# Exa.TrkX plugin¶

This plugin contains a track finding module based on Graph Neural Networks (GNNs) which is developed by the Exa.TrkX team. Build instructions and dependencies can be found in the README of the plugin.

## Model¶

The Exa.TrkX pipeline is a three-stage GNN-based algorithm:

1. Graph building (Embedding stage): This is done via metric learning approach. A neural network tries to learn a mapping that minimizes the distance between points of the same track in the embedded space. In this embedded space then a graph is built using a fixed nearest-neighbor search.

2. Graph size reduction (Filter stage): The resulting graph is typically to large for processing with a GNN. Therefore a binary classifier reduces the graph size further and removes easy to identify not matching edges.

3. Edge classification (GNN stage): Finally, a GNN is used to find the edges in the Graph that belong to tracks. This is done by scoring each edge with a number between 0 and 1, and a corresponding edge cut.

Finally, the track candidates must be extracted by a algorithm that finds the weakly connected components in the graph depending on the edge cut.

## Implementation¶

### Neural network backend¶

Currently there are two backends available:

• The TorchScript backend requires besides libtorch also TorchScatter that implements the scatter operators used in the graph neural network. The corresponding class is Acts::ExaTrkXTrackFindingTorch.

• The ONNX backend is currently not as well maintained as the TorchScript backend. The main reason is, that some scattering operators are not available in ONNX, so that the graph neural network cannot be exported correctely in the .onnx format. The corresponding class is Acts::ExaTrkXTrackFindingOnnx.

### Graph building¶

Both backends use currently different libraries for graph building.

• The TorchScript backend uses Boost.Graph for graph building.

• The ONNX backend uses the cugraph library for graph building

## API and examples integration¶

The interface of the backends is defined by Acts::ExaTrkXTrackFindingBase which is also used by ActsExamples::TrackFindingAlgorithmExaTrkX. The inference can be called with the getTracks function:

class ExaTrkXTrackFindingBase

Public Functions

virtual std::optional<ExaTrkXTime> getTracks(std::vector<float> &inputValues, std::vector<int> &spacepointIDs, std::vector<std::vector<int>> &trackCandidates, Acts::LoggerWrapper logger = Acts::getDummyLogger(), bool recordTiming = false) const = 0

This function takes the the input data as a std::vector<double> (e.g., a flattened $$N \times 3$$ array in cylindric coordinates like $$[r_0, \varphi_0, z_0, r_1, \dots \varphi_N, z_N]$$), as well as some corresponding spacepoint ids as a std::vector<int>. It then fills a std::vector<std::vector<int>> with the found track candidates using the provided spacepoint ids. Logging and timing measurements can be enabled with the remaining arguments. The hyperparameters of the models are defined in the Config member structs.

Note

Any kind of preprocessing (scaling, …) of the input values must be done before passing them to the inference.

See here for the corresponding python example.