# Minimal realization of light thermal Dark Matter

Johannes Herms<EMAIL_ADDRESS>Max-Planck-Institut für Kernphysik,
Saupfercheckweg 1, 69117 Heidelberg, Germany  Sudip Jana sudip.jana@mpi-
hd.mpg.de Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117
Heidelberg, Germany  Vishnu P.K<EMAIL_ADDRESS>Department of Physics,
Oklahoma State University, Stillwater, OK, 74078, USA  Shaikh Saad
<EMAIL_ADDRESS>Department of Physics, University of Basel,
Klingelbergstrasse 82, CH-4056 Basel, Switzerland

###### Abstract

We propose a minimal UV-complete model for kinematically forbidden Dark Matter
(DM) leading to a sub-GeV thermal relic. Our crucial realization is that the
two-Higgs-doublet model can provide a light mediator through which the DM can
annihilate into SM leptons, avoiding indirect detection constraints. The DM
mass is predicted to be very close to the mass of the leptons, which can
potentially be identified from DM annihilation into gamma-rays. Due to sizable
couplings to muons in reproducing the DM relic abundance, this framework
naturally favors a resolution to the $(g-2)_{\mu}$ anomaly. Furthermore, by
embedding this setup to the Zee model, we show that the phenomenon of neutrino
oscillations is inherently connected to the observed relic abundance of DM.
All new physics involved in our framework lies at or below the electroweak
scale, making it testable at upcoming colliders, beam-dump experiments, and
future sub-GeV gamma-ray telescopes.

_Introduction_.– Dark matter (DM) is a central part of our understanding of
the cosmos, and identifying its nature is a key goal of contemporary
cosmology, astro- and particle physics. A prime candidate for DM is thermal
relic particles – a new neutral, long-lived particle species that was in
thermal equilibrium with the particles of the Standard Model (SM) in the early
Universe before the connecting interactions froze-out when it reached the DM
abundance we observe today.

This archetypal Weakly Interacting Massive Particle (WIMP) DM scenario
motivated great experimental efforts to identify these particles.
Traditionally, the focus has been on electroweak-scale WIMPs (see eg.
Bertone:2016nfn ; Lee:1977ua ) since these are expected in many theories
beyond the Standard Model and can naturally decouple at the correct abundance.
With, on the one hand, the experimental program to search for EW-scale DM
particles well underway, and on the other hand, the degree of confidence in
new physics at the EW-scale waning in the face of the success of the SM at the
LHC, thermal relics at smaller masses have become a focus of attention. This
trend in DM studies is supported by connections to low-energy anomalies in
particle physics, in particular, the $(g-2)_{\mu}$ tension Muong-2:2021ojo ,
and can relate to neutrino physics, see, e.g., Ref. Jana:2020joi .

Figure 1: Schematic diagram for light DM annihilation to SM charged leptons
via 2HDM-portal.

Thermal DM in the mass range $\,\mathrm{MeV}\lesssim m_{\mathrm{DM}}\lesssim
10\,\mathrm{GeV}$ requires a few general conditions. It typically requires a
stabilizing symmetry to forbid decay, in contrast to lighter, keV-scale DM
candidates like sterile neutrinos Dodelson:1993je ; Roach:2019ctw ;
Heeba:2018wtf . Equilibration with the SM in the early Universe then proceeds
via annihilation, as in the WIMP scenario. The annihilation products cannot be
much heavier than the DM candidate, necessitating a coupling to light SM
particles. In contrast to heavier WIMPs, successful sub-GeV freeze-out DM
generically requires the existence of a new light mediator to enable a
sufficiently large annihilation rate 111This is true also in scenarios where
DM does not annihilate directly to SM particles, such as secluded DM
Pospelov:2007mp  or to a lesser extent SIMP DM Hochberg:2015vrg , where the
heat produced in DM annihilation is ultimately transferred to the SM bath. For
this reason, many models in the literature propose to extend the gauge
symmetry 222For non-Abelian gauge extension that offers vector dark matter
candidate, see, e.g., Ref. Chowdhury:2021tnm . of the theory by a $U(1)_{D}$,
with a dark photon that can mediate between the dark and visible sectors (for
instance, see e.g., Refs. Boehm:2003hm ; DAgnolo:2015ujb ; Lee:2015gsa ;
Pospelov:2007mp ).

