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Endcap predictions overlaid with target hit coordinates
Found track in the barrel of ITk like geometry](https://image.slidesharecdn.com/mlonfpgaforum-250126182000-e0bd2570/85/The-basic-ML-architecture-for-all-modern-PCs-and-game-consoles-is-similar-13-320.jpg)
The basic ML architecture for all modern PCs and game consoles is similar
- 1. ML Methods for Online Tracking Alex Gekow 08 Feb 2024 1
- 2. Online Vs. Offline Tracking Offline Tracking ● ∞ time to run algorithms ● Huge amount of available cpu ● Highly specialized precision algorithms 2 Online Tracking ● L1 Latency constraint ● Limited budget for hardware ● Balance tracking precision with computational cost/speed EF Tracking Goal: to run tracking at trigger level in 𝝁=200 pileup conditions Tracking Performance Computational Performance
- 3. Why Machine Learning? Machine learning algorithms and the hardware and software required to deploy them is a rapidly expanding domain⸺we can utilize, learn from, and contribute to this development (e.g Tesla FSD, Apple neural engine, Google tensor…) 3
- 4. Why Machine Learning? Neural networks have proven to be a powerful and versatile tool over a wide range of problems They Excel at exploiting correlations between input parameters to produce a non-linear mapping f: ℝinput ⟶ ℝouptut Adapting offline algorithms for new hardware has proven difficult. Why not try to develop ML algorithms for tracking to leverage newer, faster hardware? 4
- 5. Start Simple - Fake Track Classifier Classification is the most common task for Neural Networks Train a NN to classify track candidates as True/Fake The output of the NN is highly dependent on the definition of fake “tracks” which are in turn highly dependent on the algorithm used to generate the fake tracks 5
- 6. ● Hough transform is another inexpensive & fast algorithm being studied in parallel ○ Comes at the cost of a large number of fake hit combinations ● The algorithm requires a fake removal step ● Offline tracking does this via 𝝌2 calculation ○ Can we approximate this figure of merit (or come up with another) using a NN? Problem statement in ML language: “Classify a sequence of hits as true or fake given the 3D coordinates of the candidate tracks hits” ML Classifier = fast figure of merit generator 6 Hough Transform Filter
- 7. Hough Transform Filter Classification is the most common application of ML! Operating on HT output offers a perfect environment to test our hypothesis 1. Pre-processing a. Rotate all proto-tracks to initially lie along 𝜙=0 b. Scale each hit x/y/z coordinate to be O(1) 2. Score each proto-track with NN Classifier 3. Overlap removal via hit warrior a. Compare proto-tracks with more than X shared hits b. Keep only the highest scored proto-track Reduces the number of fake tracks by a factor two orders of magnitude while retaining a high purity of true track candidates *Similar in principle to scoring of conformal map here, but using all hits instead of only three https://indico.cern.ch/event/1002734/contributions/4231250/attachments/2192619/3706144/CommodityTF_210218.pdf 7
- 8. Path Finder Step up complexity: Can we use ML to find proto-tracks? 8 Assume spacepoint formation of hits and seeds of three hits in the inner-most pixel layers are available upstream for the pattern recognition algorithm 1. Input 3 hits into a NN 2. Predict the coordinate of the 4th hit 3. Look for hits in the detector nearby the predicted location 4. Append all compatible hits to the seed 5. Repeat until the edge of the detector is reached or no compatible hits are found
- 9. Parallelized Predictions Without much external information (i.e magnetic field, detector geometry…) during run time, we can get simultaneous predictions for O(100-1000) proto-tracks at a time 9 The un-reliance of external information being bussed to FPGA saves time and memory :)
- 10. Performance Metrics Our goal is to produce sufficiently few proto-tracks for overlap/fake removal while retaining high efficiency 1. Study the residuals between predicted and true hits to minimize the search window as a function of (r,η) 2. Count the number of fake proto-tracks generated per event a. Most will be removed by hit warrior 3. Tune the fake track classifier threshold cut At this stage we are NOT interested in precision. Simply constrain the number of found proto-tracks in order to remain within latency budget Precision fit will come afterwards 10 For all tracks within |η|<0.8 |z0 | < 150mm |d0 | < 2mm. Most tracks are true duplicates due to multiple hits in SCT layers.
