Machine-Learned Particle Flow (MLPF)

• Machine-Learned Particle Flow (MLPF) is a supervised, set-to-set learning framework that replaces hand-crafted particle flow rules with scalable neural architectures.
• MLPF implementations using graph neural networks and transformers demonstrate improved jet energy resolution and faster inference on heterogeneous computing platforms.
• The method integrates seamlessly with CMS software, enabling robust calibration, transferability across detectors, and reuse of latent representations for downstream tasks.

Machine-Learned Particle Flow (MLPF) is a family of supervised event-reconstruction algorithms that reformulates particle flow as a set-to-set learning problem from detector signals—principally tracks and calorimeter clusters—to particle candidates. In collider detectors, particle flow is the procedure that constructs a global description of each collision by combining information from multiple subdetectors to identify and measure final-state particles. MLPF replaces hand-crafted association and decision logic with trainable neural architectures, first in graph-neural-network form and later in transformer-based form, with the dual aim of preserving or improving physics performance and making reconstruction more portable to heterogeneous computing platforms such as GPUs (Pata et al., 2021, Pata et al., 2022, Collaboration, 24 Jan 2026).

1. Origins, scope, and relation to particle flow

The conceptual starting point for MLPF is the central role of particle flow in collider reconstruction. In CMS, standard particle flow reconstructs stable particles from calorimeter clusters and tracks and is crucial for jets and missing transverse energy; the same general principle appears in future-detector studies that formulate reconstruction from tracks and calorimeter clusters as supervised learning (Pata et al., 2022, Pata et al., 2023). MLPF is therefore not a separate analysis tool layered on top of reconstructed events, but a learned replacement for the reconstruction stage that produces the particle list on which downstream observables depend.

The first fully articulated MLPF formulation introduced an end-to-end trainable, machine-learned particle-flow algorithm based on parallelizable, computationally efficient, and scalable graph neural networks, evaluated on simulated top quark-antiquark events in conditions similar to those expected for the high-luminosity LHC (Pata et al., 2021). A precursor line of work attacked a narrower but fundamental PFlow subproblem—separating neutral from charged calorimeter energy deposits with computer-vision models—and reported a significantly improved reconstruction of the neutral particle calorimeter energy deposits in a context of large overlaps with the deposits from charged particles (Bello et al., 2020). This suggests that the later event-level MLPF program can be read as a generalization from specialized learned submodules to unified full-event reconstruction.

Paper	Context	Contribution
(Pata et al., 2021)	HL-LHC-like simulation	GNN-based end-to-end MLPF with scalable graph construction
(Pata et al., 2022)	CMS software implementation	GNN-based PF in CMSSW with validation on jets and $E_T^{\text{miss}}$
(Collaboration, 24 Jan 2026)	CMS Run-3 conditions and data	Transformer-based MLPF with GPU inference and improved jet energy resolution

A recurrent source of ambiguity is nomenclature. In collider physics, MLPF denotes machine-learned particle-flow reconstruction; it should not be conflated with unrelated uses of “particle flow” in fluid mechanics and trajectory prediction, such as TrajectoryFlowNet (Wan et al., 13 Jul 2025).

2. Problem formulation, inputs, and supervision

MLPF treats event reconstruction as a variable-cardinality mapping from a set of detector elements to a set of reconstructed particles. In the CMS GNN implementation, the inputs are the full list of detector signals per event, including ECAL, HCAL, and HF calorimeter clusters, ECAL superclusters, KF tracks, GSF tracks, and BREMS points for electrons, with features such as energies, positions, extrapolated track coordinates, hit multiplicities, charge, muon-system information, and electron-seeding flags (Pata et al., 2022). In the later CMS transformer implementation, the model again consumes all tracks and calorimeter clusters per event, with track features such as $p_T$, $\eta$, $\phi$, uncertainties, Cartesian momentum, charge, number of hits, and perigee parameters, and cluster features including $x,y,z$, $E_T$, corrected energy, timing, cluster shapes, and detailed per-layer energy distributions (Collaboration, 24 Jan 2026).

The output is a particle list with per-candidate type and kinematics. In the CMS GNN model, for each input object the network predicts a particle ID among eight categories—charged hadron, neutral hadron, HFEM, HFHAD, photon, electron, muon, or none/ghost—and a momentum vector $(p_T,\eta,\phi,E,q)$ (Pata et al., 2022). Other implementations use closely related target spaces, often parameterizing four-momentum as $(p_T,\eta,\sin\phi,\cos\phi,E)$ and, in some later CMS developments, adding a binary pileup label (Mokhtar, 28 Aug 2025).