In contrast to these previous DM theories that include new gauge sectors (e.g.
Boehm:2003hm ; DAgnolo:2015ujb ; Lee:2015gsa ; Pospelov:2007mp ) or multi-
fermionic extensions (e.g. Boehm:2003hm ; Batell:2017kty ; DAgnolo:2020mpt ),
this letter presents a minimal, ultraviolet complete (UV) model of sub-GeV
thermal DM. Our proposal is based on the crucial fact that adding a second
Higgs doublet Branco:2011iw  to the SM allows for a light scalar Jana:2020pxx
that can couple to the light SM degrees of freedom and DM particles.
Specifically, we work in the two-Higgs-doublet model (2HDM) framework, where
DM annihilates into SM leptons via a light mediator emerging from the 2HDM.
The simplest DM candidate is a real scalar stabilized by a $\mathbb{Z}_{2}$
symmetry that can easily reproduce the observed relic abundance utilizing the
2HDM-portal.

After taking into account constraints on the DM annihilation today and during
the epoch of CMB decoupling, the DM mass is required to be in the ‘forbidden’
regime Griest:1990kh ; DAgnolo:2015ujb ; DAgnolo:2020mpt , where it is just
slightly lighter than the SM particle it annihilates into. This makes for a
predictive and positively identifiable framework, motivating particularly for
searches for sub-GeV gamma-ray lines close to SM lepton masses in the simplest
scenario. Furthermore, the favored parameter space implies a positive shift
for muon $g-2$ with the proper sign and strength to account for the
measurement at Fermilab Muong-2:2021ojo .

Additionally, we consider the possibility of neutrino mass generation by a
simple extension of this setup. Introducing a charged scalar allows for non-
zero neutrino mass via one-loop quantum corrections. Within this framework,
the same Yukawa couplings reproducing the correct DM relic abundance also
participate in neutrino mass generation while remaining consistent with lepton
flavor violating constraints.

To demonstrate the versatility of the light 2HDM scalar portal, next, we
entertain the scenario of fermionic DM (see also Batell:2016ove ; Jia:2021mwk
). A singlet fermion (either Dirac or Majorana) DM can annihilate into SM
leptons via a singlet scalar that mixes with the light scalar arising from the
2HDM. Annihilation of fermion DM through a scalar mediator is velocity-
suppressed, evading bounds on energy release during CMB decoupling. This
allows for a wide range of DM and mediator masses, illustrating the broad
potential of the light 2HDM-portal.

In the following, before presenting minimal models for scalar and fermionic
sub-GeV DM, we first recapitulate the thermal freeze-out mechanism for DM
production. We present constraints from DM relic density, $(g-2)_{\mu}$,
flavor violation, and DM indirect detection. Before concluding, we briefly
demonstrate how neutrino masses can be naturally incorporated into the
light-2HDM scenario.

_Forbidden DM_.– The relic density of thermal DM is calculated by tracing its
evolution in the early Universe. If the decay of DM into SM particles is
precluded by symmetry, the leading number-changing term in the Boltzmann
equation stems from annihilations of pairs of DM particles

$\frac{dn_{\mathrm{DM}}}{dt}+3Hn_{\chi}=\zeta{\langle\sigma
v\rangle}\left(n_{\mathrm{DM}}^{2}-n_{\mathrm{DM}}^{\mathrm{eq}2}\right)\,,$
(1)

where $n_{\mathrm{DM}}$ is the total DM number density, $H$ is the Hubble
expansion rate, and ${\langle\sigma v\rangle}$ is the thermally averaged
cross-section of DM annihilating into other bath particles ($\zeta=(1/2)\,1$
for (non-)self-conjugate DM particles). In the freeze-out scenario, the relic
density is determined by the time (marked by the corresponding temperature of
the SM bath, $T_{\mathrm{fo}}$) when the annihilation rate drops below the
Hubble rate

$\zeta{\langle\sigma v\rangle}n_{\mathrm{DM}}^{\mathrm{eq}}=H\,.$ (2)

It is often sufficient to work in the instantaneous freeze-out approximation,
where the comoving DM density (denoted in terms of the abundance $Y\equiv
n/s$, with $s$ the SM entropy density) stays constant after freeze-out

$Y_{\mathrm{DM}}^{\mathrm{today}}=Y_{\mathrm{DM}}^{\mathrm{eq}}\left(T_{\mathrm{fo}}\right)\,.$
(3)

This is to be compared to value corresponding to the observed DM density
$\Omega_{\mathrm{DM}}h^{2}=0.12$ Planck:2018vyg ,

$Y_{\mathrm{DM}}^{\mathrm{obs}}=\frac{n_{\mathrm{DM}}}{s_{0}}=\Omega_{\mathrm{DM}}\frac{\rho_{C}}{m_{\mathrm{DM}}s_{0}}=4.35\cdot
10^{-10}\left(\frac{m_{\mathrm{DM}}}{\,\mathrm{GeV}}\right)^{-1}\,.$ (4)

Requiring freeze-out at the correct temperature to reproduce the observed
relic abundance leads to a constraint on ${\langle\sigma v\rangle}$.

