k4PFHitML is the key4hep/Gaudi inference implementation of the hit-based particle-flow algorithm described in arXiv:2603.04084. The standalone Python reference implementation used for training (and for inference validation against this package) lives at github.com/doloresgarcia/HitPF.

The package handles data preparation from EDM4hep input collections, runs the trained models (converted to ONNX) via k4FWCore::MultiTransformer, and writes out particle-flow objects as standard EDM4hep collections.

This package targets the CLD detector concept and geometry: input collection names (ECALBarrel, ECALEndcap, HCALBarrel, HCALEndcap, HCALOther, MUON, SiTracks_Refitted, see the KeyValues in PFHitML.cpp), the truth-matching barrel/endcap geometry constants (truth_barrel_radius, truth_n_barrel_sides, truth_endcap_z), and the models themselves.

Reconstruction proceeds in two model stages per event:

1. Condensation/clustering model -- embeds every calorimeter hit and track into a learned space and predicts, per hit/track, a condensation point/beta value. Density Peak Clustering (DPC) on that embedding groups hits and tracks belonging to the same particle into a Shower (Clustering.h/.cpp, ShowerBuilder.h/.cpp). The DPC algorithm itself is a reimplementation of pgoltstein/densitypeakclustering (ρ local density, δ distance-to-higher-density, core/halo cluster assignment).
2. Regression/PID model -- per shower (charged and neutral run through separate models), regresses energy and classifies particle type (electron / charged hadron / neutral hadron / photon / muon) (PFParticleBuilder.h/.cpp).

Training data/samples:

• Both models are trained on CLD full simulation.
• The condensation model is trained on a Z→uds sample.
• The regression model is trained on a jet-like particle gun sample.

Truth matching is done via IoU (intersection-over-union) between a reconstructed shower's constituent hits/tracks and each MCParticle's, resolved with Hungarian matching (TruthMatcher.h). This produces the HitPFMCTruthLink output collection, and is what any downstream fake-rate / efficiency definition should be built on (a reconstructed particle with no truth match is a fake; a truth particle with no reconstructed match is missed).

• HitPF (ReconstructedParticleCollection): the reconstructed particle-flow objects -- momentum, energy, mass, charge, PDG, reference point.
• HitPFIDs (ParticleIDCollection): PID hypothesis per particle (type, likelihood, PDG, full per-class score vector).
• HitPFMCTruthLink (RecoMCParticleLinkCollection): reco-to-truth links from the IoU matching above, weight = IoU.
• HitPFUnassociatedTracks (TrackCollection, opt-in): tracks that never ended up in any shower (DPC noise, or removed by the E/p consistency cut), so never made it onto any HitPF particle -- see below.

• ROOT

• PODIO

• Gaudi

• k4FWCore

Run, from the k4PFHitML directory:

cd /your/path/to/this/repo/k4PFHitML/
source ./setup.sh
k4_local_repo
mkdir build
cd build
cmake .. -DCMAKE_INSTALL_PREFIX=../install -G Ninja -DPython_EXECUTABLE=$(which python3)
ninja install

Alternatively you can source the nightlies instead of the releases:

source /cvmfs/sw-nightlies.hsf.org/key4hep/setup.sh

k4run k4PF-HitML/options/PerformMLPF.py --inputFiles <input.edm4hep.root> --outputFile output_HitPF.edm4hep.root

PerformMLPF.py also accepts all the configurable parameters listed below (--dpc_d_c, --bFieldTesla, --write_unassociated_tracks, etc. -- run with --help for the full list).

The output is a ROOT file containing the input collections (keep *) plus the HitPF/HitPFIDs/HitPFMCTruthLink (and, if enabled, HitPFUnassociatedTracks) collections described above.

• PFHitML.cpp -- the main Gaudi MultiTransformer algorithm; orchestrates the full per-event pipeline (data prep -> clustering ONNX -> DPC -> shower building -> regression ONNX -> particle assembly) and declares all configurable Gaudi::Propertys.
• DataPreprocessing.h/.cpp -- builds the clustering model's input graph (calorimeter hits and tracks as nodes), and prepares per-shower inputs for the regression model.
• Clustering.h/.cpp -- Density Peak Clustering (DPC) on the clustering model's embedding output, plus the post-clustering E/p consistency cut (remove_bad_tracks_from_cluster) that can evict a track from its cluster.
• ShowerBuilder.h/.cpp -- turns DPC cluster labels into Shower objects, assigning each hit/track node back to its shower.
• Shower.h/.cpp -- per-shower data container (hits, tracks, betas) and shower-level derived quantities (mean track momentum, chi2, energy/momentum sums).
• PFParticleBuilder.h/.cpp -- turns a Shower plus regression/PID output into a final HitPF/HitPFIDs entry (fillRecoParticle), including all the charged/neutral-specific conventions documented below.
• TruthMatcher.h -- IoU-based Hungarian matching between reconstructed showers and MCParticles; produces HitPFMCTruthLink.
• EvaluationSummary.h/.cpp -- collects per-event reco/truth summary rows (used for validation/debug logging, not part of the physics output).
• ONNXHelper.h/.cpp -- thin wrapper around ONNX Runtime for loading a model and running named inference.
• Helpers.h/.cpp -- shared small utility functions used across the above.

