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| CMS-PFT-25-001 ; CERN-EP-2025-300 | ||
| Full event interpretation with machine-learning-based particle-flow reconstruction in the CMS detector | ||
| CMS Collaboration | ||
| 24 January 2026 | ||
| Submitted to Eur. Phys. J. C | ||
| Abstract: The particle-flow (PF) algorithm constructs a global description of each particle collision by producing a comprehensive list of final-state particles, and is central to event reconstruction in the CMS experiment at the CERN LHC. The existing PF implementation relies on physics-motivated heuristics and assumptions that can be replaced by machine-learning (ML) models trained directly on simulated data and naturally suited to modern graphics processing units (GPUs). A state-of-the-art ML-based PF (MLPF) reconstruction algorithm, implemented within the CMS software framework, is presented. The MLPF algorithm performs a learnable full-event reconstruction on GPUs, generalizes across detector conditions and collision energies, and replaces multiple modular reconstruction steps with a single unified model. Physics performance comparable to standard PF reconstruction is achieved in both simulation and data, with improved jet energy resolution and inference time. In simulated top quark-antiquark events under LHC Run-3 (2023-2024) conditions, the jet energy resolution improves by 10-20% for jets with transverse momentum between 30-100 GeV. Inference time is evaluated using simulated multijet events, with a median of 20 ms per event on an Nvidia L4 GPU, compared to approximately 110 ms for the standard CMS PF reconstruction. | ||
| Links: e-print arXiv:2601.17554 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Validation of the MLPF particle-level target, after removing the contributions from the pileup particles, using $ \mathrm{t} \overline{\mathrm{t}} $ simulation with pileup. The $ p_{\mathrm{T}} $ distribution of target particles and truth particles derived from PYTHIA stable particles (upper left). The $ p_{\mathrm{T}} $ distribution of jets clustered from each particle set (upper right). The jet response relative to particle-level jets (lower left). The target $ p_{\mathrm{T}}^\text{miss} $ as a function of the PYTHIA truth $ p_{\mathrm{T}}^\text{miss} $ (lower right). The target particle set, after removing the contribution from pileup, generally aligns well with the pileup-free PYTHIA truth. |
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Figure 1-a:
Validation of the MLPF particle-level target, after removing the contributions from the pileup particles, using $ \mathrm{t} \overline{\mathrm{t}} $ simulation with pileup. The $ p_{\mathrm{T}} $ distribution of target particles and truth particles derived from PYTHIA stable particles (upper left). The $ p_{\mathrm{T}} $ distribution of jets clustered from each particle set (upper right). The jet response relative to particle-level jets (lower left). The target $ p_{\mathrm{T}}^\text{miss} $ as a function of the PYTHIA truth $ p_{\mathrm{T}}^\text{miss} $ (lower right). The target particle set, after removing the contribution from pileup, generally aligns well with the pileup-free PYTHIA truth. |
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Figure 1-b:
Validation of the MLPF particle-level target, after removing the contributions from the pileup particles, using $ \mathrm{t} \overline{\mathrm{t}} $ simulation with pileup. The $ p_{\mathrm{T}} $ distribution of target particles and truth particles derived from PYTHIA stable particles (upper left). The $ p_{\mathrm{T}} $ distribution of jets clustered from each particle set (upper right). The jet response relative to particle-level jets (lower left). The target $ p_{\mathrm{T}}^\text{miss} $ as a function of the PYTHIA truth $ p_{\mathrm{T}}^\text{miss} $ (lower right). The target particle set, after removing the contribution from pileup, generally aligns well with the pileup-free PYTHIA truth. |
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Figure 1-c:
Validation of the MLPF particle-level target, after removing the contributions from the pileup particles, using $ \mathrm{t} \overline{\mathrm{t}} $ simulation with pileup. The $ p_{\mathrm{T}} $ distribution of target particles and truth particles derived from PYTHIA stable particles (upper left). The $ p_{\mathrm{T}} $ distribution of jets clustered from each particle set (upper right). The jet response relative to particle-level jets (lower left). The target $ p_{\mathrm{T}}^\text{miss} $ as a function of the PYTHIA truth $ p_{\mathrm{T}}^\text{miss} $ (lower right). The target particle set, after removing the contribution from pileup, generally aligns well with the pileup-free PYTHIA truth. |
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Figure 1-d:
