Gage DeZoort

Savannah Thais, Paolo Calafiura, Grigorios Chachamis et al.

Many physical systems can be best understood as sets of discrete data with associated relationships. Where previously these sets of data have been formulated as series or image data to match the available machine learning architectures, with the advent of graph neural networks (GNNs), these systems can be learned natively as graphs. This allows a wide variety of high- and low-level physical features to be attached to measurements and, by the same token, a wide variety of HEP tasks to be accomplished by the same GNN architectures. GNNs have found powerful use-cases in reconstruction, tagging, generation and end-to-end analysis. With the wide-spread adoption of GNNs in industry, the HEP community is well-placed to benefit from rapid improvements in GNN latency and memory usage. However, industry use-cases are not perfectly aligned with HEP and much work needs to be done to best match unique GNN capabilities to unique HEP obstacles. We present here a range of these capabilities, predictions of which are currently being well-adopted in HEP communities, and which are still immature. We hope to capture the landscape of graph techniques in machine learning as well as point out the most significant gaps that are inhibiting potentially large leaps in research.

Gage DeZoort, Boris Hanin

This article derives and validates three principles for initialization and architecture selection in finite width graph neural networks (GNNs) with ReLU activations. First, we theoretically derive what is essentially the unique generalization to ReLU GNNs of the well-known He-initialization. Our initialization scheme guarantees that the average scale of network outputs and gradients remains order one at initialization. Second, we prove in finite width vanilla ReLU GNNs that oversmoothing is unavoidable at large depth when using fixed aggregation operator, regardless of initialization. We then prove that using residual aggregation operators, obtained by interpolating a fixed aggregation operator with the identity, provably alleviates oversmoothing at initialization. Finally, we show that the common practice of using residual connections with a fixup-type initialization provably avoids correlation collapse in final layer features at initialization. Through ablation studies we find that using the correct initialization, residual aggregation operators, and residual connections in the forward pass significantly and reliably speeds up early training dynamics in deep ReLU GNNs on a variety of tasks.

Kilian Lieret, Gage DeZoort, Devdoot Chatterjee et al. · princeton

Recent work has demonstrated that graph neural networks (GNNs) can match the performance of traditional algorithms for charged particle tracking while improving scalability to meet the computing challenges posed by the HL-LHC. Most GNN tracking algorithms are based on edge classification and identify tracks as connected components from an initial graph containing spurious connections. In this talk, we consider an alternative based on object condensation (OC), a multi-objective learning framework designed to cluster points (hits) belonging to an arbitrary number of objects (tracks) and regress the properties of each object. Building on our previous results, we present a streamlined model and show progress toward a one-shot OC tracking algorithm in a high-pileup environment.

Shitij Govil, Jack P. Rodgers, Yuan-Tang Chou et al.

Charged particle track reconstruction is a foundational task in collider experiments and the main computational bottleneck in particle reconstruction. Graph neural networks (GNNs) have shown strong performance for this problem, but costly graph construction, irregular computations, and random memory access patterns substantially limit their throughput. The recently proposed Hashing-based Efficient Point Transformer (HEPT) offers a theoretically guaranteed near-linear complexity for large point cloud processing via locality-sensitive hashing (LSH) in attention computations; however, its evaluations have largely focused on embedding quality, and the object condensation pipeline on which HEPT relies requires a post-hoc clustering step (e.g., DBScan) that can dominate runtime. In this work, we make two contributions. First, we present a unified, fair evaluation of physics tracking performance for HEPT and a representative GNN-based pipeline under the same dataset and metrics. Second, we introduce HEPTv2 by extending HEPT with a lightweight decoder that eliminates the clustering stage and directly predicts track assignments. This modification preserves HEPT's regular, hardware-friendly computations while enabling ultra-fast end-to-end inference. On the TrackML dataset, optimized HEPTv2 achieves approximately 28 ms per event on an A100 while maintaining competitive tracking efficiency. These results position HEPTv2 as a practical, scalable alternative to GNN-based pipelines for fast tracking.

Abdelrahman Elabd, Vesal Razavimaleki, Shi-Yu Huang et al.

