Automatic detection of boosted Higgs boson and top quark jets in an event image

Due to the color confinement, the quarks and gluons produced in a hard process cannot be detected individually. Instead, it will go through parton showering and hadronization after production, giving rise to a collimated spray of energetic detectable color singlet hadrons, which is referred to as a jet. Establishing the correspondence between jets and partons is essential for understanding the underlying physics of collider events. It requires an infrared-safe algorithm that can attribute the related final state hadrons to its partonic ancestors and predict the four-momentum of the parton.

At the LHC and other collider experiments, the jets are reconstructed by using sequential recombination algorithms Salam:2010nqg , in which the final state hadrons are pairwise recombined according to some distance measures, such as Cambridge/Aachen algorithm Dokshitzer:1997in , anti-$k_{T}$ algorithm Cacciari:2008gp and so on Czakon:2022wam ; Gauld:2022lem ; Caola:2023wpj . In those jet clustering algorithms, an appropriate cone size parameter needs to be taken according to the configuration of the detector and the properties of the target jet. At the LHC, the anti-$k_{T}$ jet algorithm with cone size $R=0.4$ works efficiently in finding quark and gluon jets in the ATLAS and CMS detectors. Another origin of a jet is a boosted heavy particle decaying into hadronic final states, for example, the top quark and the Higgs boson. As the typical jet cone size of a heavy resonance is given by $R\sim 2m/p_{T}$, a much larger value is adopted to fully capture the jet constituents. In contrast to the jet originating from the light quark and gluon, those fat-jets are characterized by remarkable substructure. A variety of jet substructure techniques Abdesselam:2010pt ; Altheimer:2012mn ; Altheimer:2013yza ; Adams:2015hiv ; Larkoski:2017jix ; Kogler:2018hem have been proposed for tagging heavy resonant jets, such as mass-drop tagging Butterworth:2008iy for the Higgs boson, HEPTopTagger algorithm Plehn:2010st for the top quark, and N-subjettiness Thaler:2010tr ; Thaler:2011gf for general fat-jets. One practical issue for the fat-jet reconstruction at hadron colliders would be the heavy contamination from pileup events as well as underlying events. The average number of pileup events reaches $\langle\mu\rangle=35$ for LHC Run-II and $\langle\mu\rangle=140$ for High-Luminosity LHC. The large cone size of fat-jet renders many of those background particles to be included as the jet constituents. Although the jet grooming methods Krohn:2009th ; Ellis:2009su have been found to be very helpful in mitigating the pileup effects, there are still relatively large errors in obtaining the original parton momentum when it is calculated by the vector sum of momenta of the groomed jet constituents.

In terms of fat-jet tagging efficiency, machine-learning techniques have proven to substantially outperform those jet substructure techniques Larkoski:2017jix ; Guest:2018yhq ; Albertsson:2018maf ; Radovic:2018dip ; Feickert:2021ajf . According to the jet formation, a jet can be either viewed as sequences/trees formed through sequential parton showering and hadronization or viewed as graphs/point clouds with the information encoded in the adjacency nodes and edges. Moreover, the calorimeters inside the detector measure the angular position and energy of particles on fine-grained spatial cells. Considering each calorimeter cell as a pixel and the energy deposition as the intensity, a jet can be naturally viewed as a digital image. All of those three representations of the jet are common objects in machine learning. They can be proceeded by different kinds of neural network architectures, i.e. recurrent neural networks Andreassen:2018apy and transformer network vaswani2017attention for sequence, graph neural networks (GNN) Moreno:2019bmu ; Komiske:2018cqr ; Qu:2019gqs for point cloud, recursive neural networks Louppe:2017ipp ; Cheng:2017rdo for tree, 2-dimensional convolutional neural networks (CNN) deOliveira:2015xxd ; Komiske:2016rsd ; Kasieczka:2017nvn ; Macaluso:2018tck for jet image. Those delicate deep-learning approaches can better leverage the fine resolution of detectors and automatically figure out the complex pattern of a jet from the low-level inputs. However, those methods rely on traditional jet clustering algorithms to reconstruct the jet at the first stage. As a result, a predefined cone size parameter is required. And the jet representation could suffer from distortion due to inappropriate cone-size parameter or contaminations from pileup events. The ParticleNet Qu:2019gqs , Particle Transformer Qu:2022mxj , LorentzNet Gong:2022lye , and PELICAN Bogatskiy:2022czk are among the state-of-the-art methods for Higgs and top tagging in this field. They achieve typical Area Under Curve (AUC) values of over 0.98 for top tagging, without considering the pileup effects. In addition, the momentum reconstruction component of PELICAN network can predict the $p_{T}$ and mass of $W$ boson with standard deviations of a few percent.

