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

TL;DR

This paper investigates the modeling capacity of tensor models through tensor ranks and introduces the separability issue, establishing a connection between entanglement in information theory and tensor analysis to deepen understanding of tensor complexity.

Contribution

It introduces a novel approach using separability and entanglement concepts to analyze tensor rank and modeling capacity, providing new theoretical insights.

Findings

Tensor rank analysis clarifies modeling capacity limits.

Separable tensors relate to model expressiveness.

Entanglement concepts offer a new perspective on tensor complexity.

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.