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2019 CtD: A hybrid deep learning approach to vertexing

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Henry Schreiner

This document presents a hybrid deep learning approach for vertex finding using 1D convolutional neural networks. It describes generating 1D kernel densities from tracking information, building target distributions, and using a CNN architecture with an adjustable cost function to optimize the false positive rate versus efficiency. The approach achieves 93.87% efficiency with a 0.251 false positive rate on test data. Future work includes incorporating additional xy information and exploring full 2D kernel densities.

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A hybrid deep learning approach to vertexing Rui Fang1 Henry Schreiner1, 2 Mike Sokoloff1 Constantin Weisser3 Mike Williams3 April 3, 2019 1 The University of Cincinnati 2 Princeton University 3 Massachusetts Institute of Technology CtD/WIT 2019 Supported by:
0 5 10 15 20 25 30 35 40 45 50 55 60 # LHCb long tracks 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Efficiency Found 103002 of 109733 (eff 93.87%) False positive rate = 0.251 per event Asymmetric cost function Found 96616 of 109733 (eff 88.05%) False positive rate = 0.0485 per event Symmetric cost function Events in sample = 20K Training sample = 240K 0 5 10 15 20 25 30 35 40 45 50 55 60 # LHCb long tracks 102 103 104 PVs 1/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Tracking in the LHCb upgrade Introduction The changes • 30 MHz software trigger • 7.6 PVs per event (Poisson distribution) • Roughly 5.5 visible PVs per event The problem • Much higher pileup • Very little time to do the tracking • Current algorithms too slow We need to rethink our algorithms from the ground up... 2/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Vertices and tracks Introduction Vertices • Events contain ≈ 7 Primary Vertices (≈ 5 visible PVs) A PV should contain 5+ long tracks • Multiple Secondary Vertices (SVs) per event as well A SV should contain 2+ tracks Beams PV Track SV Adapt to machine learning? • Sparse 3D data (41M pixels) → rich 1D data • 1D convolutional neural nets • Highly parallelizable, GPU friendly • Opportunities to visualize learning process 3/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
A hybrid ML approach Introduction Tracking Kernel generation Make predictions CNNs Interpret results Truth Training Validation Machine learning features (so far) • Prototracking converts sparse 3D dataset to feature-rich 1D dataset • Easy and effective visualization due to 1D nature • Even simple networks can provide interesting results What follows is a proof of principle implementation for finding PVs. 4/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored • Tracking (full or partial) z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored • Tracking (full or partial) • Fill in each voxel center with Gaussian PDF z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored • Tracking (full or partial) • Fill in each voxel center with Gaussian PDF • PDF for each (proto)track is combined z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored • Tracking (full or partial) • Fill in each voxel center with Gaussian PDF • PDF for each (proto)track is combined • Fill z “histogram” with maximum KDE value in xy z axis (along the beam) x Kernel PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Example of z KDE histogram Design 100 50 0 50 100 150 200 250 300 z values [mm] 0 500 1000 1500 2000 DensityofKernel Kernel LHCb PVs Other PVs LHCb SVs Other SVs Note: All events from toy detector simulation Human learning • Peaks generally correspond to PVs and SVs Challenges • Vertex may be offset from peak • Vertices interact 6/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Target distribution Design Build target distribution • True PV position as the mean of Gaussian • σ (standard deviation) is 100 µm (simplification) • Fill bins with integrated PDF within ±3 bins (±300 µm) 