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LHCb Computing Workshop 2018: PV finding with CNNs

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Talk given at the LHCb Computing Workshop, in Chia, Sardinia, Italy.

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LHCb Computing Workshop 2018: PV finding with CNNs

  1. 1. PV finding with CNNs LHCb Computing Workshop 2018 Rui Fang Henry Schreiner Mike Sokoloff September 26, 2018 The University of Cincinnati
  2. 2. Objectives Introduction Physics • Iterative tracking and vertexing may allow high efficiency, high speed, highly parallel algorithms: Use proto-tracks to find primary vertex (PV) candidates Use PV candidates to augment more complete tracking Find more PVs plus secondary vertices • PVs available quickly Machine learning • Sparse 3D data (41M pixels) → rich 1D dataset • 1D convolutional neural net • Great opportunities to visualize learning process Computation • Highly parallelizable • Well suited to GPUs 1/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  3. 3. Tracking in the LHCb Upgrade Introduction The changes • 30 MHz software trigger • 7.6 PVs per event (Poisson distribution) 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 PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  4. 4. A Hybrid ML Approach Introduction Prototracking → Kernel generation → CNN to find PVs → Informed tracking Prototracking • Ultra-simple/fast • Triplets only • Used for kernel only Vertexing • High efficiency • Low false positive rate • Useful for other reasons Tracking • Faster (effect TBD) • Uses search windows • Higher efficiency Machine learning features (so far) • Prototracking converts sparse 3D dataset to feature-rich 1D dataset • Easy and effective visualization due to 1D nature • Can see results with simple unoptimized 2-layer CNN + 1-layer linear What follows is a proof of principle implementation for finding PVs. 3/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  5. 5. Vertices and Tracks Introduction Vertices • Events contain ≈ 7 Primary Vertices (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 • We are developing a way to find PVs and SVs using hit triplets • This will enable an iterative tracking algorithm 4/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  6. 6. Kernel Generation Design Hits • Hits lie on the 26 planes • Tracks come from PVs and SVs • For simplicity, only 3 tracks shown • Hits are sorted in r (distance from LHC beam) z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  7. 7. Kernel Generation Design Grid • 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 PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  8. 8. Kernel Generation Design Prototrack • Start with maximum r • Find triplet with χ2 < 10 • Mark “used” all other hits within χ2 < 9 • Note: triplet is stored Kernel • Fill in each voxel center with gaussian PDF • PDF is combined for each prototrack z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  9. 9. Kernel Generation Design Prototrack • Start with maximum r • Find triplet with χ2 < 10 • Mark “used” all other hits within χ2 < 9 • Note: triplet is stored Kernel • Fill in each voxel center with gaussian PDF • PDF is combined for each prototrack z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  10. 10. Kernel Generation Design Prototrack • Start with maximum r • Find triplet with χ2 < 10 • Mark “used” all other hits within χ2 < 9 • Note: triplet is stored Kernel • Fill in each voxel center with gaussian PDF • PDF is combined for each prototrack z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  11. 11. Kernel Generation Design Kernel • Highest PDF density at vertices • Stores z histogram with maximum PDF values Details • x-y grid initially very coarse • Search performed on maximum x-y grid cell using stored triplets to recalculate PDF z axis (along the beam) x PV 5/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  12. 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 Human learning • Peaks generally correspond to PVs and SVs Challenges • Vertex may be offset from peak • Vertices interact 6/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  13. 13. Target distribution Design Build target distribution • real PV position as the mean of Gaussian distribution • σ(standard deviation) is 100 µm • calculate the cdf of each bin around of the mean, within ± 3 bins (± 300 µm ) 7/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  14. 14. Neural network architecture with two convolutional layers Design • Activation function for hidden layers: Leaky ReLu • Activation function for output layer: Sigmoid 8/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  15. 15. Activation function Design Activation function for hidden layers Activation function for output layer 9/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  16. 