Validation of the MLPF particle-level target, after removing the contributions from the pileup particles, using $ \mathrm{t} \overline{\mathrm{t}} $ simulation with pileup. The $ p_{\mathrm{T}} $ distribution of target particles and truth particles derived from PYTHIA stable particles (upper left). The $ p_{\mathrm{T}} $ distribution of jets clustered from each particle set (upper right). The jet response relative to particle-level jets (lower left). The target $ p_{\mathrm{T}}^\text{miss} $ as a function of the PYTHIA truth $ p_{\mathrm{T}}^\text{miss} $ (lower right). The target particle set, after removing the contribution from pileup, generally aligns well with the pileup-free PYTHIA truth. |
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Figure 2:
The neural network structure of the model. Input and output features are visualized in purple. Pointwise FFNs are visualized in green, and layers with full-event correlations in red. The last dimension contains a binary output to predict the presence of a particle (Valid), multi-class outputs for the PID, and the predicted momentum values. |
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Figure 2-a:
The neural network structure of the model. Input and output features are visualized in purple. Pointwise FFNs are visualized in green, and layers with full-event correlations in red. The last dimension contains a binary output to predict the presence of a particle (Valid), multi-class outputs for the PID, and the predicted momentum values. |
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Figure 2-b:
The neural network structure of the model. Input and output features are visualized in purple. Pointwise FFNs are visualized in green, and layers with full-event correlations in red. The last dimension contains a binary output to predict the presence of a particle (Valid), multi-class outputs for the PID, and the predicted momentum values. |
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Figure 3:
The PID, binary classification, and regression losses for the training and validation data sets, as a function of the training epoch. We observe both the training and validation losses to be smoothly converging. The training loss is evaluated with a partially-trained model throughout the training epoch on the training events (80%), while the validation loss is computed with the model weights at the end of the epoch on the validation events (20%). The losses are measured in arbitrary units, averaged across the events. |
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Figure 3-a:
The PID, binary classification, and regression losses for the training and validation data sets, as a function of the training epoch. We observe both the training and validation losses to be smoothly converging. The training loss is evaluated with a partially-trained model throughout the training epoch on the training events (80%), while the validation loss is computed with the model weights at the end of the epoch on the validation events (20%). The losses are measured in arbitrary units, averaged across the events. |
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Figure 3-b:
The PID, binary classification, and regression losses for the training and validation data sets, as a function of the training epoch. We observe both the training and validation losses to be smoothly converging. The training loss is evaluated with a partially-trained model throughout the training epoch on the training events (80%), while the validation loss is computed with the model weights at the end of the epoch on the validation events (20%). The losses are measured in arbitrary units, averaged across the events. |
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Figure 3-c:
The PID, binary classification, and regression losses for the training and validation data sets, as a function of the training epoch. We observe both the training and validation losses to be smoothly converging. The training loss is evaluated with a partially-trained model throughout the training epoch on the training events (80%), while the validation loss is computed with the model weights at the end of the epoch on the validation events (20%). The losses are measured in arbitrary units, averaged across the events. |
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Figure 4:
The particle $ p_{\mathrm{T}} $ (left) and $ \eta $ (right) distributions split by PID for MC particles (Gen), and PF and MLPF candidates in $ \mathrm{t} \overline{\mathrm{t}} $ events. In the forward region, the PF and MLPF algorithms do not attempt to identify particles, but instead reconstruct the deposits as either electromagnetic or hadronic. |
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Figure 4-a:
The particle $ p_{\mathrm{T}} $ (left) and $ \eta $ (right) distributions split by PID for MC particles (Gen), and PF and MLPF candidates in $ \mathrm{t} \overline{\mathrm{t}} $ events. In the forward region, the PF and MLPF algorithms do not attempt to identify particles, but instead reconstruct the deposits as either electromagnetic or hadronic. |
