Source-linked AI summary
Learning representations of irregular particle-detector geometry with distance-weighted graph networks
Shah Rukh Qasim, Jan Kieseler, Yutaro Iiyama, Maurizio Pierini
TL;DR
Irregular detector geometries challenge CNN approaches that rely on regular sensor arrays, motivating graph networks for particle reconstruction. The paper introduces distance-weighted GarNet and GravNet layers and evaluates them on calorimeter shower clustering, finding comparable performance to CNN and graph baselines with favorable resource requirements.
Problem
CNN-based detector representations commonly assume regular sensor arrays, which is problematic for realistic irregular geometries.
Method
The paper introduces GarNet and GravNet distance-weighted graph layers that learn detector-hit representations for sparse, irregular data and apply them to calorimeter clustering.
Results
GarNet and GravNet achieve performance comparable to CNN and graph baselines, while GarNet has almost 10 times shorter single-core inference time than DGCNN.
Takeaways & Limitations
The architectures offer alternative particle-reconstruction solutions with fewer geometry assumptions and a compromise between clustering performance and computational resource needs.
Takeaways & Limitations
The benchmark calorimeter is only slightly irregular, and the energy-fraction loss produces prediction bias that requires a future customized loss function.
Abstract
from arXiv · showhide
We explore the use of graph networks to deal with irregular-geometry detectors in the context of particle reconstruction. Thanks to their representation-learning capabilities, graph networks can exploit the full detector granularity, while natively managing the event sparsity and arbitrarily complex detector geometries. We introduce two distance-weighted graph network architectures, dubbed GarNet and GravNet layers, and apply them to a typical particle reconstruction task. The performance of the new architectures is evaluated on a data set of simulated particle interactions on a toy model of a highly granular calorimeter, loosely inspired by the endcap calorimeter to be installed in the CMS detector for the High-Luminosity LHC phase. We study the clustering of energy depositions, which is the basis for calorimetric particle reconstruction, and provide a quantitative comparison to alternative approaches. The proposed algorithms provide an interesting alternative to existing methods, offering equally performing or less resource-demanding solutions with less underlying assumptions on the detector geometry and, consequently, the possibility to generalize to other detectors.
1 Introduction
CNN-based detector processing commonly assumes regular sensor arrays, creating difficulties for realistic irregular geometries. This work introduces graph-network architectures for calorimeter clustering that avoid geometry-specific preprocessing while targeting performance and computational efficiency.
- CNNs impose a regular-array representation of particle detectors, creating problems for realistic collider applications.
- GarNet and GravNet are proposed for particle reconstruction without specific detector-geometry assumptions or preprocessing.
- The study is motivated by future high-granularity calorimeters with many channels, high occupancy, and increased downstream computational needs.
- The benchmark clusters calorimeter energy deposits into disentangled showers, forming a basis for subsequent particle-reconstruction tasks.
- The architectures are designed to balance clustering performance and inference resource requirements for sparse detector data.
2 Related Work
Related work spans CNNs, particle-based models, and graph networks for handling detector or event representations that do not naturally fit regular grids. Learnable graph geometry is promising for irregular detectors but must address connectivity and computational costs.
- CNN-based HEP studies often represent detectors as regular 2D or 3D sensor arrays, with additional difficulties at component transitions.
- Alternative HEP models include recurrent, recursive, graph-based, and DeepSets architectures, often using particle-level event representations.
- Graph networks represent unstructured point-wise data as vertices whose edges define information-exchange paths.
- Learnable graph geometry infers neighbor relations from input data rather than imposing detector connectivity during preprocessing.
- Connecting every vertex is computationally challenging, motivating limited neighbor connections in learned feature spaces such as EdgeConv and DGCNN.
3 The GravNet and GarNet layers
GarNet and GravNet construct distance-weighted graph representations from detector-hit features, enabling learned geometric relationships for sparse irregular data. Their principal architectural difference is how vertices are connected in the learned space.
- The layers transform batches of detector hits with FIN features into graph-network representations designed to retain learned spatial structure at low computational cost.
- A shared dense network maps each hit to learned coordinates or aggregator distances and to learned vertex features FLR.
- GravNet connects each vertex to its closest N neighbors using Euclidean distances in the learned S-dimensional space.
- GarNet connects every vertex to dim(S) aggregators, with learned values representing distances from vertices to aggregators.
- After graph construction, vertices or aggregators collect FLR information across their edges through distance-weighted aggregation steps.
1. The quantities
The layer quantities are produced from detector-hit features and used to weight information exchange by learned geometric distances. Aggregation combines edge features into collective representations that are returned to the original vertices for GarNet.
- A shared dense layer applies a learnable weight matrix and bias to the last feature dimension while sharing parameters across vertices.
- Each edge feature is scaled by a decreasing distance-dependent potential, using Gaussian weighting for GravNet and exponential weighting for GarNet.
