Track finding in particle data is a challenging pattern recognition problem in High Energy Physics. It takes as inputs a point cloud of space points and labels them so that space points created by the same particle have the same label. The list of space points with the same label is a track candidate. We argue that this pattern recognition problem can be formulated as a sorting problem, of which the inputs are a list of space points sorted by their distances away from the collision points and the outputs are the space points sorted by their labels. In this paper, we propose the TrackSorter algorithm: a Transformer-based algorithm for pattern recognition in particle data. TrackSorter uses a simple tokenization scheme to convert space points into discrete tokens. It then uses the tokenized space points as inputs and sorts the input tokens into track candidates. TrackSorter is a novel end-to-end track finding algorithm that leverages Transformer-based models to solve pattern recognition problems. It is evaluated on the TrackML dataset and has good track finding performance.

Track reconstruction is a crucial task in particle experiments and is traditionally very computationally expensive due to its combinatorial nature. Recently, graph neural networks (GNNs) have emerged as a promising approach that can improve scalability. Most of these GNN-based methods, including the edge classification (EC) and the object condensation (OC) approach, require an input graph that needs to be constructed beforehand. In this work, we consider a one-shot OC approach that reconstructs particle tracks directly from a set of hits (point cloud) by recursively applying graph attention networks with an evolving graph structure. This approach iteratively updates the graphs and can better facilitate the message passing across each graph. Preliminary studies on the TrackML dataset show better track performance compared to the methods that require a fixed input graph.

The application of Graph Neural Networks (GNN) in track reconstruction is a promising approach to cope with the challenges arising at the High-Luminosity upgrade of the Large Hadron Collider (HL-LHC). GNNs show good track-finding performance in high-multiplicity scenarios and are naturally parallelizable on heterogeneous compute architectures. Typical high-energy-physics detectors have high resolution in the innermost layers to support vertex reconstruction but lower resolution in the outer parts. GNNs mainly rely on 3D space-point information, which can cause reduced track-finding performance in the outer regions. In this contribution, we present a novel combination of GNN-based track finding with the classical Combinatorial Kalman Filter (CKF) algorithm to circumvent this issue: The GNN resolves the track candidates in the inner pixel region, where 3D space points can represent measurements very well. These candidates are then picked up by the CKF in the outer regions, where the CKF performs well even for 1D measurements. Using the ACTS infrastructure, we present a proof of concept based on truth tracking in the pixels as well as a dedicated GNN pipeline trained on $t\bar{t}$ events with pile-up 200 in the OpenDataDetector.

We introduce a novel variant of GNN for particle tracking--called Hierarchical Graph Neural Network (HGNN). The architecture creates a set of higher-level representations which correspond to tracks and assigns spacepoints to these tracks, allowing disconnected spacepoints to be assigned to the same track, as well as multiple tracks to share the same spacepoint. We propose a novel learnable pooling algorithm called GMPool to generate these higher-level representations called "super-nodes", as well as a new loss function designed for tracking problems and HGNN specifically. On a standard tracking problem, we show that, compared with previous ML-based tracking algorithms, the HGNN has better tracking efficiency performance, better robustness against inefficient input graphs, and better convergence compared with traditional GNNs.