∎

<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>(corresponding author)

11institutetext:  Key Laboratory of Quark and Lepton Physics (MOE) and
Institute of Particle Physics, Central China Normal University, Wuhan 430079,
China 22institutetext: School of Mathematics and Physics, China University of
Geosciences (Wuhan), Wuhan 430074, China

# Strange particle production in jets and underlying events in pp collisions
at $\sqrt{s}~{}=~{}7$ TeV with PYTHIA8 generator

Pengyao Cuie1, addr1  Zhongbao Yine2, addr1  Liang Zhenge3, addr2, addr1

(Received: date / Accepted: date)

###### Abstract

Strange hadron production in pp collisions at $\sqrt{s}~{}=~{}7$ TeV is
studied in jets and underlying events using the PYTHIA8 event generator.
Matching strange hadrons to the jet area and the underlying event area is
expected to help us disentangle the strange particles produced in hard and
soft processes. The yield and the relative production of strange hadrons
dependent on the event multiplicity are investigated with the color
reconnection and color rope mechanisms implemented in the PYTHIA8 framework.
It is found that the inclusive strange hadron productions can be reasonably
described by the color reconnection and color rope combined effects. A
significant multiplicity dependent enhancement of the strange baryon
production in the jet area is observed induced by the modified string
fragmentation mechanisms, indicating the strange baryon enhancement persists
in both the hard and the soft process. Multi-strange baryons are found to be
more collimated with the jet axis than other strange hadrons in the string
fragmentation picture with the jet shape analysis technique. Future
experimental examination of these jet related strange hadron productions will
provide more insight to the origin of strangeness enhancement in small
systems.

††journal: Eur. Phys. J. A

##  1 Introduction

In heavy-ion collisions at ultra-relativistic energies, it is well established
that a new state of nuclear matter called Quark-Gluon-Plasma (QGP) can be
created Adams:2005dq ; Adcox:2004mh ; Arsene:2004fa ; Back:2004je ;
Schukraft:2011na ; Satz:2000bn ; Shuryak:1983ni ; Jacak:2012dx ;
Cleymans:1985wb ; Bass:1998vz ; BraunMunzinger:2007zz . Proton-proton (pp),
proton-nucleus (p–A) collisions have been suggested to serve as the references
to study heavy-ion collisions and quantify the properties of the QGP. However,
recent measurements have revealed strong flow-like effects in high
multiplicity pp and p–A collisions at LHC energies which are qualitatively
similar to that observed in heavy-ion collisions Abelev:2012sk ;
Chatrchyan:2013eya ; Khachatryan:2010gv ; CMS:2012qk ; Abelev:2012ola ;
Aad:2012gla ; Aad:2013fja ; Chatrchyan:2013nka ; Adare:2013esx ; Adams:2006nd
; Aad:2015gqa ; ABELEV:2013wsa ; Khachatryan:2015waa ; Acharya:2019vdf ;
Abelev:2014uua ; Adam:2015vsf . These include the long-range two particle
angular correlations Aad:2015gqa ; Abelev:2012ola ; ABELEV:2013wsa , non-
vanishing 2nd order Fourier coefficients ($v_{2}$) in multi-particle cumulant
studies Acharya:2019vdf ; Khachatryan:2015waa , the baryon-to-meson
enhancement at intermediate transverse momentum ($p_{\mathrm{T}}$) range
ALICE:2018pal  and the strangeness enhancement effects ALICE:2016fzo .
Therefore, it is of great interest to investigate the origin of the
collectivity-driven features in small systems both experimentally and
theoretically.

In particular, the strangeness enhancement, referring to the enhanced
production of multi-strange baryons, has been historically regarded as an
important signature of the QGP formation. For hadronic collisions in small
systems like pp and p–A collisions, the production of particles containing
strange quarks are supposed to be suppressed due to the large strange quark
mass. The chemically equilibrated QGP medium, on the other hand, may create a
large number of strange quarks via the thermal gluon fusion process and
enhance the formation of multi-strange hadrons. It is therefore a striking
observation that a universal multi-strange hadron enhancement feature is
reported by the ALICE collaboration ALICE:2016fzo ; ALICE:2018pal  across
collision systems from pp, p–A to AA collisions. The measured multiplicity
dependent strange (${\rm K}^{0}_{\rm{S}}$, ${\rm\Lambda}$ and
$\overline{{\rm\Lambda}}$) and multi-strange (${\rm\Xi^{-}}$,
${\rm\overline{\Xi}}^{+}$, ${\rm\Omega^{-}}$ and $\overline{{\rm\Omega}}^{+}$)
particle production in pp collisions at $\sqrt{s}~{}=~{}7$ TeV is
qualitatively similar to that observed in Pb–Pb collisions and cannot be
easily reproduced by the conventional string fragmentation model. It is found
that the improvements considering the inter-string interactions like color
reconnection or color rope mechanisms are needed to describe these novel
flavor dependent observables Nayak:2018xip ; Bierlich:2016vgw;
OrtizVelasquez:2013ofg .

In this paper, we will study the production of strange hadrons, ${\rm
K}^{0}_{\rm{S}}$, ${\rm\Lambda}$, ${\rm\Xi}^{\pm}$, ${\rm\Omega}^{\pm}$ and
the resonance states ${\rm K}^{*0}$ and ${\rm\phi}$ within the jet and the
underlying event region which separates the contribution associated with hard
and soft processes. The rest of the paper is organized as follows: in Sec. 2,
we give a short introduction about the modified string fragmentation models
implemented in the PYTHIA8 framework. The analysis method involving jet
observables is described in Sec. 3. We compare the model calculations with the
experimental data and make predictions for the in-jet and underlying event
strange hadron productions in Sec. 4. In the end, we come to our summary in
Sec. 5.

##  2 Color reconnection and color rope models

In this work, we perform the study using the PYTHIA8 (version 8.2.4) event
generator together with the hadronization models considering color
reconnection and color rope mechanisms. Within the multiple parton interaction
(MPI) framework AxialFieldSpectrometer:1986dfj ; UA2:1991apc ; CDF:1997yfa
implemented in PYTHIA8, a large number of final state string objects can be
generated over limited transverse space in high energy collisions. The
traditional string fragmentation process is expected to be modified in the
high parton density environment due to the inter-string interactions. Based on
the Monash 2013 tune, color reconnection Christiansen:2015yqa ;
Sjostrand:2014zea  and color rope Biro:1984cf ; Bialas:1984ye  effects will be
included to investigate strange hadron production from both hard processes
related to the jet production and soft processes in underlying events.

#### Color reconnection model

Color reconnection (CR) deals with the formation of strings by connecting
different final state partons via color lines in a way that the total string
length is as short as possible. Within the MPI framework, partons from
independent hard scatterings at mid-rapidity can reconnect and make a
significant transverse boost to the created string piece due to the
involvement of more mid-rapidity partons OrtizVelasquez:2013ofg . Different CR
models have been developed based on the calculation of the probability to
connect partons by incorporating various color flow structures. In this work,
we employ the beyond leading color (BLC) CR model, in which strings are
allowed to form between both leading and non-leading connected partons
Christiansen:2015yqa . As the CR model connects both low and high
$p_{\mathrm{T}}$ partons, both soft and hard processes will be affected by
this mechanism. With the possibility to form junction in beyond leading color
CR as additional source for baryon production, a multiplicity dependent baryon
enhancement is observed in this model Bierlich:2015rha . The parameters of BLC
mode used in this paper are listed in Table 1 with respect to the default
settings of the Monash Tune.