The determination of charged particle trajectories in collisions at the CERN Large Hadron Collider (LHC) is an important but challenging problem, especially in the high interaction density conditions expected during the future high-luminosity phase of the LHC (HL-LHC). Graph neural networks (GNNs) are a type of geometric deep learning algorithm that has successfully been applied to this task by embedding tracker data as a graph -- nodes represent hits, while edges represent possible track segments -- and classifying the edges as true or fake track segments. However, their study in hardware- or software-based trigger applications has been limited due to their large computational cost. In this paper, we introduce an automated translation workflow, integrated into a broader tool called $\texttt{hls4ml}$, for converting GNNs into firmware for field-programmable gate arrays (FPGAs). We use this translation tool to implement GNNs for charged particle tracking, trained using the TrackML challenge dataset, on FPGAs with designs targeting different graph sizes, task complexites, and latency/throughput requirements. This work could enable the inclusion of charged particle tracking GNNs at the trigger level for HL-LHC experiments.

Gage DeZoort, Savannah Thais, Javier Duarte et al.

Recent work has demonstrated that geometric deep learning methods such as graph neural networks (GNNs) are well suited to address a variety of reconstruction problems in high energy particle physics. In particular, particle tracking data is naturally represented as a graph by identifying silicon tracker hits as nodes and particle trajectories as edges; given a set of hypothesized edges, edge-classifying GNNs identify those corresponding to real particle trajectories. In this work, we adapt the physics-motivated interaction network (IN) GNN toward the problem of particle tracking in pileup conditions similar to those expected at the high-luminosity Large Hadron Collider. Assuming idealized hit filtering at various particle momenta thresholds, we demonstrate the IN's excellent edge-classification accuracy and tracking efficiency through a suite of measurements at each stage of GNN-based tracking: graph construction, edge classification, and track building. The proposed IN architecture is substantially smaller than previously studied GNN tracking architectures; this is particularly promising as a reduction in size is critical for enabling GNN-based tracking in constrained computing environments. Furthermore, the IN may be represented as either a set of explicit matrix operations or a message passing GNN. Efforts are underway to accelerate each representation via heterogeneous computing resources towards both high-level and low-latency triggering applications.

Xiangyang Ju, Daniel Murnane, Paolo Calafiura et al.

The Exa.TrkX project has applied geometric learning concepts such as metric learning and graph neural networks to HEP particle tracking. Exa.TrkX's tracking pipeline groups detector measurements to form track candidates and filters them. The pipeline, originally developed using the TrackML dataset (a simulation of an LHC-inspired tracking detector), has been demonstrated on other detectors, including DUNE Liquid Argon TPC and CMS High-Granularity Calorimeter. This paper documents new developments needed to study the physics and computing performance of the Exa.TrkX pipeline on the full TrackML dataset, a first step towards validating the pipeline using ATLAS and CMS data. The pipeline achieves tracking efficiency and purity similar to production tracking algorithms. Crucially for future HEP applications, the pipeline benefits significantly from GPU acceleration, and its computational requirements scale close to linearly with the number of particles in the event.

Savannah Thais, Gage DeZoort

3D instance segmentation remains a challenging problem in computer vision. Particle tracking at colliders like the LHC can be conceptualized as an instance segmentation task: beginning from a point cloud of hits in a particle detector, an algorithm must identify which hits belong to individual particle trajectories and extract track properties. Graph Neural Networks (GNNs) have shown promising performance on standard instance segmentation tasks. In this work we demonstrate the applicability of instance segmentation GNN architectures to particle tracking; moreover, we re-imagine the traditional Cartesian space approach to track-finding and instead work in a conformal geometry that allows the GNN to identify tracks and extract parameters in a single shot.

Aneesh Heintz, Vesal Razavimaleki, Javier Duarte et al.

We develop and study FPGA implementations of algorithms for charged particle tracking based on graph neural networks. The two complementary FPGA designs are based on OpenCL, a framework for writing programs that execute across heterogeneous platforms, and hls4ml, a high-level-synthesis-based compiler for neural network to firmware conversion. We evaluate and compare the resource usage, latency, and tracking performance of our implementations based on a benchmark dataset. We find a considerable speedup over CPU-based execution is possible, potentially enabling such algorithms to be used effectively in future computing workflows and the FPGA-based Level-1 trigger at the CERN Large Hadron Collider.