Maria Spiropulu

Chang Sun, Zhiqiang Que, Bakhtiar Zadeh et al.

Lookup-table (LUT) based neural networks can deliver ultra-low latency and excellent hardware efficiency on FPGAs by mapping arithmetic operations directly onto the logic primitives. However, state-of-the-art LUT-aware training (LAT) approaches remain difficult to use in practice: they are often orders of magnitude slower to train than conventional networks, require non-trivial manual tuning for hardware efficiency, and lack an end-to-end workflow. This work presents HGQ-LUT, integrated in https://github.com/calad0i/HGQ2, a new LAT approach that achieves state-of-the-art hardware efficiency while accelerating training by over 100 times on modern GPUs. HGQ-LUT introduces LUT-Dense and LUT-Conv layers that are implemented with regular, accelerator-efficient tensor operations during training, which are then compiled into logic LUTs for hardware. By combining these layers with fine-grained, element-wise heterogeneous quantization (including zero-bit pruning) and a LUT-aware resource surrogate, HGQ-LUT enables the automatic exploration of accuracy-resource trade-offs without manual bit-width tuning. We further integrate HGQ-LUT into open-source toolchains, enabling unified design, compilation, and bit-exact verification of hybrid architectures that mix LUT-based with conventional arithmetic blocks. These features make LAT-based DNNs practical for real-world deployment, such as at the CERN Large Hadron Collider's experiments.

Ryan Liu, Abhijith Gandrakota, Jennifer Ngadiuba et al.

Model-agnostic anomaly detection is one of the promising approaches in the search for new beyond the standard model physics. In this paper, we present Set-VAE, a particle-based variational autoencoder (VAE) anomaly detection algorithm. We demonstrate a 2x signal efficiency gain compared with traditional subjettiness-based jet selection. Furthermore, with an eye to the future deployment to trigger systems, we propose the CLIP-VAE, which reduces the inference-time cost of anomaly detection by using the KL-divergence loss as the anomaly score, resulting in a 2x acceleration in latency and reducing the caching requirement.

Ryan Liu, Abhijith Gandrakota, Jennifer Ngadiuba et al.

The challenging environment of real-time data processing systems at the Large Hadron Collider (LHC) strictly limits the computational complexity of algorithms that can be deployed. For deep learning models, this implies that only models with low computational complexity that have weak inductive bias are feasible. To address this issue, we utilize knowledge distillation to leverage both the performance of large models and the reduced computational complexity of small ones. In this paper, we present an implementation of knowledge distillation, demonstrating an overall boost in the student models' performance for the task of classifying jets at the LHC. Furthermore, by using a teacher model with a strong inductive bias of Lorentz symmetry, we show that we can induce the same inductive bias in the student model which leads to better robustness against arbitrary Lorentz boost.

Chang Sun, Zhiqiang Que, Vladimir Loncar et al.

Neural networks with a latency requirement on the order of microseconds, like the ones used at the CERN Large Hadron Collider, are typically deployed on FPGAs fully unrolled and pipelined. A bottleneck for the deployment of such neural networks is area utilization, which is directly related to the required constant matrix-vector multiplication (CMVM) operations. In this work, we propose an efficient algorithm for implementing CMVM operations with distributed arithmetic (DA) on FPGAs that simultaneously optimizes for area consumption and latency. The algorithm achieves resource reduction similar to state-of-the-art algorithms while being significantly faster to compute. The proposed algorithm is open-sourced and integrated into the \texttt{hls4ml} library, a free and open-source library for running real-time neural network inference on FPGAs. We show that the proposed algorithm can reduce on-chip resources by up to a third for realistic, highly quantized neural networks while simultaneously reducing latency, enabling the implementation of previously infeasible networks.

Zhiqiang Que, Chang Sun, Sudarshan Paramesvaran et al.

Graph Neural Networks (GNNs), particularly Interaction Networks (INs), have shown exceptional performance for jet tagging at the CERN High-Luminosity Large Hadron Collider (HL-LHC). However, their computational complexity and irregular memory access patterns pose significant challenges for deployment on FPGAs in hardware trigger systems, where strict latency and resource constraints apply. In this work, we propose JEDI-linear, a novel GNN architecture with linear computational complexity that eliminates explicit pairwise interactions by leveraging shared transformations and global aggregation. To further enhance hardware efficiency, we introduce fine-grained quantization-aware training with per-parameter bitwidth optimization and employ multiplier-free multiply-accumulate operations via distributed arithmetic. Evaluation results show that our FPGA-based JEDI-linear achieves 3.7 to 11.5 times lower latency, up to 150 times lower initiation interval, and up to 6.2 times lower LUT usage compared to state-of-the-art GNN designs while also delivering higher model accuracy and eliminating the need for DSP blocks entirely. This is the first interaction-based GNN to achieve less than 60~ns latency and currently meets the requirements for use in the HL-LHC CMS Level-1 trigger system. This work advances the next-generation trigger systems by enabling accurate, scalable, and resource-efficient GNN inference in real-time environments. Our open-sourced templates will further support reproducibility and broader adoption across scientific applications.

