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IML Meeting
4 June 2018
IML Workshop 2018 Challenge Solution (+ Automatic Feature Engineering)
Marcel Rieger, David Schmidt, Martin Erdmann, Erik Geiser, Yannik Rath
Marcel Rieger - 4.6.18 2 IML challenge 2018
● Challenge:
■ “Regress the generator-level soft drop mass of reconstructed high-pT jets (O(TeV))”
● Conditions:
■ Simulated Future Circular Collider (FCC) conditions
■ Detector simulation via Delphes with CMS phase II config
■ 1000 additional (pile-up) interactions
msoftdrop,GEN?
Marcel Rieger - 4.6.18 2 IML challenge 2018
● Challenge:
■ “Regress the generator-level soft drop mass of reconstructed high-pT jets (O(TeV))”
● Conditions:
■ Simulated Future Circular Collider (FCC) conditions
■ Detector simulation via Delphes with CMS phase II config
■ 1000 additional (pile-up) interactions
msoftdrop,GEN?
un-cluster (C/A)
by one step
mMDTSoftdrop
• Find hard substructure using step-wise unclustering
• No pure soft divergences
• Analytically calculable to high precision
Towards an understanding of jet substructureM Dasgupta, A Fregoso, S Marzani, G Salam
JHEP 1309 029 Soft Drop
A Larkoski, S Marzani, G Soyez, J ThalerJHEP 1405 146
Factorization for groomed jet substructure beyond the next-to-leading logarithm
C Frye, AJ Larkoski, MD Schwartz, K Yan JHEP 1607 064
logR0
✓
log1
z
log1
zcut
� > 0
� = 0
� < 0
Figure 1: Phase space for emissions on the (log 1
z , log R0✓ ) plane. In the strongly-ordered
limit, emissions above the dashed line (Eq. (2.2)) are vetoed by the soft drop condition. For
� > 0, soft emissions are vetoed while much of the soft-collinear region is maintained. For
� = 0 (mMDT), both soft and soft-collinear emissions are vetoed. For � < 0, all (two-prong)
singularities are regulated by the soft drop procedure.
and ✓ behavior:
soft modes: z ! 0, ✓ = constant,
soft-collinear modes: z ! 0, ✓ ! 0,
collinear modes: z = constant, ✓ ! 0.
No relative scaling is assumed between energy fraction z and splitting angle ✓ for soft-collinear
modes. In these logarithmic coordinates, the emission probability is flat in the soft-collinear
limit. In the soft limit, the soft drop criteria reduces to
z > zcut
✓✓
R0
◆�
) log1
z< log
1
zcut+ � log
R0
✓. (2.2)
Thus, vetoed emissions lie above a straight line of slope � on the (log 1
z , log R0✓ ) plane, as
shown in Fig. 1.
For � > 0, collinear radiation always satisfies the soft drop condition, so a soft-drop jet
still contains all of its collinear radiation. The amount of soft-collinear radiation that satisfies
the soft drop condition depends on the relative scaling of the energy fraction z to the angle ✓.
As � ! 0, more of the soft-collinear radiation of the jet is removed, and in the � = 0 (mMDT)
limit, all soft-collinear radiation is removed. Therefore, we expect that the coe�cient of the
double logarithms of observables like groomed jet mass (and C(↵)1
) will be proportional to �,
– 6 –
1 Introduction
The study of jet substructure has significantly matured over the past five years [1–3], with
numerous techniques proposed to tag boosted objects [4–46], distinguish quark from gluon jets
[44, 47–51], and mitigate the e↵ects of jet contamination [6, 52–61]. Many of these techniques
have found successful applications in jet studies at the Large Hadron Collider (LHC) [50, 62–
89], and jet substructure is likely to become even more relevant with the anticipated increase
in energy and luminosity for Run II of the LHC.
In addition to these phenomenological and experimental studies of jet substructure, there
is a growing catalog of first-principles calculations using perturbative QCD (pQCD). These
include more traditional jet mass and jet shape distributions [90–95] as well as more so-
phisticated substructure techniques [44, 59, 60, 96–103]. Recently, Refs. [59, 60] considered
the analytic behavior of three of the most commonly used jet tagging/grooming methods—
trimming [53], pruning [54, 55], and mass drop tagging [6]. Focusing on groomed jet mass
distributions, this study showed how their qualitative and quantitative features could be un-
derstood with the help of logarithmic resummation. Armed with this analytic understanding
of jet substructure, the authors of Ref. [59] developed the modified mass drop tagger (mMDT)
which exhibits some surprising features in the resulting groomed jet mass distribution, in-
cluding the absence of Sudakov double logarithms, the absence of non-global logarithms [104],
and a high degree of insensitivity to non-perturbative e↵ects.