Table 1: Parameters of Beyond Leading Color reconnection model with respect to
the default settings of the Monash Tune

Parameters | Monash | BLC
---|---|---
MultiPartonInteractions:pT0Ref | 2.28 | 2.15
BeamRemnants:remnantMode | 0 | 1
BeamRemnants:saturation | - | 5
ColourReconnection:reconnect | on | on
ColourReconnection:mode | 0 | 1
ColourReconnection:allowDoubleJunRem | on | off
ColourReconnection:m0 | - | 0.3
ColourReconnection:allowJunctions | - | on
ColourReconnection:junctionCorrection | - | 1.2
ColorReconnection:timeDilationMode | - | 2
ColourReconnection:timeDilationPar | - | 0.18

#### Color rope model

The color rope hadronization model is constructed based on the idea that
strings overlapped with each other in geometric space may act coherently to
form a color rope Flensburg:2011kk . Each string piece is treated as a flux
tube with a model dependent transverse size, which allows to calculate the
amount of overlap between strings with a given impact parameter of the event.
The interfered strings ended up forming ropes are hadronized with higher
effective string tensions, reflecting the fact that more energy is available
for the hadronization process. This effect can be implemented by connecting
the relevant Lund string fragmentation parameters in PYTHIA to the effective
string tension values following the Schwinger tunneling mechanism
Bierlich:2014xba ; Zheng:2018yxq . The breakup of strings with higher string
tension in the dense environment is expected to produce more di-quarks and
strange quarks, resulting in enhanced production of baryons and strange
hadrons. The parameters of color rope model used in this paper are listed in
the Table 2.

Table 2: Color rope hadronization model parameters used in this study. Parameters | Values
---|---
Ropewalk:RopeHadronization | on
Ropewalk:doShoving | on
Ropewalk:tInit | 1.5
Ropewalk:deltat | 0.05
Ropewalk:tShove | 0.1
Ropewalk:gAmplitude | 0.
Ropewalk:doFlavour | on
Ropewalk:r0 | 0.5
Ropewalk:m0 | 0.2
Ropewalk:beta | 0.1

##  3 Method

The analysis is done by generating around 2.5 billion non-diffractive events
for pp collisions at $\sqrt{s}$ = 7 TeV with CR, Rope hadronization and
combined CR and Rope hadronization (labeled as “CR + Rope”) processes,
respectively. The Monash tune is used as a reference to quantify the effects
of each model. The events are categorized into ten different event classes
based on the final state charge multiplicities within the pseudorapidity range
of 2 $<$ $|\eta|$ $<$ 5\. The mean pseudorapidity density of charged
particles, $\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ is
estimated for $|\eta|$ $<$ 0.5. We present the
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ in each event class
from our simulation compared to that measured by ALICE ALICE:2016fzo  in Table
3.

Table 3: Definition of the event multiplicity classes as fractions of the
analyzed event sample and their corresponding
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$ within
$|\eta_{\mathrm{lab}}|<0.5$.

Event class | I | II | III | IV | V | VI | VII | VIII | IX | X
---|---|---|---|---|---|---|---|---|---|---
$\sigma/\sigma_{\mathrm{INEL>0}}$ | 0-0.95% | 0.95-4.7% | 4.7-9.5% | 9.5-14% | 14-19% | 19-28% | 28-38% | 38-48% | 48-68% | 68-100%
Exp data | 21.3 $\pm$ 0.6 | 16.5 $\pm$ 0.5 | 13.5 $\pm$ 0.4 | 11.5 $\pm$ 0.3 | 10.1 $\pm$ 0.3 | 8.45 $\pm$ 0.25 | 6.72 $\pm$ 0.21 | 5.40 $\pm$ 0.17 | 3.90 $\pm$ 0.14 | 2.26 $\pm$ 0.12
Monash | 19.2 | 15.6 | 13.1 | 11.4 | 10.0 | 8.4 | 6.7 | 5.1 | 3.5 | 2.2
CR | 18.8 | 15.6 | 13.3 | 11.5 | 10.3 | 8.6 | 6.7 | 5.4 | 3.8 | 2.2
Rope | 20.3 | 16.6 | 13.9 | 12.2 | 10.8 | 9.2 | 7.5 | 5.9 | 4.3 | 2.6
CR + Rope | 18.3 | 15.2 | 12.9 | 11.4 | 10.0 | 8.5 | 6.8 | 5.5 | 4.1 | 2.5

We study the strange hadron productions from soft and hard processes following
the same analysis procedure done in the ALICE experiment ALICE:2021cvd  with
the help of jet observables. The strange hadrons considered in this work are
usually reconstructed via their charged decay channels in the experiment. In
our simulation, we turn off their decays in PYTHIA8 and calculate the yield of
each strange hadron after considering the realistic experimental acceptance.
We use the charged-particle jet reconstructed using the anti-$k_{\rm T}$
algorithm Cacciari:2008gp  from the FastJet package Cacciari:2011ma ;
Cacciari:2005hq . The anti-$k_{\rm T}$ algorithm is the most widely used jet
finding algorithm in heavy ion physics, providing a much faster replacement
compared to the older cone algorithms and removing the irregular jet
boundaries existed in the $k_{\rm T}$algorithm Cacciari:2008gp . We use the
jet resolution parameter $R=0.4$ to match the ALICE experimental condition in
a wide range of jet related studies ALICE:2021cvd ; ALICE:2018ype ;
ALICE:2017svf . A transverse momentum cut of $p_{\rm T,~{}jet}>10$ GeV/$c$ has
been applied to the reconstructed charged-particle jets to select the jet
events ALICE:2021cvd . The strange hadron production associated with hard
processes is explored by investigating the particles produced inside the jet
cone. To ensure that the in-jet particle acceptance is fully overlapping with
the acceptance of strange particles ($|\eta_{\mathrm{par}}|<0.75$), the jet
axis cut is set to $|\eta_{\mathrm{jet}}|<0.35~{}(0.75-0.4)$. Particles with
distances to the jet axis $R(\mathrm{p,~{}jet})$ less than a cone size $R_{\rm
cone}=0.4$ are defined as the in-jet particles, in which
$R(\mathrm{p,~{}jet})$ is calculated in the pseudorapidity and azimuthal angle
space ($\eta-\varphi$ plane) as follows

$R(\mathrm{p,~{}jet})=\sqrt{\left(\eta_{\mathrm{jet}}-\eta_{\mathrm{par}}\right)^{2}+\left(\varphi_{\mathrm{jet}}-\varphi_{\mathrm{par}}\right)^{2}}.$

The background contribution to in-jet particles from the underlying event
(UE), which refers to particles not associated with hard scatterings in jet
$R$ (p, jet) $<$ 0.4 region, is estimated in the perpendicular cone (PC) to
the jet axis with a radius $R_{\rm cone}=0.4$, as shown in Fig. 1.

Figure 1: Diagram illustrating the particle in jet cone region ($R$ (p, jet)
$<$ 0.4) and perpendicular cone region (UE).