16. Cost Function Design Approach • Cost function should be similar to Cross-Entropy for y → 0, y → 1; cost = − y ln ˆy + (1 − y) ln(1 − ˆy) • Should be symmetric with respect to r = (ˆy/y) & 1/r Sum Over Bins ri ≡ (ˆyi + )/(yi + ) (1) zi ≡ 2 ri ri + 1/ri (2) our cost = bins − ln zi (3) 10/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  17. 17. Cost, efficiency, and false positive rate: 2 convolutionial layers Results 11/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  18. 18. Cost, efficiency, and false positive rate: 3 convolutionial layers Results 12/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  19. 19. Compare Predictions with Targets (3 convolutional layers) Results 86.00 87.00 88.00 89.00 90.00 z values [mm] 0 50 100 150 200 250 300 350 400 KernelDensity True: 88.062 mm Event 0: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 99.00 100.00 101.00 102.00 103.00 z values [mm] 0 500 1000 1500 KernelDensity True: 100.825 mm Pred: 100.726 mm : 99 µm Event 0: PV found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 135.00 136.00 137.00 138.00 139.00 z values [mm] 0 200 400 600 800 1000 1200 1400 1600 KernelDensity True: 136.602 mm Pred: 136.601 mm : 2 µm Event 0: PV found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 182.00 183.00 184.00 185.00 186.00 z values [mm] 0 200 400 600 800 1000 1200 KernelDensity True: 183.668 mm Pred: 183.734 mm : 66 µm Event 0: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 13/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  20. 20. Compare Predictions with Targets (3 convolutional layers) Results 60.00 61.00 62.00 63.00 64.00 z values [mm] 0 100 200 300 400 500 600 KernelDensity Pred: 61.784 mm Event 2: False positive Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 89.00 90.00 91.00 92.00 93.00 z values [mm] 0 200 400 600 800 1000 KernelDensity True: 91.279 mm Pred: 91.244 mm : 35 µm Event 2: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 109.00 110.00 111.00 112.00 113.00 z values [mm] 0 50 100 150 200 KernelDensity True: 110.675 mm Event 2: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 127.00 128.00 129.00 130.00 131.00 z values [mm] 0 500 1000 1500 2000 KernelDensity True: 128.742 mm Pred: 128.720 mm : 22 µm Event 2: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 14/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  21. 21. Efficiencies and False Positive Rates Results parameter 2 CVN Layers 3 CVN Layers 4 CVN Layers (Efficiency) = TP TP+FN ≈ 58% ≈ 70% ≈ 75% False Positive rate = FP number of events ≈ 0.07 ≈ 0.08 ≈ 0.13 Found Not found Real PV True positive False negative Not a real PV False positive True negative True Positive • search ±5 bins (±500µm) around a real PV • at least 3 (4) bins with predicted probability > 1% and integrated probability > 20%. False Positive • at least 3 (4) bins with individual probabilities > 1% and integrated probability > 20%. • no real PV within ±5 bins (±500µm) of that cluster. 15/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  22. 22. Future Plans Future Plans Some Ideas • Model PV resolution as a function of the number of tracks; right now, the target function is always generated assuming σz = 100 µm; • Extract σz from predicted signals; • Extend algorithm to find PV (x, y, z) target functions, not just PV z target functions. • Mask PVs with < 5 long tracks (not labeled as PVs now) • Ask the algorithm (very nicely) to find Secondary Vertices as well; it should probably use both the original KDE histogram and the learned PV histogram as inputs. It may be possible to re-use some of the features generated by the convolutional layers. • Integrate KDE plus PV-finding code into an iterative tracking and vertexing algorithm; well-defined vertex positions may be able to serve as anchors for good tracks, restricting the roads to be searched. • Optimize NN architecture to (i) improve learning, (ii) improve learning speed, (iii) minimize inference costs (cycles and memory). Increase training sample. 16/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  23. 23. Compare Predictions with Targets (3 convolutional layers) Backup 31.00 32.00 33.00 34.00 35.00 z values [mm] 0 200 400 600 800 KernelDensity True: 32.975 mm Pred: 32.766 mm : 209 µm Event 1: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 92.00 93.00 94.00 95.00 96.00 z values [mm] 0 50 100 150 200 250 300 350 400 KernelDensity True: 93.727 mm Event 1: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 107.00 108.00 109.00 110.00 111.00 112.00 z values [mm] 0 100 200 300 400 500 KernelDensity True: 109.659 mm Pred: 109.530 mm : 129 µm Event 1: PV found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 116.00 117.00 118.00 119.00 120.00 z values [mm] 0 200 400 600 800 1000 KernelDensity True: 118.176 mm Pred: 118.224 mm : 48 µm Event 1: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Probability Target Predicted 17/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  24. 