7/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Neural network architecture Design Inputs 1 2 3 · · · 25 26 · · · 3998 3999 4000 Convolution Width: 25 Channels: 1 → 25 25 Channels 1 2 3 · · · 15 16 · · · 3998 3999 4000 Convolution Width: 15 Channels: 25 → 25 25 Channels 1 2 3 · · · 15 16 · · · 3998 3999 4000 Convolution Width: 15 Channels: 25 → 25 25 Channels 1 2 3 4 5 6 · · · 3998 3999 4000 Convolution Width: 5 Channels: 25 → 1 1 Channel 1 2 3 · · · 91 92 · · · 3998 3999 4000 Convolution Width: 91 Channels: 1 → 1 Output 1 2 3 4 5 · · · 3997 3998 3999 4000 -x x y Leaky relu -x x y Leaky relu -x x y Leaky relu -x x y Leaky relu -x x y Softplus 8/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Cost function Design 10 6 10 5 10 4 10 3 10 2 10 1 100 yhat 0 10 20 30 40 50 60 cost 0.0 0.2 0.4 0.6 0.8 yhat 0 5 10 15 20 25 30 cost Asym. Cost for y = 0.10 Symm. Cost for y = 0.10 Asym. Cost for y = 0.30 Symm. Cost for y = 0.30 Asym. Cost for y = 1e-5 Symm. Cost for y = 1e-5 0.2 0.4 0.6 0.8 1.0 yhat 0 2 4 6 8 10 cost Approach • Symmetric cost function: low FP but low efficiency • Adding asymmetry term controls trade-off for FP vs. efficiency 9/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
False Positive and efficiency rates Results 88 89 90 91 92 93 94 Efficiency [%] 0.05 0.10 0.15 0.20 0.25FPperevent Symm cost Most asymm cost 88 89 90 91 92 93 94 Efficiency [%] 10 1 6×10 2 2×10 1 FPperevent Symm cost Most asymm cost Search for PVs (handwritten, maybe not optimial) • Search ±5 bins (±500µm) around a true PV • At least 3 bins with predicted probability > 1% and integrated probability > 20%. Tunable efficiency vs. FP • The asymmetry parameter controls FP vs. efficiency 10/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Compare predictions with targets: Examples Results 0 100 200 300 400 500 KernelDensity True: 197.461 mm Pred: 197.396 mm : -65 µm Event 5 @ 197.4 mm: PV found Kernel Density 195.00 196.00 197.00 198.00 199.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked PV found example 0 200 400 600 800 1000 1200 1400 1600 KernelDensity True: 36.068 mm Pred: 36.400 mm : 332 µm Event 6 @ 36.1 mm: PV found Kernel Density 34.00 35.00 36.00 37.00 38.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked PV found example 11/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Compare predictions with targets: When it works Results 0 200 400 600 800 1000 1200 KernelDensity True: 48.904 mm Pred: 48.954 mm : 50 µm Event 0 @ 48.9 mm: PV found Kernel Density 47.00 48.00 49.00 50.00 51.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked PV found example 0 50 100 150 200 KernelDensity Pred: 0.976 mm Event 0 @ 1.0 mm: Masked Kernel Density -1.00 0.00 1.00 2.00 3.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked Masked (<5 tracks) example 12/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Compare predictions with targets: When it fails Results 0 50 100 150 200 250 KernelDensity Pred: 65.696 mm Event 2 @ 65.7 mm: False positive Kernel Density 64.00 65.00 66.00 67.00 68.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted False Positive example 0 100 200 300 400 500 KernelDensity True: 51.898 mm Event 3 @ 51.9 mm: PV not found Kernel Density 50.00 51.00 52.00 53.00 54.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked PV not found example 13/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Future addition: xy information Future plans Adding xy information • Point of maximum z in xy available • Extra information: sharp discontinuities between PVs • Need iterative approach or “reduced importance” What about a full 2D kernel? • Not needed for LHCb currently (large xy, “low” z overlap) • Might be useful for other detectors! 0 500 1000 1500 2000 KernelDensity True: 114.622 mm Pred: 114.597 mm : -26 µm Event 2 @ 114.6 mm: PV found Kernel Density 113.00 114.00 115.00 116.00 117.