To subtract the UE component from the jet cone selection, a particle density
per unit area $\rho$ is defined as

$\rho=N_{\mathrm{par}}/(N_{\mathrm{jet,ev}}A_{\mathrm{jet}}),$

where $N_{\mathrm{par}}$ is integrated yields of strange hadrons located in
the jet cone or PC, $N_{\mathrm{jet,ev}}$ is the number of generated events
containing at least one selected charged-particle jets, $A_{\mathrm{jet}}$ is
the area of all jet cones or PC occupied area in $\eta-\varphi$ plane in an
event. Note that the inclusive strange hadron distributions are usually
obtained with $|y|<0.5$, slightly different from that of the in-jet particle
acceptance $|\eta_{\mathrm{par}}|<0.75$.

##  4 Results

Figure 2: Charged particle pseudo-rapidity distribution
($\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$) (top) and multiplicity
distribution (bottom) in pp collisions at $\sqrt{s}~{}=~{}7$ TeV. The
experimental data are taken from ALICE:2010mty .

The results of ${\rm K}^{0}_{\rm{S}}$, ${\rm K}^{*0}$, ${\rm\phi}$,
${\rm\Lambda}$, ${\rm\Xi}^{\pm}$ and ${\rm\Omega}^{\pm}$ productions in pp
collisions at $\sqrt{s}~{}=~{}7$ TeV from PYTHIA8 will be compared to the
ALICE measurements in this section. The inclusive charged particle
pseudorapidity distribution ($\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$) and
the multiplicity distribution with color reconnection and color rope effects
are compared with the corresponding experimental data in Fig. 2. The
experimental data are shown in black point with the error box. The PYTHIA8
results with the Monash tune are shown in the black solid line. The CR and
rope model effects are presented with the red dashed line and the blue dotted
line, respectively. The green dash-dotted line includes both CR and rope
effects. In the BLC CR model, reformulated strings may produce more heavy
hadrons and hadrons with larger $p_{\mathrm{T}}$, the multiplicity in this
model is therefore supposed to be suppressed compared to the normal string
fragmentation picture. Previous studies suggest that the MPI regulating
parameter pT0Ref needs to be decreased to compensate this effect
Bierlich:2015rha , as already seen in Tab. 1. We see in the comparison of Fig.
2 (top) that the charged particle densities with the CR effect are consistent
with the experimental data. It is also interesting to see that the charged
particle yields are increased by about 10% in the rope model with respect to
the Monash tune. We also notice that the different fragmentation models can
hardly reproduce the experimental data shown by Fig. 2 (bottom) in the high
multiplicity region. A more exclusive study to describe the charge particle
distribution over a wide multiplicity range requires a systematic tuning to
the relevant model parameters, which is beyond the scope of this work and
should not change our conclusions on the strange hadron productions discussed
in the rest of this paper.

###  4.1 Inclusive strange particle production

The integrated yields of ${\rm K}^{0}_{\rm{S}}$, ${\rm K}^{*0}$, ${\rm\phi}$,
${\rm\Lambda}$, ${\rm\Xi}^{\pm}$, and ${\rm\Omega}^{\pm}$ in pp collisions at
$\sqrt{s}~{}=~{}7$ TeV varying with the event multiplicity are shown in Fig.
3. The Monash reference results are shown with the black solid lines. Color
reconnection and rope model effects are represented by the red dashed lines
and the blue dotted lines, while the CR and rope combined effects are
presented in the green dash-dotted lines. It is observed that the CR effects
generally enhance the productions in the baryon sector and suppress the meson
productions due to the creation of additional junction structures at the
beyond the leading color level. The rope model, however, slightly increases
the yield of all hadrons. Combining the CR and rope model, the meson
suppression due to CR is compensated and the enhancement to the baryon
production becomes stronger in the multi-strange particles as an outcome of
the string tension changes.

Figure 3: Integrated yields d$N/$d$y$ of various hadrons, ${\rm
K}^{0}_{\rm{S}}$, ${\rm K}^{*0}$, $\phi$, ${\rm\Lambda}$, ${\rm\Xi}$, and
${\rm\Omega}$, as functions of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$. The
mesons yields are shown in the top plots, and the baryons yields are shown in
the bottom plots. Model results are show for pp collisions at
$\sqrt{s}~{}=~{}7$ TeV, data for pp collisions at $\sqrt{s}~{}=~{}7$ TeV and
$\sqrt{s}~{}=~{}13$ TeV (only for $\phi$ particle). The data point are taken
from ALICE:2016fzo ; ALICE:2019etb .

Figure 4: Hadrons to $\pi$ ratios, ${\rm K}^{0}_{\rm{S}}/\pi$,
${\rm\phi}/\pi$, ${\rm\Lambda}/\pi$, ${\rm\Xi}/\pi$, and ${\rm\Omega}/\pi$, as
function of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$
distributions in pp collisions at $\sqrt{s}~{}=~{}7$ TeV. The mesons to $\pi$
ratios are shown in the top plots, and the baryons to $\pi$ ratios are shown
in the bottom plots. The data point are taken from ALICE:2016fzo ;
ALICE:2018pal .

The multiplicity dependent distributions of all the strange particle to pion
ratios are presented in Fig. 4. It is clearly seen that the baryon to meson
ratio increases with the event multiplicity in the CR model as shown by the
red dashed lines, resulted from the fact that more non-leading connected
partons can form junctions in the high multiplicity events. The resonance
meson states ${\rm K}^{*0}$ and ${\rm\phi}$ to pion ratios are gradually
decreasing with $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$, consistent with
the previous observation that lower mass states are preferred in the breakup
of strings with shorter length in the color reconnection model Goswami:2019mta
; Acconcia:2017bjv . After including the baryon enhancement from CR, the CR
combined rope model reasonably describes especially the multi-strange baryon
to meson ratio, which is an important signature of the strangeness
enhancement. The rapid growth of the ${\rm\Xi}^{\pm}$ and ${\rm\Omega}^{\pm}$
to pion ratio with $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ is a result of
the large string tension of color rope fragmentations in the high multiplicity
events. Strange quarks and spin 1 $ss$ diquarks are more likely to be produced
with larger string tensions during the string breakups in the rope
hadronization model. It is also noted that the resonance production feature in
the rope model is different from CR effects. ${\rm K}^{*0}$ and ${\rm\phi}$
meson to pion ratios are both enhanced in high multiplicity events with only
the color rope mechanism. The combined model, however, brings down the ${\rm
K}^{*0}$ yield while the ${\rm\phi}$ yield is further enhanced. To sum up, the
color rope model combined with CR effects is expected to provide the best
inclusive strange hadron production estimations.

###  4.2 Strange particle production in jets and UE

Figure 5: The integrated yields of ${\rm K}^{0}_{\rm{S}}$, ${\rm K}^{*0}$,
$\phi$, ${\rm\Lambda}$, ${\rm\Xi}$, and ${\rm\Omega}$ in underlying events
(left) and in charged-particle jets (right) as a function of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$
distributions in pp collisions at $\sqrt{s}~{}=~{}7$ TeV.

In this section, we study the strange hadron productions associated with hard
processes with the help of jet measurements. We estimate the strange hadron
yield from soft processes by investigating the hadron productions
perpendicular to the jet cone direction. The strange hadron yields normalized
to per unit acceptance area $\rho$ in PC as a function of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$ are
shown in the left panel of Fig. 5. Similar to what has been shown in Fig. 3,
the CR induced meson suppression and baryon enhancement persists in the PC
hadron productions. The strangeness number dependent baryon enhancement is
also observed in the CR and rope combined model. It can be inferred from this
resemblance that the inclusive strange hadron production is largely dominated
by the UE effects.

