The new algorithm, dubbed MLPF, replaces the modular, physics-motivated heuristics of standard PF with a transformer neural network trained end-to-end on simulated collision events. Instead of linking tracks and calorimeter clusters through geometric proximity rules refined over years of tuning, the model learns those correlations directly from data-like simulation, processing the entire event in a single inference step rather than through sequential iterations. The architecture embeds each reconstructed track and calorimeter cluster into a 256-dimensional latent space and passes them through parallel transformer encoders for classification and regression, using scaled dot-product attention to learn pairwise correlations across the full event. With roughly 5.1 million trainable parameters, the model is compact by modern deep-learning standards, comparable in size to the unified particle transformer CMS already uses for jet flavor tagging.

Training such a model required solving a deceptively hard problem: defining what the network should learn. The collaboration constructed a particle-level training target from the Geant4 detector simulation, selecting only particles that genuinely leave detectable signals, excluding those that fall outside the detector acceptance or below energy thresholds, and treating charged hadrons that fail to produce a reconstructed track as neutral hadrons. A per-particle loss function assigns each target particle to exactly one input element, its primary track or cluster, combining a binary classification loss, a particle-identification loss computed with focal loss to handle class imbalance, and a regression loss on the four-momentum expressed in logarithmic ratios relative to the primary element. A transverse-momentum-dependent weighting factor emphasizes high-energy particles in the training tails, and all three loss components converge smoothly with no signs of overfitting.

The training itself ran on eight AMD MI250X GPUs at the LUMI supercomputer in Finland, taking about six hours per epoch for ten epochs using the PyTorch framework and a LAMB optimizer with cosine annealing. Simulated samples were generated under LHC Run-3 2023 conditions at a center-of-mass energy of 14 TeV, with testing events generated under 2024 conditions at 13.6 TeV, deliberately shifted from the training configuration to demonstrate that the model generalizes across detector conditions and collision energies rather than memorizing a single operating point. Events contained between 55 and 75 additional proton-proton interactions per bunch crossing, the pileup that contaminates real LHC collisions and makes reconstruction dramatically harder.

The physics performance numbers are striking. In simulated top quark-antiquark events, MLPF improves jet energy resolution by 10 to 20 percent compared to standard PF for jets with transverse momentum between 30 and 100 GeV, an improvement that holds consistently in both top and quantum chromodynamics multijet samples. Because the model is trained only on individual particles and never explicitly optimized on jets, the better jet performance emerges purely from improved particle-level reconstruction. MLPF also achieves higher efficiency for reconstructing neutral hadrons while maintaining the same misidentification rate as standard PF, a combination that is difficult to achieve with rule-based linking, and the reconstructed missing transverse momentum distributions remain generally consistent with the standard algorithm.

Crucially, the team did not stop at simulation. The model was commissioned on a small sample of real CMS data collected in 2024 with a dijet trigger, corresponding to an integrated luminosity of 375 inverse picobarns. Running both PF and MLPF on the same data events, the collaboration found comparable jet distributions and consistent dijet asymmetry, an observable particularly sensitive to relative jet resolutions. The MLPF-reconstructed missing transverse momentum spectrum was somewhat harder in the tails, matching the trend seen in simulation. This data validation makes MLPF the first machine-learning-based full-event reconstruction pipeline ever applied to data from a hadron collider experiment, a milestone that could reshape reconstruction strategies across the field.

The computational gains are equally significant. Standard PF runs on CPUs and took approximately 110 milliseconds per event in the benchmark, while MLPF performed inference on an Nvidia L4 GPU with a median of 20 milliseconds per event, a roughly fivefold speedup. Because of the iterative nature of the baseline PF block algorithms, no performant GPU implementation exists for standard PF; MLPF unlocks accelerator use for this critical step. The FlashAttention kernel keeps memory and runtime scaling manageable despite the nominally quadratic cost of full-event attention, and a single L4 GPU supported 64 parallel inference streams using less than 10 GB of memory. The model also produces fully reproducible outputs, with repeated evaluations on the same GPU yielding identical results and CPU and GPU inference agreeing within numerical precision.

