Graph Neural Networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum Computing (QC) offers a promising avenue to address these issues and inspires new algorithmic approaches. In particular, Quantum Graph Neural Networks (QGNNs) have been explored in recent literature. However, current quantum hardware limits the dimension of the data that can be effectively encoded. Existing approaches either simplify datasets manually or use artificial graph datasets. This work introduces the Guided Graph Compression (GGC) framework, which uses a graph autoencoder to reduce both the number of nodes and the dimensionality of node features. The compression is guided to enhance the performance of a downstream classification task, which can be applied either with a quantum or a classical classifier. The framework is evaluated on the Jet Tagging task, a classification problem of fundamental importance in high energy physics that involves distinguishing particle jets initiated by quarks from those by gluons. The GGC is compared against using the autoencoder as a standalone preprocessing step and against a baseline classical GNN classifier. Our numerical results demonstrate that GGC outperforms both alternatives, while also facilitating the testing of novel QGNN ansatzes on realistic datasets.
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.
In high energy physics, self-supervised learning (SSL) methods have the potential to aid in the creation of machine learning models without the need for labeled datasets for a variety of tasks, including those related to jets -- narrow sprays of particles produced by quarks and gluons in high energy particle collisions. This study introduces an approach to learning jet representations without hand-crafted augmentations using a jet-based joint embedding predictive architecture (J-JEPA), which aims to predict various physical targets from an informative context. As our method does not require hand-crafted augmentation like other common SSL techniques, J-JEPA avoids introducing biases that could harm downstream tasks. Since different tasks generally require invariance under different augmentations, this training without hand-crafted augmentation enables versatile applications, offering a pathway toward a cross-task foundation model. We finetune the representations learned by J-JEPA for jet tagging and benchmark them against task-specific representations.
Machine learning (ML) algorithms, particularly attention-based transformer models, have become indispensable for analyzing the vast data generated by particle physics experiments like ATLAS and CMS at the CERN LHC. Particle Transformer (ParT), a state-of-the-art model, leverages particle-level attention to improve jet-tagging tasks, which are critical for identifying particles resulting from proton collisions. This study focuses on interpreting ParT by analyzing attention heat maps and particle-pair correlations on the $\eta$-$\phi$ plane, revealing a binary attention pattern where each particle attends to at most one other particle. At the same time, we observe that ParT shows varying focus on important particles and subjets depending on decay, indicating that the model learns traditional jet substructure observables. These insights enhance our understanding of the model's internal workings and learning process, offering potential avenues for improving the efficiency of transformer architectures in future high-energy physics applications.
Discovering new phenomena at the Large Hadron Collider (LHC) involves the identification of rare signals over conventional backgrounds. Thus binary classification tasks are ubiquitous in analyses of the vast amounts of LHC data. We develop a Lie-Equivariant Quantum Graph Neural Network (Lie-EQGNN), a quantum model that is not only data efficient, but also has symmetry-preserving properties. Since Lorentz group equivariance has been shown to be beneficial for jet tagging, we build a Lorentz-equivariant quantum GNN for quark-gluon jet discrimination and show that its performance is on par with its classical state-of-the-art counterpart LorentzNet, making it a viable alternative to the conventional computing paradigm.
In high-energy physics, particle jet tagging plays a pivotal role in distinguishing quark from gluon jets using data from collider experiments. While graph-based deep learning methods have advanced this task beyond traditional feature-engineered approaches, the complex data structure and limited labeled samples present ongoing challenges. However, existing contrastive learning (CL) frameworks struggle to leverage rationale-aware augmentations effectively, often lacking supervision signals that guide the extraction of salient features and facing computational efficiency issues such as high parameter counts. In this study, we demonstrate that integrating a quantum rationale generator (QRG) within our proposed Quantum Rationale-aware Graph Contrastive Learning (QRGCL) framework significantly enhances jet discrimination performance, reducing reliance on labeled data and capturing discriminative features. Evaluated on the quark-gluon jet dataset, QRGCL achieves an AUC score of $77.53\%$ while maintaining a compact architecture of only 45 QRG parameters, outperforming classical, quantum, and hybrid GCL and GNN benchmarks. These results highlight QRGCL's potential to advance jet tagging and other complex classification tasks in high-energy physics, where computational efficiency and feature extraction limitations persist.