The in-jet integrated yields of ${\rm K}^{0}_{\rm{S}}$, ${\rm K}^{*0}$,
$\phi$, ${\rm\Lambda}$, ${\rm\Xi}$, and ${\rm\Omega}$ as a function of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$ are
presented in the right panel of Fig. 5. It is distinguishing that the strange
hadron productions in PC are largely driven by the event multiplicity while
the in-jet strange meson yields are quite stable over a wide multiplicity
range. This is not unexpected as the hadron production in UE is strongly
related to the number of multiple parton interactions in an event but the in-
jet hadron yield is more sensitive to the jet fragmentation effects.
Therefore, the in-jet meson yield only slightly changes with the event
charged-partice multiplicity density since the per jet energy, which dictates
the in-jet hadron productions, is hardly changed at different event activity.
On the other hand, the CR effect with or without color rope mechanism leads to
significant increase of the baryon yield inside the jet cone as a function of
the event multiplicity, indicating the CR effect is important for both soft
and hard processes. The faster increasing trend of the baryon production
inside jets also suggests that the junction structure due to color
reconnection is more likely to be formed inside jets. This is consistent with
the picture that beyond leading color reconnections often happen between
different MPI initiated string ends, thus quite impressive to the high
$p_{\mathrm{T}}$ physics.

Figure 6: The integrated yield ratios of strange hadrons to $\pi$ in
underlying events (left) and in charged-particle jets (right) as a function of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$
distributions in pp collisions at $\sqrt{s}~{}=~{}7$ TeV.

The strange hadron to $\pi$ ratios, ${\rm K}^{0}_{\rm{S}}/\pi$, $\phi/\pi$,
${\rm\Lambda}/\pi$, ${\rm\Xi}/\pi$, and ${\rm\Omega}/\pi$ as functions of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$
distributions in underlying evens of pp collisions at $\sqrt{s}~{}=~{}7$ TeV
derived by the integrated yields are shown in the left panel of Fig. 6. The
similar increasing trend compared to Fig. 4 confirms that the event activity
dependence of the strange to non-strange particle ratio observed in the
inclusive distribution is from soft processes.

The in-jet strange hadron to pion ratios in pp collisions at
$\sqrt{s}~{}=~{}7$ TeV varying with
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$ are
presented in the right panel of Fig. 6. It is found that the strange meson to
pion ratios including those for the strange resonance in jets are almost
independent of the
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$,
suggesting the high $p_{\mathrm{T}}$ parton flavor is more likely to be
determined by the hard QCD process and not sensitive to the fragmentation
details. The striking increase of the in-jet baryon yield is manifested in the
strange baryon to pion ratio as well. The rope model combined with CR effect
delivers the strangeness number dependent baryon enhancement feature like that
found in the inclusive distributions. It is also observed that unlike the
strange baryon to pion ratios in the inclusive distributions and PC, which
saturate at the intermediate $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$, the
in-jet strange baryon to pion ratios grow faster in the high multiplicity
events.

The jet shape dependence of the strange hadron yields is also investigated. In
Fig. 7. The yields of ${\rm K}^{0}_{\rm{S}}$, ${\rm K}^{*0}$, ${\rm\phi}$,
${\rm\Lambda}$, ${\rm\Xi}$ and ${\rm\Omega}$ as functions of the distance
between particle to the jet axis $R$(p, jet) are presented. It is found that
the decreasing trend of ${\rm K}^{0}_{\rm{S}}$, ${\rm K}^{*0}$, ${\rm\phi}$
and ${\rm\Lambda}$ strange hadron with $R$(p, jet) are almost the same. A
faster decreasing is observed for multi-strange baryons, ${\rm\Xi}$ and
${\rm\Omega}$, at large $R$(p, jet).

Figure 7: The integrated yields of ${\rm K}^{0}_{\rm{S}}$, ${\rm K}^{*0}$,
${\rm\phi}$, ${\rm\Lambda}$ (left) and ${\rm\Xi}$, and ${\rm\Omega}$ (right)
in jet cone as a function of $R$ (p, jet).

Figure 8: The ratios of ${\rm K}^{*0}$/${\rm K}^{0}_{\rm{S}}$,
${\rm\phi}$/${\rm K}^{0}_{\rm{S}}$, ${\rm\Lambda}$/${\rm K}^{0}_{\rm{S}}$
(left) and ${\rm\Xi}$/${\rm K}^{0}_{\rm{S}}$, and ${\rm\Omega}$/${\rm
K}^{0}_{\rm{S}}$ (right) in jet cone as a function of $R$ (p, jet).

We also investigate the jet shape dependence of the relative strange hadron
yield ratios in Fig. 8. In this comparison, the ratios of ${\rm K}^{*0}$,
${\rm\phi}$, ${\rm\Lambda}$, ${\rm\Xi}$, and ${\rm\Omega}$ to ${\rm
K}^{0}_{\rm{S}}$ in jet cone as function of distance between particle to jet
axis $R$(p, jet) are presented. It is found in the Monash reference all the
strange hadron to ${\rm K}^{0}_{\rm{S}}$ ratios are decreasing with $R$(p,
jet). The slow variation of strange resonances and ${\rm\Lambda}$ to ${\rm
K}^{0}_{\rm{S}}$ ratios implies that the in-jet strange resonance mesons and
${\rm\Lambda}$ baryons are uniformly produced along the string piece similar
to ${\rm K}^{0}_{\rm{S}}$. The more pronouncing $R$(p, jet) dependence for the
multi-strange baryons indicates that multi-strange baryon formations in the
string fragmentation framework are strongly related to the junction structures
created at the string ends. The multi-strange baryons are thus more likely to
be produced close to the jet axis, possibly being the leading hadron inside
the jet. It is interesting to see that the CR model provides different
behaviors for ${\rm\Lambda}$ to ${\rm K}^{0}_{\rm{S}}$ and multi-strange
baryon to ${\rm K}^{0}_{\rm{S}}$ ratios. This feature can result from that
${\rm\Lambda}$ baryons can be created with the reconnected junctions formed
between the beam remnant parts, thus pulling the ${\rm\Lambda}$ baryons away
from the jet axis direction close to the high $p_{\mathrm{T}}$ side of the
string end. The enhancement of multi-strange baryons in the CR model comes
from the connection of two already formed $s$ quarks, which are expected to be
associated with the hard production, leading to the enhanced production of
strange baryons close to the jet axis direction. This feature suggests the in-
jet multi-strange baryon productions can be potentially unique probes to the
hard QCD process related physics in the string fragmentation picture.

##  5 Summary

In summary, the production of strange hadrons is studied in pp collisions at
$\sqrt{s}~{}=~{}7$ TeV with the modified string fragmentation models within
the PYTHIA8 framework. The inclusive integrated yields and relative production
ratios to pion of strange particles as functions of the event multiplicity can
be well described by the combined color reconnection and color rope effects.
The CR model generally enhances the productions in the baryon sector and
suppress the meson productions with respect to Monash tune. The strange hadron
productions are also studied in events with energetic jets by dividing the
particles into the in-jet region and the underlying event region which are
expected to represent the hard and soft process effects, respectively. The
results indicate the inclusive strange particle production is dominated by the
underlying event contributions. The multiplicity dependence of the strange
particle yield in jets is found to be much weaker compared to the rapid growth
in underlying events, suggesting that the in-jet hadron production is more
sensitive to the jet fragmentation process. However, the color reconnection
and color rope induced enhancement of multi-strange hadron to pion ratio is
visible both in the soft and the hard process. The untamed increasing of the
in-jet strange baryon yield implies the strange baryon productions are largely
related to the hard process. The in-jet yields of strange particles are also
dependent on their distance to the jet axis. The multi-strange baryons are
more likely to be produced close to the jet axis compared to the strange
mesons. These observations may shed more light on the understanding to the
multiplicity dependent strangeness enhancement in pp collisions at LHC
energies.

