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Efficient and accurate algorithms are necessary to reconstruct particles in the highly granular detectors anticipated at the High-Luminosity Large Hadron Collider and the Future Circular Collider. We study scalable machine learning models for event reconstruction in electron-positron collisions based on a full detector simulation. Particle-flow reconstruction can be formulated as a supervised learning task using tracks and calorimeter clusters. We compare a graph neural network and kernel-based transformer and demonstrate that we can avoid quadratic operations while achieving realistic reconstruction. We show that hyperparameter tuning significantly improves the performance of the models. The best graph neural network model shows improvement in the jet transverse momentum resolution by up to 50% compared to the rule-based algorithm. The resulting model is portable across Nvidia, AMD and Habana hardware. Accurate and fast machine-learning based reconstruction can significantly improve future measurements at colliders.

 

The Earth mover’s distance (EMD) is a useful metric for image recognition and classification, but its usual implementations are not differentiable or too slow to be used as a loss function for training other algorithms via gradient descent. In this paper, we train a convolutional neural network (CNN) to learn a differentiable, fast approximation of the EMD and demonstrate that it can be used as a substitute for computing-intensive EMD implementations. We apply this differentiable approximation in the training of an autoencoder-inspired neural network (encoder NN) for data compression at the high-luminosity LHC at CERN The goal of this encoder NN is to compress the data while preserving the information related to the distribution of energy deposits in particle detectors. We demonstrate that the performance of our encoder NN trained using the differentiable EMD CNN surpasses that of training with loss functions based on mean squared error.

 

In-time particle trajectory reconstruction in the Large Hadron Collider is challenging due to the high collision rate and numerous particle hits. Using GNN (Graph Neural Network) on FPGA has enabled superior accuracy with flexible trajectory classification. However, existing GNN architectures have inefficient resource usage and insufficient parallelism for edge classification. This paper introduces a resource-efficient GNN architecture on FPGAs for low latency particle tracking. The modular architecture facilitates design scalability to support large graphs. Leveraging the geometric properties of hit detectors further reduces graph complexity and resource usage. Our results on Xilinx UltraScale+ VU9P demonstrate 1625x and 1574x performance improvement over CPU and GPU respectively. 

In high energy physics, one of the most important processes for collider data analysis is the comparison of collected and simulated data. Nowadays the state-of-the-art for data generation is in the form of Monte Carlo (MC) generators. However, because of the upcoming high-luminosity upgrade of the Large Hadron Collider (LHC), there will not be enough computational power or time to match the amount of needed simulated data using MC methods. An alternative approach under study is the usage of machine learning generative methods to fulfill that task. Since the most common final-state objects of high-energy proton collisions are hadronic jets, which are collections of particles collimated in a given region of space, this work aims to develop a convolutional variational autoencoder (ConVAE) for the generation of particle-based LHC hadronic jets. Given the ConVAE’s limitations, a normalizing flow (NF) network is coupled to it in a two-step training process, which shows improvements on the results for the generated jets. The ConVAE+NF network is capable of generating a jet in$18.30\pm 0.04\mu \text{s}$, making it one of the fastest methods for this task up to now.

 

There has been significant work recently in developing machine learning (ML) models in high energy physics (HEP) for tasks such as classification, simulation, and anomaly detection. Often these models are adapted from those designed for datasets in computer vision or natural language processing, which lack inductive biases suited to HEP data, such as equivariance to its inherent symmetries. Such biases have been shown to make models more performant and interpretable, and reduce the amount of training data needed. To that end, we develop the Lorentz group autoencoder (LGAE), an autoencoder model equivariant with respect to the proper, orthochronous Lorentz group$$\textrm{SO}^+(3,1)$$${\text{SO}}^{+}(3,1)$, with a latent space living in the representations of the group. We present our architecture and several experimental results on jets at the LHC and find it outperforms graph and convolutional neural network baseline models on several compression, reconstruction, and anomaly detection metrics. We also demonstrate the advantage of such an equivariant model in analyzing the latent space of the autoencoder, which can improve the explainability of potential anomalies discovered by such ML models.

 

The findable, accessible, interoperable, and reusable (FAIR) data principles provide a framework for examining, evaluating, and improving how data is shared to facilitate scientific discovery. Generalizing these principles to research software and other digital products is an active area of research. Machine learning models—algorithms that have been trained on data without being explicitly programmed—and more generally, artificial intelligence (AI) models, are an important target for this because of the ever-increasing pace with which AI is transforming scientific domains, such as experimental high energy physics (HEP). In this paper, we propose a practical definition of FAIR principles for AI models in HEP and describe a template for the application of these principles. We demonstrate the template’s use with an example AI model applied to HEP, in which a graph neural network is used to identify Higgs bosons decaying to two bottom quarks. We report on the robustness of this FAIR AI model, its portability across hardware architectures and software frameworks, and its interpretability.

 

We study how to use deep variational autoencoders (VAEs) for a fast simulation of jets of particles at the Large Hadron Collider. We represent jets as a list of constituents, characterized by their momenta. Starting from a simulation of the jet before detector effects, we train a deep VAE to return the corresponding list of constituents after detection. Doing so, we bypass both the time-consuming detector simulation and the collision reconstruction steps of a traditional processing chain, speeding up significantly the events generation workflow. Through model optimization and hyperparameter tuning, we achieve state-of-the-art precision on the jet four-momentum, while providing an accurate description of the constituents momenta, and an inference time comparable to that of a rule-based fast simulation.

 

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 are 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.

 

Efficient machine learning implementations optimized for inference in hardware have wide-ranging benefits, depending on the application, from lower inference latency to higher data throughput and reduced energy consumption. Two popular techniques for reducing computation in neural networks are pruning, removing insignificant synapses, and quantization, reducing the precision of the calculations. In this work, we explore the interplay between pruning and quantization during the training of neural networks for ultra low latency applications targeting high energy physics use cases. Techniques developed for this study have potential applications across many other domains. We study various configurations of pruning during quantization-aware training, which we term quantization-aware pruning , and the effect of techniques like regularization, batch normalization, and different pruning schemes on performance, computational complexity, and information content metrics. We find that quantization-aware pruning yields more computationally efficient models than either pruning or quantization alone for our task. Further, quantization-aware pruning typically performs similar to or better in terms of computational efficiency compared to other neural architecture search techniques like Bayesian optimization. Surprisingly, while networks with different training configurations can have similar performance for the benchmark application, the information content in the network can vary significantly, affecting its generalizability.