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.

Jet classification in high-energy particle physics is important for understanding fundamental interactions and probing phenomena beyond the Standard Model. Jets originate from the fragmentation and hadronization of quarks and gluons, and pose a challenge for identification due to their complex, multidimensional structure. Traditional classification methods often fall short in capturing these intricacies, necessitating advanced machine learning approaches. In this paper, we employ two neural networks simultaneously as an ensemble to tag various jet types. We convert the jet data to two-dimensional histograms instead of representing them as points in a higher-dimensional space. Specifically, this ensemble approach, hereafter referred to as Ensemble Model, is used to tag jets into classes from the JetNet dataset, corresponding to: Top Quarks, Light Quarks (up or down), and W and Z bosons. For the jet classes mentioned above, we show that the Ensemble Model can be used for both binary and multi-categorical classification. This ensemble approach learns jet features by leveraging the strengths of each constituent network achieving superior performance compared to either individual network.

--This article presents, for the first time, the application of diffusion models for generating jet images corresponding to proton-proton collision events at the Large Hadron Collider (LHC). The kinematic variables of quark, gluon, W-boson, Z-boson, and top quark jets from the JetNet simulation dataset are mapped to two-dimensional image representations. Diffusion models are trained on these images to learn the spatial distribution of jet constituents. We compare the performance of score-based diffusion models and consistency models in accurately generating class-conditional jet images. Unlike approaches based on latent distributions, our method operates directly in image space. The fidelity of the generated images is evaluated using several metrics, including the Fr echet Inception Distance (FID), which demonstrates that consistency models achieve higher fidelity and generation stability compared to score-based diffusion models. These advancements offer significant improvements in computational efficiency and generation accuracy, providing valuable tools for High Energy Physics (HEP) research. IFFUSION models have been used for a wide range of image generation tasks, including grayscale images, RGB color images, hyperspectral images, and physics-based images. Grayscale and color image generation using diffusion models have demonstrated significant advancements in capturing details and color distributions. In grayscale image generation, these models effectively reproduce variations in intensity and texture, as shown in recent studies [1], [2].

Weak supervision combines the advantages of training on real data with the ability to exploit signal properties. However, training a neural network using weak supervision often requires an excessive amount of signal data, which severely limits its practical applicability. In this study, we propose addressing this limitation through data augmentation, increasing the training data's size and diversity. Specifically, we focus on physics-inspired data augmentation methods, such as $p_{\text{T}}$ smearing and jet rotation. Our results demonstrate that data augmentation can significantly enhance the performance of weak supervision, enabling neural networks to learn efficiently from substantially less data.

A framework is presented to extract and understand decision-making information from a deep neural network (DNN) classifier of jet substructure tagging techniques. The general method studied is to provide expert variables that augment inputs ("eXpert AUGmented" variables, or XAUG variables), then apply layerwise relevance propagation (LRP) to networks both with and without XAUG variables. The XAUG variables are concatenated with the intermediate layers after network-specific operations (such as convolution or recurrence), and used in the final layers of the network. The results of comparing networks with and without the addition of XAUG variables show that XAUG variables can be used to interpret classifier behavior, increase discrimination ability when combined with low-level features, and in some cases capture the behavior of the classifier completely. The LRP technique can be used to find relevant information the network is using, and when combined with the XAUG variables, can be used to rank features, allowing one to find a reduced set of features that capture part of the network performance. In the studies presented, adding XAUG variables to low-level DNNs increased the efficiency of classifiers by as much as 30-40\%. In addition to performance improvements, an approach to quantify numerical uncertainties in the training of these DNNs is presented.

Autoencoders are widely used in machine learning applications, in particular for anomaly detection. Hence, they have been introduced in high energy physics as a promising tool for model-independent new physics searches. We scrutinize the usage of autoencoders for unsupervised anomaly detection based on reconstruction loss to show their capabilities, but also their limitations. As a particle physics benchmark scenario, we study the tagging of top jet images in a background of QCD jet images. Although we reproduce the positive results from the literature, we show that the standard autoencoder setup cannot be considered as a model-independent anomaly tagger by inverting the task: due to the sparsity and the specific structure of the jet images, the autoencoder fails to tag QCD jets if it is trained on top jets even in a semi-supervised setup.

Classification of jets with deep learning has gained significant attention in recent times. However, the performance of deep neural networks is often achieved at the cost of interpretability. Here we propose an interpretable network trained on the jet spectrum $S_{2}(R)$ which is a two-point correlation function of the jet constituents. The spectrum can be derived from a functional Taylor series of an arbitrary jet classifier function of energy flows. An interpretable network can be obtained by truncating the series. The intermediate feature of the network is an infrared and collinear safe C-correlator which allows us to estimate the importance of a $S_{2}(R)$ deposit at an angular scale R in the classification. The performance of the architecture is comparable to that of a convolutional neural network (CNN) trained on jet images, although the number of inputs and complexity of architecture is significantly simpler than the CNN classifier. We consider two examples: one is the classification of two-prong jets which differ in color charge of the mother particle, and the other is a comparison between Pythia 8 and Herwig 7 generated jets.

Modern machine learning techniques, such as convolutional, recurrent and recursive neural networks, have shown promise for jet substructure at the Large Hadron Collider. For example, they have demonstrated effectiveness at boosted top or W boson identification or for quark/gluon discrimination. We explore these methods for the purpose of classifying jets according to their electric charge. We find that neural networks that incorporate distance within the jet as an input can provide significant improvement in jet charge extraction over traditional methods. We find that both convolutional and recurrent networks are effective and both train faster than recursive networks. The advantages of using a fixed-size input representation (as with the CNN) or a smaller input representation (as with the RNN) suggest that both convolutional and recurrent networks will be essential to the future of modern machine learning at colliders.

We provide a bridge between generative modeling in the Machine Learning community and simulated physical processes in High Energy Particle Physics by applying a novel Generative Adversarial Network (GAN) architecture to the production of jet images -- 2D representations of energy depositions from particles interacting with a calorimeter. We propose a simple architecture, the Location-Aware Generative Adversarial Network, that learns to produce realistic radiation patterns from simulated high energy particle collisions. The pixel intensities of GAN-generated images faithfully span over many orders of magnitude and exhibit the desired low-dimensional physical properties (i.e., jet mass, n-subjettiness, etc.). We shed light on limitations, and provide a novel empirical validation of image quality and validity of GAN-produced simulations of the natural world. This work provides a base for further explorations of GANs for use in faster simulation in High Energy Particle Physics.

Artificial intelligence offers the potential to automate challenging data-processing tasks in collider physics. To establish its prospects, we explore to what extent deep learning with convolutional neural networks can discriminate quark and gluon jets better than observables designed by physicists. Our approach builds upon the paradigm that a jet can be treated as an image, with intensity given by the local calorimeter deposits. We supplement this construction by adding color to the images, with red, green and blue intensities given by the transverse momentum in charged particles, transverse momentum in neutral particles, and pixel-level charged particle counts. Overall, the deep networks match or outperform traditional jet variables. We also find that, while various simulations produce different quark and gluon jets, the neural networks are surprisingly insensitive to these differences, similar to traditional observables. This suggests that the networks can extract robust physical information from imperfect simulations.