Integration into the CMS software framework was designed to be minimally invasive. The model is exported as a frozen Open Neural Network Exchange file and loaded through ONNX Runtime, taking reconstructed tracks and calorimeter clusters as inputs and producing particle candidates that downstream modules consume without modification. Upstream tracking and cluster-building algorithms remain untouched, making MLPF fully complementary to ongoing GPU-based developments elsewhere in the reconstruction chain. This separation of concerns means analyses can switch between PF and MLPF with a configuration flag, enabling the side-by-side comparisons that underpinned the validation campaign.

The motivation extends well beyond Run 3. At the high-luminosity upgrade of the LHC, expected to begin operation later this decade, average pileup will reach up to 200 simultaneous interactions per bunch crossing, roughly three times the conditions tested here. Reconstruction complexity grows rapidly with pileup, and hand-engineered algorithms whose combinatorics scale poorly with detector occupancy face diminishing returns. Machine-learning approaches offer favorable scaling, faster retraining when detector geometries change, and even the possibility of baking analysis-specific optimizations directly into reconstruction, as CMS already demonstrated by improving missing transverse momentum resolution for its W boson mass measurement. For proposed future colliders, ML-based particle-flow can accelerate detector design studies through rapid iteration and differentiable programming pipelines.

For now, the collaboration is careful about what has and has not been proven. Electron reconstruction sequences have not yet been retuned for MLPF, the forward detector region needs re-optimization ahead of the high-granularity endcap calorimeter upgrade, and deploying the algorithm in production requires further validation against simulation across a wide range of samples. But the demonstration is complete in its essentials: a transformer trained on simulation runs faster, generalizes across operating conditions, matches the physics performance of decades of hand-tuned software, and has already interpreted real collision data. The era in which the world’s most complex detectors are read out by learned models rather than rulebooks has effectively begun.

Subject of Research: Machine-learning-based particle-flow reconstruction in the CMS detector

Article Title: Full event interpretation with machine-learning-based particle-flow reconstruction in the CMS detector

Article References: Full event interpretation with machine-learning-based particle-flow reconstruction in the CMS detector. (n.d.). https://doi.org/10.1140/epjc/s10052-026-15754-5

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-15754-5

Keywords: CMS, particle-flow reconstruction, machine learning, transformers, CERN, LHC, jet energy resolution, GPU computing, high-energy physics, pileup, HL-LHC, graph attention

The standard remedy for rising noise is blunt but simple. Experimenters apply a fixed energy threshold to each individual calorimeter cell, typically set a few standard deviations above the measured noise level, so that any fluctuation below that cut is discarded as spurious. The trouble is that the threshold cannot tell the difference between noise and a real, low-energy piece of an electromagnetic shower. When a photon slams into the crystal array, it deposits its energy across many neighboring cells, and the outer cells of that shower often carry only small amounts of energy. A rigid threshold discards exactly those contributions, underestimating the total energy of the particle and worsening the resolution that precision analyses depend on, from Higgs boson mass measurements to searches for new particles and detailed studies of jet substructure.

The new study, led by Suman Das Gupta and colleagues at the Saha Institute of Nuclear Physics in Kolkata, together with collaborators in France, the United States and India, proposes a data-driven alternative. Instead of judging each cell in isolation, a machine learning model looks at the full picture: the complete shape of the electrical pulse in each crystal, the spatial pattern of energy deposits across the cluster, and the correlations among neighboring cells. The researchers framed the task as a binary classification problem at the level of individual cells, asking the network to label each one as a genuine signal hit or a noise hit, and then to use that information to reconstruct the photon’s energy more faithfully than any fixed cut could.

To train and test the approach realistically, the team built a standalone Geant4 simulation of an 11 by 11 matrix of lead-tungstate crystals, each 2.2 by 2.2 square centimeters in cross section and 22 centimeters long, arranged to mimic the geometry of the barrel section of the CMS electromagnetic calorimeter. Monoenergetic electrons were fired perpendicularly into the front face of the array, and the deposited energy in each crystal was recorded and converted into digitized waveforms following the same methodology used in the current CMS detector. Each pulse was sampled at 40 megahertz, matching the LHC bunch crossing rate, and engineered with three presamples for pedestal subtraction, with the peak timed to fall at the sixth of ten retained sampling points.

