Clifford Group Equivariant Neural Networks

Explore the innovative concept of Clifford Group Equivariant Neural Networks in this comprehensive lecture. Delve into the Clifford group, a subgroup within the Clifford algebra, and its unique properties that enable the construction of E(n)-equivariant networks. Discover how the group's action forms an orthogonal automorphism extending to the entire Clifford algebra while respecting multivector grading. Learn about the non-equivalent subrepresentations corresponding to multivector decomposition and how the action respects both vector space structure and multiplicative structure of the Clifford algebra. Understand the implications of these findings for parameterizing equivariant neural network layers, including their ability to operate directly on a vector basis and generalize to any dimension. Examine state-of-the-art performance demonstrations on various tasks, including a three-dimensional n-body experiment, a four-dimensional Lorentz-equivariant high-energy physics experiment, and a five-dimensional convex hull experiment. Gain insights into the methodology behind linear layers and geometric product layers, and participate in a Q&A session to further explore this cutting-edge approach in AI and drug discovery.

- Intro
- The Clifford Algebra
- Clifford Group Equivariant Networks: Theoretical Results
- Methodology: Linear Layers
- Methodology: Geometric Product Layers
- Experiments
- Final Remarks
- Q+A