Using Line Segment Tracking to enable ML-based Track Reconstruction in CMS

The gist The first CMS demonstration of a track-reconstruction model built on Transformers and object condensation takes Line Segment Tracking objects as tokens to enable ML-based track reconstruction in high-pileup conditions.

Line Segment Tracking Objects as Tokens

Line Segment Tracking (LST) is designed around a distinctive feature of the Phase-2 OT geometry, where each layer is instrumented with pT modules of two closely spaced silicon sensors, so a charged particle deposits a hit in each; because the trajectory is bent in the 3.8 T solenoidal field, the displacement between the two hits encodes the local bending and hence a coarse estimate of its transverse momentum Every OT layer therefore supplies not just a position but a directional and momentum constraint, which LST exploits at every level of a bottom-up hierarchy of objects, each formed from those of the preceding level using only local geometric information (Figure 1). Mini-doublets (MD) link the two hits of a single pT module when their displacement is consistent with a track above 0.8 GeV, the offline counterpart of the on-detector stub. Line segments (LS) join two MDs in neighbouring layers whose positions and directions are compatible with a single trajectory, with the allowed pairings fixed in advance by precomputed module connection maps. Triplets (T3) merge two LSs sharing a middle MD into a threelayer object whose curvature gives a refined local pT estimate, and quintuplets (T5) combine two T3s sharing a middle MD into a five-layer object, the principal pure-OT track candidate. Triplets serve as the tokens for the model described below: they are already rich in physics content while remaining combinatorially manageable enough to preserve the flexibility to form longer candidates.

Model Architecture and Training

Each event is an unordered point cloud of T3 objects, and each mini-doublet is represented by its anchor hit, the hit in the better-resolved sensor of the module: the macro-pixel P-side in PS modules, whereas in 2S modules both sensors are strips and the resolution is the coarsest in the OT. Every triplet is then described by 49 features, including "(x, y,z) coordinates of both hits, the η and ϕ of the anchor hit, and the intra-mini-doublet differences (∆ϕ, ∆ϕ', ∆z); for each of its two line segments, ∆ϕ, ∆ϕ' and the angles (∆αinner, ∆αouter, ∆αinner-outer) between the segment direction and that of its inner mini-doublet, of its outer mini-doublet, and between the two mini-doublet directions; and the pT, η and ϕ of the triplet itself". The model utilizes a Transformer encoder with geometrically masked sparse self-attention to embed these objects in a learned latent space. To bound the memory footprint, attention is sparsified by a geometrically motivated mask where "a given T3 attends only to other T3s whose closest hits lie within ∆R < 0.1 in η–ϕ space". The model is trained under an object condensation objective, which assigns such triplets a low condensation likelihood, providing a natural first-pass fake-rejection step before clustering.

Object Condensation and Inference

The number of tracks in an event is not known in advance, so the network output must be converted into a variable-length list of objects using object condensation [8, 9]. Each input point is embedded in a low-dimensional latent space and additionally assigned a condensation charge βi ∈ [0, 1], the likelihood that it acts as the representative, or condensation point, of an object. The objective or loss function combines an attractive term pulling the constituents of an object towards its condensation point, a repulsive term separating points of different objects, and a term that rewards a high charge on each condensation point while suppressing the charge of noise points. At inference, the learned embeddings are clustered into track candidates with the density-based algorithm DBSCAN, which requires no prior specification of the number of clusters and so adapts to the track multiplicity of each event.

Performance Evaluation

Performance is evaluated on simulated tt¯ events at ⟨µ⟩ = 200 and √s = 14 TeV in the Phase2 detector geometry. Reconstructed candidates are associated to simulated particles through their constituent mini-doublets, where a candidate is matched if more than 75% of its mini-doublets originate from a single simulated particle and is otherwise counted as a misidentified (fake) track. Three metrics are reported as functions of η and pT: the tracking efficiency, the fraction of simulated particles associated to at least one reconstructed track; the fake rate, the fraction of misidentified reconstructed tracks; and the duplicate rate, the fraction of reconstructed tracks associated multiple times to the same simulated particle.

Key Findings

The model achieves a fake rate roughly three times lower than the LST quintuplet baseline and a duplicate rate consistent with zero. When shorter trajectories are admitted (NL ≥ 4), the model matches or exceeds the T5 baseline across the full range, reaching 0.80–0.87 against 0.70–0.80, with the gain concentrated at 1 ≲ η ≲ 2. This work establishes LST objects as an effective, physics-rich tokenization for learned tracking, and shows that a physics-informed model can match, and in places surpass, a state-of-the-art combinatorial algorithm under the harshest conditions foreseen at the HL-LHC. The natural next steps are to integrate the model into the CMS reconstruction and trigger software alongside LST, to measure its throughput against the latency budget of the Phase-2 HLT, and to extend it from the Outer Tracker towards the full tracking volume.

