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: TBC
Title: TBC
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.