Cannikin's Law in Tensor Modeling: A Rank Study for Entanglement and Separability in Tensor Complexity and Model Capacity

2022/04/16 by Tong Yang, Yang, Tong
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Quantum Physics (quant-ph) #cs.LG #cs.NA #math.NA #quant-ph

paper · pdf · doi:10.48550/arxiv.2204.07760

7 pages

arxiv created 2022/04/16 · arxiv updated 2022/04/19

Abstract

This study clarifies the proper criteria to assess the modeling capacity of a general tensor model. The work analyze the problem based on the study of tensor ranks, which is not a well-defined quantity for higher order tensors. To process, the author introduces the separability issue to discuss the Cannikin's law of tensor modeling. Interestingly, a connection between entanglement studied in information theory and tensor analysis is established, shedding new light on the theoretical understanding for modeling capacity problems.

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