Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics
This work addresses the need for high-precision and data-efficient learning in high-energy physics, offering a novel architecture that could enhance analysis in this domain, though it appears incremental in combining existing concepts like transformers and equivariance.
The paper tackles the challenge of extracting insights from particle-physics data by proposing the Lorentz Geometric Algebra Transformer (L-GATr), a versatile architecture that is equivariant under Lorentz transformations and based on geometric algebra. It demonstrates competitive or superior performance on regression and classification tasks and introduces the first Lorentz-equivariant generative model using continuous normalizing flow.
Extracting scientific understanding from particle-physics experiments requires solving diverse learning problems with high precision and good data efficiency. We propose the Lorentz Geometric Algebra Transformer (L-GATr), a new multi-purpose architecture for high-energy physics. L-GATr represents high-energy data in a geometric algebra over four-dimensional space-time and is equivariant under Lorentz transformations, the symmetry group of relativistic kinematics. At the same time, the architecture is a Transformer, which makes it versatile and scalable to large systems. L-GATr is first demonstrated on regression and classification tasks from particle physics. We then construct the first Lorentz-equivariant generative model: a continuous normalizing flow based on an L-GATr network, trained with Riemannian flow matching. Across our experiments, L-GATr is on par with or outperforms strong domain-specific baselines.