The rapid data surge from the high-luminosity Large Hadron Collider introduces critical computational challenges requiring novel approaches for efficient data processing in particle physics. Quantum machine learning, with its capability to leverage the extensive Hilbert space of quantum hardware, offers a promising solution. However, current quantum graph neural networks (GNNs) lack robustness to noise and are often constrained by fixed symmetry groups, limiting adaptability in complex particle interaction modeling. This paper demonstrates that replacing the Lorentz Group Equivariant Block modules in LorentzNet with a dressed quantum circuit significantly enhances performance despite using nearly 5.5 times fewer parameters. Additionally, quantum circuits effectively replace MLPs by inherently preserving symmetries, with Lorentz symmetry integration ensuring robust handling of relativistic invariance. Our Lorentz-Equivariant Quantum Graph Neural Network (Lorentz-EQGNN) achieved $74.00\%$ test accuracy and an AUC of $87.38\%$ on the Quark-Gluon jet tagging dataset, outperforming the classical and quantum GNNs with a reduced architecture using only 4 qubits. On the Electron-Photon dataset, Lorentz-EQGNN reached $67.00\%$ test accuracy and an AUC of $68.20\%$, demonstrating competitive results with just 800 training samples. Evaluation of our model on generic MNIST and FashionMNIST datasets confirmed Lorentz-EQGNN's efficiency, achieving $88.10\%$ and $74.80\%$ test accuracy, respectively. Ablation studies validated the impact of quantum components on performance, with notable improvements in background rejection rates over classical counterparts. These results highlight Lorentz-EQGNN's potential for immediate applications in noise-resilient jet tagging, event classification, and broader data-scarce HEP tasks.
The use of machine learning methods in high energy physics typically relies on large volumes of precise simulation for training. As machine learning models become more complex they can become increasingly sensitive to differences between this simulation and the real data collected by experiments. We present a generic methodology based on contrastive learning which is able to greatly mitigate this negative effect. Crucially, the method does not require prior knowledge of the specifics of the mismodeling. While we demonstrate the efficacy of this technique using the task of jet-tagging at the Large Hadron Collider, it is applicable to a wide array of different tasks both in and out of the field of high energy physics.
Jet point cloud images are high dimensional data structures that needs to be transformed to a separable feature space for machine learning algorithms to distinguish them with simple decision boundaries. In this article, the authors focus on jet category separability by particle and jet feature extraction, resulting in more efficient training of a simple deep neural network, resulting in a computational efficient interpretable model for jet classification. The methodology is tested with three to five categories of jets from the JetNet benchmark jet tagging dataset, resulting in comparable performance to particle flow network. This work demonstrates that high dimensional datasets represented in separable latent spaces lead to simpler architectures for jet classification.
Jet tagging is an essential categorization problem in high energy physics. In recent times, Deep Learning has not only risen to the challenge of jet tagging but also significantly improved its performance. In this article, we proposed an idea of a new architecture, Particle Multi-Axis transformer (ParMAT) which is a modified version of Particle transformer (ParT). ParMAT contains local and global spatial interactions within a single unit which improves its ability to handle various input lengths. We trained our model on JETCLASS, a publicly available large dataset that contains 100M jets of 10 different classes of particles. By integrating a parallel attention mechanism and pairwise interactions of particles in the attention mechanism, ParMAT achieves robustness and higher accuracy over the ParT and ParticleNet. The scalability of the model to huge datasets and its ability to automatically extract essential features demonstrate its potential for enhancing jet tagging.
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.
