Invertible Networks for LHC Theory
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Invertible
Networks
Tilman Plehn
Simulations
Events
Unfolding
Inverting
Measurements
Invertible Networks for LHC Theory
Tilman Plehn
Universität Heidelberg
Würzburg, 4/2021
Invertible
Networks Briefest introduction ever
Tilman Plehn
Neural network just a function
Simulations
Events – think fθ (x) just as f (x)
Unfolding – no parametrization, just very many values θ
Inverting
– θ-space the cool space [latent space]
Measurements
Construction through minimization
– define loss function L
– minimize through task
– evaluate x → f (x) in test/use case
LHC applications
– regression: parton momentum from jet constituents
matrix element over phase space
– classification: gluon/quark/bottom/top inside jet
– generation: sample r → f (r )
...
Invertible
Networks Challenges towards HL-LHC
Tilman Plehn
Paradigm shift: model searches −→ fundamental understanding of data
Simulations
Events – precision QCD
Unfolding – precision simulations
Inverting
– precision measurements
Measurements
⇒ Nothing fundamental without simulations [not even unsupervised...]
ATLAS Preliminary
2020 Computing Model -CPU: 2030: Aggressive R&D
2% 10%
8%
12%
13% Data Proc
7% MC-Full(Sim)
MC-Full(Rec)
MC-Fast(Sim)
MC-Fast(Rec)
EvGen
16% Heavy Ions
18% Data Deriv
MC Deriv
5% Analysis
8%
Invertible
Networks Challenges towards HL-LHC
Tilman Plehn
Paradigm shift: model searches −→ fundamental understanding of data
Simulations
Events – precision QCD
Unfolding – precision simulations
Inverting
– precision measurements
Measurements
⇒ Nothing fundamental without simulations [not even unsupervised...]
10-year HL-LHC requirements
– simulated event numbers ∼ expected events [factor 25 for HL-LHC]
– general move to NLO/NNLO [1%-2% error]
– higher relevant multiplicities [jet recoil, extra jets, WBF, etc.]
– new low-rate high-multiplicity backgrounds
– cutting-edge predictions not through generators [N3 LO in Pythia?]Invertible
Networks Challenges towards HL-LHC
Tilman Plehn
Paradigm shift: model searches −→ fundamental understanding of data
Simulations
Events – precision QCD
Unfolding – precision simulations
Inverting
– precision measurements
Measurements
⇒ Nothing fundamental without simulations [not even unsupervised...]
10-year HL-LHC requirements
– simulated event numbers ∼ expected events [factor 25 for HL-LHC]
– general move to NLO/NNLO [1%-2% error]
– higher relevant multiplicities [jet recoil, extra jets, WBF, etc.]
– new low-rate high-multiplicity backgrounds
– cutting-edge predictions not through generators [N3 LO in Pythia?]
Three ways to use ML
– improve current tools: iSherpa, ML-MadGraph, etc
– new tools: ML-generator-networks
– conceptual ideas in theory simulations and analysesInvertible
Networks Generative networks
Tilman Plehn
GANGogh [Bonafilia, Jones, Danyluk (2017)]
Simulations
Events – neural network: learned function f (x) [regression, classification]
Unfolding – can networks create new pieces of art?
Inverting map random numbers to image pixels?
Measurements – train on 80,000 pictures [organized by style and genre]
– generate flowersInvertible
Networks Generative networks
Tilman Plehn
GANGogh [Bonafilia, Jones, Danyluk (2017)]
Simulations
Events – neural network: learned function f (x) [regression, classification]
Unfolding – can networks create new pieces of art?
Inverting map random numbers to image pixels?
Measurements – train on 80,000 pictures [organized by style and genre]
– generate portraitsInvertible
Networks Generative networks
Tilman Plehn
GANGogh [Bonafilia, Jones, Danyluk (2017)]
Simulations
Events – neural network: learned function f (x) [regression, classification]
Unfolding – can networks create new pieces of art?
Inverting map random numbers to image pixels?
