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. PV finding with CNNs LHCb Computing Workshop 2018 Rui Fang Henry Schreiner Mike Sokoloff September 26, 2018 The University of Cincinnati
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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