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In this paper, a way of generalizing the tensor renormalization group(TRG) isproposed. Mathematically, the connection between patterns of tensorrenormalization group and the concept of truncation sequence in polytopegeometry is discovered. A theoretical contraction framework is thereforeproposed. Furthermore, the canonical polyadic decomposition is introduced totensor network theory. A lowest order numerical verification of this method onthe 3-D Ising model is carried out.

Generalization of the tensor renormalization group approach to 3-D or higher dimensions