In this paper, we introduce a new tagging/grooming method called “soft drop decluster-
ing”, with the aim of generalizing (and in some sense simplifying) the mMDT procedure. Like
any grooming method, soft drop declustering removes wide-angle soft radiation from a jet in
order to mitigate the e↵ects of contamination from initial state radiation (ISR), underlying
event (UE), and multiple hadron scattering (pileup). Given a jet of radius R0 with only two
constituents, the soft drop procedure removes the softer constituent unless
Soft Drop Condition:min(pT1, pT2)
pT1 + pT2
> zcut
✓�R12
R0
◆�
, (1.1)
where pT i are the transverse momenta of the constituents with respect to the beam, �R12
is their distance in the rapidity-azimuth plane, zcut is the soft drop threshold, and � is an
angular exponent. By construction, Eq. (1.1) fails for wide-angle soft radiation. The degree
of jet grooming is controlled by zcut and �, with � ! 1 returning back an ungroomed jet. As
we explain in Sec. 2, this procedure can be extended to jets with more than two constituents
with the help of recursive pairwise declustering.1
Following the spirit of Ref. [59], the goal of this paper is to understand the analytic
behavior of the soft drop procedure, particularly as the angular exponent � is varied. There
are two di↵erent regimes of interest. For � > 0, soft drop declustering removes soft radiation
1The soft drop procedure takes some inspiration from the “semi-classical jet algorithm” [58], where a variant
of Eq. (1.1) with zcut = 1/2 and � = 3/2 is tested at each stage of recursive clustering (unlike declustering
considered here).
– 2 –
!6
!6
Soft drop mass distribution
Figure: Soft drop jet mass distribution of probe jets in a sample enriched with tt for jets with pT > 400
GeV. The probe jets are anti-kT jets with R = 0.8,
with soft drop and the PUPPI pile-up corrections applied. The tt processes are simulated with POWHEG interfaced with PYTHIA8. The “Merged QB” tt contribution consists of events in which the b-quark from the top decay and just one of the quarks from the W decay are clustered into the jet. The tt templates have been fit to the data. The hatched region shows the total uncertainty on the simulation. In the lower panel, the dark and a light grey bands show the statistical and the total posterior uncertainties, respectively.
CMS DP-2017/26
j2
j1Do j1, j2 fulfill
no
yes
repeat with j1
Soft drop mass := m1
Initial jet
m1 < µ ·minit<latexit sha1_base64="h58qwtu8PfjGw60YTShn0SNxfNc=">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</latexit><latexit sha1_base64="h58qwtu8PfjGw60YTShn0SNxfNc=">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</latexit><latexit sha1_base64="h58qwtu8PfjGw60YTShn0SNxfNc=">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</latexit><latexit sha1_base64="h58qwtu8PfjGw60YTShn0SNxfNc=">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</latexit>
Marcel Rieger - 4.6.18 2 IML challenge 2018
● Challenge:
■ “Regress the generator-level soft drop mass of reconstructed high-pT jets (O(TeV))”
● Conditions:
■ Simulated Future Circular Collider (FCC) conditions
■ Detector simulation via Delphes with CMS phase II config
■ 1000 additional (pile-up) interactions
msoftdrop,GEN?
un-cluster (C/A)
by one step
mMDTSoftdrop
• Find hard substructure using step-wise unclustering
• No pure soft divergences
• Analytically calculable to high precision
Towards an understanding of jet substructureM Dasgupta, A Fregoso, S Marzani, G Salam
JHEP 1309 029 Soft Drop
A Larkoski, S Marzani, G Soyez, J ThalerJHEP 1405 146
Factorization for groomed jet substructure beyond the next-to-leading logarithm
C Frye, AJ Larkoski, MD Schwartz, K Yan JHEP 1607 064
logR0
✓
log1
z
log1
zcut
� > 0
� = 0
� < 0
Figure 1: Phase space for emissions on the (log 1
z , log R0✓ ) plane. In the strongly-ordered
limit, emissions above the dashed line (Eq. (2.2)) are vetoed by the soft drop condition. For
� > 0, soft emissions are vetoed while much of the soft-collinear region is maintained. For
� = 0 (mMDT), both soft and soft-collinear emissions are vetoed. For � < 0, all (two-prong)
singularities are regulated by the soft drop procedure.