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 14/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Conclusions and plans Future plans 0 5 10 15 20 25 30 35 40 45 50 55 60 # LHCb long tracks 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Efficiency • Proof-of-Principle established: a hybrid ML algorithm using a 1-dimensional KDE processed by a 5-layer CNN finds primary vertices with efficiencies and false positive rates similar to traditional algorithms. • Efficiency is tunable; increasing the efficiency also increases the false positive rate. • Adding information should improve performance. • can add KDE (x,y) information to algorithm • can associate tracks to PV candidates, then iterate. • Next steps: train with full LHCb MC and deploy inference engine in LHCb Hlt1 framework. • Beyond LHCb • approach might work for ATLAS and CMS (in 2D?); • algorithm is an interesting ML laboratory. 15/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Final words Future plans Source code: • https://gitlab.cern.ch/LHCb-Reco-Dev/pv-finder • Runnable with Conda on macOS and Linux Run: conda env create -f environment-gpu.yml Python 3.6+ and PyTorch used for machine learning code Generation now available too using the new Conda-Forge ROOT and Pythia8 packages Supported by: • NSF OAC-1836650: IRIS-HEP • NSF OAC-1740102: SI2:SSE • NSF OAC-1739772: SI2:SSE 16/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Final words Future plans Questions? Source code: • https://gitlab.cern.ch/LHCb-Reco-Dev/pv-finder • Runnable with Conda on macOS and Linux Run: conda env create -f environment-gpu.yml Python 3.6+ and PyTorch used for machine learning code Generation now available too using the new Conda-Forge ROOT and Pythia8 packages Supported by: • NSF OAC-1836650: IRIS-HEP • NSF OAC-1740102: SI2:SSE • NSF OAC-1739772: SI2:SSE 16/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
More predictions with targets (1) Backup 0 50 100 150 200 KernelDensity True: 221.595 mm Pred: 221.546 mm : -49 µm Event 5 @ 221.5 mm: PV found Kernel Density 219.00 220.00 221.00 222.00 223.00 224.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 0 500 1000 1500 2000 KernelDensity True: 114.622 mm Pred: 114.597 mm : -26 µm Event 2 @ 114.6 mm: PV found Kernel Density 113.00 114.00 115.00 116.00 117.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 17/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
More predictions with targets (2) Backup 0 200 400 600 800 1000 1200 1400 1600 KernelDensity True: 129.336 mm Pred: 129.337 mm : 1 µm Event 6 @ 129.3 mm: PV found Kernel Density 127.00 128.00 129.00 130.00 131.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 0 500 1000 1500 2000 KernelDensity True: 143.224 mm Pred: 143.199 mm : -25 µm Event 6 @ 143.2 mm: PV found Kernel Density 141.00 142.00 143.00 144.00 145.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 18/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
More predictions with targets (3) Backup 0 50 100 150 200 250 300 350 400 KernelDensity True: 150.650 mm Pred: 150.416 mm : -234 µm Event 6 @ 150.4 mm: PV found Kernel Density 148.00 149.00 150.00 151.00 152.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 0 500 1000 1500 2000 2500 KernelDensity True: 179.560 mm Pred: 179.591 mm : 31 µm Event 6 @ 179.6 mm: PV found Kernel Density 178.00 179.00 180.00 181.00 182.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 19/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
The VELO Backup Tracks • Originate from vertices (not shown) • Hits originate from tracks • We only know the true track in simulation • Nearly straight, but tracks may scatter in material The VELO • A set of 26 planes that detect tracks • Tracks should hit one or more pixels per plane • Sparse 3D dataset (41M pixels) 20/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
Questions for other experiments Backup • Beam width (x, y): 40 µm for LHCb, what is yours? • Transverse resolution: 5–15 µm for LHCb depending on number of tracks, what is yours? • Longitudinal resolution: 40–100 µm for LHCb depending on number of tracks, what is yours? • Cleaning up prototracks based on IP could simplify kernel • Can prototracking be done in the triggers? 21/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019