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References [1] E. Vourliotis, P. Chang, P. Elmer, Y. Gu, J. Guiang, V. Krutelyov, B.V.S. Narayanan, G Niendorf, M Reid, M Silva et al., Line Segment Tracking: Improving the Phase 2 CMS high level trigger tracking with a novel hardware-agnostic pattern recognition algorithm CMS-CR-2024-141 (2024), 2407.18231, https://arxiv.org/abs/2407.18231 [5] CMS Collaboration, Extended ML Selections and Track Embeddings for Duplicate Removal in Line Segment Tracking (LST), CMS Detector Performance Summary CERNCMS-DP-2025-048 (2025), https://cds.cern.ch/record/2941435 [7] CMS Collaboration, Using Line Segment Tracking to enable ML-based Track Reconstruction in Phase-2 of the CMS Experiment, CMS Detector Performance Summary CERN-CMS-DP-2026-030 (2026), https://cds.cern.ch/record/2961686 [8] J. Kieseler, Object condensation: one-stage grid-free multi-object reconstruction in physics detectors, graph, and image data, Eur. Phys. J. C 80, 886 (2020), 10.1140/epjc/s10052-020-08461-2 [9] K Lieret, G DeZoort, D Chatterjee, J Park, S Miao, P Li, High pileup particle tracking with object condensation, 8th International Connecting the Dots Workshop (2312.03823), https://arxiv.org/abs/2312.03823 [10] M Ester, H P Kriegel, J Sander, X Xu, A density-based algorithm for discovering clusters in large spatial databases with noise, in Proc. 2nd Int. Conf. on Knowledge Discovery and Data Mining (KDD-96) (AAAI Press, 1996), pp. 226–231 [11] A Bocci, V Innocente, M Kortelainen, F Pantaleo, M Rovere, Heterogeneous reconstruction of tracks and primary vertices with the CMS pixel tracker, Front.

1. Bold feature-rich tokenization of LST triplets enables physics-informed modeling: "The LST objects, namely the triplets used in this study, are built according to geometry- and physics-driven criteria and carry richer local structure, geometrical cues, and physics quantities such as transverse momentum. This allows the model to incorporate detector-level information from the start" rather than learning magnetic field effects from scratch.

2. Sparse geometric attention mechanism for Transformer efficiency: The system implements a geometrically masked sparse self-attention where "a given T3 attends only to other T3s whose closest hits lie within ∆R < 0.1 in η–ϕ space, scaling the cost to O(Nk) rather than O(N2)" while preserving physical locality.

3. Object condensation for variable-length output: The model uses an object condensation objective which assigns a likelihood, where the loss function combines terms that pull the constituents of an object towards its condensation point, a repulsive term separating points of different objects. This allows the system to produce a variable-length list of objects and form track candidates in a single inference step.

4. Single-step track assembly via DBSCAN: Instead of sequential fitting, the system uses object condensation to organize triplets into clusters, which are then assembled by DBSCAN [10] to form track candidates in a single inference step. This eliminates the need for a final track-fitting stage and reduces duplicate rates.

5. Physics-informed prior integration: The model processes input as an unordered point cloud of T3 objects, where the tokens are not raw hits but triplets already containing physics content, leading to embeddings that represent a strong physics prior in the latent space.

High-pileup conditions in CMS during the HL-LHC era make charged-particle tracking increasingly challenging as detector occupancy and combinatorics grow. We present a hybrid approach that exploits Line Segment Tracking (LST) objects rather than individual hits to enable the first CMS ML-based track reconstruction algorithm. The LST objects, namely the triplets used in this study, are built according to geometry- and physics-driven criteria and carry richer local structure, geometrical cues, and physics quantities such as transverse momentum, which helps the model incorporate detector-level information from the start. We apply a Transformer encoder with geometrically masked sparse self-attention to embed these objects in a learned latent space, and use object condensation to assemble full tracks in a single inference step. This object-based representation reduces complexity in dense environments and makes the model less sensitive to ambiguities introduced by high pileup. Evaluated on CMS Phase-2 simulation of t events at μ = 200, the approach achieves reconstruction efficiency comparable to the LST quintuplet baseline while reducing the fake rate by roughly a factor of three and suppressing duplicates almost entirely, demonstrating the promise of advanced ML architectures for next-generation particle tracking.