and ✓ behavior:
soft modes: z ! 0, ✓ = constant,
soft-collinear modes: z ! 0, ✓ ! 0,
collinear modes: z = constant, ✓ ! 0.
No relative scaling is assumed between energy fraction z and splitting angle ✓ for soft-collinear
modes. In these logarithmic coordinates, the emission probability is flat in the soft-collinear
limit. In the soft limit, the soft drop criteria reduces to
z > zcut
✓✓
R0
◆�
) log1
z< log
1
zcut+ � log
R0
✓. (2.2)
Thus, vetoed emissions lie above a straight line of slope � on the (log 1
z , log R0✓ ) plane, as
shown in Fig. 1.
For � > 0, collinear radiation always satisfies the soft drop condition, so a soft-drop jet
still contains all of its collinear radiation. The amount of soft-collinear radiation that satisfies
the soft drop condition depends on the relative scaling of the energy fraction z to the angle ✓.
As � ! 0, more of the soft-collinear radiation of the jet is removed, and in the � = 0 (mMDT)
limit, all soft-collinear radiation is removed. Therefore, we expect that the coe�cient of the
double logarithms of observables like groomed jet mass (and C(↵)1
) will be proportional to �,
– 6 –
1 Introduction
The study of jet substructure has significantly matured over the past five years [1–3], with
numerous techniques proposed to tag boosted objects [4–46], distinguish quark from gluon jets
[44, 47–51], and mitigate the e↵ects of jet contamination [6, 52–61]. Many of these techniques
have found successful applications in jet studies at the Large Hadron Collider (LHC) [50, 62–
89], and jet substructure is likely to become even more relevant with the anticipated increase
in energy and luminosity for Run II of the LHC.
In addition to these phenomenological and experimental studies of jet substructure, there
is a growing catalog of first-principles calculations using perturbative QCD (pQCD). These
include more traditional jet mass and jet shape distributions [90–95] as well as more so-
phisticated substructure techniques [44, 59, 60, 96–103]. Recently, Refs. [59, 60] considered
the analytic behavior of three of the most commonly used jet tagging/grooming methods—
trimming [53], pruning [54, 55], and mass drop tagging [6]. Focusing on groomed jet mass
distributions, this study showed how their qualitative and quantitative features could be un-
derstood with the help of logarithmic resummation. Armed with this analytic understanding
of jet substructure, the authors of Ref. [59] developed the modified mass drop tagger (mMDT)
which exhibits some surprising features in the resulting groomed jet mass distribution, in-
cluding the absence of Sudakov double logarithms, the absence of non-global logarithms [104],
and a high degree of insensitivity to non-perturbative e↵ects.
In this paper, we introduce a new tagging/grooming method called “soft drop decluster-
ing”, with the aim of generalizing (and in some sense simplifying) the mMDT procedure. Like
any grooming method, soft drop declustering removes wide-angle soft radiation from a jet in
order to mitigate the e↵ects of contamination from initial state radiation (ISR), underlying
event (UE), and multiple hadron scattering (pileup). Given a jet of radius R0 with only two
constituents, the soft drop procedure removes the softer constituent unless
Soft Drop Condition:min(pT1, pT2)
pT1 + pT2
> zcut
✓�R12
R0
◆�
, (1.1)
where pT i are the transverse momenta of the constituents with respect to the beam, �R12
is their distance in the rapidity-azimuth plane, zcut is the soft drop threshold, and � is an
angular exponent. By construction, Eq. (1.1) fails for wide-angle soft radiation. The degree
of jet grooming is controlled by zcut and �, with � ! 1 returning back an ungroomed jet. As
we explain in Sec. 2, this procedure can be extended to jets with more than two constituents
with the help of recursive pairwise declustering.1
Following the spirit of Ref. [59], the goal of this paper is to understand the analytic
behavior of the soft drop procedure, particularly as the angular exponent � is varied. There
are two di↵erent regimes of interest. For � > 0, soft drop declustering removes soft radiation
1The soft drop procedure takes some inspiration from the “semi-classical jet algorithm” [58], where a variant
of Eq. (1.1) with zcut = 1/2 and � = 3/2 is tested at each stage of recursive clustering (unlike declustering
considered here).