Measurements – train on 80,000 pictures [organized by style and genre]
Edmond de Belamy [Caselles-Dupre, Fautrel, Vernier (2018)]
– trained on 15,000 portraits
– sold for $432.500
⇒ ML all marketing and salesInvertible
Networks Generative networks
Tilman Plehn
GANGogh [Bonafilia, Jones, Danyluk (2017)]
Simulations
Events – neural network: learned function f (x) [regression, classification]
Unfolding – can networks create new pieces of art?
Inverting map random numbers to image pixels?
Measurements – train on 80,000 pictures [organized by style and genre]
Edmond de Belamy [Caselles-Dupre, Fautrel, Vernier (2018)]
– trained on 15,000 portraits
– sold for $432.500
⇒ ML all marketing and sales
Jet portraits [de Oliveira, Paganini, Nachman (2017)]
– calorimeter or jet images
sparsity the technical challenge
1- reproduce valid jet images from training data
2- organize them by QCD vs W -decay jets
– high-level observables m, τ21 as check
⇒ GANs generating QCD jetsInvertible
Networks GAN algorithm
Tilman Plehn
Generating events [phase space positions, possibly with weights]
Simulations
Events – training: true events {xT }
Unfolding
output: generated events {r } → {xG }
Inverting
– discriminator constructing D(x) by minimizing [classifier D(x) = 1, 0 true/generator]
Measurements LD = − log D(x) xT
+ − log(1 − D(x)) xG
– generator constructing r → xG by minimizing [D needed]
LG = − log D(x) xG
– equilibrium D = 0.5 ⇒ LD /2 = LG = − log 0.5
⇒ statistically independent copy of training eventsInvertible
Networks GAN algorithm
Tilman Plehn
Generating events [phase space positions, possibly with weights]
Simulations
Events – training: true events {xT }
Unfolding
output: generated events {r } → {xG }
Inverting – discriminator constructing D(x) by minimizing [classifier D(x) = 1, 0 true/generator]
Measurements – generator constructing r → xG by minimizing [D needed]
⇒ statistically independent copy of training events
Generative network studies
– Jets [de Oliveira (2017), Carrazza-Dreyer (2019)]
– Detector simulations [Paganini (2017), Musella (2018), Erdmann (2018), Ghosh (2018), Buhmann (2020,2021)]
– Events [Otten (2019), Hashemi, DiSipio, Butter (2019), Martinez (2019), Alanazi (2020), Chen (2020), Kansal (2020)]
– Unfolding [Datta (2018), Omnifold (2019), Bellagente (2019), Bellagente (2020), Vandegar (2020), Howard (2020)]
– Templates for QCD factorization [Lin (2019)]
– EFT models [Erbin (2018)]
– Event subtraction [Butter (2019)]
– Phase space [Bothmann (2020), Gao (2020), Klimek (2020)]
– Basics [GANplification (2020), DCTR (2020)]
– Unweighting [Verheyen (2020), Backes (2020)]
– Superresolution [DiBello (2020), Baldi (2020)]
– Parton densities [Carrazza (2021)]
– Uncertainties [Bellagente (2021)]Invertible
Networks GANplification
Tilman Plehn
Gain beyond training data [Butter, Diefenbacher, Kasieczka, Nachman, TP]
Simulations
Events – true function known 0.18
compare GAN vs sampling vs fit 10 quantiles truth
Unfolding 0.16 GAN trained on 100 data points fit
Sample
Inverting – quantiles with χ2 -values 0.14 GAN
0.12
Measurements – fit like 500-1000 sampled points
0.10
GAN like 500 sampled points [amplifictation factor 5]
p(x)
0.08
requiring 10,000 GANned events
0.06
– interpolation and resolution the key [NNPDF]
0.04
⇒ GANs beyond training data 0.02
0.00 8 6 4 2 0 2 4 6 8
x
50 quantiles
GAN 100 data points
quantile MSE
sample
10 2 200
300
fit
101 102 103 104 105 106
number GANedInvertible
Networks How to GAN LHC events