Several studies Grigoriev:2003tn ; Mackey:2015hwa ; Cerro:2021abp ; Mukhopadhyaya:2023rsb attempt to propose jet definitions alternative to the clustering methods, so that the presumed cone size parameter is no longer mandatory. Meanwhile, the techniques of object detection and semantic segmentation in computer vision provide new ways to label the jet constituents. In the Monte-Carlo simulation of collider events, the final state hadrons can be attributed to their ancestor parton without ambiguity. So it will be possible to build a neural network to label the jet constituents among final state particles based on supervised learning. Ref. Ju:2020tbo studies the construction of a $W$ boson jet from final state particles with the supervised GNN. In Ref. Guo:2020vvt , we improve the GNN with focal loss function, such that the method can remain efficient when heavy pileup contaminations are taken into account. Moreover, we demonstrate that the GNN, which is trained on events of the $H$+jets process, is capable of detecting a Higgs jet in events of several different processes. The image segmentation with the convolutional network also works well in detecting the Higgs jets in event images. In Ref. Li:2020grn , we take the event information as a digital image and adopt the Mask R-CNN framework 2017arXiv170306870H to reconstruct the Higgs jet in the event image. Those deep learning methods reach higher efficiency of Higgs jet detection and higher accuracy of Higgs momentum reconstruction than the traditional jet clustering and substructure tagging methods.

However, those methods have not been tested for detecting multiple jets of different kinds in an event. In this work, based on the event image representation, we adopt a modified version of Mask R-CNN to detect/reconstruct all Higgs and top quark jets in an event. Since the top quark is carrying a color charge, its energy flow is interconnected with other colored particles in the production process and with the beam remnants. There is no unique way to associate the hadronic final states with it. Based on the rule that the vector sum of top jet constituents can reproduce the top quark momentum well, we propose a pattern of attribution for the top quark final states in the training sample. As a result, the Mask R-CNN can be trained to detect the top quark jet in a supervised way, similar to the Higgs jet. Moreover, the Mask R-CNN can only predict regions with masks which will also include a large number of particles from pileup events. The Higgs and top quark momenta can not be simply obtained by the vector sum of momenta of masked pixels (calorimeter cells) in the jet image. We add a new fully connected network component to the Mask R-CNN, which takes the input of bounding box information to predict the Higgs and top quark momenta. Given the Higgs and top quark momenta at the ground truth level, this network component is capable of pileup mitigation in an automatic way after supervised learning. It turns out that the modified Mask R-CNN can not only provide the jet regions (masks) of Higgs and top jets in an event but also predict the four-momenta of the Higgs and top parton precisely. We compare the Higgs and top jet tagging performance with LorentzNet and the momentum regression performance with PELICAN.

This paper is organized as follows. In Sec. II, we describe the event generation and the event preprocessing. In Sec. III, we briefly introduce the Mask R-CNN framework and illustrate how events proceed. The changes to the Mask R-CNN are discussed in detail. In Sec. IV, the performances of the network being applied to the $Ht\bar{t}$ process as well as other processes that have not been used for training are presented. We summarise our work and conclude in Sec. V.