– 2 –
!6
!6
Soft drop mass distribution
Figure: Soft drop jet mass distribution of probe jets in a sample enriched with tt for jets with pT > 400
GeV. The probe jets are anti-kT jets with R = 0.8,
with soft drop and the PUPPI pile-up corrections applied. The tt processes are simulated with POWHEG interfaced with PYTHIA8. The “Merged QB” tt contribution consists of events in which the b-quark from the top decay and just one of the quarks from the W decay are clustered into the jet. The tt templates have been fit to the data. The hatched region shows the total uncertainty on the simulation. In the lower panel, the dark and a light grey bands show the statistical and the total posterior uncertainties, respectively.
CMS DP-2017/26
j2
j1Do j1, j2 fulfill
no
yes
repeat with j1
Soft drop mass := m1
Initial jet
m1 < µ ·minit<latexit sha1_base64="h58qwtu8PfjGw60YTShn0SNxfNc=">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</latexit><latexit sha1_base64="h58qwtu8PfjGw60YTShn0SNxfNc=">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</latexit><latexit sha1_base64="h58qwtu8PfjGw60YTShn0SNxfNc=">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</latexit><latexit sha1_base64="h58qwtu8PfjGw60YTShn0SNxfNc=">AAACN3icbVDLSgMxFM34rOOr6tJNsAiuykw3KrgounFZwdpCZxgyadqGJpMhuSMtQz/Ar3Gr/ok7V+LWHxDTx8K2HggczrmP3BOnghvwvHdnZXVtfWOzsOVu7+zu7RcPDh+MyjRldaqE0s2YGCZ4wurAQbBmqhmRsWCNuH8z9huPTBuuknsYpiyUpJvwDqcErBQVS0HLlZGPr3AgMxzQtgIsowDYAHKecBi5QWirvLI3AV4m/oyU0Ay1qPgTtBXNJEuACmJMy/dSCHOigVPB7MjMsJTQPumylqUJkcyE+eSYET61Sht3lLYvATxR/3bkRBozlLGtlAR6ZtEbi/95rQw6F6E9Ks2AJXS6qJMJDAqPk8FtrhkFMbSEUM3tXzHtEU0o2PzmtsRK9YHEZu6SvKtJ2uN0MHJtYP5iPMukXilflv27Sql6PUuugI7RCTpDPjpHVXSLaqiOKHpCz+gFvTpvzofz6XxNS1ecWc8RmoPz/QvwV6yW</latexit>
Marcel Rieger - 4.6.18 3 Challenge dataset
● 1M jets for training (20% used for validation)
● Input features:
■ Jet + soft drop jet
▻ pT, eta, phi, mass
■ Jet constituents (up to ∼300):
▻ pT, eta, phi
▻ Charge, dxy + dz impact parameters
▻ Energy deposit in ECAL + HCALNconstituents
Marcel Rieger - 4.6.18 3 Challenge dataset
● 1M jets for training (20% used for validation)
● Input features:
■ Jet + soft drop jet
▻ pT, eta, phi, mass
■ Jet constituents (up to ∼300):
▻ pT, eta, phi
▻ Charge, dxy + dz impact parameters
▻ Energy deposit in ECAL + HCALNconstituents
● Pre-processing of constituents:
■ Use first N = 200 constituents sorted by pT
■ Zero-padding when N < 200
■ Determine full 4-vector:
▻ E = EECAL + EHCAL
▻ Identify µ’s via E/p < 1 → use mµ (O(mπ))
!! Only keep 4-vectors, discard charge, etc. E / p (= β-1)
Interpret as µ’s
Marcel Rieger - 4.6.18
● Network output:
■ Predicted soft drop mass
● Metric:
■ Resolution of truth-normalized masses
■ Practical definition, overall offset could
be subject to calibration
!! Insensitive to tails, i.e. 32% of all jets, take into account in loss function
4 Challenge metric
M =a� b
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0.5 1.0 1.5 2.00
#50% (c)
16% (b)
84% (a)
R =mpred
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≠ 0
percentiles
Marcel Rieger - 4.6.18 5 Loss function
● Using the challenge metric itself as loss does not yield strong performance !! Back-prop. through percentiles ...
