Lower and Upper Bounds on the VC-Dimension of Tensor Network Models

Explore lower and upper bounds on the VC-dimension of tensor network models in this 53-minute lecture from the Workshop on Tensors: Quantum Information, Complexity and Combinatorics. Delve into tensor network methods and their applications in condensed matter physics and machine learning. Examine the derivation of VC dimension and pseudo-dimension bounds for various tensor network structures used in classification, regression, and completion tasks. Investigate generalization bounds for low-rank matrix classifiers and common tensor decomposition models. Learn about the resolution of an open problem regarding the VC dimension of matrix product state classifiers. Cover topics including tensor networks, decomposition tasks, learning relationships, quantum physics examples, and future research directions in this comprehensive presentation by Guillaume Rabusseau from the Centre de recherches mathématiques.

Intro
Tensor Networks
Decomposition
Task
Learning
Relationship
Quantum Physics
Examples
VCDimension of Hypothesis Classes
Generalization Bond
Proof
Example
Lower Bounds
Future Work