Accelerating Tracking with Symbolic Regression

Tracking charged particles is a core task in high-energy physics experiments. It plays a central role in reconstructing and identifying the particles produced in collisions, and in interpreting the resulting physics. This task is especially challenging in high-luminosity environments, where many particles cross the detector simultaneously, producing complex and overlapping patterns of hits.

Graph neural networks (GNNs) have emerged as a powerful and flexible tool for particle tracking, as they can naturally represent the detector hits and their relationships in graph form. These models have shown strong performance in terms of accuracy and generalization. However, their computational complexity makes them difficult to deploy in environments where fast decision-making is required—such as in real-time processing or hardware-level trigger systems.

In this work, we introduce an approach that approximates graph-based tracking models using symbolic regression [1]. Instead of relying on fully learned neural networks, we use symbolic regression to discover simple mathematical expressions that can replace the core components of the GNN. These expressions retain the structure and logic of the original graph model, including message passing between nodes, but are far more efficient to compute. The resulting models are suitable for fast inference on standard CPUs or hardware like FPGAs. 

[1] Nathalie Soybelman et al 2024 Mach. Learn.: Sci. Technol. 5 045042