###### Acknowledgements.

This work is supported by the National Key Research and Development Program of
China (2016YFE0100900), the National Natural Science Foundation of China
(11875143, 11905188 and 12061141008) and the Innovation Fund of Key Laboratory
of Quark and Lepton Physics LPL2020P01 (LZ). At the end we would like to thank
Christian Bierlich for providing us the input parameters for the color
reconnection and the color rope model.

## Appendix

To clarify the reliability of the treatment to the UE contribution in this
work, we provide in the Appendix additional details for the jet number
distributions in different multiplicity bins, which explores the multi-jet
impacts on our analysis.

Figure 9: Jet number distribution varying with the event multiplicity in each
minimum bias events (top), jet number with the event multiplicity distribution
in events with at least one high $p_{\mathrm{T}}$ jet (middle), and jet number
probability distribution in the most high multiplicity event class (bottom)
compared to that in inclusive events.

The top panel of Fig. 9 presents the yields of $p_{\rm T,~{}jet}^{\rm ch}>10$
GeV/$c$ jets dependent on the event multiplicity from the default PYTHIA8
simulations. The jet yields grow rapidly with the event multiplicity, while
the per-event high $p_{\mathrm{T}}$ jet number is around 0.02 even in the
highest multiplicity bin. We also explore the multiplicity dependence of jet
yields normalized to the events with at least one high $p_{\mathrm{T}}$ jet in
the middle panel of Fig. 9. It is shown that the produced jet number in each
jet event is very close to one and almost independent of the event activity.
The jet number probability distribution in high multiplicity jet events is
found to be similar to that in the minbias jet events as shown in the bottom
panel of Fig. 9. Most of the events contain only one jet and the probability
to have more than one back-to-back di-jet in an event is very low. In that
sense, the contamination to UE from jet particles is negligible within the
accessible multiplicity range which can be covered by the current experiments
in pp collisions at the LHC energy. Like what has been done in many jet
related experimental studies ALICE:2021cvd ; ALICE:2019mmy , the UE
contribution can be safely estimated simply by taking the perpendicular region
to the leading jet direction, which is denoted as the perpendicular cone
method in this work.

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# COLA: COarse LAbel pre-training for 3D semantic segmentation of sparse LiDAR
datasets

Jules Sanchez  MINES ParisTech, PSL University,
Centre for Robotics,
75006 Paris, France
<EMAIL_ADDRESS>Jean-Emmanuel Deschaud  MINES ParisTech, PSL
University,
Centre for Robotics,
75006 Paris, France
<EMAIL_ADDRESS>Francois Goulette  MINES ParisTech,
PSL University,
Centre for Robotics,
75006 Paris, France
<EMAIL_ADDRESS>
###### Abstract

Transfer learning is a proven technique in 2D computer vision to leverage the
large amount of data available and achieve high performance with datasets
limited in size due to the cost of acquisition or annotation. In 3D,
annotation is known to be a costly task; nevertheless, pre-training methods
have only recently been investigated. Due to this cost, unsupervised pre-
training has been heavily favored.

In this work, we tackle the case of real-time 3D semantic segmentation of
sparse outdoor LiDAR scans. Such datasets have been increasingly released, but
each has a unique label set. We propose here an intermediate-level label set
called coarse labels, which can easily be used on any existing and future
datasets, thus allowing all the data available to be leveraged at once without
any additional manual labeling.

This way, we have access to a larger dataset, alongside a simple task of
semantic segmentation. With it, we introduce a new pre-training task: coarse
label pre-training, also called COLA.

We thoroughly analyze the impact of COLA on various datasets and architectures
and show that it yields a noticeable performance improvement, especially when
only a small dataset is available for the finetuning task.

###### Index Terms:

LiDAR, semantic segmentation, pre-training

##  I Introduction

LiDAR-based deep learning has been gaining a lot of traction in recent years,
especially for autonomous driving. Thus, an increasing amount of data has been
released for scene understanding, such as KITTI [1] and Argoverse 2 [2] for
detection or SemanticKITTI [3] and nuScenes [4] for semantic segmentation.

So far, 3D semantic segmentation methods have focused on architecture design
and tuning rather than data-driven approaches to improve performance. Some
works have started to emerge on domain adaptation and transfer learning to
ensure good performances when the amount of target annotations is limited or
nonexistent.

Transfer learning is the ability to reuse previously learned information in a
deep learning model. We can decompose transfer learning into two parts: first,
a pre-training task for which there is usually a large amount of data
available, and then a finetuning task, which is the task we want our model to
achieve in the end. The pre-training task helps the network to learn useful
representations that should speed up the training and improve the results of
the finetuning task.

Domain adaptation is a subset of transfer learning, aiming specifically to
transfer knowledge when the pre-training and finetuning tasks are similar.
However, it is applied in a specific scope where the pre-training data and the
finetuning data are available simultaneously.

(a) SemanticKITTI coarse labels.
8 different labels

(b) SemanticPOSS fine labels.
13 different labels

Figure 1: COLA pipeline.

Thus far, most of the work done in 3D pre-training has been leveraging
contrastive learning (see subsection II-B). Existing work studying semantic
segmentation as the finetuning task focused on dense point clouds [5], whereas
work looking into outdoor LiDAR scans focused on object detection [6].

We propose a new pre-training method that leverages a set of heterogeneous
source datasets thanks to a simple label unification techniques for LiDAR
point cloud semantic segmentation. Contrary to domain adaptation methods,
access to the pre-training data is not required when finetuning our models.
This way, we can provide off-the-shelf pre-trained models that can be directly
finetuned on any autonomous driving semantic segmentation dataset and
systematically increase performance on the finetuning task.

We introduce an intermediate-level label set called coarse labels that can be
applied to any autonomous driving semantic segmentation dataset. We
demonstrate that using this intermediate label set enables us to use all
datasets together to pre-train neural architectures and improve performance
after finetuning.

Furthermore, we highlight the limitation of existing contrastive-based methods
for the task of autonomous driving semantic segmentation by looking at CSC
results. For a fairer comparison, we also train our own contrastive learning-
based method by following PointContrast [5] and applying it to sparse
autonomous driving data. We call it SPC, for Sparse PointContrast.

The mapping from existing available datasets to the proposed label set
alongside links to our pre-trained models using the largest source dataset can
be found at https://github.com/JulesSanchez/CoarseLabel.

In practice, our contributions are as follows:

  * •

Studying the limitations of current contrastive based methods for autonomous
driving 3D semantic segmentation.

  * •

Introducing a label set specific to the task of semantic segmentation of
autonomous driving (sparse LiDAR scan) generic enough to leverage every
dataset at once.

  * •

Thoroughly experimenting on a new pre-training that leverages this new label
set. This method, called COLA (COarse LAbel pre-training) is shown in Figure
1. It is quantitatively and qualitatively studied, showing a mIoU improvement
of up to +6.4% on the target dataset.

##  II Related Works

###  II-A 3D autonomous driving semantic segmentation

Semantic segmentation for autonomous driving has two main challenges:
achieving real-time inference and dealing with the unordered structure of the
LiDAR point clouds.