Tilman Plehn
Idea: replace ME for hard process [Butter, TP, Winterhalder]
Simulations
Events – medium-complex final state t t̄ → 6 jets
Unfolding t/t̄ and W ± on-shell with BW 6 × 4 = 18 dof
Inverting on-shell external states → 12 dof [constants hard to learn]
Measurements parton level, because it is harder
– flat observables flat [phase space coverage okay]
– standard observables with tails [statistical error indicated]
3
⇥10
6.0 True
[GeV 1]
GAN
4.0
dpT,t
2.0
1 d
0.0
1.2
GAN
True
1.0
0.8
1.0 pT,t [GeV]
Ntail
20%
p1
0.1
0 50 100 150 200 250 300 350 400
pT,t [GeV]Invertible
Networks How to GAN LHC events
Tilman Plehn
Idea: replace ME for hard process [Butter, TP, Winterhalder]
Simulations
Events – medium-complex final state t t̄ → 6 jets
Unfolding t/t̄ and W ± on-shell with BW 6 × 4 = 18 dof
Inverting on-shell external states → 12 dof [constants hard to learn]
Measurements parton level, because it is harder
– flat observables flat [phase space coverage okay]
– standard observables with tails [statistical error indicated]
– improved resolution [1M training events]
1M true events ×101
3
5.0
2
4.0
1
φ j2
0 3.0
−1 2.0
−2
1.0
−3
−3 −2 −1 0 1 2 3
φ j1Invertible
Networks How to GAN LHC events
Tilman Plehn
Idea: replace ME for hard process [Butter, TP, Winterhalder]
Simulations
Events – medium-complex final state t t̄ → 6 jets
Unfolding t/t̄ and W ± on-shell with BW 6 × 4 = 18 dof
Inverting on-shell external states → 12 dof [constants hard to learn]
Measurements parton level, because it is harder
– flat observables flat [phase space coverage okay]
– standard observables with tails [statistical error indicated]
– improved resolution [10M generated events]
10M generated events ×102
3
3.5
2
1 3.0
φ j2
0 2.5
−1 2.0
−2
1.5
−3
−3 −2 −1 0 1 2 3
φ j1Invertible
Networks How to GAN LHC events
Tilman Plehn
Idea: replace ME for hard process [Butter, TP, Winterhalder]
Simulations
Events – medium-complex final state t t̄ → 6 jets
Unfolding t/t̄ and W ± on-shell with BW 6 × 4 = 18 dof
Inverting on-shell external states → 12 dof [constants hard to learn]
Measurements parton level, because it is harder
– flat observables flat [phase space coverage okay]
– standard observables with tails [statistical error indicated]
– improved resolution [50M generated events]
50M generated events ×103
– Forward simulation working 3 1.8
2 1.6
1 1.4
φ j2
0
1.2
−1
1.0
−2
0.8
−3
−3 −2 −1 0 1 2 3
φ j1Invertible
Networks Bonus: unweighting & errors without binning
Tilman Plehn
Gaining from unweighting [Butter, TP, Winterhalder]
Simulations
Events – phase space sampling: weighted events [PS weight ×|M|2 ]
Unfolding events: constant weights Train
10−1
Unweighted
Inverting – unweighting the weak spot of standard MC 10−2 uwGAN
Measurements
σ dEµ−
– learn phase space patterns 10−3
1 dσ
[density estimation]
generate unweighted events [through loss] 10−4
10−5
10−6
2.0
1.5
Truth
X
1.0
0.5
0 1000 2000 3000 4000 5000 6000
Eµ− [GeV]Invertible
Networks Bonus: unweighting & errors without binning
Tilman Plehn
Gaining from unweighting [Butter, TP, Winterhalder]
Simulations
Events – phase space sampling: weighted events [PS weight ×|M|2 ]
Unfolding
events: constant weights Train
10−1
Unweighted
Inverting – unweighting the weak spot of standard MC 10−2 uwGAN
σ dEµ−
Measurements – learn phase space patterns 10−3
1 dσ
[density estimation]
generate unweighted events [through loss] 10−4
10−5
10−6
2.0
1.5
Truth
X
1.0
0.5
0 1000 2000 3000 4000 5000 6000
