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End-to-end Particle Reconstruction with Transformers in High-Granularity Calorimeters

This study demonstrates that end-to-end transformer-based methods, specifically diffusion, flow matching, and query-based set prediction architectures, offer highly effective and scalable solutions for accurately reconstructing overlapping particle showers in high-granularity calorimeters for the High-Luminosity LHC.

Original authors: Qiming Bao, Haotian Bi, Benedikt Maier, Alex Tapper, Lauri Laatu

Published 2026-10-30

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CC BY 4.0

Original authors: Qiming Bao, Haotian Bi, Benedikt Maier, Alex Tapper, Lauri Laatu

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 Europe, beneath the border of France and Switzerland, lies the Large Hadron Collider, a machine built to smash particles together at speeds approaching that of light. When these collisions occur, they create a chaotic spray of new particles, each leaving behind a faint trace of energy as it passes through massive detectors. For decades, physicists have relied on traditional methods to piece together these traces, grouping them into clusters to guess what kind of particle created them. However, the next generation of this machine, the High-Luminosity Large Hadron Collider, promises to increase the number of collisions so dramatically that the resulting energy sprays will overlap like a dense fog. In this crowded environment, the old methods of sorting particles begin to fail, leaving scientists unable to see the individual particles hidden within the mess. The challenge is not just to see the energy, but to count the particles and understand their properties when they are packed so tightly together that their signals merge into a single, confusing cloud.

To solve this, researchers at Imperial College London turned to a new kind of artificial intelligence, one that learns to see patterns in data much like a human brain might, but with the speed and precision of a computer. They focused on a specific detector called the High Granularity Calorimeter, which is designed to capture the three-dimensional shape of these energy sprays with incredible detail. Instead of using the standard clustering algorithms that have been the industry norm, the team tested three different advanced machine learning frameworks. These frameworks were designed to take the raw, unordered points of energy deposited in the detector and directly predict the number, type, and path of the particles that caused them. The researchers simulated a scenario where ten different particles, ranging from electrons to heavier kaons, were fired into the detector at once, creating a complex, overlapping shower of energy that mimics the difficult conditions expected in the future collider.

The team compared their new methods against a standard baseline algorithm known as CLUEstering, which works by finding the densest points of energy and grouping nearby hits around them. In their simulations, the traditional method struggled significantly when the particles were close together, often missing entire particles or merging them into a single, incorrect blob. In contrast, the three new artificial intelligence models, which use a mathematical structure called a transformer to process information, showed a remarkable ability to untangle the mess. These models did not just guess; they learned to reconstruct the particles directly from the raw data. One model, which uses a process of learning from random noise to find the correct answer, and another, which uses a set of learned questions to hunt for particles, both succeeded in identifying nearly all the particles in the simulation. They recovered about 96 percent of the true particles, a significant improvement over the 87 percent recovered by the traditional method.

Beyond simply counting the particles, the new models were also far better at measuring their energy. When the researchers looked at how accurately the models could determine the energy of each particle, the traditional method showed a wide spread of errors, often underestimating the energy of the particles. The new models, however, produced much tighter and more accurate results. The most precise of the new methods had a significantly lower error margin compared to the traditional approach. This precision held true even when the particles were very close to one another, a situation where the old method faltered the most. As the distance between particles increased, all models improved, but the artificial intelligence approaches maintained a clear advantage in accuracy across the board.

The study also looked at how fast these new systems could run, a critical factor for a machine that produces millions of collisions every second. The researchers tested their models on powerful computer chips designed for artificial intelligence. They found that two of the new models could process more than 12,000 events per second, outpacing the traditional method which managed just over 10,000. A third model, which used a slightly different mathematical approach requiring more steps to reach a conclusion, was slower but still capable of handling the workload. This speed, combined with the superior accuracy, suggests that these new methods are not just theoretical curiosities but practical tools ready for the future. The researchers concluded that while the problem of overlapping particles remains difficult, these end-to-end machine learning approaches offer a highly effective and scalable way to resolve the complex showers expected in the next era of particle physics, providing a clear path forward for the High-Luminosity Large Hadron Collider.

Technical Summary: End-to-end Particle Reconstruction with Transformers in High-Granularity Calorimeters

Problem Statement
The High-Luminosity Large Hadron Collider (HL-LHC) upgrade presents a severe challenge to particle reconstruction due to the drastic increase in simultaneously interacting particles. While next-generation High Granularity Calorimeters (HGCAL), such as the one for the CMS experiment, offer unprecedented 3D measurement capabilities with approximately 5 million independent channels, reconstructing particles from heavily overlapping energy showers remains computationally difficult. Traditional clustering methods often fail when incident particles are unknown in number, collide simultaneously, and produce overlapping energy deposits. This study addresses the specific challenge of reconstructing particle identities and properties directly from raw, sparse, unordered 3D detector hits in conditions simulating high particle density.