● Custom loss (per batch):
■ Select predictions in central 74% range
of prediction / truth
▻ Increased range w.r.t. metric to be robust against boundary effects
■ Compute MSE, scaled to arbitrary value
that is subject to tuning
▻ t = 3 found to result in best training (interferes with weight init.,
batch norm., etc)
R =mpred
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13% 87%50%
}
MSEt =1
nbatch · t
sX
i
(t�Ri)2
<latexit sha1_base64="SUcecWG2qyCdm1TAOs6myV5Ap1w=">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</latexit><latexit sha1_base64="SUcecWG2qyCdm1TAOs6myV5Ap1w=">AAACZXicbVDLbhMxFHWGVwnQhofYsOCKCKksiGayARZIFQiJDVILhFbKDKM7jiex4rEH+w5qZM138S1ddAt8BcJ5LEjLkSwdnXMfvqeolXQUx2ed6MrVa9dv7Nzs3rp9Z3evd/feF2cay8WIG2XsSYFOKKnFiCQpcVJbgVWhxHExf7v0j78L66TRn2lRi6zCqZal5EhByntH6bgLkJI4Jf/h07s2J3gNaWmR+6T1Ol87BRKftZDyiSGgQNw3Sz51TZVL2Cd4Dh9z+ezrsO2mWd7rx4N4BbhMkg3psw0O896fdGJ4UwlNXKFz4ySuKfNoSXIlwsjGiRr5HKdiHKjGSrjMr05v4WlQJlAaG54mWKn/dnisnFtURaiskGbuorcU/+eNGypfZl7quiGh+XpR2SggA8scYSKt4KQWgSC3MvwV+AxDbhTS3tpSGDMnLNzWJX5qsZ5Jftp2Q2DJxXguk9Fw8GqQHA37B282ye2wR+wJ22cJe8EO2Ht2yEaMsx/snP1kvzq/o93oQfRwXRp1Nj332Raix38Bq/66zA==</latexit><latexit sha1_base64="SUcecWG2qyCdm1TAOs6myV5Ap1w=">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</latexit><latexit sha1_base64="SUcecWG2qyCdm1TAOs6myV5Ap1w=">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</latexit>
→ Final resolution: 41.3%
Marcel Rieger - 4.6.18
● Fully connected (FCN) architecture
● 5 hidden layers, 2048→1024→512→256→128
● ELU activation
● ADAM, r = 2.0e-4 @ batch size 4096
● L2 regularization, λ = 1.5e-5
● Batch normalization
6 Network architecture
Input
4 vectors of jet,
soft drop jet, constituents
additional constituent
data
✂ Output
╳
Trainable feature
generator (LBN)
(next slides)
→ Final resolution: 41.3%
Marcel Rieger - 4.6.18 7 Feature engineering in HEP
Low-level features
High-level features
Physicist
Baseline result
DNN
Marcel Rieger - 4.6.18 7 Feature engineering in HEP
Low-level features
High-level features
Physicist
Baseline result
DNN
Best result
Marcel Rieger - 4.6.18 7 Feature engineering in HEP
Low-level features
High-level features
Physicist
Baseline result
DNN
Best result
Worse than
baseline
Marcel Rieger - 4.6.18 7 Feature engineering in HEP
Low-level features
High-level features
Physicist
Baseline result
DNN
Best result
● Problem statement
1. Physicists’ crafted high-level features might not exploit all available information 2. In practice, it is hard for “standard” DNNs to learn representations of complex features
Marcel Rieger - 4.6.18 7 Feature engineering in HEP
Low-level features
High-level features
Physicist
Baseline result
DNN
Best result
● Problem statement
1. Physicists’ crafted high-level features might not exploit all available information 2. In practice, it is hard for “standard” DNNs to learn representations of complex features
W
l
ν
tb θ*
5 ttH Event Reconstruction
hmi [GeV] �m [GeV]
thad 178.91 20.79tlep 171.88 24.91Whad 84.62 12.08
Table 5.1: Expectation values and uncertainties for the calculation of the �2 inputvariable derived from the simulated event sample using generator data.