Chang Sun, Thea K. Årrestad, Vladimir Loncar et al.

Model size and inference speed at deployment time, are major challenges in many deep learning applications. A promising strategy to overcome these challenges is quantization. However, a straightforward uniform quantization to very low precision can result in significant accuracy loss. Mixed-precision quantization, based on the idea that certain parts of the network can accommodate lower precision without compromising performance compared to other parts, offers a potential solution. In this work, we present High Granularity Quantization (HGQ), an innovative quantization-aware training method that could fine-tune the per-weight and per-activation precision by making them optimizable through gradient descent. This approach enables ultra-low latency and low power neural networks on hardware capable of performing arithmetic operations with an arbitrary number of bits, such as FPGAs and ASICs. We demonstrate that HGQ can outperform existing methods by a substantial margin, achieving resource reduction by up to a factor of 20 and latency improvement by a factor of 5 while preserving accuracy.

Chang Sun, Jennifer Ngadiuba, Maurizio Pierini et al.

We explore the innovative use of MLP-Mixer models for real-time jet tagging and establish their feasibility on resource-constrained hardware like FPGAs. MLP-Mixers excel in processing sequences of jet constituents, achieving state-of-the-art performance on datasets mimicking Large Hadron Collider conditions. By using advanced optimization techniques such as High-Granularity Quantization and Distributed Arithmetic, we achieve unprecedented efficiency. These models match or surpass the accuracy of previous architectures, reduce hardware resource usage by up to 97%, double the throughput, and half the latency. Additionally, non-permutation-invariant architectures enable smart feature prioritization and efficient FPGA deployment, setting a new benchmark for machine learning in real-time data processing at particle colliders.

Michael Chen, Raghav Kansal, Abhijith Gandrakota et al.

We present a systematic evaluation of representation learning objectives for particle physics within a unified framework. Our study employs a shared transformer-based particle-cloud encoder with standardized preprocessing, matched sampling, and a consistent evaluation protocol on a jet classification dataset. We compare contrastive (supervised and self-supervised), masked particle modeling, and generative reconstruction objectives under a common training regimen. In addition, we introduce targeted supervised architectural modifications that achieve state-of-the-art performance on benchmark evaluations. This controlled comparison isolates the contributions of the learning objective, highlights their respective strengths and limitations, and provides reproducible baselines. We position this work as a reference point for the future development of foundation models in particle physics, enabling more transparent and robust progress across the community.

Lauri Laatu, Chang Sun, Arianna Cox et al.

We present the first sub-microsecond transformer implementation on an FPGA achieving competitive performance for state-of-the-art high-energy physics benchmarks. Transformers have shown exceptional performance on multiple tasks in modern machine learning applications, including jet tagging at the CERN Large Hadron Collider (LHC). However, their computational complexity prohibits use in real-time applications, such as the hardware trigger system of the collider experiments up until now. In this work, we demonstrate the first application of transformers for jet tagging on FPGAs, achieving $\mathcal{O}(100)$ nanosecond latency with superior performance compared to alternative baseline models. We leverage high-granularity quantization and distributed arithmetic optimization to fit the entire transformer model on a single FPGA, achieving the required throughput and latency. Furthermore, we add multi-head attention and linear attention support to hls4ml, making our work accessible to the broader fast machine learning community. This work advances the next-generation trigger systems for the High Luminosity LHC, enabling the use of transformers for real-time applications in high-energy physics and beyond.

Zichun Hao, Raghav Kansal, Abhijith Gandrakota et al.

A common challenge with supervised machine learning (ML) in high energy physics (HEP) is the reliance on simulations for labeled data, which can often mismodel the underlying collision or detector response. To help mitigate this problem of domain shift, we propose RINO (Renormalization Group Invariance with No Labels), a self-supervised learning approach that can instead pretrain models directly on collision data, learning embeddings invariant to renormalization group flow scales. In this work, we pretrain a transformer-based model on jets originating from quantum chromodynamic (QCD) interactions from the JetClass dataset, emulating real QCD-dominated experimental data, and then finetune on the JetNet dataset -- emulating simulations -- for the task of identifying jets originating from top quark decays. RINO demonstrates improved generalization from the JetNet training data to JetClass data compared to supervised training on JetNet from scratch, demonstrating the potential for RINO pretraining on real collision data followed by fine-tuning on small, high-quality MC datasets, to improve the robustness of ML models in HEP.

