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Using Graph Neural Networks for the segmentation of overlapping objects in high granularity calorimeters

This paper presents an optimized Graph Neural Network pipeline that efficiently disentangles overlapping two-photon showers in high-granularity calorimeters by predicting node-level energy fractions with reduced algorithmic complexity.

Original authors: Matthieu Melennec, Frédéric Magniette

Published 2026-09-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Matthieu Melennec, Frédéric Magniette

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the heart of modern particle physics, scientists are preparing for a future where the universe's most fundamental secrets are revealed not by looking at a single event, but by watching nearly two hundred collisions happen at the exact same time. This is the challenge of the High-Luminosity Large Hadron Collider, an upgrade to the world's most powerful particle accelerator. When protons smash together with such frequency, the energy they release creates a chaotic storm of debris. In traditional detectors, this storm looks like a single, messy blob of energy, making it impossible to tell which particle came from which collision. To solve this, the next generation of experiments is building detectors with unprecedented detail, capable of seeing the individual threads of energy as they spread out. However, seeing the threads is only half the battle; the real difficulty lies in untangling them. When two particles fly out from the same collision and their energy trails cross, they overlap, creating a complex puzzle that old computer algorithms cannot solve.

This is where a new approach comes in, using a type of artificial intelligence designed to understand relationships between points in space. Researchers at the École Polytechnique in France have developed a specialized system to separate these overlapping energy trails, specifically focusing on pairs of photons, which are particles of light. In their simulations, they created a scenario where two photons, born from the decay of a neutral pion, travel into a detector and their energy deposits mix together. The goal was to teach a computer to look at this mixed mess and decide, for every single piece of energy it sees, how much of it belongs to the first photon and how much belongs to the second. The team found that by treating the detector's data as a network of connected points, they could successfully disentangle the two showers, recovering the original energy and direction of each particle with high accuracy.

The detector used in this study is a sampling calorimeter, a device that measures energy by capturing the cascade of particles created when a high-energy photon strikes matter. The simulated detector has twenty-six layers of electromagnetic sensors followed by twenty-four layers of hadronic sensors, creating a three-dimensional map of the energy deposits. When two photons arrive close together, their energy hits the same sensors, and the detector simply records the sum of the energy. To test their method, the researchers generated millions of simulated events where two photons entered the detector at angles between one and four and a half degrees apart. They then fed this data into a Graph Neural Network, a type of machine learning model that excels at processing data where the connections between items matter more than the items themselves. Instead of treating the detector as a grid, the model treats each energy deposit as a node in a graph, connected to its neighbors based on physical proximity.

A major hurdle in using these networks for particle physics has been the sheer cost of building the connections between points. Usually, a computer must compare every single point to every other point to see if they are close enough to be connected, a process that becomes impossibly slow as the number of points grows. The researchers solved this by using a pre-computed map of distances, allowing the system to find neighbors quickly without doing the heavy math for every single event. This optimization reduced the complexity of the task significantly, making it feasible to run on the massive datasets required for future experiments. The network was then trained to predict two things for every point of energy: the fraction of that energy that came from the dominant photon, and the estimated location where that photon first entered the detector.

The results showed that the system could effectively separate the overlapping showers. By predicting where each photon entered the detector, the model could group the energy deposits into two distinct clusters, even when they were heavily mixed. The researchers measured the success of this separation by looking at how well the total energy of each reconstructed photon matched the true energy. They found that as the distance between the two entering photons increased, the separation became more accurate, which is expected since the trails overlap less. Even when the photons were very close, the system managed to recover the energy with a high degree of precision, though a small bias remained where the system slightly underestimated the total energy. This bias was attributed to the fact that the final step of grouping the points relied on a statistical clustering method that was not fully integrated into the training process.

The study demonstrates that graph-based neural networks can handle the extreme complexity of high-granularity detectors without needing the prohibitively expensive calculations of older methods. While the current system still relies on a post-processing step to finalize the grouping of particles, the core ability to predict energy fractions and entry points directly from the raw data is a significant step forward. The researchers acknowledge that future improvements will be needed to make the entire process, including the grouping step, fully differentiable and trainable, which would allow the system to correct its own biases more effectively. For now, this optimized pipeline offers a competitive way to untangle the chaotic energy showers of the future High-Luminosity LHC, ensuring that the unprecedented detail of new detectors can be fully utilized to reveal the physics hidden within the noise.

Technical Summary: SOOP Pipeline for Overlapping Object Segmentation

Problem Statement
The High-Luminosity LHC (HL-LHC) upgrade will introduce severe pileup, with nearly 200 simultaneous collisions per bunch crossing, causing spatial overlaps of energy deposits in conventional calorimeters. While next-generation experiments like CMS are deploying High Granularity Calorimeters (HGCAL) to capture unprecedented detail in shower development, legacy algorithms struggle to generalize to these high-dimensional outputs without prohibitive computational complexity. Specifically, standard Graph Neural Network (GNN) approaches, while promising for particle reconstruction, often rely on graph construction and dynamic adjacency updates that scale quadratically with the number of nodes, making them computationally expensive for real-time or high-pileup applications.

