DeepCore: Convolutional Neural Network for high p_T jet tracking

Introduction

High p_T jet problem

The tracking inside jet core becomes inefficient in high transverse momentum jets, because the collimated environment produces merged cluster from different tracks on the pixel detector. The splitting of the merged cluster is inefficient and it degrades the quality of seeding of the CMS tracking algorithm, based on a combinatorial Kalman Filter (cKF).

CNN High p_T jet tracking: DeepCore

• The presented algorithm is a Convolutional Neural Network which produces the track-seeds directly from the raw pixel information of the four layers in the jet core region. In this way, it is possible to improve the tracking performance by skipping the pixel clustering.
• DeepCore has been trained on 22 millions of inputs from 2 millions of Monte Carlo QCD events (1.8 TeV <p̂_T< 2.4 TeV, p_T^jet> 1 TeV, |η^jet|<1.4)

Integration and validation

• DeepCore replaces the seeding step of the cKF of CMS reconstruction in the iteration dedicate to the jet core region only.
• The performance of the algorithm integrated in the CMS reconstruction has been validated on a Monte Carlo sample of 2 x 104 QCD events (1.8 TeV < p̂_T < 2.4 TeV, p_T^jet> 1 TeV, |η^jet|<1.4)
• The typical selection is applied on simulated tracks used for validation: |η^jet|<2.5, r_prod<3 cm, |z_prod|<30 cm, p_T> 0.9 GeV.

DeepCore Network

Input

A single input of the network is composed by:

• four 30x30 pixel maps (one per layer), aligned with the directions of a merged cluster present on layer one (or layer 2 if layer 1 is missing)
• jet η and jet p_T

Target

For each pixel in 30x30 window of layer 2:

• 1 if a track cross that pixel, 0 otherwise (TCP map)
• the 5 track parameters in local parametrization (with respect to the centre of the pixel) for the TCP and in a circle of radius 2 pixel (NCP)
• 3 repetitions of this target are given to take into account of overlap

Prediction

• Same structure of the target
• The seeds are selected as the track parameters of the most probable (TCP>0.85, 0.75, 0.65 in the 3 repetitions, or 0.50,0.40,0.30 if layer 2 is missing) pixels.

Architecture

• 9 2D Convolutional layers branched at layer 5 in two, to predict the TCP Map and the Track Parameters Map
• Activation functions: ReLU for all the layers, except Sigmoid for the last TCP layer
• Loss functions: 2 custom functions for the two branches
• TCP: Binary Cross Entropy weighted on TCP/NCP/other pixels fractions
• Track Parameters: Mean Square Error, clipped between [-5,5], averaged on TCP and NCP only

Definitions

Tracking Efficiency

Number of simulated tracks associated to a reconstructed one divided by the number of simulated tracks. A simulated track is flagged as “associated” if the χ² between its parameters and the reconstructed is lower than 25.

Fake Rate

Number of reconstructed tracks not associated to a simulated one divided by the number of reconstructed tracks.

Duplicate rate

Number of tracks duplicate divided by the number of reconstructed tracks. A reconstructed track is flagged as “duplicate” if at least another reconstructed track is associated to the same simulated track of the first one.

Current status

• DeepCore has been fully trained and integrated in CMSSW in the barrel region only ( |η^jet|<1.4)
• DeepCore-endcap is currently under development (optimization of the training)
• DeepCore can be enabled, in cmsDriver commands, with the option ----procModifiers seedingDeepCore. In the endcap the standard jetCore is still used.

Workflow

• prepare the input and build the ntuple, using the ntuplizer present in this branch/Module of CMSSW: https://github.com/vberta/cmssw/tree/CMSSW_12_0_0_pre4_DeepCoreTraining/RecoTracker/DeepCoreTraining
• train DeepCore, using the DeepCore.py script
• convert the trained model .h5 in a .pb model for CMSSW and place in the proper repository, accessible from CMSSW (https://github.com/vberta/RecoTracker-TkSeedGenerator/tree/DeepCore)
• cmsRun with ----procModifiers seedingDeepCore

Last pull requests:

• Integration: https://github.com/cms-sw/cmssw/pull/32222
• Speedup of validation: https://github.com/cms-sw/cmssw/pull/33731
• Barrel DeepCore and endcap jetCore solution: https://github.com/cms-sw/cmssw/pull/33531

Code location:

• Ntuplizer: https://github.com/vberta/cmssw/tree/CMSSW_12_0_0_pre4_DeepCoreTraining/RecoTracker/DeepCoreTraining
• Training script and documentation: https://github.com/vberta/DeepCore
• Trained model: https://github.com/vberta/RecoTracker-TkSeedGenerator/tree/DeepCore

References

Detector Performance Summary: [ https://cds.cern.ch/record/2669826/files/DP2019_007.pdf ]

Connecting The Dots 2019 Proceeding: [ https://arxiv.org/abs/1910.08058 ]

Connecting The Dots 2019 Talk: [ https://indico.cern.ch/event/742793/contributions/3274301/attachments/1822584/2981871/bertacchi_deepcore_ConnectingTheDots.pdf ]

CMS track reconstruction reference: [ arXiv:1405.6569v2 ]

Performance Plots

Training

plots	Description
pdf png	Residual between the seed η parameter predicted by DeepCore and the target (simulated) track η parameter.
pdf png	Correlation between prediction of DeepCore and target parameters shown with seed η parameter predicted against the simulated track η parameter.

CMS reconstruction performance

plots	plots	Description
pdf png	pdf png	Tracking efficiency (left figure) and fake rate (right figure) in the jet core region (ΔR<0.1, between the reconstructed jet axis and the simulated track direction). The contribution of the different iterations of the cKF are shown as stacked histograms. The DeepCore algorithm is used in the iteration dedicated to the cores of the jets [jetCore (purple)]. In the efficiency the shared reconstructed tracks (duplicated) between various iterations are not removed.

CMS Compared reconstruction performance

plots	plots	Description
pdf png	pdf png	Tracking efficiency (left figure) and fake rate (right figure) in the jet core region (ΔR<0.1, between the reconstructed jet axis and the simulated track direction). The light blue filled histogram is obtained with the standard CMS tracking algorithm. The dark blu histogram is obtained removing the cKF iteration dedicated to the jet cores. The red histogram is obtained using the DeepCore in the seeding for the interation dedicated to the jet cores. The green histrogram is obtained producing the seed for the jet core iteration using the simulated track information (i.e. equivalent to 100% of seeding efficiency). In the lower pads are shown the differences between various tracking efficiencies (fake rates) and the MC truth seeding one, divided by the MC truch seeding efficiency (fake rate).

Qualitative Plots

plots	plots	plots	plots	plots	Description
pdf png	pdf png	pdf png	pdf png	pdf png	Example of of the pixel maps used as input for the DeepCore neural network (four left plots): the maps shows a windows on the four pixel detecor layer of CMS, aligned to the jet direction. The most right figure is the map of the predicted crossing point on the window of layer 2, expressed as probability.
pdf png	pdf png	pdf png	pdf png	pdf png	Example of of the pixel maps used as input for the DeepCore neural network (four left plots): the maps shows a windows on the four pixel detecor layer of CMS, aligned to the jet direction. On the top are also shown the crosses of the crossing point of the target (simulated) tracks and the correspondent predicion of DeepCore for the most probable hits. The prediction is produced on layer 2 and propagated linearly on the other layer. The most right figure is the map of the predicted crossing point on the window of layer 2, expressed as probability, with the crosses of the predictions and the targets.