Eric A. Moreno, Jean-Roch Vlimant, Maria Spiropulu et al.

We present an application of anomaly detection techniques based on deep recurrent autoencoders to the problem of detecting gravitational wave signals in laser interferometers. Trained on noise data, this class of algorithms could detect signals using an unsupervised strategy, i.e., without targeting a specific kind of source. We develop a custom architecture to analyze the data from two interferometers. We compare the obtained performance to that obtained with other autoencoder architectures and with a convolutional classifier. The unsupervised nature of the proposed strategy comes with a cost in terms of accuracy, when compared to more traditional supervised techniques. On the other hand, there is a qualitative gain in generalizing the experimental sensitivity beyond the ensemble of pre-computed signal templates. The recurrent autoencoder outperforms other autoencoders based on different architectures. The class of recurrent autoencoders presented in this paper could complement the search strategy employed for gravitational wave detection and extend the reach of the ongoing detection campaigns.

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.

Joosep Pata, Javier Duarte, Jean-Roch Vlimant et al.

In general-purpose particle detectors, the particle-flow algorithm may be used to reconstruct a comprehensive particle-level view of the event by combining information from the calorimeters and the trackers, significantly improving the detector resolution for jets and the missing transverse momentum. In view of the planned high-luminosity upgrade of the CERN Large Hadron Collider (LHC), it is necessary to revisit existing reconstruction algorithms and ensure that both the physics and computational performance are sufficient in an environment with many simultaneous proton-proton interactions (pileup). Machine learning may offer a prospect for computationally efficient event reconstruction that is well-suited to heterogeneous computing platforms, while significantly improving the reconstruction quality over rule-based algorithms for granular detectors. We introduce MLPF, a novel, end-to-end trainable, machine-learned particle-flow algorithm based on parallelizable, computationally efficient, and scalable graph neural networks optimized using a multi-task objective on simulated events. We report the physics and computational performance of the MLPF algorithm on a Monte Carlo dataset of top quark-antiquark pairs produced in proton-proton collisions in conditions similar to those expected for the high-luminosity LHC. The MLPF algorithm improves the physics response with respect to a rule-based benchmark algorithm and demonstrates computationally scalable particle-flow reconstruction in a high-pileup environment.

Nicholas Choma, Daniel Murnane, Xiangyang Ju et al.

To address the unprecedented scale of HL-LHC data, the Exa.TrkX project is investigating a variety of machine learning approaches to particle track reconstruction. The most promising of these solutions, graph neural networks (GNN), process the event as a graph that connects track measurements (detector hits corresponding to nodes) with candidate line segments between the hits (corresponding to edges). Detector information can be associated with nodes and edges, enabling a GNN to propagate the embedded parameters around the graph and predict node-, edge- and graph-level observables. Previously, message-passing GNNs have shown success in predicting doublet likelihood, and we here report updates on the state-of-the-art architectures for this task. In addition, the Exa.TrkX project has investigated innovations in both graph construction, and embedded representations, in an effort to achieve fully learned end-to-end track finding. Hence, we present a suite of extensions to the original model, with encouraging results for hitgraph classification. In addition, we explore increased performance by constructing graphs from learned representations which contain non-linear metric structure, allowing for efficient clustering and neighborhood queries of data points. We demonstrate how this framework fits in with both traditional clustering pipelines, and GNN approaches. The embedded graphs feed into high-accuracy doublet and triplet classifiers, or can be used as an end-to-end track classifier by clustering in an embedded space. A set of post-processing methods improve performance with knowledge of the detector physics. Finally, we present numerical results on the TrackML particle tracking challenge dataset, where our framework shows favorable results in both seeding and track finding.

Dawit Belayneh, Federico Carminati, Amir Farbin et al.

