Event Generation and Statistical Sampling with Deep Generative - - PowerPoint PPT Presentation

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Event Generation and Statistical Sampling with Deep Generative - - PowerPoint PPT Presentation

Nov 02, 2022 443 likes •686 views

Event Generation and Statistical Sampling with Deep Generative Models Rob Verheyen Introduction Event generation is really hard! 2 Introduction Can we use deep neural networks to do event generation? Possible applications: Faster

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Event Generation and Statistical Sampling with Deep Generative Models

Rob Verheyen

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Introduction

Event generation is really hard!

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Introduction

Can we use deep neural networks to do event generation? Possible applications:

  • Faster
  • Data driven generators
  • Targeted event generation
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Introduction

Study of different types of unsupervised generative models

  • Generative Adversarial Networks
  • Variational Autoencoders
  • Buffer Variational Autoencoder

Can these networks be used for event generation?

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Generative Adversarial Networks (GANs)

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Generative Adversarial Networks

Two networks (Generator & Discriminator) that play a game against each other

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Generative Adversarial Networks

Loss function: Nash equilibrium:

pdata(x) = pgen(x)

D(x) = 1 2

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Generative Adversarial Networks

1812.04948

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Variational Autoencoders (VAEs)

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Autoencoders

  • Data is encoded into latent space
  • Dim of latent space is often lower than dim of data
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Variational Autoencoders

Add degree of randomness to training procedure

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Variational Autoencoders

Points in latent space are ordered

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Variational Autoencoders

Loss function

Mean squared error Kullback–Leibler divergence

LVAE = (1 − ) 1 N (~ xi − ~ yi)2 + DKL(N(µi, i), N(0, 1))

MSE : Gaussians prefer being very narrow KL Div: Gaussians prefer being close to

N(0, 1)

is a hyperparameter: tune by hand

β

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Information Buffer

The latent space representation of our datapoints are now ordered But we can do better: Create information buffer

p(z) = 1 n

n

X

i

N(µi, σi)

Representation of distribution of training data in latent space Normally, one would now sample from in latent space

N(0, 1)

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Results

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Toy Model

1 → 2

decay with uniform angles and no exact momentum conservation Trained on four-vectors

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Top pair production

  • One top required to decay leptonically

5 × 105

  • Number of training points
  • Jets with pT > 20 GeV

Event generation with the B-VAE is faster!

O(108)

MG5 aMC@NLO 6.3.2 + Pythia 8.2 + Delphes 3

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Top pair production

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Latent space distributions

Distributions are still Gaussian-like Some have sharp cutoffs: Unphysical events outside Information buffer very important!

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Latent Space Principal Component Analysis

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Latent Space Principal Component Analysis

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Possible Applications

Most direct application: Importance sampling for ME generation

σ ∝ Z dΦ|M(Φ)|2 = Z dΦ p(Φ)|M(Φ)|2 p(Φ)

Current methods: VEGAS Recent ML techniques: Latent variable models

1810.11509

e+e− → qg¯ q efficiency:

  • VEGAS: ~4%
  • LVM: ~ 65%
  • B-VAE: ???
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Applications?

  • Data-driven event generators
  • Targeted event generation
  • Applications outside High Energy Physics?
  • ???