Compact Matrix Quantum Group Equivariant Neural Networks

Abstract: In deep learning, we would like to develop principled approaches for constructing neural networks. One important approach involves identifying symmetries that are inherent in data and then encoding them into neural network architectures using representations of groups. However, there exist so-called “quantum symmetries” that cannot be understood formally by groups. In this talk, we show how to construct neural networks that are equivariant to compact matrix quantum groups using Woronowicz’s version of Tannaka-Krein duality. We go on to characterise the linear weight matrices that appear in these neural networks for a class of compact matrix quantum groups known as “easy”. In particular, we show that every compact matrix group equivariant neural network is a compact matrix quantum group equivariant neural network.

category theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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