Using detailed simulations of calorimeter showers as training data, we investigate the use of deep learning algorithms for the simulation and reconstruction of particles produced in high-energy physics collisions. We train neural networks on shower data at the calorimeter-cell level, and show significant improvements for simulation and reconstruction when using these networks compared to methods which rely on currently-used state-of-the-art algorithms. We define two models: an end-to-end reconstruction network which performs simultaneous particle identification and energy regression of particles when given calorimeter shower data, and a generative network which can provide reasonable modeling of calorimeter showers for different particle types at specified angles and energies. We investigate the optimization of our models with hyperparameter scans. Furthermore, we demonstrate the applicability of the reconstruction model to shower inputs from other detector geometries, specifically ATLAS-like and CMS-like geometries. These networks can serve as fast and computationally light methods for particle shower simulation and reconstruction for current and future experiments at particle colliders.

Alexander Zlokapa, Alex Mott, Joshua Job et al.

Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, a novel algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the ROC curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a new class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks.

Alexander Zlokapa, Abhishek Anand, Jean-Roch Vlimant et al.

At the High Luminosity Large Hadron Collider (HL-LHC), traditional track reconstruction techniques that are critical for analysis are expected to face challenges due to scaling with track density. Quantum annealing has shown promise in its ability to solve combinatorial optimization problems amidst an ongoing effort to establish evidence of a quantum speedup. As a step towards exploiting such potential speedup, we investigate a track reconstruction approach by adapting the existing geometric Denby-Peterson (Hopfield) network method to the quantum annealing framework and to HL-LHC conditions. Furthermore, we develop additional techniques to embed the problem onto existing and near-term quantum annealing hardware. Results using simulated annealing and quantum annealing with the D-Wave 2X system on the TrackML dataset are presented, demonstrating the successful application of a quantum annealing-inspired algorithm to the track reconstruction challenge. We find that combinatorial optimization problems can effectively reconstruct tracks, suggesting possible applications for fast hardware-specific implementations at the LHC while leaving open the possibility of a quantum speedup for tracking.

Olmo Cerri, Thong Q. Nguyen, Maurizio Pierini et al.

Using variational autoencoders trained on known physics processes, we develop a one-sided threshold test to isolate previously unseen processes as outlier events. Since the autoencoder training does not depend on any specific new physics signature, the proposed procedure doesn't make specific assumptions on the nature of new physics. An event selection based on this algorithm would be complementary to classic LHC searches, typically based on model-dependent hypothesis testing. Such an algorithm would deliver a list of anomalous events, that the experimental collaborations could further scrutinize and even release as a catalog, similarly to what is typically done in other scientific domains. Event topologies repeating in this dataset could inspire new-physics model building and new experimental searches. Running in the trigger system of the LHC experiments, such an application could identify anomalous events that would be otherwise lost, extending the scientific reach of the LHC.

Jesus Arjona Martinez, Olmo Cerri, Maurizio Pierini et al.

At the Large Hadron Collider, the high transverse-momentum events studied by experimental collaborations occur in coincidence with parasitic low transverse-momentum collisions, usually referred to as pileup. Pileup mitigation is a key ingredient of the online and offline event reconstruction as pileup affects the reconstruction accuracy of many physics observables. We present a classifier based on Graph Neural Networks, trained to retain particles coming from high-transverse-momentum collisions, while rejecting those coming from pileup collisions. This model is designed as a refinement of the PUPPI algorithm, employed in many LHC data analyses since 2015. Thanks to an extended basis of input information and the learning capabilities of the considered network architecture, we show an improvement in pileup-rejection performances with respect to state-of-the-art solutions.

Thong Q. Nguyen, Daniel Weitekamp, Dustin Anderson et al.

We show how event topology classification based on deep learning could be used to improve the purity of data samples selected in real time at at the Large Hadron Collider. We consider different data representations, on which different kinds of multi-class classifiers are trained. Both raw data and high-level features are utilized. In the considered examples, a filter based on the classifier's score can be trained to retain ~99% of the interesting events and reduce the false-positive rate by as much as one order of magnitude for certain background processes. By operating such a filter as part of the online event selection infrastructure of the LHC experiments, one could benefit from a more flexible and inclusive selection strategy while reducing the amount of downstream resources wasted in processing false positives. The saved resources could be translated into a reduction of the detector operation cost or into an effective increase of storage and processing capabilities, which could be reinvested to extend the physics reach of the LHC experiments.

Dustin Anderson, Jean-Roch Vlimant, Maria Spiropulu

We present a lightweight Python framework for distributed training of neural networks on multiple GPUs or CPUs. The framework is built on the popular Keras machine learning library. The Message Passing Interface (MPI) protocol is used to coordinate the training process, and the system is well suited for job submission at supercomputing sites. We detail the software's features, describe its use, and demonstrate its performance on systems of varying sizes on a benchmark problem drawn from high-energy physics research.