The proton-proton collision events are simulated by the MG5_aMC@NLO framework madgraph with center-of-mass-energy $\sqrt{s}=13$ TeV. The Pythia8pythia is used for the quark parton showering, hadronization, and hadron decay. The detector effects are not considered except for the angular granularity of calorimeters ¹¹1The effects of energy smearing will be discussed separately later.. The angular size of the calorimeter cell is assumed to be $0.02\times 0.02$ on the $\eta\times\phi$ plane. This is an idealized setup since the hadron calorimeter at the LHC usually has $\eta/\phi$ resolution larger than $\sim 0.15$. Although the precision of momentum reconstruction is limited by the cell size, we find that the network performance, i.e. the Higgs/top detection efficiency, is barely changing with the cell size. The event image is built by presenting each calorimeter cell on the $\eta\times\phi$ plane as a pixel of an image, and the transverse momentum of the cell as the intensity (or grayscale color) of that pixel.

The network is trained on one million events of the $Ht\bar{t}$ process, where both the Higgs and top quark jets are marked. It should be noted that training our network on other processes is certainly possible and the performance of the network should be similar. To show the generality of the network, the performances on various test samples are studied, including $Ht\bar{t}$, $t\bar{t}t\bar{t}$, $HHt\bar{t}$ production in the SM model as well as the neutralino pair production and top squark pair production with subsequent decay $\tilde{\chi}^{0}_{2}\to H\tilde{\chi}_{1}^{0}$ and $\tilde{t}\rightarrow t\tilde{\chi}_{1}^{0}$ in the supersymmetric (SUSY) model. The transverse momenta of Higgs and top quark in the SM processes are required to be greater than 200 GeV and 300 GeV, respectively. As for the SUSY case, we set the masses $m_{\tilde{\chi}^{0}_{2}}=450$ GeV, $m_{\tilde{t}}=650$ GeV and $m_{\tilde{\chi}^{0}_{1}}=100$ GeV. We do not specify the decay modes of the Higgs and top quark in the training sample. However, we find the network exhibit better performance on events with hadronically decaying Higgs ($H\to b\bar{b}$) and top quark ($t\to bW,W\to qq$). Therefore the Higgs and top quark in the test sample are forced to decay through those modes.

Moreover, there are multiple proton-proton collisions (referred to as pileup) in each bunch crossing at the LHC. Those collisions are dominated by nondiffractive events with small transverse momentum transfer. Simulation of the pileup events requires perturbative parton shower, Lund-string hadronization, multiple parton interaction and colour reconnection, which are usually described by phenomenological models. The parameters in the models are not unique and need to be inferred from experimental data. The set of appropriately chosen parameters is dubbed Pythia tunes ATLAS:2012uec . We adopt the A3 tune of Pythia8 with phenomenological parameters provided in Refs. Skands:2014pea ; ATLAS:2016puo to simulate pileup events. The number of pileup events per bunch crossing at the LHC follows the Poisson distribution with an average value around $\langle\mu\rangle$ = 35 at the LHC run-II and $\langle\mu\rangle$ = 200 at High-Luminosity LHC. We took the average number of pileup events of $\langle\mu\rangle$ = 50 in our simulation. A detailed study on the effects of different pileup levels will be given later. Finally, we note that particles flying into the same calorimeter cell can only be identified with the summation of their momenta. So, the pileup will increase the momenta of the target jet constituents, and the pileup mitigation procedure is essential to obtain a precise parton momentum.

Mask R-CNN 8237584 is a state-of-the-art framework for object detection and instance segmentation. It was progressively developed from region-based convolutional neural networks (R-CNNs) that first take candidate regions from separate region proposal methods, and then use a convolutional network to extract features for classifications and bounding box regressions. The original R-CNN 6909475 was computationally expensive as it performs a CNN for each region proposal. By extracting a feature map from the entire input image to share across region proposals, SPPnet 10.1007/978-3-319-10578-9_23 greatly reduced the computational cost, and Fast R-CNN 7410526 streamlined a multi-stage pipeline of the predecessors as the classifier and box regressor are jointly trained with the feature extraction network. While the previous models take the region proposals from separate region proposal methods, Faster R-CNN NIPS2015_14bfa6bb has brought them into one unified network by introducing region proposal networks (RPNs) that can share the convolutional feature map, showing remarkable gains in speed and accuracy. Finally, Mask R-CNN extends Faster R-CNN by adding a mask branch for instance segmentation in parallel with the classifier and box regressor.