All exposed as Gaudi::Propertys on PFHitML, settable from options/PerformMLPF.py:

• The three ONNX model paths (model_path_clustering, model_path_properties_neutral, model_path_properties_charged -- --onnx_model_clustering/--onnx_model_properties_neutral/ --onnx_model_properties_charged on the command line).
• Density Peak Clustering parameters (dpc_d_c, dpc_rho_min, dpc_delta_min, dpc_core_radius).
• Truth matching parameters (truth_iou_threshold, truth_barrel_radius, truth_n_barrel_sides, truth_endcap_z).
• Magnetic field strength (bFieldTesla), used for track pT reconstruction from curvature.
• reassign_low_p_muons / muon_to_charged_hadron_p_threshold: reassigns a charged candidate predicted as muon below a momentum threshold to charged hadron instead (on by default) -- a punch-through/misidentified hadron is more likely than a genuine muon at that momentum.
• writeUnassociatedTracks: write tracks never assigned to any shower into the HitPFUnassociatedTracks output collection (off by default) -- e.g. for invariant-mass calculations that want to recover tracks HitPF itself drops (charged particles that curl up before reaching the calorimeter).

• Reference point (referencePoint): for charged particles this is the energy-weighted shower barycenter minus the driving track's calorimeter-entry position (PFParticleBuilder.cpp::buildChargedRecoInfo), matching Python's PickPAtDCA.predict() (tools_for_regression.py: barycenters - p_xyz). For neutral particles, referencePoint is instead an absolute shower-barycenter position (computeNeutralReferencePoint)

• Energy (energy): for neutral particles this is a regression output. For charged particles it is the driving track's momentum magnitude |p|.

• Predicted class (HitPFIDs.type): the canonical field for "which of the 5 classes did the model predict" is HitPFIDs' type (ParticleID.type, set via pid.setType(recoInfo.physicsClass)) -- 0=electron, 1=charged hadron, 2=neutral hadron, 3=photon, 4=muon. Use this, not PDG, to identify the predicted class: PDG (both HitPF.PDG and HitPFIDs.PDG) is derived from type via a fixed mass/species assumption per class (see below), not an independent measurement -- e.g. every charged hadron gets PDG ±211 (pion) regardless of whether it's actually a pion, kaon, or proton/

• Mass / PDG: fixed per predicted class, not species-specific -- electron 0.511 MeV / PDG ±11, charged hadron assumed pion 139.57 MeV / PDG ±211, neutral hadron assumed neutron 939.57 MeV / PDG 2112, photon 0 / PDG 22, muon 105.658 MeV / PDG ±13 (PFParticleBuilder.cpp::massFromPredictedClass, pdgFromChargedClass/pdgFromNeutralClass). Note that the PID classifier only differentiates e, gamma, CH, NH, mu.

• Charge: derived from the driving track's curvature sign (chargeSignFromTrack, omega > 0 -> +1), 0 for neutral particles.

• Tracks: only the single driving track (lowest chi2/ndf, pickBestTrack) is attached to a charged HitPF particle's tracks relation, even if DPC clustered more than one track into the same shower. Recover unassociated tracks via the HitPFUnassociatedTracks subset collection (e.g. for invariant-mass calculations that want to include tracks HitPF itself drops).

• HitPFIDs.parameters: the full per-class softmax vector (not just the winning class), in chargedClassMap/neutralClassMap order (PFHitML.cpp) -- 3 entries {e, CH, mu} for charged particles, 2 entries {NH, gamma} for neutral. Lets a downstream consumer define their own PID working point instead of only seeing the argmax decision already baked into physicsClass/mass/PDG.

1. arXiv:2603.04084 -- hit-based particle-flow algorithm this package implements.
2. HitPF -- Python training/inference reference implementation.
3. pgoltstein/densitypeakclustering -- reference for the Density Peak Clustering algorithm reimplemented in Clustering.h/.cpp.

Parts of this codebase and README were drafted with AI assistance, then reviewed and adapted if necessary.