Mixed-precision fully-connected tensor network decomposition

doi:10.1016/j.aml.2026.110068

Mixed-precision fully-connected tensor network decomposition

2026-07-01

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DOI：10.1016/j.aml.2026.110068

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Fully-connected tensor network (FCTN) decomposition has received extensive attention due to its ability to capture the interaction between any two factors, which brings powerful representation power. However, the high computational complexity of the FCTN decomposition hinders its widespread application. To solve this problem, we propose a novel mixed-precision gradient descent FCTN decomposition algorithm (FCTN-MPGD) to accelerate the FCTN decomposition. Specifically, we first adopt the low-precision GD with a low cost to obtain a decent initial point, and then employ the high-precision GD to achieve rapid convergence with a few iterations. The proposed method not only significantly reduces the computational time but also maintains high accuracy. Theoretically, we also provide rigorous analysis to demonstrate the convergence property of the proposed FCTN-MPGD. Extensive experiments on both synthetic and real-world tensor datasets validate that our FCTN-MPGD achieves markedly higher efficiency than the high-precision FCTN decomposition methods.

Keywords:

Mixed-precision computation

Tensor network decomposition

Gradient descent

Mixed-precision fully-connected tensor network decomposition

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