Let us briefly review the structure of Mask R-CNN (Figure 3). It can be mainly divided into three modules, a backbone architecture for feature extraction, an RPN for region proposal generation, and a detection head for classification, box regression, mask segmentation. The RPN and detection head share the backbone such that the features are used for both regional proposals and detections. Although the backbone can be any convolutional architectures, Feature Pyramid Network (FPN) 8099589 is commonly used to take advantage of multi-scale features in addition to the base architecture such as residual neural networks (ResNets) he2016residual . The ResNet extracts features from an input image by successively scaling down its spatial size through convolutions, which in turn produces a pyramid of outputs at several scales. The FPN then uses a top-down pathway with lateral connections to the outputs at each scale in order to build a feature pyramid. The feature map at each level of the pyramid is fed into the RPN to propose candidate bounding boxes, referred to as regions of interest (RoIs). An anchor is a reference box whose center is at a pixel of the feature pyramid. By default every pixel has three anchors with aspect ratio of 1:1, 1:2, and 2:1, where the anchor scale is different according to the level of the feature pyramid. Through a small convolutional network, the RPN outputs an objectness score and box regression for each anchor. It is trained so that an anchor has a high score if its Intersection over Union (IoU) with a ground truth box greater than a threshold, and the box regression refines the size and location of positive anchors to fit their ground truth boxes better. The refined positive boxes are the RoIs that are passed on to RoI Pooling. While the RoIs have variable sizes due to the refinement in the RPN, the detection head requires a fixed-size input. Therefore, we pool RoI features of a fixed size by cropping the RoIs from the feature pyramid and resizing them using bilinear interpolation ⁴⁴4 We use the crop and resize operation following the source code matterport_maskrcnn_2017 for simplicity. The original paper 8237584 proposed a more elaborate method, called RoIAlign, to reduce misalignment between the RoIs and the extracted features.. The RoI features are then fed to the detection head that has two branches. The classification branch consists of two fully-connected layers followed by classification and box regression outputs. The mask branch is a small fully convolutional network to predict binary masks.

In the jet reconstruction task, the original Mask R-CNN can be used to tag jets and predict the jet areas. On the other hand, the jet areas, especially the convex hull areas, are susceptible to the pileup contamination since they include background particles as well. Furthermore, the preselection process to define jet areas may exclude some constituents that significantly contribute to the four-momentum of their parton. Therefore, in order to accurately obtain four-momenta of partons from jet area predictions, one needs separate methods carrying out the pileup mitigation as well as compensating for the preselection. On the contrary, instead of using separate methods, we bring a pileup mitigation and compensation network into Mask R-CNN to facilitate end-to-end jet reconstructions. In other words, we extend Mask R-CNN by adding an additional branch for predicting the mass, $p_{T}$, and coordinates of partons ⁵⁵5In practice, the vector sum of the constituents momenta is used as ground truth instead of the momentum of the original parton in training our network, because vector sum is more directly related to the masked constituents. However, in the training sample, the momentum difference between the vector sum and the parton is less than 2% for Higgs and 5% for top, for more than 90% events., which we call jet branch. The jet branch has the same architecture as the classification branch, i.e., two fully-connected layers, and also shares the RoI inputs with the classification branch (Figure 4). It is worth noting that we predict two boxes and two masks for each RoI (denoted by ‘$\times 2$’ in the figure), although it is usual to predict one box and mask per class so that the default number of predictions for each RoI is $3$ corresponding to the three classes (background/Higgs/top). If objects in each class have their typical shape or ratio, the class-specific prediction may be more effective. However, the Higgs jets are indistinguishable from top jets by their bounding box or mask. Therefore, we predict for two classes (background/jet) considering Higgs and top as one class. On the other hand, the jet branch outputs a single four-momentum (coordinates, $p_{T}$, and mass) for each RoI regardless of class. This reflects the fact that it is always possible to calculate the four-momentum even for a background region in a consistent way. Furthermore, this approach also can tell the network that the mass of an RoI is essential to determine its class. Consequently, the mass and class prediction tasks will be closely intertwined and enhance each other.