As such, several types of methods have emerged: using only a permutation
invariant operation [7][8][9], redefining the convolution [10][11][12][13],
projecting the point clouds in 2D with a range-based image [14][15] and
bird’s-eye-view images [16] or leveraging sparse convolution-based
architectures as introduced by MinkowskiNet [17], under the name Sparse
Residual U-Net (SRU-Net).

SRU-Nets have been used as the backbone for more refined methods [17], [18],
[19], [20] that are the best performing methods on the various benchmarks.

Figure 2: The proposed coarse labels and their mapping to SemanticKITTI fine
labels.

###  II-B 3D transfer learning

As mentioned in the introduction, 3D transfer learning has mainly relied on
unsupervised contrastive pre-training tasks such as in PointContrast [5], CSC
[21], DepthContrast [22] or CrossPoint [23]. PC-FractalDB [24] proposes an
alternative to contrastive learning by learning fractal geometry as the pre-
training task. Point-BERT [25] looks into pre-training of point cloud
transformers specifically.

All those methods look into either shape understanding, indoor dense scene
understanding or outdoor dense scene understanding as they rely on the large
availability of such data [26] [27] [28] to perform their pre-training task.

Fewer methods have looked into pre-training for outdoor sparse point clouds.
GCC-3D [6] applies a two-step self-supervised method, first learning
contrastive features and then leveraging the sequential nature of the data to
generate pseudo instances that can be used to learn semantic clustering.
ProposalContrast [29] proposes learning contrastive information at the
proposal level rather than point or voxel levels. These outdoor methods are
specifically designed for object detection and are not evaluated on any
semantic segmentation finetuning tasks.

None of the aforementioned methods has looked into autonomous driving semantic
segmentation as the finetuning task, highlighting a gap in the study of the
pre-training effect on this case.

###  II-C Leveraging heterogeneous datasets

Using several datasets at once for supervised learning is a nontrivial task.
Datasets, even for a similar task, usually have vastly different label sets.
This variation can come from the type of elements in the scene or annotation
choices.

To leverage as much of these data as possible , several techniques have been
implemented. Some approaches have chosen to only leverage common labels across
datasets [30] [31] or the union [32], to have one shared encoder and one
decoder for each dataset [33] [34], to leverage label relationships [35] [36]
[37], finally some have chosen to unify annotations through remapping [38] and
re-annotation [39].

Category-shift multi-source domain adaptation, as defined in the proposed
taxonomy of [40], aims to tackle a similar issue as it leverages a set of
heterogeneously labeled source datasets to improve the performance of a target
dataset presenting a different label set, as in Deep Cocktail Network [41] and
mDALU [40].

Inspired by the first type of method, COLA focuses on leveraging the
annotations of all the pre-training data without any additional human cost.
Furthermore, contrary to domain adaptation methods, COLA provides off-the-
shelf pre-trained models that can be finetuned without requiring access to the
pre-training data.

##  III COLA

###  III-A Shortcomings of simple contrastive approaches

Contrastive learning has been the main approach for the pre-training of 3D
models. As such, we want to investigate them for our specific finetuning task.
As one of the founding and reference methods for dense point clouds, we
investigate specifically CSC [21].

In Table I, we show the results after finetuning on three major autonomous
driving 3D semantic segmentation datasets when the model is pre-trained with
CSC and with a LiDAR-based adaptation Sparse PointContrast (SPC). Whereas CSC
is trained on dense point clouds (ScanNetV2 [26]), SPC follows the same
training methodology but with 100K LiDAR scans, leveraging mainly KITTI-360
[42]. We see that CSC results in small to moderate improvement (from +$0.2\%$
to +$1.1\%$), whereas SPC pre-training systematically decreases results in the
finetuning task.

Results could be different with more recent methods working on LiDAR scans
such as GCC-3D, but their work is not available.

In total, the SPC pre-training took the equivalent of 50 GPU days of training.
In comparison, CSC takes approximately 15 GPU days to be trained. This
discrepancy stems from the difference in scan sizes regarding number of points
and their range in meters. The duration of the SPC pre-training makes it
unrealistic to perform it on 1M scans such as the ONCE dataset [43], which is
10 times larger than the dataset used for SPC, as it would amount to 500 GPU
days.

|  | No pre-
---
training
| CSC
---
| SPC
---
nuScenes | 67.2 | 68.3 (+1.1) | 66.3 (-0.9)
SemanticKITTI | 50.5 | 50.7 (+0.2) | 48.9 (-1.6)
SemanticPOSS | 55.0 | 55.5 (+0.5) | 54.4 (-0.6)
TABLE I: Test set mIoU for each target dataset. No pre-training, dense
contrastive pre-training (CSC), and sparse contrastive pre-training (SPC) with
the SRU-Net architecture.

We see that contrastive pre-training at the moment is not suited for our
specific case, and scaling the method to leverage more data would require
significant time and computing power. We believe that discarding human
annotations to rely solely on unsupervised pre-training is a waste of
information, and supervised methods are still relevant.

To the best of our knowledge, we propose the first method of pre-training in
the case of semantic segmentation of LiDAR point clouds in the context of
autonomous driving. Furthermore, we propose a novel approach using a
supervised pre-train task as opposed to the self-supervised and unsupervised-
centered methods that are the typical approaches.

###  III-B Available semantic segmentation data

Since the release of SemanticKITTI in 2019, other autonomous driving semantic
segmentation LiDAR datasets have been available. We focus on five different
datasets, which are the most important at the time of the writing due to the
variety in size, scene types, and hardware used for acquisition. As seen in
Table II, limiting a method to one dataset would be omitting a large amount of
data. However, thus far, it is impossible to use them all at once, as there is
no unique fine label set.

Dataset | Size | Scene type | #Labels
---|---|---|---
KITTI-360 [42] | 80K | Suburbs | 27
nuScenes [4] | 35K | Urban | 16
SemanticKITTI [3] | 23K | Suburbs | 19
PandaSet [44] | 6K | Urban & Road | 37
SemanticPOSS [45] | 3K | Campus | 13
TABLE II: Summary of the datasets used in the different experiments. The size
corresponds to the number of labeled scans. Labels correspond to the labels
used at the inference time.

Despite this obvious obstacle, a study of the datasets shows that labels are
organized in a tree-like structure with more or less refined labels, similar
to the one highlighted by [35]. Moreover, higher levels of trees are more
uniform across datasets.

###  III-C Coarse Labels

Based on these observations, we propose a set of coarse labels such that we
can easily map fine labels from any dataset to this one. These coarse labels
define categories that retain information relevant to the end task, are
consensual across all existing and future datasets, and display little
ambiguity; furthermore, they come at no additional annotation cost.

Besides these technical advantages, we believe that those coarse labels can
still represent effectively the major elements of a typical road scene such
thaht a model trained with them would still be relevant for autonomous
driving. The coarse labels we propose are as follows:

  * •

Driveable ground covers areas where cars are expected to be driving.

  * •

Other ground corresponds to other large planar surfaces, where pedestrians can
be found.

  * •

Structure corresponds to fixed human-made structures, which can be hard to
subdivide into smaller groups.

  * •

Vehicles are the typical road users.

  * •

Nature corresponds to the vegetation-like components of the scene.

  * •

Living being groups humans and animals alike, who can interact with all the
other elements.

  * •

Dynamic objects are objects that can typically move, such as strollers.