The supervision strategy has evolved. Early CMS work deliberately mirrored the established PF input schema and target definitions so that the learned model could reproduce the behavior of standard PF within the existing reconstruction chain (Pata et al., 2022). A subsequent CMS report stated that the improved implementation was “optimized using generator/simulation-level particle information as the target for the first time,” with the explicit goal of potentially improving detector response in terms of physical quantities of interest (Mokhtar et al., 2023). In the 2026 CMS implementation, the training target is built from simulated Monte Carlo truth comprising all stable, reconstructable particles leaving signals in the detector, while another CMS development described a “RECO-level” truth target that includes only particles that generate detectable hits and survive reconstruction (Collaboration, 24 Jan 2026, Mokhtar, 28 Aug 2025). A plausible implication is that MLPF has moved from imitation of legacy PF toward direct optimization against simulation-level notions of reconstructable truth.

3. Architectures and learning objectives

The original MLPF lineage is graph-neural-network based. The 2021 formulation constructed a unified event graph whose nodes are detector inputs and used approximate $k$-nearest neighbors via locality sensitive hashing to obtain scalable graph building; classification and regression were then performed with a multi-task objective on per-node outputs (Pata et al., 2021). In the CMS implementation described in 2022, the model used local context binning in a learned latent space, built fully connected graphs within bins, and defined connection strength or neighborhood through a Gaussian kernel over the embedding space. Successive graph convolution and message-passing layers aggregated information, and separate branches predicted particle classification and momentum/charge regression. The loss was written as

$$L(Y, Y') = \sum_{k=1}^{|X|} \mathrm{focal}(y_k, y'_k) + \mathrm{Huber}(y_k, y'_k),$$

with focal loss for categorical classification and Huber loss for regression; the model used the object condensation paradigm to enable a scalable set-to-set mapping (Pata et al., 2022).

Interpretability studies have clarified what these GNNs use internally. One explanatory analysis adapted layerwise-relevance propagation to MLPF and reported that charged hadron candidates rely extensively on neighboring node information, whereas neutral hadrons need less neighbor information; it also found that only a subset of closest neighbors receive nonzero relevance because the dynamic graph uses $p_T$0 nearest neighbors in the learned embedding space (Mokhtar et al., 2021). This is significant because it shows that the learned replacement for PF is not merely memorizing detector-object types; it is using relational structure in a class-dependent way.

The architectural center of gravity later shifted toward transformers. In the 2026 CMS model, tracks and clusters are embedded into a 1024-dimensional space and processed by two parallel transformer encoders, one for classification and one for regression, each with three transformer blocks, with scaled dot-product attention implemented using FlashAttention for memory and runtime optimization on GPUs (Collaboration, 24 Jan 2026). A parallel literature on future detectors compared a scalable GNN with a kernel-based transformer that avoids quadratic operations and reported that the best GNN model improved jet transverse momentum resolution by up to 50% compared to the rule-based algorithm, while remaining portable across Nvidia, AMD and Habana hardware (Pata et al., 2023).

Training has required substantial hyperparameter optimization. One dedicated study used the MLPF GNN as a benchmark for distributed HPO on HPC systems and found that ASHA in combination with Bayesian optimization gave the largest performance increase per compute resources spent; the total campaign used 19,574 core-hours on JUWELS Booster and 56,730 core-hours on CoreSite, and would have required about 6 months on a single-GPU machine compared to approximately 83 hours in the distributed setup (Wulff et al., 2022).

4. CMS implementation and physics validation

A defining feature of the CMS program has been integration into the experiment’s software rather than isolated benchmarking. The 2022 implementation was fully integrated into CMSSW for validation, using the same downstream reconstruction of jets and $p_T$1 as standard PF. On realistic samples including unseen QCD events and typical Run-3 pileup, particle-level $p_T$2 and $p_T$3 spectra showed good agreement for most candidate types, while jet $p_T$4 and $p_T$5 distributions using PUPPI were very similar between MLPF and PF (Pata et al., 2022). The same study reported a high-$p_T$6 tail in QCD events not used during training, suggesting that rare, high-energy neutral particles were occasionally misreconstructed and that enlarging the high-energy portion of the training set could mitigate the effect (Pata et al., 2022).

The later CMS transformer implementation moved beyond broad compatibility and reported explicit gains. In simulated top quark-antiquark events under LHC Run-3 conditions, jet energy resolution improved by 10–20% for jets with transverse momentum between 30 and 100 GeV; particle-level studies found higher efficiency for neutral hadrons at similar misidentification rates as standard PF, as well as more efficient identification of charged hadrons and photons (Collaboration, 24 Jan 2026). The same paper stated that MLPF- and PF-reconstructed kinematic distributions in real CMS Run-3 data are in agreement, which is the critical condition for direct use on data rather than simulation-only studies (Collaboration, 24 Jan 2026).