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2019 CtD: A hybrid deep learning approach to vertexing

  • 1. A hybrid deep learning approach to vertexing Rui Fang1 Henry Schreiner1, 2 Mike Sokoloff1 Constantin Weisser3 Mike Williams3 April 3, 2019 1 The University of Cincinnati 2 Princeton University 3 Massachusetts Institute of Technology CtD/WIT 2019 Supported by:
  • 2. 0 5 10 15 20 25 30 35 40 45 50 55 60 # LHCb long tracks 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Efficiency Found 103002 of 109733 (eff 93.87%) False positive rate = 0.251 per event Asymmetric cost function Found 96616 of 109733 (eff 88.05%) False positive rate = 0.0485 per event Symmetric cost function Events in sample = 20K Training sample = 240K 0 5 10 15 20 25 30 35 40 45 50 55 60 # LHCb long tracks 102 103 104 PVs 1/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 3. Tracking in the LHCb upgrade Introduction The changes • 30 MHz software trigger • 7.6 PVs per event (Poisson distribution) • Roughly 5.5 visible PVs per event The problem • Much higher pileup • Very little time to do the tracking • Current algorithms too slow We need to rethink our algorithms from the ground up... 2/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 4. Vertices and tracks Introduction Vertices • Events contain ≈ 7 Primary Vertices (≈ 5 visible PVs) A PV should contain 5+ long tracks • Multiple Secondary Vertices (SVs) per event as well A SV should contain 2+ tracks Beams PV Track SV Adapt to machine learning? • Sparse 3D data (41M pixels) → rich 1D data • 1D convolutional neural nets • Highly parallelizable, GPU friendly • Opportunities to visualize learning process 3/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 5. A hybrid ML approach Introduction Tracking Kernel generation Make predictions CNNs Interpret results Truth Training Validation Machine learning features (so far) • Prototracking converts sparse 3D dataset to feature-rich 1D dataset • Easy and effective visualization due to 1D nature • Even simple networks can provide interesting results What follows is a proof of principle implementation for finding PVs. 4/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 6. Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 7. Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 8. Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored • Tracking (full or partial) z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 9. Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored • Tracking (full or partial) • Fill in each voxel center with Gaussian PDF z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 10. Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored • Tracking (full or partial) • Fill in each voxel center with Gaussian PDF • PDF for each (proto)track is combined z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 11. Kernel generation Design Tracking procedure • Hits lie on the 26 planes • For simplicity, only 3 tracks shown • Make a 3D grid of voxels (2D shown) • Note: only z will be fully calculated and stored • Tracking (full or partial) • Fill in each voxel center with Gaussian PDF • PDF for each (proto)track is combined • Fill z “histogram” with maximum KDE value in xy z axis (along the beam) x Kernel PV 5/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 12. Example of z KDE histogram Design 100 50 0 50 100 150 200 250 300 z values [mm] 0 500 1000 1500 2000 DensityofKernel Kernel LHCb PVs Other PVs LHCb SVs Other SVs Note: All events from toy detector simulation Human learning • Peaks generally correspond to PVs and SVs Challenges • Vertex may be offset from peak • Vertices interact 6/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 13. Target distribution Design Build target distribution • True PV position as the mean of Gaussian • σ (standard deviation) is 100 µm (simplification) • Fill bins with integrated PDF within ±3 bins (±300 µm) 7/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 14. Neural network architecture Design Inputs 1 2 3 · · · 25 26 · · · 3998 3999 4000 Convolution Width: 25 Channels: 1 → 25 25 