Events with error bars [Bellagente, Haußmann, Luchmann, TP]
Eµ− [GeV]
(1) learn phase space density as usual ×10−2
(2) learn error from weight distributions 2.0
[Bayesian network] BINN
Training Data
– generate events with error bars 1.5
+/- σpred
Normalized
1.0
0.5
0.0
1.1
BINN
Data
1.0
0.9
0 100 200 300
Ee+ [GeV]Invertible
Networks How to GAN away detector effects
Tilman Plehn
Goal: invert Monte Carlo [Bellagente, Butter, Kasiczka, TP, Winterhalder]
Simulations
Events
– parton shower, detector simulation typical examples [drawing random numbers]
Unfolding – inversion possible, in principle [entangled convolutions, model assumed]
Inverting – GAN task
Measurements DELPHES GAN
partons −→ detector −→ partons
⇒ Full phase space unfolded
Conditional GAN
– random numbers −→ parton level
hadron level as condition
matched event pairsInvertible
Networks Detector unfolding
Tilman Plehn
Reference process pp → ZW → (``) (jj)
Simulations
– broad jj mass peak
Events
narrow `` mass peak
Unfolding
modified 2 → 2 kinematics
Inverting fun phase space boundaries
Measurements
– GAN same as event generation [with MMD]
Model (in)dependence
2 1
⇥10 ⇥10
2.5 Truth 3.0 Truth
FCGAN FCGAN
2.0 2.5
[GeV 1]
[GeV 1]
Delphes Delphes
2.0
1.5
1.5
dpT,j1
dmjj
1.0
1 d
1 d
1.0
0.5 0.5
0.0 0.0
1.2 1.2
FCGAN
FCGAN
Truth
Truth
1.0 1.0
0.8 0.8
0 25 50 75 100 125 150 175 200 70.0 72.5 75.0 77.5 80.0 82.5 85.0 87.5 90.0
pT,j1 [GeV] mjj [GeV]Invertible
Networks Detector unfolding
Tilman Plehn
Reference process pp → ZW → (``) (jj)
Simulations
– broad jj mass peak
Events narrow `` mass peak
Unfolding modified 2 → 2 kinematics
Inverting fun phase space boundaries
Measurements – GAN same as event generation [with MMD]
Model (in)dependence
– detector-level cuts [14%, 39% events, no interpolation, MMD not conditional]
pT ,j1 = 30 ... 50 GeV pT ,j2 = 30 ... 40 GeV pT ,`− = 20 ... 50 GeV (12)
pT ,j1 > 60 GeV (13)
2 1
⇥10 ⇥10
4.0
6.0 Truth Truth
FCGAN 3.5 FCGAN
5.0 Eq.(12) 3.0 Eq.(12)
Eq.(13) Eq.(13)
4.0 2.5
dpT,j1
dmjj
2.0
1 d
1 d
3.0
1.5
2.0
1.0
1.0 0.5
0.0 0.0
0 25 50 75 100 125 150 175 200 70.0 72.5 75.0 77.5 80.0 82.5 85.0 87.5 90.0
pT,j1 [GeV] mjj [GeV]Invertible
Networks Detector unfolding
Tilman Plehn
Reference process pp → ZW → (``) (jj)
Simulations
– broad jj mass peak
Events narrow `` mass peak
Unfolding modified 2 → 2 kinematics
Inverting fun phase space boundaries
Measurements – GAN same as event generation [with MMD]
Model (in)dependence
– detector-level cuts [14%, 39% events, no interpolation, MMD not conditional]
pT ,j1 = 30 ... 50 GeV pT ,j2 = 30 ... 40 GeV pT ,`− = 20 ... 50 GeV (12)
pT ,j1 > 60 GeV (13)
×10−3
– model dependence [Thank you to BenN] 6.0 Truth (W’)
FCGAN
– train: SM events 5.0 Truth (SM)
test: 10% events with W 0 in s-channel
[GeV−1]
4.0
⇒ Working fine, but ill-defined
3.0
σ dm``jj
1 dσ
2.0
1.0
0.0
600 800 1000 1200 1400 1600 1800 2000
m``jj [GeV]Invertible
Networks Proper inverting
Tilman Plehn
Invertible networks [Bellagente, Butter, Kasieczka, TP, Rousselot, Winterhalder, Ardizzone, Köthe]
Simulations
Events – network as bijective transformation — normalizing flow
Unfolding Jacobian tractable [specifically: coupling layer]
Inverting
evaluation in both directions — INN [Ardizzone, Rother, Köthe]
Measurements – standard setup, random-number-padded working like FCGAN
– conditional: parton-level events from {r }
– maximum likelihood loss
L = − hlog p(θ|xp , xd )ix ,x
p d
∂g(xp , xd )
= − log p(g(xp , xd )) + log − log p(θ) + const.
