Top Tagging with Lorentz Boost Networks and Simulation of Electromagnetic Showers with a Wasserstein GAN

Transcription

1 Top Tagging with Lorentz Boost Networks and Simulation of Electromagnetic Showers with a Wasserstein GAN Y. Rath, M. Erdmann, B. Fischer, L. Geiger, E. Geiser, J.Glombitza, D. Noll, T. Quast, M. Rieger, D. Schmidt, M. Wirtz III. Physikalisches Institut A, RWTH Aachen University

2 2 Introduction Presenting two applications of deep learning related to jet physics Lorentz Boost Networks (LBN) as a network architecture exploiting physical structure Application to top-tagging Fast simulation of electromagnetic showers with a Wasserstein GAN using label conditioning

3 Top Tagging with Lorentz Boost Networks

4 LBN - Motivation 4 Success of deep learning in computer science through dedicated architectures exploiting problem structure [Zeiler & Fergus 2013], adapted by Yann LeCun Udacity Course 730, Deep Learning Similar developments in physics, e.g. LoLa, Recursive NN (and others!) LBN: Utilize knowledge of particle combinations, rest frames through Lorentz boosts

5 LBN Structure 5 Input: Particle four vectors Combine into particles and rest frames (trainable), perform Lorentz boost Physical interpretation of network weights

6 6 LBN Structure (II) Build generic features from boosted particles, e.g. masses, pair-wise angles Fully connected layers to combine information

7 7 Feature Construction Example of feature construction: cos(θ*)

8 8 Top Tagging with LBN Example application: Top-tagging Distinguish boosted top quarks from QCD jets Use public dataset based on arxiv: enables comparison of diferent algorithms

9 9 LBN Setup Input ordering: Based on clustering history Cluster sub-jets with anti-kt, R=0.25 Order constituents based on clustering history Order sub-jets based on clustering order with anti-kt, R=0.8 LBN architecture: 50 combined particles and rest frames 4 feedforward layers at the end

10 10 Performance LBN competitive with other sophisticated approaches Only minor diferences, hitting physical limit of dataset? Additional method comparisons will follow

11 Simulation of Electromagnetic Showers

12 12 Introduction - WGAN Calorimeter simulations computationally very expensive Ongoing research into simulation with Generative Adversarial Networks (GANs) See e.g. LAGAN, CaloGAN Promise speed-up of several orders of magnitude (~10³ to 10⁵) compared to full simulation

13 13 Experimental Setup Electromagnetic compartment of a CMS High Granularity Calorimeter (HGCAL) prototype Seven sensitive layers with >100 hexagonal pixels each Training data: Geant4 based simulation of electron showers with GeV, diferent impact positions

14 14 Generative Adversarial Networks Concept: NN generates samples from noise following 'real' data distribution Adversary tries to distinguish generated from real events Feedback to the generator Training requires careful balance of both networks Variant: Wasserstein GAN

15 15 WGAN Concept Wasserstein metric as distance measure Earth mover distance : Work required to move one distribution to the other (mass x distance) Can be realized by a neural network with limited gradients, the 'critic' Meaningful gradients everywhere

16 WGAN Setup 16 Translate hexagonal pixels to cartesian coordinate system Add starting conditions (energy, impact position) to inputs Generator Latent input + starting conditions (10 + 3) x 1 x 1 Critic Shower (12x15x7) linear 192x1x1 22xxFully connected 192x1x1 2 x Reshape Fully connected 192x1x1 Reshape 3x4x16 3x4x16 7x Reshape DeConv 33xxDeConv 3 x Convolution DeConv Convolution Conv2D 3x4x16 24x32x64 24x32x64 24x32x64 20x24x1 20x24x1 20x24x1... concat 3 x Conv2D Starting conditions 3x1x1 2 x Fully con. 192x1x1 Reshape 3 x Conv2D 14x17x128 Locally connected 12x15x7 14x17x128 Locally connected 12x15x7 Shower (12x15x7) Critic (1x1x1) 3x4x16

17 17 Constrainer Networks Simulated events should depend on starting conditions (here: initial particle energy, impact position) Use label conditioning Introduced by auxiliary classifer GANs (AC-GANs) Starting conditions given to both the generator and the critic Train constrainer networks to reconstruct energy/impact position of real samples Additional loss term for the generator

18 18 Shower Generation Visual inspection: Showers scale with electron energy, move according to impact position To study full set of events, look at average occupancy

19 19 Validation Compare observable distributions between GEANT4 and WGAN Overall good agreement 70 GeV electrons (grey) not part of training set Assess interpolation capabilities

20 20 Validation (II) Beyond observable distributions: Correlations also well modelled Only diference: Low energy densities underrepresented Sparsity related variables challenge for GANs ~10% contribution to the signal

21 21 Summary LBN physics-motivated NN architecture Integrates particle combinations and Lorentz boosting Example application of top-tagging Simulation of electromagnetic showers with GAN Wasserstein distance to improve training stability Constrainer networks to incorporate initial conditions