Channels 1 2 3 · · · 15 16 · · · 3998 3999 4000 Convolution Width: 15 Channels: 25 → 25 25 Channels 1 2 3 · · · 15 16 · · · 3998 3999 4000 Convolution Width: 15 Channels: 25 → 25 25 Channels 1 2 3 4 5 6 · · · 3998 3999 4000 Convolution Width: 5 Channels: 25 → 1 1 Channel 1 2 3 · · · 91 92 · · · 3998 3999 4000 Convolution Width: 91 Channels: 1 → 1 Output 1 2 3 4 5 · · · 3997 3998 3999 4000 -x x y Leaky relu -x x y Leaky relu -x x y Leaky relu -x x y Leaky relu -x x y Softplus 8/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 15. Cost function Design 10 6 10 5 10 4 10 3 10 2 10 1 100 yhat 0 10 20 30 40 50 60 cost 0.0 0.2 0.4 0.6 0.8 yhat 0 5 10 15 20 25 30 cost Asym. Cost for y = 0.10 Symm. Cost for y = 0.10 Asym. Cost for y = 0.30 Symm. Cost for y = 0.30 Asym. Cost for y = 1e-5 Symm. Cost for y = 1e-5 0.2 0.4 0.6 0.8 1.0 yhat 0 2 4 6 8 10 cost Approach • Symmetric cost function: low FP but low efficiency • Adding asymmetry term controls trade-off for FP vs. efficiency 9/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 16. False Positive and efficiency rates Results 88 89 90 91 92 93 94 Efficiency [%] 0.05 0.10 0.15 0.20 0.25FPperevent Symm cost Most asymm cost 88 89 90 91 92 93 94 Efficiency [%] 10 1 6×10 2 2×10 1 FPperevent Symm cost Most asymm cost Search for PVs (handwritten, maybe not optimial) • Search ±5 bins (±500µm) around a true PV • At least 3 bins with predicted probability > 1% and integrated probability > 20%. Tunable efficiency vs. FP • The asymmetry parameter controls FP vs. efficiency 10/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 17. Compare predictions with targets: Examples Results 0 100 200 300 400 500 KernelDensity True: 197.461 mm Pred: 197.396 mm : -65 µm Event 5 @ 197.4 mm: PV found Kernel Density 195.00 196.00 197.00 198.00 199.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked PV found example 0 200 400 600 800 1000 1200 1400 1600 KernelDensity True: 36.068 mm Pred: 36.400 mm : 332 µm Event 6 @ 36.1 mm: PV found Kernel Density 34.00 35.00 36.00 37.00 38.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked PV found example 11/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 18. Compare predictions with targets: When it works Results 0 200 400 600 800 1000 1200 KernelDensity True: 48.904 mm Pred: 48.954 mm : 50 µm Event 0 @ 48.9 mm: PV found Kernel Density 47.00 48.00 49.00 50.00 51.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked PV found example 0 50 100 150 200 KernelDensity Pred: 0.976 mm Event 0 @ 1.0 mm: Masked Kernel Density -1.00 0.00 1.00 2.00 3.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked Masked (<5 tracks) example 12/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 19. Compare predictions with targets: When it fails Results 0 50 100 150 200 250 KernelDensity Pred: 65.696 mm Event 2 @ 65.7 mm: False positive Kernel Density 64.00 65.00 66.00 67.00 68.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted False Positive example 0 100 200 300 400 500 KernelDensity True: 51.898 mm Event 3 @ 51.9 mm: PV not found Kernel Density 50.00 51.00 52.00 53.00 54.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked PV not found example 13/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 20. Future addition: xy information Future plans Adding xy information • Point of maximum z in xy available • Extra information: sharp discontinuities between PVs • Need iterative approach or “reduced importance” What about a full 2D kernel? • Not needed for LHCb currently (large xy, “low” z overlap) • Might be useful for other detectors! 0 500 1000 1500 2000 KernelDensity True: 114.622 mm Pred: 114.597 mm : -26 µm Event 2 @ 114.6 mm: PV found Kernel Density 113.00 114.00 115.00 116.00 117.