## Talks

Talks

### 2024

2024

### Workshop on Symmetry and Equivariance in Deep Learning, Paris, France

Workshop on Symmetry and Equivariance in Deep Learning, Paris, France

### Date: Wednesday, 4th September 2024, 11:30am CET

Date: Wednesday, 4th September 2024, 11:30am CET

### Title: Diagrammatic Mathematics for Equivariant Deep Learning Architectures

Title: Diagrammatic Mathematics for Equivariant Deep Learning Architectures

### In deep learning, we would like to develop principled approaches for constructing neural network architectures. One important approach involves encoding symmetries into neural network architectures using representations of groups such that the learned functions are equivariant to the group. In this talk, we show how certain group equivariant neural network architectures can be built using set partition diagrams. In many cases, we can establish a category theory framework both for the set partition diagrams and for the equivariant linear maps between layer spaces. We extend this framework to characterise the weight matrices that appear in neural networks that are equivariant to the automorphism group of a graph.

In deep learning, we would like to develop principled approaches for constructing neural network architectures. One important approach involves encoding symmetries into neural network architectures using representations of groups such that the learned functions are equivariant to the group. In this talk, we show how certain group equivariant neural network architectures can be built using set partition diagrams. In many cases, we can establish a category theory framework both for the set partition diagrams and for the equivariant linear maps between layer spaces. We extend this framework to characterise the weight matrices that appear in neural networks that are equivariant to the automorphism group of a graph.

### Quantum Groups Seminar (Online)

Quantum Groups Seminar (Online)

### Date: Monday, 20th May 2024, 4:00pm CET

Date: Monday, 20th May 2024, 4:00pm CET

### Compact Matrix Quantum Group Equivariant Neural Networks

Compact Matrix Quantum Group Equivariant Neural Networks

### 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.

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.

### The Royal Institution of Great Britain, London, UK

The Royal Institution of Great Britain, London, UK

### Date: Thursday, 29th February 2024, 2:00pm GMT

Date: Thursday, 29th February 2024, 2:00pm GMT

### Exploring Group Equivariant Neural Networks Using Set Partition Diagrams

Exploring Group Equivariant Neural Networks Using Set Partition Diagrams

### 2023

2023

### Fortieth International Conference on Machine Learning, Honolulu, Hawaii, United States

Fortieth International Conference on Machine Learning, Honolulu, Hawaii, United States

### Date: Wednesday, July 26th, 5:12pm HST (Thursday, July 27th, 4:12am BST)

Date: Wednesday, July 26th, 5:12pm HST (Thursday, July 27th, 4:12am BST)

### Brauer's Group Equivariant Neural Networks

Brauer's Group Equivariant Neural Networks

Live Presentation (SlidesLive)

### We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$ for three symmetry groups that are missing from the machine learning literature: $O(n)$, the orthogonal group; $SO(n)$, the special orthogonal group; and $Sp(n)$, the symplectic group. In particular, we find a spanning set of matrices for the learnable, linear, equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$ when the group is $O(n)$ or $SO(n)$, and in the symplectic basis of $\mathbb{R}^{n}$ when the group is $Sp(n)$.

We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$ for three symmetry groups that are missing from the machine learning literature: $O(n)$, the orthogonal group; $SO(n)$, the special orthogonal group; and $Sp(n)$, the symplectic group. In particular, we find a spanning set of matrices for the learnable, linear, equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$ when the group is $O(n)$ or $SO(n)$, and in the symplectic basis of $\mathbb{R}^{n}$ when the group is $Sp(n)$.

### Date: Wednesday, June 21st, 10am BST

Date: Wednesday, June 21st, 10am BST

### Exploring Group Equivariant Neural Networks Using Set Partition Diagrams

Exploring Group Equivariant Neural Networks Using Set Partition Diagrams

Video (YouTube), Slides

### What do jellyfish and an 11th century Japanese novel have to do with neural networks? In recent years, much attention has been given to developing neural network architectures that can efficiently learn from data with underlying symmetries. These architectures ensure that the learned functions maintain a certain geometric property called group equivariance, which determines how the output changes based on a change to the input under the action of a symmetry group. In this talk, we will describe a number of new group equivariant neural network architectures that are built using tensor power spaces of $R^n$ as their layers. We will show that the learnable, linear functions between these layers can be characterised by certain subsets of set partition diagrams. This talk will be based on several papers that are to appear in ICML 2023.

What do jellyfish and an 11th century Japanese novel have to do with neural networks? In recent years, much attention has been given to developing neural network architectures that can efficiently learn from data with underlying symmetries. These architectures ensure that the learned functions maintain a certain geometric property called group equivariance, which determines how the output changes based on a change to the input under the action of a symmetry group. In this talk, we will describe a number of new group equivariant neural network architectures that are built using tensor power spaces of $R^n$ as their layers. We will show that the learnable, linear functions between these layers can be characterised by certain subsets of set partition diagrams. This talk will be based on several papers that are to appear in ICML 2023.