∂xp x p ,xdInvertible
Networks Proper inverting
Tilman Plehn
Invertible networks [Bellagente, Butter, Kasieczka, TP, Rousselot, Winterhalder, Ardizzone, Köthe]
Simulations
Events
– network as bijective transformation — normalizing flow
Unfolding
Jacobian tractable [specifically: coupling layer]
evaluation in both directions — INN [Ardizzone, Rother, Köthe]
Inverting
Measurements
– standard setup, random-number-padded working like FCGAN
– conditional: parton-level events from {r }
– maximum likelihood loss
Again pp → ZW → (``) (jj)
– performance on distributions like FCGAN
– parton-level probability distribution for single detector event
⇒ Well-defined statistical inversion
single detector event
3200 unfoldings
1.4 FCGAN Parton Truth
1.2
events normalized
1.0
0.8
0.6
0.4
0.2 cINN eINN
0.0
10 15 20 25 30 35 40 45 50
pT,q1 [GeV]Invertible
Networks Proper inverting
Tilman Plehn
Invertible networks [Bellagente, Butter, Kasieczka, TP, Rousselot, Winterhalder, Ardizzone, Köthe]
Simulations
Events
– network as bijective transformation — normalizing flow
Unfolding
Jacobian tractable [specifically: coupling layer]
evaluation in both directions — INN [Ardizzone, Rother, Köthe]
Inverting
Measurements
– standard setup, random-number-padded working like FCGAN
– conditional: parton-level events from {r }
– maximum likelihood loss
Again pp → ZW → (``) (jj)
– performance on distributions like FCGAN
– parton-level probability distribution for single detector event
⇒ Well-defined statistical inversion
single detector event
3200 unfoldings 1.0
1.4 FCGAN Parton Truth
1.2 0.8
events normalized
fraction of events
1.0
0.6
0.8
FCGAN
eINN
0.6 0.4
0.4 N
0.2 N
cINN eINN cI
0.2
0.0 0.0
10 15 20 25 30 35 40 45 50 0.0 0.2 0.4 0.6 0.8 1.0
pT,q1 [GeV] quantile pT, q1Invertible
Networks Inverting to hard process
Tilman Plehn
What theorists want: undo ISR
Simulations
Events
– detector-level process pp → ZW +jets [variable number of objects]
Unfolding – ME vs PS jets decided by network
Inverting – training jet-inclusively or jet-exclusively
Measurements parton-level hard process chosen 2 → 2
×10−2 ×10−2
2.5
2 jet incl. 2.5 2 jet excl.