  * •

Static objects are objects that are fixed, such as poles.

An illustration of the labels and the mapping of the fine labels from
SemanticKITTI to the proposed label set can be found in Figure 2. All mappings
are available in our public GitHub
repository111https://github.com/JulesSanchez/CoarseLabel.

###  III-D COLA (Coarse Label pre-training)

Given this new coarse label set, we can perform semantic segmentation on all
the data at once. This supervised learning is the proposed COarse LAbel (COLA)
pre-training presented in the introduction. To reuse such a pre-trained model,
only the last layer of the model needs to be replaced for finetuning, to
account for the new number of labels (see Figure 1). Due to the size of the
architecture, no layers need to be frozen at the time of finetuning. In this
way, COLA is expected to learn representations tailored for the specific task
of autonomous driving semantic segmentation. The validation mIoU of the pre-
training reaches between $65$% and $78$%, depending on the target dataset,
which is sufficient to conclude that the architecture has learned relevant
features, confirmed in subsection III-E.

In practice, COLA took the equivalent of 10 GPU days of training time,
resulting in a much shorter pre-training procedure than SPC.

We expect COLA to perform well for several reasons. First, seeing various
sensor and environment settings in its training set will help generalize to
new scenes and sensors. Second, aligning the pre-training and finetuning tasks
to be very similar ensures the relevance of the learned features, both
geometrically and semantically.

###  III-E Pre-training feature analysis

In this section, we proceed to a feature analysis of the last layer, before
the classification of a SRU-Net model after the COLA pre-training. We base the
analysis on the SemanticPOSS dataset to study COLA when the largest amount of
pre-training data is available.

To conduct the analysis, we give point clouds extracted from SemanticPOSS
until we reach at least 200 points for each ground truth category and extract
their associated last layer features. We then do a t-SNE analysis and plot the
2D projection in Figure 3, where points are colored according to either their
coarse ground truth or fine ground truth. We observe the ability of the model
to correctly cluster points in both the coarse label set and in the fine label
set, even though it was not yet finetuned and had never seen any SemanticPOSS
data. This demonstrates the ability of COLA to generalize the segmentation to
unseen data and furthermore shows the relevance of learning coarse labels even
when fine labels are the end goal.

We focus on a particular case of the COLA t-SNE analysis in Figure 3. In the
right image, we highlighted (points are circled in black) points belonging to
either car or bike categories. We observe a highly desirable pattern, which is
that COLA learned to distinguish bikes from cars feature-wise, even if they
were not annotated as such in the coarse labels. This highlights that the pre-
training method leverages both semantics and geometry, and thus, COLA does not
rely on a perfect intermediate label set to learn relevant features.

(a) t-SNE analysis of COLA
colored with coarse labels

(b) t-SNE analysis of COLA
colored with fine labels

Figure 3: t-SNE analysis of the last feature layers of SRU-Net trained with
COLA. Inference performed on SemanticPOSS.

##  IV Experiments

In this section, we describe the experimental setup used to evaluate the
performance of the proposed coarse label pre-training (COLA).

###  IV-A Experimental cases

For all our experiments, we split the data into two categories: the target
data, which is the data we used for finetuning, on which we compute
performance metrics, and the pre-training data. KITTI-360 is not used for pre-
training in the case of the SemanticKITTI target as there is a significant
geographic overlap of their scenes.

The four cases we chose correspond to experimenting on the two reference
datasets in the community (nuScenes and SemanticKITTI), as well as on two
limited data availability setups (SemanticPOSS and partial nuScenes).
Additional details can be found in Table III. Partial nuScenes is a homemade
set of datasets, which corresponds to subsets of nuScenes to provide access to
a wider range of dataset sizes; otherwise, we would be limited to
SemanticPOSS.

As highlighted in Table II, target datasets present different scene types, and
furthermore, nuScenes and SemanticKITTI are acquired with sensors of very
different resolutions. In this way, we can evaluate the methods in many
settings.

We experiment on two architectures, SPVCNN [18] and SRU-Net [17] which are
staples of the autonomous driving semantic segmentation field, either as
state-of-the-art architecture or typical backbone.

To study COLA, we compute the mean Intersection over Union (mIoU) computed on
an extracted test set. All experiments are performed on NVIDIA GeForce RTX
3090 GPUs.

Pre-training data |  | # Scans for
---
pre-training
Target |  | # Size ratio
---
| SK + K360 + SP + PS
---
110K | NS | 25%
| SK + K360 + PS + NS
---
140K | SP | 2%
| SP + NS + PS
---
45K | SK | 33%
| SK + K360 + SP + PS
---
110K |  | PartialNS
---
| 2.5%-25%
---
| SK + K360 + SP + PS
---
110K |  | PartialSP
---
| 0.7%
---
TABLE III: Datasets used for pre-training depending on the target and the size
ratio between the target set and the pre-training set. The various datasets
are SemanticKITTI (SK), KITTI-360 (K360), nuScenes (NS), SemanticPOSS (SP) and
PandaSet (PS)

###  IV-B Partial nuScenes and partial SemanticPOSS

We introduced partial nuScenes previously. Partial nuScenes is a subset of
nuScenes, based on the number of scenes. We propose three levels: 10%, 25%,
and 50%, which represent 95, 235, and 470 scenes (respectfully 1900, 4700, and
9400 scans), respectively, for training and validation, which are split in the
same proportion as the full nuScenes 70/30. The test set is the same one as
the full nuScenes test set and represents 230 scenes (4500 scans).

To have an even smaller dataset available, we similarly introduce partial
SemanticPOSS, composed of one sequence (00) for training and one for
validation. The same test set is used as for SemanticPOSS.

###  IV-C Networks and parameters

We experimented on two architectures, one state of the art (SPVCNN [18]) and a
traditional backbone (SRU-Net [17]), to demonstrate the ability of COLA to be
helpful independantly of the chosen architecture.

####  IV-C1 SRU-Net

For the COLA pre-training, we used the SGD optimizer, with an initial learning
rate of 0.4, a momentum of 0.9, and a cosine annealing scheduler. We had a
batch size of 48 over 10 epochs.

For finetuning, whether the model has been pre-trained or not, we use the same
parameters. We used the SGD optimizer, with an initial learning rate of 0.8, a
momentum of 0.9, and a cosine annealing scheduler. We had a batch size of 36
over 30 epochs.

The model used is the same as the one used in [21].

####  IV-C2 SPVCNN

For the COLA pre-training and the finetuning, we used the SGD optimizer, with
an initial learning rate of 0.24, a momentum of 0.9, and a cosine warmup
scheduler. We had a batch size of 16 over 15 epochs.

The model used is the one provided by the original authors in the official
GitHub repository [18].

All models are trained with the mixed Lovasz loss function and following the
same data augmentation as [17].

##  V Results

In this section, we show the results from the thorough experiments described
in the previous sections. They are divided into two parts. First, we look at
results on full datasets (SemanticKITTI, SemanticPOSS, and nuScenes), and on
each network architectures, and then, we investigate more precisely the case
of limited data with partial nuScenes. In each case, we show the mIoU over a
test set, which we extract from the training set, representing between 10% and
20% of the available data. We compare all COLA results to the no pre-training
case. Due to the lack of methods tackling the same finetuning task we cannot
compare our methods to any baseline besides the work done in subsection III-A.

