxiv.org/abs/2604.10858

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