- 11. Barrel Only Application 11 The algorithm was tested and validated in the barrel of ITK Efficiency defined as : NMatched / NConstructed where a “track” is considered matched iff there exists a constructed proto-track such that more than half of the hits after the seed come from a unique particle Comparable performance to ODD geometry https://arxiv.org/abs/2212.02348 Prediction Residuals, NOT track resolution! Residuals to be compared to green band in CKF analogy Limited/worse precision is OK so long as the gain in speed outweighs the number of found proto-tracks
- 12. Overview of Algorithms 12 The irregular orientation of detector layers of ITk make straightforward coordinate prediction difficult for a NN If spacepoints and the detector layer are given as input, the NN learns to associate discrete sets of coordinates to each detector layer https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PLOTS/ITK-2020-002/ NN Classifier Xt-2 Yt-2 Zt-2 Xt-1 Yt-1 Zt-1 Xt Yt Zt Volume ID Layer ID NN Hit Predictor Xt+1 Yt+1 Zt+1
- 13. Full Detector Predictions 13 ● Target Hits ● Predicted Hits Z (normalized coordinates) ⍴ (normalized coordinates) Y [mm] Predicted True X [mm] 0 -200 -400 -600 True Seed Endcap predictions overlaid with target hit coordinates Found track in the barrel of ITk like geometry
- 14. Improvements to ML Models Improving the predictive power of the NN improves efficiency and reduces the fake rate. Several methods under investigation 1. Metric learning for layer/volume encodings a. Exploit relationships between neighboring regions of the detector 2. Recurrent models a. Exploit the sequential nature of our data 3. Fine tuned loss functions a. Mean-squared-error assumes constant uncertainty. Remove this assumption for better results (more difficult to train) 14
- 15. Track Parameter Estimation 15 Seeding Track Finding Fake Removal Linear Fit Precision Track Fit Potential EF-Tracking Pipline: … Hough Transform GNN ML Path Finding Hit Condensation NN Fake Track Filter Parameter Estimation to provide initial guess for Kalman Filter Is the linear fit redundant? Can the NN used for fake track removal also provide track parameter estimates?
- 16. 16 Track Parameter Estimation Warning! Not realistic results. Proof of principle only ● Initial non-rigorous testing shows promise in NN capability to estimate track parameters ● NN = Linear fit under certain conditions ● Can it outperform linear fit? Does it need to? 1. Currently generating and studying optimal training data 2. Interface to precision fitting to determine the effects of estimates used as initial guess Extremely Preliminary! Bug in z0 being fixed
- 17. FPGA Implementation We have been using relatively small networks (2-3 hidden layers, 32-64 nodes) Execution on FPGA takes only 50 ns (10 clock cycles) and is perfectly pipelined To make N predictions, we require N+10 clock cycles 17 Clock Output Perfectly pipelined Input
- 18. FPGA Implementation NN Models should be compact so as to easily fit on FPGA Sharing resources with other algorithms also running on FPGA Firmware and test vectors actively being developed! 18 Latency (ns) LUT (%) FF (%) BRAM/URAM (%) DSP (%) Ambiguity Resolution 50 18 1 <0.01 31 Hit Prediction 50 7 0.5 <0.01 21 Xilinx Alveo U250 FPGA resource usage estimates for neural networks * rough estimates as NN architecture may change Hit prediction only includes coordinate hit prediction and not layer classification Classification network is smaller than hit prediction network
- 19. Conclusion ● Online tracking involves re-evaluating particle tracking problems under light of new constraints (latency, throughput, hardware…) ● Versatility makes for a large space of potential solutions ○ Full ML tracking (GNN) ○ ML as a tool in a larger toolkit (Fake track filter, pattern recognition, parameter estimation) ● Smaller scale ML approaches can be very flexible and fit readily on FPGA/GPU ● Need to interface new algorithms with existing “traditional” algorithms ■ Core software and firmware development ongoing by EF-Tracking team 19 + = (?)