###  V-A Results on SemanticKITTI, nuScenes, and SemanticPOSS

| SRU-Net | SPVCNN
---|---|---
|  | No pre-
---
training
| COLA
---
(Ours)
| No pre-
---
training
| COLA
---
(Ours)
nuScenes | 67.2 | 69.3 (+2.1) | 65.9 | 66.2 (+0.3)
SemanticKITTI | 50.5 | 52.4 (+1.9) | 57.7 | 58.4 (+0.7)
SemanticPOSS | 55 | 55.8 (+0.8) | 49.9 | 53.8 (+3.9)
TABLE IV: Test set mIoU on each target dataset. No pre-training, and COLA pre-
training.

Overall, the models pre-trained with the proposed COLA pre-training show
significant improvement compared with the other methods, with a gain of up to
+$2\%$ for SRU-Net and up to +$4\%$ for SPVCNN Table IV, in every case
displaying significant improvement when compared with naive contrastive
approaches (Table I).

###  V-B Results on partial nuScenes and partial SemanticPOSS

% scenes | # of scans | SRU-Net | SPVCNN
---|---|---|---
|  |  | No
---
pre-training
| COLA
---
(Ours)
| No
---
pre-training
| COLA
---
(Ours)
10% | 1900 | 46.2 | 48.4 (+2.2) | 44.9 | 51.3 (+6.4)
25% | 4700 | 58.0 | 60.0 (+2.0) | 52.5 | 55.6 (+3.1)
50% | 9400 | 62.4 | 65.0 (+2.6) | 56.8 | 57.2 (+0.4)
100% | 16000 | 67.2 | 69.3 (+2.1) | 65.9 | 66.2 (+0.3)

TABLE V: Test set mIoU on each partial nuScenes. No pre-training, and COLA
pre-training.

# of scans | SRU-Net | SPVCNN
---|---|---
|  | No pre-training
---
| COLA (Ours)
---
| No pre-training
---
| COLA (Ours)
---
500 | 35.2 | 37.9 (+2.7) | 32.9 | 36.8 (+3.9)
1500 (full) | 55 | 55.8 (+0.8) | 49.9 | 53.8 (+3.9)

TABLE VI: Test set mIoU on partial SemanticPOSS. No pre-training and COLA pre-
training.

We compiled results for partial nuScenes for both architectures in Table V and
the ones for partial SemanticPOSS in Table VI. We confirmed the previous
conclusions that the proposed COLA pre-training improves the performance
significantly, whatever the architecture, when a small dataset is available.
this is even more significant for SPVCNN.

###  V-C Qualitative results

We show some qualitative results on SemanticKITTI with SRU-Net in Figure 4.
Segmentation errors are red, and we can see a significant decrease in mistakes
thanks to COLA pre-training especially for buildings and vegetation. More
visualization of semantic results on SemanticPOSS comparing the baseline (no
pre-training) with COLA pre-training is presented in Figure 5. Zoom in for a
better visualization.

(a) Results for
no pre-training

(b) Results for
COLA training

Figure 4: Example of results on SemanticKITTI after finetuning with SRU-Net.
In blue, points with correct semantic segmentation. In red, errors.

(a) Results for no pre-training

(b) Results for COLA

Figure 5: Example of results on SemanticPOSS after finetuning with SRU-Net.
Highlighted in pink (resp. orange), some pedestrian (resp. cars) misclassified
without pre-training and corrected by COLA.

###  V-D Ablation study

In the ablation study presented in Table VII, we analyze the importance of the
different steps that are part of our proposed COLA pre-training. We conduct
our analysis with SemanticPOSS as the target dataset as this is the one with
largest size ratio (see Table III). We are comparing four cases: no pre-
training, pre-training with only KITTI-360 labeled with its original fine
labels, pre-training with only KITTI-360 labeled with our proposed coarse
labels, and finally, applying the full COLA, that is, all the pre-training
data labeled with the coarse labels.

First, we arrive at the same conclusions as the one presented in PointContrast
[5]. In the case of 3D scene understanding, pre-trainings still provide a
substantial gain compared with training from scratch, and the data ceiling is
not reached yet, as shown by the increase in performance between COLA and pre-
training with only KITTI-360 (+1.4 mIoU) (Table VII).

The second highlight is the impact of the coarse labels compared with the fine
labels. We demonstrate an improvement in using the coarse labels rather than
the fine labels as a pre-training task (+0.6 mIoU). This means than beside
providing a simpler mapping in between label sets, it also serves a purpose
model-wise. This stems from the simplicity of the labels provided by the
coarse labels. When finetuning the model does not need to unlearn anything,
unlike the pre-training with the fine labels, where some labels and objects do
not exist anymore.

Finally, we compare our approach (COLA) with a more naive pre-training
approach that would have a classification module for each of the pre-training
datasets rather than having a unified classification module. In this way, each
dataset is trained with its fine labels rather than using the coarse label
set. This method is referred to MH (multi-head) in Table VII. COLA
demonstrates a significant improvement (+1.1 mIoU) over MH and highlights the
effectiveness of using an intermediate label set rather than naively using
fine label sets.

In subsection III-C, we proposed a coarse label set we deemed representative
of autonomous driving data. We showed that it managed to learn useful geometry
information beyond the annotated coarse label: nevertheless, the choice of the
label set could still be discussed. In Table VIII, we study the impact of the
coarse label set choice: more precisely, we compare the results when we use
coarser category (5 instead of 8 by grouping driveable ground and other
ground, and grouping dynamic and static objects and structure) or finer
categories (10 categories instead of 8 by subdividing static objects into
poles and other objects, and subdividing vehicles into 2-wheeled and 4-wheeled
vehicles). We can see that the pre-training is robust to the number and choice
of coarse labels, allowing in all cases a gain of about +2% mIoU, with a
slight advantage for our 8 categories.

Methodology | mIoU
---|---
Only finetuned on SemanticPOSS = (1) | 49.9
Pre-trained with KITTI-360 (fine labels) + (1) | 51.8 (+1.9)
Pre-trained with KITTI-360 (coarse labels) + (1) | 52.4 (+2.5)
Pre-trained with MH (all datasets) + (1) | 52.7 (+2.8)
Pre-trained with COLA (all datasets) + (1) | 53.8 (+3.9)
TABLE VII: Ablation study of the method focusing on the impact of the coarse labels and the amount of pre-training data with SPVCNN. The target dataset on which the test set mIoU is computed is SemanticPOSS. Methodology | mIoU
---|---
Only finetuned on SemanticPOSS = (1) | 49.9
Pre-trained with KITTI-360 with 5 coarse labels + (1) | 52.2 (+2.3)
Pre-trained with KITTI-360 with 10 coarse labels + (1) | 52.1 (+2.2)
Pre-trained with KITTI-360 with the same labels as COLA + (1) | 52.4 (+2.5)
TABLE VIII: Ablation study of the method focusing on the impact of the number
of coarse labels with SPVCNN. The target dataset on which the test set mIoU is
computed is SemanticPOSS.

##  VI Conclusion

In this paper, we proposed a new supervised pre-training method for autonomous
driving semantic segmentation in order to leverage existing annotations and
extract meaningfully semantic and geometric information from the available
data.

We demonstrated that the proposed COLA method shows great promises.
Specifically, it works very well when the amount of data is limited, but the
proposed method is not restricted to this use case. Furthermore, we have shown
the proposed method works on various data setups and manages to improve
performance even when the target setup is not seen during the pre-training.
COLA needs fewer raw data than typical contrastive approaches followed thus
far, in addition to needing significantly less computational power and time.

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