Nowadays, there has been a growing trend in the field of high-energy physics (HEP), in both its experimental and phenomenological studies, to incorporate machine learning (ML) and its specialized branch, deep learning (DL). This review paper provides a thorough illustration of these applications using different ML and DL approaches. The first part of the paper examines the basics of various particle physics types and establishes guidelines for assessing particle physics alongside the available learning models. Next, a detailed classification is provided for representing Jets that are reconstructed in high-energy collisions, mainly in proton-proton collisions at well-defined beam energies. This section covers various datasets, preprocessing techniques, and feature extraction and selection methods. The presented techniques can be applied to future hadron-hadron colliders (HHC), such as the high-luminosity LHC (HL-LHC) and the future circular collider - hadron-hadron (FCChh). The authors then explore several AI techniques analyses designed specifically for both image and point-cloud (PC) data in HEP. Additionally, a closer look is taken at the classification associated with Jet tagging in hadron collisions. In this review, various state-of-the-art (SOTA) techniques in ML and DL are examined, with a focus on their implications for HEP demands. More precisely, this discussion addresses various applications in extensive detail, such as Jet tagging, Jet tracking, particle classification, and more. The review concludes with an analysis of the current state of HEP using DL methodologies. It highlights the challenges and potential areas for future research, which are illustrated for each application.
Foundation models are multi-dataset and multi-task machine learning methods that once pre-trained can be fine-tuned for a large variety of downstream applications. The successful development of such general-purpose models for physics data would be a major breakthrough as they could improve the achievable physics performance while at the same time drastically reduce the required amount of training time and data. We report significant progress on this challenge on several fronts. First, a comprehensive set of evaluation methods is introduced to judge the quality of an encoding from physics data into a representation suitable for the autoregressive generation of particle jets with transformer architectures (the common backbone of foundation models). These measures motivate the choice of a higher-fidelity tokenization compared to previous works. Finally, we demonstrate transfer learning between an unsupervised problem (jet generation) and a classic supervised task (jet tagging) with our new OmniJet-$\alpha$ model. This is the first successful transfer between two different and actively studied classes of tasks and constitutes a major step in the building of foundation models for particle physics.
Compact symbolic expressions have been shown to be more efficient than neural network models in terms of resource consumption and inference speed when implemented on custom hardware such as FPGAs, while maintaining comparable accuracy~\cite{tsoi2023symbolic}. These capabilities are highly valuable in environments with stringent computational resource constraints, such as high-energy physics experiments at the CERN Large Hadron Collider. However, finding compact expressions for high-dimensional datasets remains challenging due to the inherent limitations of genetic programming, the search algorithm of most symbolic regression methods. Contrary to genetic programming, the neural network approach to symbolic regression offers scalability to high-dimensional inputs and leverages gradient methods for faster equation searching. Common ways of constraining expression complexity often involve multistage pruning with fine-tuning, which can result in significant performance loss. In this work, we propose $\tt{SymbolNet}$, a neural network approach to symbolic regression specifically designed as a model compression technique, aimed at enabling low-latency inference for high-dimensional inputs on custom hardware such as FPGAs. This framework allows dynamic pruning of model weights, input features, and mathematical operators in a single training process, where both training loss and expression complexity are optimized simultaneously. We introduce a sparsity regularization term for each pruning type, which can adaptively adjust its strength, leading to convergence at a target sparsity ratio. Unlike most existing symbolic regression methods that struggle with datasets containing more than $\mathcal{O}(10)$ inputs, we demonstrate the effectiveness of our model on the LHC jet tagging task (16 inputs), MNIST (784 inputs), and SVHN (3072 inputs).
Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such as graph neural networks (GNNs), have been leveraged for various data analysis tasks in high-energy physics. One typical task is jet tagging, where jets are viewed as point clouds with distinct features and edge connections between their constituent particles. The increasing size and complexity of the LHC particle datasets, as well as the computational models used for their analysis, greatly motivate the development of alternative fast and efficient computational paradigms such as quantum computation. In addition, to enhance the validity and robustness of deep networks, one can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. In this paper, we perform a fair and comprehensive comparison between classical graph neural networks (GNNs) and equivariant graph neural networks (EGNNs) and their quantum counterparts: quantum graph neural networks (QGNNs) and equivariant quantum graph neural networks (EQGNN). The four architectures were benchmarked on a binary classification task to classify the parton-level particle initiating the jet. Based on their AUC scores, the quantum networks were shown to outperform the classical networks. However, seeing the computational advantage of the quantum networks in practice may have to wait for the further development of quantum technology and its associated APIs.
Artificial Intelligence for Science (AI4S) is an emerging research field that utilizes machine learning advancements to tackle complex scientific computational issues, aiming to enhance computational efficiency and accuracy. However, the data-driven nature of AI4S lacks the correctness or accuracy assurances of conventional scientific computing, posing challenges when deploying AI4S models in real-world applications. To mitigate these, more comprehensive benchmarking procedures are needed to better understand AI4S models. This paper introduces a novel benchmarking approach, known as structural interpretation, which addresses two key requirements: identifying the trusted operating range in the problem space and tracing errors back to their computational components. This method partitions both the problem and metric spaces, facilitating a structural exploration of these spaces. The practical utility and effectiveness of structural interpretation are illustrated through its application to three distinct AI4S workloads: machine-learning force fields (MLFF), jet tagging, and precipitation nowcasting. The benchmarks effectively model the trusted operating range, trace errors, and reveal novel perspectives for refining the model, training process, and data sampling strategy. This work is part of the SAIBench project, an AI4S benchmarking suite.
Machine learning has played a pivotal role in advancing physics, with deep learning notably contributing to solving complex classification problems such as jet tagging in the field of jet physics. In this experiment, we aim to harness the full potential of neural networks while acknowledging that, at times, we may lose sight of the underlying physics governing these models. Nevertheless, we demonstrate that we can achieve remarkable results obscuring physics knowledge and relying completely on the model's outcome. We introduce JetLOV, a composite comprising two models: a straightforward multilayer perceptron (MLP) and the well-established LundNet. Our study reveals that we can attain comparable jet tagging performance without relying on the pre-computed LundNet variables. Instead, we allow the network to autonomously learn an entirely new set of variables, devoid of a priori knowledge of the underlying physics. These findings hold promise, particularly in addressing the issue of model dependence, which can be mitigated through generalization and training on diverse data sets.
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.
As particle accelerators increase their collision rates, and deep learning solutions prove their viability, there is a growing need for lightweight and fast neural network architectures for low-latency tasks such as triggering. We examine the potential of one recent Lorentz- and permutation-symmetric architecture, PELICAN, and present its instances with as few as 19 trainable parameters that outperform generic architectures with tens of thousands of parameters when compared on the binary classification task of top quark jet tagging.
Jet tagging is a classification problem in high-energy physics experiments that aims to identify the collimated sprays of subatomic particles, jets, from particle collisions and tag them to their emitter particle. Advances in jet tagging present opportunities for searches of new physics beyond the Standard Model. Current approaches use deep learning to uncover hidden patterns in complex collision data. However, the representation of jets as inputs to a deep learning model have been varied, and often, informative features are withheld from models. In this study, we propose a graph-based representation of a jet that encodes the most information possible. To learn best from this representation, we design Particle Chebyshev Network (PCN), a graph neural network (GNN) using Chebyshev graph convolutions (ChebConv). ChebConv has been demonstrated as an effective alternative to classical graph convolutions in GNNs and has yet to be explored in jet tagging. PCN achieves a substantial improvement in accuracy over existing taggers and opens the door to future studies into graph-based representations of jets and ChebConv layers in high-energy physics experiments. Code is available at https://github.com/YVSemlani/PCN-Jet-Tagging.