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 14/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 21. Conclusions and plans Future plans 0 5 10 15 20 25 30 35 40 45 50 55 60 # LHCb long tracks 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Efficiency • Proof-of-Principle established: a hybrid ML algorithm using a 1-dimensional KDE processed by a 5-layer CNN finds primary vertices with efficiencies and false positive rates similar to traditional algorithms. • Efficiency is tunable; increasing the efficiency also increases the false positive rate. • Adding information should improve performance. • can add KDE (x,y) information to algorithm • can associate tracks to PV candidates, then iterate. • Next steps: train with full LHCb MC and deploy inference engine in LHCb Hlt1 framework. • Beyond LHCb • approach might work for ATLAS and CMS (in 2D?); • algorithm is an interesting ML laboratory. 15/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 22. Final words Future plans Source code: • https://gitlab.cern.ch/LHCb-Reco-Dev/pv-finder • Runnable with Conda on macOS and Linux Run: conda env create -f environment-gpu.yml Python 3.6+ and PyTorch used for machine learning code Generation now available too using the new Conda-Forge ROOT and Pythia8 packages Supported by: • NSF OAC-1836650: IRIS-HEP • NSF OAC-1740102: SI2:SSE • NSF OAC-1739772: SI2:SSE 16/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 23. Final words Future plans Questions? Source code: • https://gitlab.cern.ch/LHCb-Reco-Dev/pv-finder • Runnable with Conda on macOS and Linux Run: conda env create -f environment-gpu.yml Python 3.6+ and PyTorch used for machine learning code Generation now available too using the new Conda-Forge ROOT and Pythia8 packages Supported by: • NSF OAC-1836650: IRIS-HEP • NSF OAC-1740102: SI2:SSE • NSF OAC-1739772: SI2:SSE 16/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 24. More predictions with targets (1) Backup 0 50 100 150 200 KernelDensity True: 221.595 mm Pred: 221.546 mm : -49 µm Event 5 @ 221.5 mm: PV found Kernel Density 219.00 220.00 221.00 222.00 223.00 224.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 0 500 1000 1500 2000 KernelDensity True: 114.622 mm Pred: 114.597 mm : -26 µm Event 2 @ 114.6 mm: PV found Kernel Density 113.00 114.00 115.00 116.00 117.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 17/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 25. More predictions with targets (2) Backup 0 200 400 600 800 1000 1200 1400 1600 KernelDensity True: 129.336 mm Pred: 129.337 mm : 1 µm Event 6 @ 129.3 mm: PV found Kernel Density 127.00 128.00 129.00 130.00 131.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 0 500 1000 1500 2000 KernelDensity True: 143.224 mm Pred: 143.199 mm : -25 µm Event 6 @ 143.2 mm: PV found Kernel Density 141.00 142.00 143.00 144.00 145.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 18/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 26. More predictions with targets (3) Backup 0 50 100 150 200 250 300 350 400 KernelDensity True: 150.650 mm Pred: 150.416 mm : -234 µm Event 6 @ 150.4 mm: PV found Kernel Density 148.00 149.00 150.00 151.00 152.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 0 500 1000 1500 2000 2500 KernelDensity True: 179.560 mm Pred: 179.591 mm : 31 µm Event 6 @ 179.6 mm: PV found Kernel Density 178.00 179.00 180.00 181.00 182.00 z values [mm] 150 100 50 0 50 100 150 xymaximum[m] x y 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted Masked 19/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 27. The VELO Backup Tracks • Originate from vertices (not shown) • Hits originate from tracks • We only know the true track in simulation • Nearly straight, but tracks may scatter in material The VELO • A set of 26 planes that detect tracks • Tracks should hit one or more pixels per plane • Sparse 3D dataset (41M pixels) 20/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019
  • 28. Questions for other experiments Backup • Beam width (x, y): 40 µm for LHCb, what is yours? • Transverse resolution: 5–15 µm for LHCb depending on number of tracks, what is yours? • Longitudinal resolution: 40–100 µm for LHCb depending on number of tracks, what is yours? • Cleaning up prototracks based on IP could simplify kernel • Can prototracking be done in the triggers? 21/16Fang, Schreiner, Sokoloff, Weisser, Williams A hybrid deep learning approach to vertexing April 3, 2019