Methodology
The authors propose and evaluate three distinct end-to-end transformer-based architectures designed to map raw calorimeter hits to particle states (energy, position, and class). All models utilize a Perceiver encoder to reduce up to 12,000 input hits (position $x, y, z$ and energy) into a latent representation. The output is a set of up to 15 particles. The three frameworks compared are:

QueryDETR: An adaptation of the Detection Transformer (DETR). It employs 15 learned queries, each containing a latent representation and a reference state. These queries interact via self-attention to prevent duplicates and cross-attention to extract relevant shower data from the encoded hits. The model iteratively refines particle candidates through 6 blocks, using Hungarian matching during training to pair predictions with ground truth.
DiffReco: A generative approach based on diffusion models (inspired by DiffusionDet). It treats reconstruction as a denoising process. During training, candidate slots (comprising real particles and background) are corrupted with Gaussian noise. The network learns to reverse this corruption using Feature-wise Linear Modulation (FiLM) to adapt to noise levels. Inference involves an iterative sampling procedure (DDIM) starting from noisy candidates to recover clean particle states over 16 steps.
FlowReco: A generative approach using flow matching. The model learns a continuous, straight-line path (vector field) between random noise candidates and true targets. During inference, it evolves candidates from noise to final states by solving an ordinary differential equation (ODE) using Heun's method (a 2-step solver requiring two network evaluations per step).

A baseline model, CLUEstering, based on the CLUstering by Energy (CLUE) algorithm, is used for comparison. It calculates local energy density to group hits into seeds, outliers, and followers.

The evaluation uses a dataset of 100,000 Geant4 events simulating local detector regions with 1–10 particles (energies 20–200 GeV) emitted within a narrow cone to simulate overlapping showers. The dataset is split 80%-10%-10% for training, validation, and testing.

Key Results
The study demonstrates that all three transformer-based methods significantly outperform the CLUEstering baseline across multiple metrics:

Particle Multiplicity Recovery: The neural networks recover approximately 96% of truth particles (QueryDETR: 96.57%, FlowReco: 96.55%, DiffReco: 95.92%), compared to 87.20% for CLUEstering. The neural networks show a strong concentration along the diagonal in particle multiplicity matrices, indicating accurate counting of overlapping particles.
Energy Resolution: For correctly reconstructed particles ( $\Delta R \le 0.1$ ), the neural networks exhibit sharp peaks near zero error. QueryDETR achieves the narrowest energy-residual width ( $\sigma = 12.69 \pm 0.37$ GeV), followed by FlowReco ( $13.09 \pm 0.39$ GeV) and DiffReco ( $14.30 \pm 0.49$ GeV). In contrast, CLUEstering shows a substantially broader distribution ( $\sigma = 44.53$ GeV) with a pronounced negative tail, indicating systematic underestimation of energy.
Handling Overlaps: As particle separation decreases, energy resolution degrades for all methods. However, the neural networks maintain superior precision compared to CLUEstering across all angular distances.
Classification Accuracy: Combined accuracy (grouping predictions into electromagnetic, hadronic, and background) exceeds 97% for all three neural network models.
Computational Throughput: On an A100 GPU, QueryDETR and FlowReco achieve throughputs of 12,725 and 12,042 events per second, respectively, surpassing the CLUEstering baseline (10,145 ev/s). DiffReco is slower (7,455 ev/s) due to its requirement for 16 denoising steps.

Significance and Claims
The paper claims that learned queries (QueryDETR), diffusion processes (DiffReco), and flow matching (FlowReco) are all highly capable of mapping raw detector data into reconstructed particles with accurate kinematic properties. The authors assert that these end-to-end methods provide highly effective and scalable alternatives for resolving complex overlapping particle showers, a critical requirement for future calorimeters like the HGCAL.

Specifically, the study highlights that:

Transformer-based architectures can effectively replace traditional clustering methods in high-density environments where those methods fail.
Query-based set prediction (QueryDETR) and flow matching (FlowReco) offer a favorable balance of high reconstruction accuracy and inference speed, making them promising candidates for the HL-LHC era.
While resolving highly overlapping showers remains challenging (evidenced by reduced precision at small angular separations), the neural networks outperform the evaluated baseline in both particle recovery and energy resolution.

The authors conclude that these findings motivate further evaluation with larger datasets and more realistic detector conditions, positioning end-to-end machine learning as a viable pathway for particle reconstruction in future high-energy physics experiments.

Technical Summary: End-to-end Particle Reconstruction with Transformers in High-Granularity Calorimeters

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