cjchbb The combined jet charge (CJC) of the two bottom quarks from the Higgsboson decay,
CJC =��JCbH
� JCb̄H
�� . (5.9)
The electric charges of the two quarks are expected to have opposite signs andhence, CJC is larger for signal events and has a theoretical value of 2/3 e onparton level.
cjcbhadblep The combined jet charge of the two bottom quarks from the top quarkdecays,
CJC = |JCbhad � JCblep| . (5.10)
Its theoretical value on parton level is 2/3 e as well.
cjcj1j2 The combined jet charge of the two light jets,
CJC = �Qlep · (JClj1 + JClj2). (5.11)
The factor �Qlep, i.e. the charge of the lepton, causes the combination to be+1 e on parton level.
cjcall The combined jet charge of the two light jets and the two bottom quarks fromthe top quark decays,
CJC = Qlep · (JCbhad � JCblep � JClj1 � JClj2), (5.12)
with an expectation value of 5/3 e on parton level.
wlephelicity The angle ✓⇤ between W ⇤lep
(boosted into the tlep system) and lep⇤
(boosted into the Wlep system) determined as
cos ✓⇤ =
# »W ⇤
lep·
# »lep⇤���
# »W ⇤
lep
��� ·
���# »lep⇤
���. (5.13)
Another illustration of the angle ✓⇤ is shown in figure 5.1.
48
Marcel Rieger - 4.6.18
● Aim: “”Encode first-principles of domain (physics) into network structure”
● Similar situation to FCNs → CNNs:
■ Images contain information in translation invariant adjacency of pixels
→ Exploit by changing the network structure!
● Already successful applications out there (selection):
● Event classification by learning a rest frame with a “Lorentz Layer” (J.-R. Vlimant, link, link)
8 Networks motivated by Physics
arXiv 1707.08966 arXiv 1702.00748
Marcel Rieger - 4.6.18 9 Lorentz Boost Networks
N x 4
Input (4-vectors)
Combine to Particles
& Rest framesBoost
P into R
2 x (M x 4) M x 4
Feature engineering
F x 1
I
P
R
B F
Paper public soon
Trainable
Marcel Rieger - 4.6.18 10 LBN: Boosting
● Lorentz transformation with boost matrix
● Vectorized formulation to run efficiently on GPUs
■ 4D tensor (batch x particle x 4 x 4)
2 Network Architecture
q =
"EÆp
#(2.1)
⇤ =
266666664
� ���nx ���ny ���nz���nx 1 + (� � 1)n2
x (� � 1)nxny (� � 1)nxnz���ny (� � 1)nynx 1 + (� � 1)n2
y (� � 1)nynz���nz (� � 1)nznx (� � 1)nzny 1 + (� � 1)n2
z
377777775(2.2)
with Æn = Æ�/� (2.3)
q⇤ = ⇤ · q (2.4)
MR, EG - 16.4.18 12 Basic LNN architecture
N x 4
Input(4-vectors)
Clustering Boosting(C1 into C2)
2 x (M x 4) M x 4
Features(Engineered)
F x 1
Batch norm.(optional)
Gate(optional)
F x 1 F x 1
I
C1
C2
B F N G
Figure 2. LBN architecture. TODO: Better image.
X =
2666666664
E1 px,1 py,1 pz,1E2 px,2 py,2 pz,2......
......
EN px,N py,N pz,N
3777777775(2.5)
– 2 –
Pm,i =
N’n=1
Wparticlesm,n · Xn,i (2.6)
Rm,i =
N’n=1
W restframesm,n · Xn,i (2.7)
(2.8)
⇤ = I + (U � �) � ((U + 1) � � � U) � (e ⇥ eT ) (2.9)
with U =
"�1
1⇥10
1⇥3
03⇥1 �1
3⇥3
#(2.10)
and e =
"1
1⇥1
�Æn3⇥1
#(2.11)
with � the element-wise addition and � the element-wise multiplication TODO: rephrase?.
In practice, ⇤ is implemented as a 4-dimensional tensor over multiple batches, a predefined
number of particles per batch (TODO: refer to Fig. 2 here), and the 4 ⇥ 4 ... TODO: todo.