The longer historical arc is therefore mixed rather than monotonic. Early CMS integration showed that MLPF could faithfully reproduce the core physics response of hand-optimized PF in an operational framework (Pata et al., 2022); later CMS work showed improved jet energy resolution and improved inference time in both simulation and data (Collaboration, 24 Jan 2026). This progression addresses a common misconception that learned reconstruction is evaluated only in simplified or stand-alone settings.

5. Computational scaling, deployment, and heterogeneous hardware

Computational portability has been an explicit design objective from the beginning. The 2022 CMS GNN was implemented in TensorFlow 2.6 using only standard dense matrix operations and no custom CUDA, which was intended to maximize portability across CPUs, GPUs, and other accelerators. The trained model could be exported to ONNX for inference in CMSSW via ONNXRUNTIME (Pata et al., 2022). In that implementation, runtime and memory usage scaled linearly with event size, and inference for typical LHC Run-3 events with pileup required approximately 10 ms per event and approximately 1 GB RAM on a single NVIDIA RTX2060S GPU (Pata et al., 2022).

The transformer generation strengthened the hardware case. In the 2026 CMS study, inference time evaluated on simulated multijet events had a median of 20 ms per event on an Nvidia L4 GPU, compared to approximately 110 ms for the standard CMS PF reconstruction. The same model supported 64 parallel streams with less than 10 GB total memory, about 150 MB per stream, and used FlashAttention to avoid the quadratic scaling of standard attention (Collaboration, 24 Jan 2026). The paper also reported that runtime remains stable even on high-occupancy events, unlike PF (Collaboration, 24 Jan 2026).

Beyond CMS, scalable MLPF models for future detectors have emphasized both asymptotic behavior and device portability. A study of electron-positron full simulation reported linearly scaling GNN inference with event size, event reconstruction with up to $p_T$7 particles, and near-linear multi-device scaling on Nvidia GPUs, AMD GPUs, and Intel Habana HPUs (Pata et al., 2023). Taken together, these results position MLPF not only as a physics-reconstruction method but also as a computing strategy for increasingly accelerator-centric offline and possibly online environments.

6. Interpretability, transfer, and the foundation-model perspective

Interpretability has been a persistent concern because MLPF replaces a rule-based chain with a learned set-to-set model. The layerwise-relevance-propagation study addressed this directly by adapting LRP to dynamic graph building and message passing, producing relevance maps that identified important nodes and features for particular predictions and verified, for example, the importance of charge for charged hadron classification (Mokhtar et al., 2021). This does not remove opacity, but it narrows the gap between learned and heuristic reconstruction.

A second major direction is transfer across detectors and tasks. A cross-detector fine-tuning study pretrained a transformer-based MLPF on the CLICdet detector and fine-tuned it on the CLD detector, showing that with an order of magnitude less samples from the second dataset it could achieve the same performance as costly training from scratch across particle-level and event-level metrics, including jet and missing transverse momentum resolution. Specifically, the fine-tuned model achieved comparable performance to the traditional rule-based particle-flow approach on event-level metrics after training on 100,000 CLD events, whereas a model trained from scratch required at least 1 million CLD events to achieve similar reconstruction performance (Mokhtar et al., 28 Feb 2025). This suggests that MLPF learns representations that are not tied rigidly to one detector geometry.

That representational view has been made explicit in the proposal to use machine-learned particle flow as a foundation model for collider physics. In that work, a pretrained MLPF backbone was repurposed for jet flavor identification, jet energy regression, and missing momentum regression by appending the per-particle latent representations learned during reconstruction as additional input features. The study reported substantial improvement over baselines using kinematic features alone and showed that a single linear layer trained only on the latent representations achieved competitive performance, outperforming the missing-momentum baseline with approximately 35 times fewer parameters (Mokhtar et al., 12 Jun 2026). In this formulation, reconstruction is no longer only an endpoint; it becomes a learned interface between detector-level data and high-level analysis.

The principal unresolved issue is therefore not whether MLPF can emulate PF, but how far a unified learned reconstruction can be pushed without sacrificing calibration, robustness to domain shift, and experimental control. Existing results establish that MLPF can reproduce standard PF behavior, improve selected reconstruction metrics, operate efficiently on GPUs, generalize across detector conditions and collision energies, and expose reusable latent representations for downstream tasks (Pata et al., 2022, Collaboration, 24 Jan 2026, Mokhtar et al., 12 Jun 2026). Whether this eventually displaces modular reconstruction wholesale remains an open experimental and computing question rather than a settled architectural fact.