The simulation then layered on the harsh realities of collider operation. Electronic noise with a root-mean-square amplitude of 150 megaelectronvolts was injected into every crystal, with correlations between time samples modeled through a covariance matrix and generated via Cholesky decomposition. On top of that came pileup: the spray of energy from dozens of unrelated proton-proton collisions overlapping in the same bunch crossing. The researchers simulated minimum-bias interactions with Pythia8 at the Run 3 collision energy of 13.6 teraelectronvolts, drawing the number of overlapping interactions per crossing from a Poisson distribution with a mean of 50, consistent with actual LHC Run 3 conditions. Contributions from fifteen preceding bunch crossings, the in-time crossing, and nine subsequent ones were all summed into each crystal’s waveform, producing readout samples that faithfully blend signal, pileup and noise.

Before the machine learning could begin, the raw waveforms were passed through the multifit algorithm, the pulse-shape fitting technique already used by CMS, which reconstructs cell energies by fitting a linear combination of known signal and pileup templates to the observed samples via nonnegative least squares. The resulting energies, together with the ten time samples of each pulse shape, the spatial coordinates of each cell, and the energy normalized to the highest-energy seed cell, formed the input features. Each event was turned into a graph, with calorimeter cells as nodes and edges connecting spatial neighbors through a k-nearest-neighbors scheme with k equal to 24, allowing the network to reason about the local geometry of the shower.

The architecture works in three stages. First, a temporal encoder built from two one-dimensional convolutional layers compresses each cell’s ten-sample waveform into a compact feature vector. These embeddings are concatenated with the cell’s position and normalized energy, and the combined node features are fed through multiple layers of a graph neural network, which propagates information between neighboring cells so that each cell’s classification is informed by its context. Finally, a small multilayer perceptron with a sigmoid output assigns each node a probability of being a genuine signal hit. The team compared four graph convolution backbones: a standard Graph Convolutional Network, a Graph Attention Network, Edge Convolution, and Dynamic Edge Convolution, all trained with a binary cross-entropy loss augmented by two physics-motivated regularization terms, one penalizing the spread of the relative energy error and another ensuring the seed cell at the shower’s center is always retained.

While all four architectures achieved nearly identical discrimination power on the signal-versus-noise task, they diverged in how well they reconstructed energy. The Graph Attention Network emerged as the clear winner, delivering the most accurate energy scale and the lowest, most uniform standard deviation of the relative energy error across the full range of photon energies from 5 to 30 gigaelectronvolts, evaluated at a pseudorapidity of 1.4, a high-pileup region of the CMS barrel chosen deliberately as a challenging scenario. The selected model contains roughly 11,300 trainable parameters, trained on a single NVIDIA Tesla V100 GPU over 1500 epochs in about eight hours, and reaches a verdict on each event in an average of just 4.38 milliseconds, fast enough to be contemplated for real reconstruction workflows.

The head-to-head comparison against the traditional method was striking. With the ML score threshold set at 0.5 and the baseline energy cut set at 150 megaelectronvolts, comparable to the simulated noise floor, the machine learning selection consistently produced better mean reconstructed photon energy, better energy resolution, and higher signal cell efficiency at every photon energy tested, a level of performance that no value of the energy cut could replicate. Visualizations of the 11 by 11 cell window around a 15 gigaelectronvolt photon show why: the simple threshold carves away the low-energy outskirts of the true shower, while the network, reading the pulse shapes and the collective pattern of deposits, keeps those cells and rejects the noise. The authors emphasize that the approach is dynamic rather than fixed, adapting to evolving detector conditions as radiation damage deepens, which makes it particularly suited to the long-term operation of calorimeters in radiation-intensive environments and could ultimately extend the physics reach of collider experiments as luminosity continues to climb.

Subject of Research: Machine learning-based noise discrimination for electromagnetic calorimeter signal reconstruction in high-radiation particle physics detectors

Article Title: Enhancing electromagnetic calorimeter signal reconstruction with machine learning-based noise discrimination

Article References: Das Gupta, S., Ghosh, S., Gazi, L., Dutta, S., Ledovskoy, A., Bhattacharya, S., & Jain, S. (2026). Enhancing electromagnetic calorimeter signal reconstruction with machine learning-based noise discrimination. The European Physical Journal C, 86(9), Article 1134. https://doi.org/10.1140/epjc/s10052-026-16346-z

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16346-z

Keywords: graph neural networks, electromagnetic calorimeter, CMS experiment, Large Hadron Collider, noise discrimination, energy resolution, radiation damage, pileup, Geant4 simulation, lead-tungstate crystals, pulse-shape fitting, machine learning