24. Compare Predictions with Targets (3 convolutional layers) Backup 138.00 139.00 140.00 141.00 142.00 z values [mm] 0 500 1000 1500 KernelDensity True: 139.889 mm Pred: 139.861 mm : 28 µm Event 1: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Probability Target Predicted 152.00 153.00 154.00 155.00 156.00 z values [mm] 0 500 1000 1500 2000 KernelDensity True: 153.906 mm Pred: 153.864 mm : 42 µm Event 1: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 194.00 195.00 196.00 197.00 198.00 z values [mm] 0 50 100 150 200 250 KernelDensity True: 195.838 mm Event 1: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 222.00 223.00 224.00 225.00 226.00 z values [mm] 0 50 100 150 200 250 300 350 400 KernelDensity True: 224.386 mm Pred: 224.583 mm : 197 µm Event 1: PV found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 18/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  25. 25. More Predictions with Targets (3 CVN layers) Backup 159.00 160.00 161.00 162.00 163.00 z values [mm] 0 20 40 60 80 100 120 KernelDensity True: 160.920 mm Event 2: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 65.00 66.00 67.00 68.00 69.00 z values [mm] 0 500 1000 1500 2000 KernelDensity True: 66.923 mm Pred: 66.964 mm : 42 µm Event 3: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 66.00 67.00 68.00 69.00 70.00 z values [mm] 0 500 1000 1500 2000 KernelDensity True: 67.930 mm Event 3: PV not found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 108.00 109.00 110.00 111.00 112.00 z values [mm] 0 200 400 600 800 1000 1200 KernelDensity True: 110.449 mm Pred: 110.413 mm : 36 µm Event 3: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 19/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  26. 26. More Predictions with Targets (3 CVN layers) Backup 120.00 121.00 122.00 123.00 124.00 z values [mm] 0 100 200 300 400 500 600 700 KernelDensity True: 122.303 mm Pred: 122.261 mm : 42 µm Event 3: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 208.00 209.00 210.00 211.00 212.00 z values [mm] 0 50 100 150 200 250 300 KernelDensity True: 210.210 mm Pred: 210.417 mm : 207 µm Event 3: PV found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 239.00 240.00 241.00 242.00 243.00 z values [mm] 0 10 20 30 40 50 60 70 KernelDensity True: 240.865 mm Event 3: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 17.00 18.00 19.00 20.00 21.00 z values [mm] 0 50 100 150 KernelDensity True: 19.440 mm Event 4: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 20/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  27. 27. More Predictions with Targets (3 CVN layers) Backup 71.00 72.00 73.00 74.00 75.00 z values [mm] 0 500 1000 1500 2000 KernelDensity True: 72.816 mm Pred: 72.764 mm : 52 µm Event 4: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 92.00 93.00 94.00 95.00 96.00 z values [mm] 0 100 200 300 400 KernelDensity True: 93.940 mm Pred: 93.959 mm : 19 µm Event 4: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 117.00 118.00 119.00 120.00 121.00 z values [mm] 0 200 400 600 800 KernelDensity True: 119.325 mm Pred: 119.513 mm : 188 µm Event 4: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 145.00 146.00 147.00 148.00 149.00 z values [mm] 0 50 100 150 200 250 300 350 400 KernelDensity True: 146.840 mm Pred: 146.923 mm : 84 µm Event 4: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 Probability Target Predicted 21/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  28. 28. More Predictions with Targets (3 CVN layers) Backup 195.00 196.00 197.00 198.00 199.00 z values [mm] 0 50 100 150 200 250 300 350 400 KernelDensity True: 197.279 mm Pred: 197.330 mm : 51 µm Event 4: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 60.00 61.00 62.00 63.00 64.00 z values [mm] 0 100 200 300 400 500 600 700 800 KernelDensity True: 62.436 mm Pred: 62.428 mm : 8 µm Event 5: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 72.00 73.00 74.00 75.00 76.00 z values [mm] 0 500 1000 1500 2000 2500 KernelDensity True: 73.592 mm Pred: 73.594 mm : 2 µm Event 5: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 98.00 99.00 100.00 101.00 102.00 z values [mm] 0 500 1000 1500 2000 2500 KernelDensity True: 100.143 mm Pred: 100.129 mm : 14 µm Event 5: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 22/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  29. 29. More Predictions with Targets (3 CVN layers) Backup 113.00 114.00 115.00 116.00 117.00 z values [mm] 0 200 400 600 800 1000 1200 KernelDensity True: 114.670 mm Pred: 114.756 mm : 86 µm Event 5: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 131.00 132.00 133.00 134.00 135.00 z values [mm] 0 50 100 150 200 250 KernelDensity True: 132.683 mm Pred: 132.622 mm : 61 µm Event 5: PV found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 156.00 157.00 158.00 159.00 160.00 z values [mm] 0 500 1000 1500 KernelDensity True: 158.211 mm Pred: 158.333 mm : 121 µm Event 5: PV found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 158.00 159.00 160.00 161.00 162.00 z values [mm] 0 500 1000 1500 KernelDensity True: 159.703 mm Event 5: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 23/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  30. 