Methodology: The SOOP Pipeline
The authors present SOOP (Segmentation of Overlapping Objects Pipeline), an optimized GNN framework designed to disentangle overlapping two-photon showers. The methodology addresses both algorithmic efficiency and the specific challenge of label ambiguity in overlapping events.

Optimized Graph Construction: To reduce computational complexity, the pipeline utilizes the PT-KNN algorithm with pre-computed proximity tables. Sensors are pre-ordered by distance, allowing edge construction via $k$ -nearest neighbors ( $k=4$ ) without performing full pairwise distance calculations during event processing. This shifts the complexity from quadratic to sub-quadratic.
Node-Level Regression Strategy: Instead of directly classifying nodes into Shower A or Shower B (which suffers from global permutation ambiguity due to the symmetric nature of the problem), the model employs a dual regression objective for each hit node $v$ $v$ :
1. Dominant Energy Fraction ( $f_v^{(X)}$ ): Predicting the fraction of energy ( $\in [0.5, 1]$ ) contributed by the locally dominant shower.
2. Detector Entry Point ( $\tilde{u}_v$ ): Predicting the 2D position where the particle contributing the dominant energy entered the detector.
Clustering and Reconstruction:
- The predicted entry points are clustered to resolve the global assignment. The pipeline first removes outliers using DBSCAN and then fits a Gaussian Mixture Model (GMM) with a tied covariance matrix to identify the two incident particle entry positions.
- Nodes are assigned to the shower corresponding to the most probable Gaussian component.
- Final shower reconstruction is achieved by weighting the hit energies: the dominant fraction is assigned to the associated shower, and the complementary fraction ( $1 - f$ ) is assigned to the other.
Training: The model is trained on the convolution layer outputs using a loss function combining position error ( $L_{pos}$ ) and energy fraction error ( $L_{frac}$ ). Notably, the GMM clustering step is performed post-hoc during inference, not during the training forward pass, to avoid the non-differentiability of the clustering operation.

Key Contributions

Algorithmic Optimization: The introduction of PT-KNN with pre-computed tables significantly accelerates graph construction, reducing the algorithmic complexity of standard GNNs that typically require dynamic adjacency updates.
Symmetry-Aware Formulation: The paper proposes a local regression formulation that bypasses the global permutation ambiguity inherent in overlapping object segmentation. By predicting a dominant fraction and an entry point, the model structurally respects input symmetries while enabling unique event-level assignment.
Static Geometry Efficiency: The work demonstrates that static geometry-aware message passing (using fixed edges based on detector proximity) can achieve competitive separation performance comparable to computationally heavy dynamic methods, without the need for iterative adjacency updates.

Results
Evaluated on the D2 dataset (simulated photon pairs in an HGCAL-inspired detector with energies between 10–100 GeV and angular separations of $1^\circ$ to $4.5^\circ$ ), the SOOP pipeline achieved the following:

Separation Efficiency: The model successfully reconstructed overlapping showers, with performance comparable to state-of-the-art dynamic methods.
Response Function: The global energy reconstruction response ( $R$ ) was evaluated. While the mean response was slightly below 1 (indicating a residual bias), the standard deviation of the response improved significantly as the separation angle between photons increased. This improvement correlates with a decrease in shared hits, reducing the number of nodes with ambiguous fractions ( $f \approx 0.5$ ).
Bias Observation: A bias was observed where reconstructed entry positions tended to cluster toward the midpoint between the true photon entry points. The authors note this is likely due to the post-hoc clustering step not being part of the training loss.

Significance and Limitations
The paper claims that SOOP provides a viable path to exploiting high-granularity data in high-pileup environments by reducing the algorithmic complexity of GNNs while maintaining high segmentation fidelity. It demonstrates that detailed spatial disentanglement and incident particle entry point recovery are possible beyond simple background rejection.

However, the authors modestly acknowledge two structural limitations:

Non-Differentiable Clustering: The reliance on a post-hoc GMM prevents full end-to-end optimization of the total shower reconstruction loss, as the clustering step cannot backpropagate gradients to correct the position predictions.
Lack of Multi-Scale Representation: As a node-level regression pipeline without graph pooling, the model suffers from message attenuation over long distances, limiting its ability to form multi-scale representations. The authors suggest that future work should explore graph encoder-decoder architectures to mitigate this.

Technical Summary: SOOP Pipeline for Overlapping Object Segmentation

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