- Edge features are combined with aggregators such as the mean and maximum, with mean aggregation improving model convergence in this study.
- GarNet sends aggregated features back to the initial vertices using the distance potential, producing outputs that include collective neighborhood information.
- The architectures and resulting models are implemented in TensorFlow.
4 Data set
The study uses a simplified irregular-geometry calorimeter and simulates overlapping particle showers to provide inputs and ground truth for graph-model clustering.
- The benchmark calorimeter has 20 longitudinal layers with fine segmentation in one quadrant and lower granularity elsewhere, producing layer-dependent sensor sizes and counts.
- Each event records cell energy deposits, positions, widths, and layer numbers as input features for the graph models.
- Events contain two overlapping showers whose cell-level energy fractions define the clustering ground truth.
- About 5% of events are discarded when the two showers share the same largest-deposit position and are therefore considered inseparable.
- The dataset contains 16,000,000 generated events, with 100,000 for validation and 250,000 for testing.
5 Clustering metrics
The clustering objective predicts each sensor’s energy fraction assigned to each shower, using an energy-weighted loss and a shower-level response definition.
- The target is to separate overlapping shower contributions without removing important parts of the original energy deposition.
- The loss compares predicted and true sensor-level shower fractions, weighting each term by the square root of the corresponding deposited energy.
- Predicted and true quantities are represented as energy fractions p_ik and t_ik for sensor i and shower k.
6 Models
The models combine local structure learning with global information exchange and compare three graph-network approaches against a CNN baseline under similar parameter budgets.
- All models use sensor energy, position, size, and layer information, and contain approximately 100,000 free parameters for comparison.
- The architectures combine message passing between neighboring sensors with direct global information exchange to capture localized and global structures.
- Binning: The comparison includes a CNN Binning baseline that imposes a regular 20 × 20 × 20 grid on the irregular detector geometry.
- GravNet model: The GravNet model repeatedly learns a four-dimensional space, connects each vertex to 40 neighbors, and propagates learned features through GravNet blocks.
- GarNet model: The GarNet model uses 11 layers with four aggregators, propagates 20 learned features, and produces 32 output nodes per layer.
7 Clustering performance
All approaches perform well at clustering overlapping calorimeter showers, with graph-based models generally outperforming the binning baseline. GravNet provides the strongest overall performance, while the shared loss introduces an energy-dependent response bias affecting every model.
- GravNet separates two heavily overlapping approximately 50 GeV pion showers and assigns energy fractions correctly, including in their overlap.The reconstructed track within the calorimeter is also well identified in this example.
- GravNet outperforms the other approaches on inclusive metrics, including the more resource-intensive DGCNN model.GarNet performs between DGCNN and binning for individual shower hit fractions, while binning slightly leads GarNet and DGCNN for clustering-response characteristics.
- Graph-based models outperform binning on overlap-specific metrics, with DGCNN and GravNet performing equally well and GarNet intermediate.
- Correcting for shower swapping enhances the response difference between GravNet and GarNet, while GravNet and DGCNN remain similarly scaled.Shower swapping can represent correctly clustered events whose test and noise labels are exchanged.
- Across the full test-shower energy range, GravNet has the best inclusive response metrics, while GarNet performs worst and DGCNN lies between them.
- The adapted mean-square-error loss causes low-energy response overestimation and high-energy underestimation for all models.Designing a customized loss to remove this bias is left for future work.
8 Resource requirements
Inference costs differ substantially across models: binning is fastest overall, while GarNet offers a favorable performance–memory trade-off and is especially fast on a CPU core.
- Binning is fastest overall, while graph models have similar GPU behavior at small batch sizes and benefit from larger batches.The comparison covers CPU and GPU inference across batch sizes.
- DGCNN uses the most memory, whereas GravNet requires about 50% less and GarNet provides a performance-compatible compromise.
- GarNet achieves almost 10× shorter inference time than DGCNN on a single CPU core.Its mostly sequential architecture explains this CPU performance.
9 Conclusions
GarNet and GravNet provide distance-weighted graph networks for sparse, irregular detector data, achieving competitive clustering performance with favorable resource requirements. Their broader applicability remains to be established beyond the benchmarked calorimeter task.
- GarNet and GravNet achieve performance comparable to CNN and graph baselines in the benchmark study.The simulated calorimeter is only slightly irregular, so stronger differences may emerge in more realistic geometries.
- GarNet is positioned for fast, accurate inference, while GravNet offers high-performance reconstruction with less resource demand than DGCNN at similar parameter counts.
- The architectures make no specific assumptions about underlying data structure and may extend to tracking and jet identification.The paper identifies exploring this usability as follow-up work.
- Inference-time comparisons span CPUs and GPUs with different batch sizes, with uncertainty shown as a shaded band.
Note added
A related study on a similar approach to jet tagging appeared after this work.
- A subsequent reference discusses applying a similar approach to jet tagging.