Parton Truth Parton Truth
2.0
Parton cINN 2.0 Parton cINN
[GeV−1 ]
[GeV−1 ]
Detector Truth Detector Truth
1.5 1.5
σ dpT,q1
σ dpT,q1
1.0 1.0
1 dσ
1 dσ
0.5 0.5
0.0 0.0
1.2 1.2
Truth
Truth
cINN
cINN
1.0 1.0
0.8 0.8
0 25 50 75 100 125 150 175 200 0 25 50 75 100 125 150 175 200
pT,q1 [GeV] pT,q1 [GeV]
×10−2 ×10−2
2.5
3 jet excl. 4 jet excl.
2.0 Parton Truth 2.0 Parton Truth
Parton cINN Parton cINN
[GeV−1 ]
[GeV−1 ]
1.5 Detector Truth 1.5 Detector Truth
1.0 1.0
σ dpT,q1
σ dpT,q1
1 dσ
1 dσ
0.5 0.5
0.0 0.0
0 25 50 75 100 125 150 175 200 0 25 50 75 100 125 150 175 200
pT,q1 [GeV] pT,q1 [GeV]Invertible
Networks Inverting to hard process
Tilman Plehn
What theorists want: undo ISR
Simulations
Events – detector-level process pp → ZW +jets [variable number of objects]
Unfolding – ME vs PS jets decided by network
Inverting – training jet-inclusively or jet-exclusively
Measurements parton-level hard process chosen 2 → 2
Towards systematic inversion
– detector unfolding known problem
– QCD parton from jet algorithm standard
– jet radiation possible
⇒ Invertible simulation in reachInvertible
Networks Inverting to QCD
Tilman Plehn
cINN for inference [Bieringer, Butter, Heimel, Höche, Köthe, TP, Radev]
Simulations
Events – condition jets with QCD parameters
Unfolding train model parameters −→ Gaussian latent space
Inverting
test Gaussian sampling −→ QCD parameter measurement
Measurements – going beyond CA vs CF [Kluth etal]
" #
2z(1 − y)
Pqq = CF Dqq + Fqq (1 − z) + Cqq yz(1 − z)
1 − z(1 − y )
!
z(1 − y) (1 − z)(1 − y )
Pgg = 2CA Dgg + + Fgg z(1 − z) + Cgg yz(1 − z)
1 − z(1 − y) 1 − (1 − z)(1 − y )
h i
2 2
Pgq = TR Fqq z + (1 − z) + Cgq yz(1 − z)Invertible
Networks Inverting to QCD
Tilman Plehn
cINN for inference [Bieringer, Butter, Heimel, Höche, Köthe, TP, Radev]
Simulations
Events
– condition jets with QCD parameters
Unfolding
train model parameters −→ Gaussian latent space
test Gaussian sampling −→ QCD parameter measurement
Inverting
Measurements
– going beyond CA vs CF [Kluth etal]
" #
2z(1 − y)
Pqq = CF Dqq + Fqq (1 − z) + Cqq yz(1 − z)
1 − z(1 − y )
!
z(1 − y) (1 − z)(1 − y )
Pgg = 2CA Dgg + + Fgg z(1 − z) + Cgg yz(1 − z)
1 − z(1 − y) 1 − (1 − z)(1 − y )
h i σ =0.9
2 2
Pgq = TR Fqq z + (1 − z) + Cgq yz(1 − z) 0.4 Posterior
0.3 Gaussian fit
– idealized shower [Sherpa] 0.2 Absolute error of 2.5
0.1
Cqq
-2.5 0 2.5
Cqq 0.08 σ =5.6
2.5
0.06
0 0.04
0.02
-2.5
Cgg Cgg
-10 0 10 -10 0 10
Cqq Cgg 0.08 σ =4.9
2.5
0.06
0
0 0.04
-10 0.02
-2.5
Cgq Cgq Cgq
-10 0 10 -10 0 10 -10 0 10Invertible
Networks Inverting to QCD
Tilman Plehn
cINN for inference [Bieringer, Butter, Heimel, Höche, Köthe, TP, Radev]
Simulations
Events
– condition jets with QCD parameters
Unfolding
train model parameters −→ Gaussian latent space
test Gaussian sampling −→ QCD parameter measurement
Inverting
Measurements
– going beyond CA vs CF [Kluth etal]
" #
2z(1 − y)
Pqq = CF Dqq + Fqq (1 − z) + Cqq yz(1 − z)
1 − z(1 − y )
!