In our implementation of Mask R-CNN, which is based on the open-source code in matterport_maskrcnn_2017 , we also employed Composite Backbone Network (CBNet) Liang_2022 as our backbone and Cascade R-CNN 8578742 as an extension of the detection head, so as to further improve accuracy. We present a brief introduction to the two architectures while referring readers to the original papers Liang_2022 ; 8578742 for details. The CBNet groups multiple identical backbones by connecting them in parallel. We use CB-ResNet50 which consists of two ResNet50s, an assisting one and a lead one, connected in such a way that the features of higher-level stages in the assisting backbone flow to the lower-level stages in the lead backbone. Therefore, the lead backbone can integrate the high-level features into its low-level convolutional stages for more effective feature extractions. Cascade R-CNN extends the detection head in order to have more accurate bounding box predictions. The detector requires an IoU threshold to decide whether an RoI is positive or negative, and the commonly used threshold value is 0.5, which will be robust to poor proposals but also can be loose, leading to noisy box predictions. To address the problem, Cascade R-CNN adds detectors and constructs a sequence of detectors with increasing thresholds at each stage. We use three detectors where the first two have only the classification branch to refine RoIs while the last detector has all three branches.

In object detection, it is usual to evaluate the network performance using Average Precision (AP). Given an IoU threshold, one can obtain the precision-recall curve by varying the score threshold as shown in the Figure 5, and AP is the area under the curve. In jet detection, however, the value itself is not directly comparable to that of other models since AP also heavily depends on the mask scheme. Nonetheless, it is a useful metric within one mask scheme, and hence we report the mask AP and box AP in Table 1 to show the performance in jet area detection (see also Figure 6 for example).

On the other hand, the main goal of the jet reconstruction task is to calculate the four-momentum of partons, which are independent of the mask scheme. Therefore, we want to measure how accurately our extended Mask R-CNN can predict the mass, $p_{T}$, and coordinates. In experimental analyses, we have prior knowledge about the type and number of jets in selecting the signal events. Let us assume we have three ground truth Higgs jets on an image for illustrative purposes. First recall that, since we use the augmented images, there may be two predictions for the same jet duplicated along the augmented $\phi$ coordinate. To sort this out, we post-process the output by taking it back to the $\phi$ range of one period and eliminating one with a lower score if two predictions are of the same class and their mask overlap is large. After the postprocessing, we choose three predictions of Higgs with the highest scores if there are more than three Higgs predictions. Otherwise, we take all available Higgs predictions. A prediction is a true positive if the distance between the predicted and ground truth coordinates is less than a threshold (we use 30 pixels $\simeq$ 0.6). We measure the coordinates, mass, and $p_{T}$ differences between the true positive prediction and its ground truth (obtained by the vector sum of the constituents momenta).

To gain an intuitive understanding of the network performance, we contrast our results with those from existing state-of-the-art object tagging architecture. We adopt LorentzNet for classification and PELICAN for momentum regression as an illustration. The validations for the application of these two networks are provided in Appendix A. These networks require a jet clustering algorithm to localize jets for a given event image, as they use a jet as the input. We retrain these networks on Higgs and top quark jets from our 0.3 million $Ht\bar{t}$ event sample (with an average number of 50 pileup events superposed on each signal event), where the Higgs ($p_{T_{H}}>$ 200 GeV) and top quark ($p_{T_{t}}>$ 300 GeV) jets are reconstructed by the anti-$k_{T}$ algorithm with cone size parameter $R$ varying from 0.8 to 1.8 in steps of 0.2. The detector effects have been ignored in this comparison study.

