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.

翻译：从粒子物理实验中提取科学理解，需要以高精度和良好的数据效率解决多样化的学习问题。我们提出了洛伦兹几何代数Transformer（L-GATr），一种用于高能物理的新型多用途架构。L-GATr在四维时空的几何代数中表示高能数据，并且在洛伦兹变换（相对论运动学的对称群）下具有等变性。同时，该架构是一个Transformer，这使其具有多功能性并可扩展至大型系统。L-GATr首先在粒子物理的回归和分类任务上得到验证。随后，我们构建了首个洛伦兹等变生成模型：一个基于L-GATr网络的连续归一化流，使用黎曼流匹配进行训练。在我们的所有实验中，L-GATr的表现与强大的领域专用基线模型相当或更优。