z(1 − y) (1 − z)(1 − y )
Pgg = 2CA Dgg + + Fgg z(1 − z) + Cgg yz(1 − z)
1 − z(1 − y) 1 − (1 − z)(1 − y )
h i
2 2 σ =0.06 Posterior
Pgq = TR Fqq z + (1 − z) + Cgq yz(1 − z) 6
Gaussian fit
Relative error of 2%
4
– idealized shower [Sherpa] Absolute error of 2.5
2
– reality hitting... Dqq
0.9 1.0 1.1
– More ML-opportunities...
Dqq 2 σ =0.2
1.1
1.0
1
0.9
Fqq Fqq
0.5 1.0 1.5 0.5 1.0 1.5
Dqq Fqq σ =2.3
1.1
1.0 1.0 0.1
0.9 0.5
Cqq Cqq Cqq
-5 0 5 -5 0 5 -5 0 5Invertible
Networks Machine learning for LHC theory
Tilman Plehn
Machine learning for the LHC
Simulations
Events – Classification/regression standard
Unfolding learning vs smart pre-processing
Inverting uncertainties?
Measurements experimental realities?
– GANs the cool kid
generator trying to produce best events
discriminator trying to catch generator
– INNs my theory hope
flow networks for control
condition for inversion
Bayesian for errors
– Progress needs crazy ideasInvertible
Networks Bonus: subtraction
Tilman Plehn
Subtract samples without binning [Butter, TP, Winterhalder]
Simulations
Events – statistical uncertainty q
Unfolding ∆B−S = ∆2B + ∆2S > max(∆B, ∆S)
Inverting
– GAN setup: differential class label, sample normalization
Measurements
– toy example
1 1
PB (x) = + 0.1 PS (x) = ⇒ PB−S = 0.1
x x
100 0.13
GAN vs Truth (B − S)GAN
B (B − S)Truth ± 1σ
0.12
S
B−S
10−1 0.11
P (x)
P (x)
0.10
−2
10 0.09
0.08
0 25 50 75 100 125 150 175 200 0 25 50 75 100 125 150 175 200
x xInvertible
Networks Bonus: subtraction
Tilman Plehn
Subtract samples without binning [Butter, TP, Winterhalder]
Simulations
Events – statistical uncertainty q
Unfolding ∆B−S = ∆2B + ∆2S > max(∆B, ∆S)
Inverting
– GAN setup: differential class label, sample normalization
Measurements
– toy example
1 1
PB (x) = + 0.1 PS (x) = ⇒ PB−S = 0.1
x x
– event-based background subtraction [weird notation, sorry]
+ − + − + −
pp → e e (B) pp → γ → e e (S) ⇒ pp → Z → e e (B-S)
1
⇥10
GAN vs Truth
2.0 B
S
[pb/GeV]
1.5 B S
1.0
dEe
d
0.5
0.0
20 40 60 80 100
Ee [GeV]Invertible
Networks Bonus: subtraction
Tilman Plehn
Subtract samples without binning [Butter, TP, Winterhalder]
Simulations
Events – statistical uncertainty q
Unfolding ∆B−S = ∆2B + ∆2S > max(∆B, ∆S)
Inverting
– GAN setup: differential class label, sample normalization
Measurements
– toy example
1 1
PB (x) = + 0.1 PS (x) = ⇒ PB−S = 0.1
x x
– event-based background subtraction [weird notation, sorry]
+ − + − + −
pp → e e (B) pp → γ → e e (S) ⇒ pp → Z → e e (B-S)
– collinear subtraction [assumed non-local]
pp → Zg (B: matrix element, S: collinear approximation)
GAN vs Truth
101 B
S
[pb/GeV]
B−S
100
10−1
dpT,g
dσ
10−2
0 20 40 60 80 100
pT,g [GeV]You can also read