It should be noted that the LorentzNet and PELICAN follow a fixed input format: a set of four momenta of the jet constituents. To simplify the training, we construct a training file for the reconstructed anti-$k_{T}$ jets mentioned above, mainly containing the following information:

• •

  Nobj: The count of jet constituents.

• •

  Pmu: The four-momentum of jet constituents $(E,p_{x},p_{y},p_{z})$, sorted in descending order of $p_{T}$. This part serves as the network input, with a shape of [N$\times$4], where N(=200) is the maximum number of jet constituents for a single input, and the insufficient parts are padded with zeros.

• •

  label: Indicates whether Pmu at a certain position is a constituent(1) or a padding value(0), with a shape of [1$\times$200].

• •

  truth_Pmu: The four-momentum of the parton to which the jet belongs, used for momentum prediction.

• •

  is_signal: The type of the jet determined by the distance from jet to parton. For example, if it is closest to the Higgs (i.e., when $\Delta R=\sqrt{\Delta\phi^{2}+\Delta y^{2}}$ is the smallest), it is classified as a Higgs jet(0), and top jet(1) is in a similar situation. This value is used for jet classification.

• •

  mass: The invariant mass of the parton to which the jet belongs.

The above file format refers to https://zenodo.org/record/7126443, and there are some other configurations mentioned in the same link, which are irrelevant to the training. For more details, please refer to the link provided above. The hyperparameters for both networks are set to the default values as shown in Refs Gong:2022lye ; Bogatskiy:2022czk .

The receiver operating characteristic (ROC) curves of the LorentzNet for top quark (signal) and Higgs (background) jet discrimination with different cone sizes are shown in the left panel of Figure 7. It can be observed that the cone size parameter has non-negligible effects on the performance of LorentzNet. In particular, the performance degrades dramatically when the cone size becomes too small to fully capture the jet constituents. On the other hand, a larger cone size does not impair jet classification much, despite distorting the jet shape. The performance of those classifiers is not directly comparable to that of Mask R-CNN. However, we may consider only the classification part of Mask R-CNN to obtain ROC curve. In Mask R-CNN, RPN does a similar job to jet clustering algorithms. The RPN in our hyperparameter setting proposes up to 500 RoIs for each image ⁶⁶6Overlaps between RoIs are allowed as long as IoU is less than a threshold (we use 0.7) such that several RoIs indicate one jet in general., which will be passed to the detection head. To calculate the ROC, we first get all those RoIs of an event from RPN, and compute IoUs between RoIs and ground truth bounding box. The RoIs with IoU greater than 0.5 are selected and fed into the classifier branch. The RoI with the highest classification score is chosen for calculating the ROC curve of the Mask R-CNN. As our network predicts three classes, we provide two ROC curves, one of which considers Higgs jet as positive class and top quark jet as negative class, while the other considers the opposite. The ROC curves are presented in Figure 7. The Mask R-CNN achieves higher performance than the LorentzNet in general, due to its more accurate jet boundaries. Those features can be quantified in terms of AUC values, as given in Table 2. In addition, the Mask R-CNN can tag top quark jet more accurately than Higgs jet in its trinary classification. The right panel of Figure 7 illustrates this fact with the classification scores distributions, where $P(H|H)$, $P(H|t)$, $P(t|t)$ and $P(t|H)$ are the probabilities of tagging true Higgs as Higgs, true top as Higgs, true top as top and true Higgs as top, respectively.

This work aims to build a deep neural network to label the constituents of target jets among hadronic final state particles based on supervised learning. In particular, the hadronic final state of the top quark can not be identified unambiguously according to the Monte Carlo simulation due to the color interconnection in hadronization. We propose an algorithm based on the ground truth information as well as the angular distance measure to determine the top quark jet constituents.