Bm = ⇤(Rm) · Pm (2.12)
F = f (B) (2.13)
f denotes the flat concatenation of the following features:
• Energy and momentum components of all particles in {E, px, py, pz} and {E, ⌘, �,m} repre-
sentation.
• Relativistic quantities � and � of all particles:
� =pE, � =
Em
(2.14)
• Distance �R in the ⌘ � � plane between all pairs of particles i and j:
�Ri j =
q��i � � j
�2+�⌘i � ⌘j
�2(2.15)
The minuend accounts for periodic boundaries.
• Distance �s in the Minkowski space between all pairs of particles i and j:
�si j =q(Ei � Ej)2 � | Æpi � Æpj |2 (2.16)
– 3 –
I
P
R
B F
Marcel Rieger - 4.6.18 11 LBN: Feature engineering
● Project features from M boosted 4-vectors:
■ Features per vector:
▻ E, pt, eta, phi, mass
■ Pairwise features:
▻ cos(φ) between vectors
■ More features possible, but not necessarily required
■ We used M = 50 → 1475 features in total
■ Input feature scaling / normalization not applicable
→ Batch normalization applied after feature layer
I
P
R
B F
W
l
ν
tb θ*
5 ttH Event Reconstruction
hmi [GeV] �m [GeV]
thad 178.91 20.79tlep 171.88 24.91Whad 84.62 12.08
Table 5.1: Expectation values and uncertainties for the calculation of the �2 inputvariable derived from the simulated event sample using generator data.
cjchbb The combined jet charge (CJC) of the two bottom quarks from the Higgsboson decay,
CJC =��JCbH
� JCb̄H
�� . (5.9)
The electric charges of the two quarks are expected to have opposite signs andhence, CJC is larger for signal events and has a theoretical value of 2/3 e onparton level.
cjcbhadblep The combined jet charge of the two bottom quarks from the top quarkdecays,
CJC = |JCbhad � JCblep| . (5.10)
Its theoretical value on parton level is 2/3 e as well.
cjcj1j2 The combined jet charge of the two light jets,
CJC = �Qlep · (JClj1 + JClj2). (5.11)
The factor �Qlep, i.e. the charge of the lepton, causes the combination to be+1 e on parton level.
cjcall The combined jet charge of the two light jets and the two bottom quarks fromthe top quark decays,
CJC = Qlep · (JCbhad � JCblep � JClj1 � JClj2), (5.12)
with an expectation value of 5/3 e on parton level.
wlephelicity The angle ✓⇤ between W ⇤lep
(boosted into the tlep system) and lep⇤
(boosted into the Wlep system) determined as
cos ✓⇤ =
# »W ⇤
lep·
# »lep⇤���
# »W ⇤
lep
��� ·
���# »lep⇤
���. (5.13)
Another illustration of the angle ✓⇤ is shown in figure 5.1.
48
Marcel Rieger - 4.6.18 12 Observations
Paper public soon
I
P
R
B F
1. LBN is not a black box
▻ Extract which (combined) particles and features are important from combinations
2. FCN behind LBN can be rather shallow
▻ Feature representation moved to LBN
▻ FCN can focus on transformation to output
FCN
LBN
Marcel Rieger - 4.6.18 13 Top tagging reference dataset
● Developed along arXiv:1707.08966 (A. Butter, G. Kasieczka, T. Plehn, M. Russell)
● Data:
■ 1.2M + 400k + 400k jets (top + QCD)
■ Only 4-vectors of up to 160 constituents
● Documentation:
[...]HEP community needs method comparisons!
Marcel Rieger - 4.6.18 14 Summary
● IML challenges & public reference datasets:
▻ Opportunities to compare methods and to open fruitful discussions
● “Which separating variable could increase my network performance?” should become
“How can I design my network to (even better) work with raw features?”
▻ Encode physics knowledge right into network rather than into variables
● Lorentz Boost Network possible candidate for many use cases
I
P
R
B F
![7/12/2015 Prof. Ehud Gudes Security Ch 1 1 Chapter 1 [SB] chapters 1,13,14,15,16,17,18 Articles J1,J2](https://img.pdfslide.us/doc/110x75/56649d775503460f94a585a5/7122015-prof-ehud-gudes-security-ch-1-1-chapter-1-sb-chapters-1131415161718.jpg)