30. More Predictions with Targets (3 CVN layers) Backup 176.00 177.00 178.00 179.00 180.00 z values [mm] 0 200 400 600 800 1000 1200 KernelDensity True: 177.635 mm Pred: 177.621 mm : 14 µm Event 5: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 10.00 11.00 12.00 13.00 14.00 z values [mm] 0 50 100 150 200 250 300 350 KernelDensity True: 11.973 mm Event 6: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 50.00 51.00 52.00 53.00 54.00 55.00 z values [mm] 0 500 1000 1500 2000 KernelDensity True: 52.597 mm Pred: 52.550 mm : 47 µm Event 6: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Probability Target Predicted 56.00 57.00 58.00 59.00 60.00 61.00 z values [mm] 0 100 200 300 400 500 600 700 KernelDensity True: 58.490 mm Pred: 58.494 mm : 4 µm Event 6: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 24/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  31. 31. More Predictions with Targets (3 CVN layers) Backup 141.00 142.00 143.00 144.00 145.00 z values [mm] 0 500 1000 1500 2000 KernelDensity True: 143.421 mm Pred: 143.445 mm : 24 µm Event 6: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 147.00 148.00 149.00 150.00 151.00 z values [mm] 0 200 400 600 800 1000 1200 KernelDensity True: 148.586 mm Pred: 148.622 mm : 36 µm Event 6: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 229.00 230.00 231.00 232.00 233.00 z values [mm] 0 100 200 300 400 500 KernelDensity True: 230.789 mm Pred: 230.886 mm : 97 µm Event 6: PV found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 61.00 62.00 63.00 64.00 65.00 z values [mm] 0 50 100 150 200 KernelDensity True: 62.706 mm Event 7: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 25/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  32. 32. More Predictions with Targets (3 CVN layers) Backup 101.00 102.00 103.00 104.00 105.00 106.00 z values [mm] 0 100 200 300 400 KernelDensity True: 103.480 mm Event 7: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 105.00 106.00 107.00 108.00 109.00 z values [mm] 0 200 400 600 800 1000 KernelDensity True: 106.733 mm Pred: 106.813 mm : 80 µm Event 7: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 165.00 166.00 167.00 168.00 169.00 z values [mm] 0 200 400 600 800 1000 KernelDensity True: 167.395 mm Pred: 167.434 mm : 40 µm Event 7: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 18.00 19.00 20.00 21.00 22.00 z values [mm] 0 500 1000 1500 2000 KernelDensity True: 19.824 mm Pred: 19.877 mm : 53 µm Event 8: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 26/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  33. 33. More Predictions with Targets (3 CVN layers) Backup 113.00 114.00 115.00 116.00 117.00 z values [mm] 0 100 200 300 400 500 KernelDensity True: 114.807 mm Event 8: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 155.00 156.00 157.00 158.00 159.00 z values [mm] 0 200 400 600 800 1000 KernelDensity True: 157.448 mm Pred: 157.432 mm : 16 µm Event 8: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 161.00 162.00 163.00 164.00 165.00 z values [mm] 0 100 200 300 400 500 600 KernelDensity True: 162.676 mm Event 8: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 162.00 163.00 164.00 165.00 166.00 z values [mm] 0 100 200 300 400 500 600 KernelDensity True: 163.772 mm Event 8: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 27/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  34. 34. More Predictions with Targets (3 CVN layers) Backup 228.00 229.00 230.00 231.00 232.00 z values [mm] 0 50 100 150 200 KernelDensity True: 230.200 mm Event 8: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 1.00 2.00 3.00 4.00 5.00 z values [mm] 0 500 1000 1500 2000 2500 3000 KernelDensity True: 3.065 mm Pred: 3.068 mm : 3 µm Event 9: PV found Kernel Density 0.0 0.2 0.4 0.6 0.8 1.0 Probability Target Predicted 64.00 65.00 66.00 67.00 68.00 z values [mm] 0 50 100 150 200 250 300 350 KernelDensity True: 65.737 mm Event 9: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 153.00 154.00 155.00 156.00 157.00 z values [mm] 0 50 100 150 200 250 KernelDensity True: 155.047 mm Event 9: PV not found Kernel Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Probability Target Predicted 28/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018
  35. 35. 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) 29/16Fang, Schreiner, Sokoloff PV finding with CNNs: LHCb Computing Workshop 2018 September 26, 2018

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