The Mask R-CNN framework is adopted to detect the Higgs jets and the top quark jets in collision events at the LHC. The network can predict the shape (or mask) of target jets of different kinds on event images. The definition of jet shape/mask is not unique, even from a theoretical perspective. Two schemes of mask definition are proposed in this work: enlargement mask and convex hull mask. More importantly, an additional jet branch is built for predicting the four-momenta of the original partons, in which the pileup mitigation is intrinsically implemented.

The network is trained on events of the $Ht\bar{t}$ process at the LHC, where the transverse momenta of the Higgs and top quarks are required to be $p_{T}(H)>200$ GeV and $p_{T}(t/\bar{t})>300$ GeV. Each event is overlaid with an average number of $\langle\mu\rangle=50$ pileup events. Compared with the LorentzNet for jet classification and the PELICAN network for jet momentum regression, the Mask R-CNN can detect and reconstruct both the Higgs and top jets in a more efficient and accurate way, mainly because it predicts jets with more accurate boundaries. The networks with two different definitions of the mask have similar performances. In terms of two-dimensional distributions on the $\Delta y\times\Delta\phi$ plane and $\frac{\Delta m}{m}\times\frac{\Delta p_{T}}{p_{T}}$ plane, about 60% of Higgs jets can be reconstructed with $\Delta y\sim\Delta\phi\in[-0.06,0.06]$, $\frac{\Delta m}{m}\in[-0.08,0.05]$ and $\frac{\Delta p_{T}}{p_{T}}\in[-0.14,0.1]$. And about 60% of top jets can be reconstructed with $\Delta y\sim\Delta\phi\in[-0.05,0.05]$, $\frac{\Delta m}{m}\in[-0.07,0.5]$ and $\frac{\Delta p_{T}}{p_{T}}\in[-0.11,0.08]$.

The generality of the method is demonstrated by applying the Mask R-CNN to processes different from the trained one, including 1) $pp\to HHt\bar{t}$ in the SM; 2) $\tilde{\chi}^{0}_{2}\tilde{\chi}^{0}_{2}$ production with decay $\tilde{\chi}^{0}_{2}\to H\tilde{\chi}^{0}_{1}$ in SUSY model; 3) $\tilde{t}\bar{\tilde{t}}$ production with decay $\tilde{t}\to t\tilde{\chi}^{0}_{1}$; 4) $pp\to t\bar{t}t\bar{t}$ in the SM. In all cases, we find the dependence of the network performance on the mask definition is little. And the network outperforms the PELICAN method in the accuracy of momenta reconstruction, especially for processes with higher visible final state multiplicity. In general, the performance is slightly worse than that for the $Ht\bar{t}$ process. About 40% of the Higgs/top jets in those test samples can be reconstructed with $\Delta y\sim\Delta\phi\in[-0.04,0.04]$, $\frac{\Delta m}{m}\in[-0.08,0.05]$ and $\frac{\Delta p_{T}}{p_{T}}\in[-0.1,0.07]$.

Moreover, we show that the network is capable of detecting the target jets even when they overlap with each other on the event image, although the accuracy of the reconstructed momentum is degraded. The network exhibits high background jet rejection power when applied to events of the QCD multijet process.

Although we have focused on the generalization capability to other processes in this work, conversely one may have the network to specialize in a particular process through the transfer learning. By training only the detection head with a small dataset of a certain process, the accuracy on the process increases while the network becomes rapidly insensitive to other processes. The Mask R-CNN method proposed in this work can be used to detect the boosted Higgs/top at the hardware trigger when being loaded to FPGA. Meanwhile, this method can also supplement the conventional analysis, by detecting the Higgs/top and removing the Higgs/top constituent before applying a usual jet clustering algorithm. In the future, we will try to generalize this method to detect all kinds of jets in collider events. Then it can simply replace the jet clustering and indentification algorithms in the conventional data analysis.