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Figure 4-b:
The particle $ p_{\mathrm{T}} $ (left) and $ \eta $ (right) distributions split by PID for MC particles (Gen), and PF and MLPF candidates in $ \mathrm{t} \overline{\mathrm{t}} $ events. In the forward region, the PF and MLPF algorithms do not attempt to identify particles, but instead reconstruct the deposits as either electromagnetic or hadronic. |
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Figure 5:
Neutral hadron efficiency (left) and misidentification rate (right) as functions of $ p_{\mathrm{T}} $ for PF (blue) and MLPF (red) in $ \mathrm{t} \overline{\mathrm{t}} $ events based on $ \Delta R $ matching to generator-level particles. The MLPF algorithm generally has higher efficiency at a lower misidentification rate. The vertical bars indicate the statistical uncertainties on the respective distributions. |
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Figure 5-a:
Neutral hadron efficiency (left) and misidentification rate (right) as functions of $ p_{\mathrm{T}} $ for PF (blue) and MLPF (red) in $ \mathrm{t} \overline{\mathrm{t}} $ events based on $ \Delta R $ matching to generator-level particles. The MLPF algorithm generally has higher efficiency at a lower misidentification rate. The vertical bars indicate the statistical uncertainties on the respective distributions. |
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Figure 5-b:
Neutral hadron efficiency (left) and misidentification rate (right) as functions of $ p_{\mathrm{T}} $ for PF (blue) and MLPF (red) in $ \mathrm{t} \overline{\mathrm{t}} $ events based on $ \Delta R $ matching to generator-level particles. The MLPF algorithm generally has higher efficiency at a lower misidentification rate. The vertical bars indicate the statistical uncertainties on the respective distributions. |
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Figure 6:
The corrected jet $ p_{\mathrm{T}} $ distribution in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) validation samples with 55--75 pileup interactions. MLPF is only trained to reconstruct particles, and is never explicitly optimized to reconstruct jets. The PUPPI algorithm is applied to both PF and MLPF jets to perform pileup subtraction. We show the jet $ p_{\mathrm{T}} $ distribution after simulated response calibration. The shaded bands indicate the statistical uncertainties on Gen. |
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Figure 6-a:
The corrected jet $ p_{\mathrm{T}} $ distribution in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) validation samples with 55--75 pileup interactions. MLPF is only trained to reconstruct particles, and is never explicitly optimized to reconstruct jets. The PUPPI algorithm is applied to both PF and MLPF jets to perform pileup subtraction. We show the jet $ p_{\mathrm{T}} $ distribution after simulated response calibration. The shaded bands indicate the statistical uncertainties on Gen. |
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Figure 6-b:
The corrected jet $ p_{\mathrm{T}} $ distribution in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) validation samples with 55--75 pileup interactions. MLPF is only trained to reconstruct particles, and is never explicitly optimized to reconstruct jets. The PUPPI algorithm is applied to both PF and MLPF jets to perform pileup subtraction. We show the jet $ p_{\mathrm{T}} $ distribution after simulated response calibration. The shaded bands indicate the statistical uncertainties on Gen. |
png pdf |
Figure 6-c:
The corrected jet $ p_{\mathrm{T}} $ distribution in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) validation samples with 55--75 pileup interactions. MLPF is only trained to reconstruct particles, and is never explicitly optimized to reconstruct jets. The PUPPI algorithm is applied to both PF and MLPF jets to perform pileup subtraction. We show the jet $ p_{\mathrm{T}} $ distribution after simulated response calibration. The shaded bands indicate the statistical uncertainties on Gen. |
png pdf |
Figure 6-d:
The corrected jet $ p_{\mathrm{T}} $ distribution in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) validation samples with 55--75 pileup interactions. MLPF is only trained to reconstruct particles, and is never explicitly optimized to reconstruct jets. The PUPPI algorithm is applied to both PF and MLPF jets to perform pileup subtraction. We show the jet $ p_{\mathrm{T}} $ distribution after simulated response calibration. The shaded bands indicate the statistical uncertainties on Gen. |
png pdf |
Figure 7:
The jet resolution in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) validation samples with 55--75 pileup interactions, after simulated response calibration. The MLPF algorithm is only trained to reconstruct particles, and is never explicitly optimized to reconstruct jets. The PUPPI algorithm is applied to both PF and MLPF jets to perform pileup subtraction. The jet resolution is parameterized by fitting a Gaussian distribution and dividing the best-fit standard deviation by the mean, showing the bin midpoints on the horizontal axis. |
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Figure 7-a:
The jet resolution in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) validation samples with 55--75 pileup interactions, after simulated response calibration. The MLPF algorithm is only trained to reconstruct particles, and is never explicitly optimized to reconstruct jets. The PUPPI algorithm is applied to both PF and MLPF jets to perform pileup subtraction. The jet resolution is parameterized by fitting a Gaussian distribution and dividing the best-fit standard deviation by the mean, showing the bin midpoints on the horizontal axis. |
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Figure 7-b:
The jet resolution in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) validation samples with 55--75 pileup interactions, after simulated response calibration. The MLPF algorithm is only trained to reconstruct particles, and is never explicitly optimized to reconstruct jets. The PUPPI algorithm is applied to both PF and MLPF jets to perform pileup subtraction. The jet resolution is parameterized by fitting a Gaussian distribution and dividing the best-fit standard deviation by the mean, showing the bin midpoints on the horizontal axis. |
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Figure 8:
Uncalibrated $ p_{\mathrm{T}}^\text{miss} $ in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) samples with pileup from offline reconstruction using PF and MLPF. The MLPF algorithm is only trained to reconstruct particles, and is never explicitly optimized to reconstruct $ p_{\mathrm{T}}^\text{miss} $. The $ p_{\mathrm{T}}^\text{miss} $ distributions from PF and MLPF are found to be generally consistent, with MLPF reconstructing a somewhat harder $ p_{\mathrm{T}}^\text{miss} $ spectrum in the tails. The vertical bars indicate the statistical uncertainties on the respective distributions, and the shaded bands in the ratio panel indicate the statistical uncertainties on PF. |
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Figure 8-a:
Uncalibrated $ p_{\mathrm{T}}^\text{miss} $ in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) samples with pileup from offline reconstruction using PF and MLPF. The MLPF algorithm is only trained to reconstruct particles, and is never explicitly optimized to reconstruct $ p_{\mathrm{T}}^\text{miss} $. The $ p_{\mathrm{T}}^\text{miss} $ distributions from PF and MLPF are found to be generally consistent, with MLPF reconstructing a somewhat harder $ p_{\mathrm{T}}^\text{miss} $ spectrum in the tails. The vertical bars indicate the statistical uncertainties on the respective distributions, and the shaded bands in the ratio panel indicate the statistical uncertainties on PF. |
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Figure 8-b:
Uncalibrated $ p_{\mathrm{T}}^\text{miss} $ in $ \mathrm{t} \overline{\mathrm{t}} $ (left) and QCD multijet (right) samples with pileup from offline reconstruction using PF and MLPF. The MLPF algorithm is only trained to reconstruct particles, and is never explicitly optimized to reconstruct $ p_{\mathrm{T}}^\text{miss} $. The $ p_{\mathrm{T}}^\text{miss} $ distributions from PF and MLPF are found to be generally consistent, with MLPF reconstructing a somewhat harder $ p_{\mathrm{T}}^\text{miss} $ spectrum in the tails. The vertical bars indicate the statistical uncertainties on the respective distributions, and the shaded bands in the ratio panel indicate the statistical uncertainties on PF. |
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Figure 9:
Distributions of the leading jet $ p_{\text{T,corr}} $ (left), the dijet asymmetry (center), and $ p_{\mathrm{T}}^\text{miss} $ (right) in a small sample of dijet data collected in Run 3. The distributions are largely compatible. The vertical bars indicate the statistical uncertainties on the respective distributions, and the shaded bands in the ratio panel indicate the statistical uncertainties on PF. |
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Figure 9-a:
Distributions of the leading jet $ p_{\text{T,corr}} $ (left), the dijet asymmetry (center), and $ p_{\mathrm{T}}^\text{miss} $ (right) in a small sample of dijet data collected in Run 3. The distributions are largely compatible. The vertical bars indicate the statistical uncertainties on the respective distributions, and the shaded bands in the ratio panel indicate the statistical uncertainties on PF. |
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Figure 9-b:
Distributions of the leading jet $ p_{\text{T,corr}} $ (left), the dijet asymmetry (center), and $ p_{\mathrm{T}}^\text{miss} $ (right) in a small sample of dijet data collected in Run 3. The distributions are largely compatible. The vertical bars indicate the statistical uncertainties on the respective distributions, and the shaded bands in the ratio panel indicate the statistical uncertainties on PF. |
png pdf |
Figure 9-c:
Distributions of the leading jet $ p_{\text{T,corr}} $ (left), the dijet asymmetry (center), and $ p_{\mathrm{T}}^\text{miss} $ (right) in a small sample of dijet data collected in Run 3. The distributions are largely compatible. The vertical bars indicate the statistical uncertainties on the respective distributions, and the shaded bands in the ratio panel indicate the statistical uncertainties on PF. |
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Figure 10:
The runtime of the baseline particle-flow reconstruction compared to the MLPF inference, directly within the CMS offline software using the native ONNXRUNTIME on GPU. |
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Figure 10-a:
The runtime of the baseline particle-flow reconstruction compared to the MLPF inference, directly within the CMS offline software using the native ONNXRUNTIME on GPU. |
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Figure 10-b:
The runtime of the baseline particle-flow reconstruction compared to the MLPF inference, directly within the CMS offline software using the native ONNXRUNTIME on GPU. |
png pdf |
Figure 10-c:
The runtime of the baseline particle-flow reconstruction compared to the MLPF inference, directly within the CMS offline software using the native ONNXRUNTIME on GPU. |
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Figure 10-d:
The runtime of the baseline particle-flow reconstruction compared to the MLPF inference, directly within the CMS offline software using the native ONNXRUNTIME on GPU. |
| Tables | |
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Table 1:
Monte Carlo simulation samples used for optimizing, validating, and testing the model. The training and validation samples are divided using an 80%/20% split, respectively. The symbols $ \text{---} $ in the 3rd column represent samples generated without pileup. |
| Summary |
| A machine-learning (ML)-based algorithm for particle-flow (PF) reconstruction in the CMS experiment has been presented. The algorithm correlates tracks and calorimeter clusters using successive transformer layers, and outputs a list of reconstructed particles with four-momenta and particle identification values. The algorithm is functionally equivalent to the standard PF algorithm currently used in CMS. The model is trained on CMS Run-3 (2023--2024) full simulation data sets that include realistic pileup conditions, and its performance is evaluated in simulated top quark-antiquark ( $ \mathrm{t} \overline{\mathrm{t}} $) and quantum chromodynamics multijet testing samples across different experimental conditions, as well as on data collected using a dijet trigger. To ensure computational efficiency, the model avoids quadratic scaling in runtime and memory by efficiently employing modern graphics processing units (GPUs). The ML-based PF (MLPF) algorithm achieves physics performance comparable to the standard PF algorithm, while enabling GPU acceleration for full event reconstruction within the CMS offline software framework. Specifically, we observe improved neutral hadron efficiency with MLPF while maintaining the same misidentification rate as standard PF. For jets with $ p_{\mathrm{T}} $ between 30--100 GeV in $ \mathrm{t} \overline{\mathrm{t}} $ events, we observe a 10--20% improvement in jet energy resolution compared to standard PF. The algorithm delivers a per-event runtime of approximately 20\unitms on an Nvidia L4 inference GPU, with 64 inference streams running in parallel per GPU. We also observe improved runtime scaling with event size compared to the standard PF algorithm, highlighting the computational robustness of the approach. While the MLPF algorithm has been successfully benchmarked under Run-3 conditions, its primary motivation lies in deployment at the high-luminosity upgrade of the LHC (HL-LHC), where the increased event complexity and pileup conditions demand both high physics performance and computational scalability. To deploy MLPF in production at the HL-LHC, several developments are foreseen. First, the model must be retrained for the upgraded detector and higher pileup conditions. Second, ensuring the portability of the inference across different GPU generations and hardware vendors is essential. Third, the model inference can be further optimized through techniques such as sparse or block attention, quantization, pruning, and asynchronous or batched execution. Finally, the physics performance and robustness can be improved through additional training and extensive cross-checks on a wide variety of simulated and data samples. |
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