The generic implication of the WIMP scenario is DM annihilation with
${\langle\sigma v\rangle}_{\mathrm{fo}}\sim\,\mathrm{pb}\,c$ at
$T_{\mathrm{fo}}\sim m_{\mathrm{DM}}/20$. This motivates the WIMP indirect
detection program, looking for DM annihilation at overdense regions of the
Universe today. For sub-GeV DM however, this can be a problem, since
${\langle\sigma v\rangle}_{\mathrm{CMB\ epoch}}={\langle\sigma
v\rangle}_{\mathrm{fo}}$ results in excessive energy injection into the SM
plasma during CMB decoupling for $m_{\mathrm{DM}}\lesssim 10\,\mathrm{GeV}$
Planck:2018vyg ; Slatyer:2015jla .

In the models considered in this work, tree-level annihilation channels are
closed at low temperatures. In this “forbidden DM” scenario DAgnolo:2015ujb ;
DAgnolo:2020mpt , DM particles $\chi\chi$ are slightly lighter than the bath
particles $l_{1}\bar{l}_{2}$ they annihilate into. The leading annihilation
rate $\chi\chi\to l_{1}\bar{l}_{2}$ is then Boltzmann suppressed 333 In the
models we consider, DM freeze-out can also be determined by forbidden
annihilations into two mediator particles, provided the mediator remains in
equilibrium with the SM bath. We have verified that this is ensured by
$\phi\leftrightarrow\nu\bar{\nu},\gamma\gamma$ processes for the relevant
values of mediator-lepton couplings. , ${\langle\sigma v\rangle}_{\chi\chi\to
l_{1}\bar{l}_{2}}\simeq\frac{1}{2\zeta}{\langle\sigma
v\rangle}_{l_{1}\bar{l}_{2}\to\chi\chi}e^{-2\Delta x}$ where $n_{l_{i}}$
denote the number density of $l_{i}$ particles plus antiparticles and
$n_{\mathrm{DM}}$ denotes the total DM number density, while
$\Delta\equiv(m_{l_{1}}+m_{l_{2}}-2m_{\mathrm{DM}})/2m_{\mathrm{DM}}$ and
$x=m_{\mathrm{DM}}/T$. Tree-level DM annihilation is strongly suppressed at
low temperature for $\Delta>0$, evading CMB and cosmic ray probes. Radiative
annihilations, however, are not forbidden, and $\gamma$-ray line signals at
energies just below SM particle masses can be a powerful and specific probe of
the present scenario, as discussed later in the text.

_Models_.– Here we present a minimal scenario for forbidden DM. Our UV-
complete model is a simple extension of the 2HDM Branco:2011iw  by an
$SU(2)_{L}$ scalar singlet $S$, which qualifies as a promising forbidden DM
candidate. The stability of the DM is ensured by a discrete $\mathcal{Z}_{2}$
symmetry, under which only the DM transforms non-trivially. In the Higgs
basis, when only one neutral Higgs acquires a nonzero vacuum expectation
value, the Higgs doublets can be parameterized as,

$\displaystyle H_{1}=\begin{pmatrix}G^{+}\\\
\frac{1}{\sqrt{2}}(v+\phi_{1}^{0}+iG^{0})\end{pmatrix},\quad
H_{2}=\begin{pmatrix}H^{+}\\\
\frac{1}{\sqrt{2}}(\phi_{2}^{0}+iA)\end{pmatrix}.$ (5)

Here $G^{+}$ and $G^{0}$ are the unphysical Goldstone modes, whereas $H^{+}$
and $\\{\phi_{1}^{0},\phi_{2}^{0},A\\}$ are the physical Higgs bosons. The VEV
of $H_{1}$, in our notation of $v\simeq 246$ GeV, governs the EW symmetry
breaking.

We choose to work in the alignment limit Branco:2011iw ; Babu:2018uik ;
Bernon:2015qea ; BhupalDev:2014bir , where the SM Higgs $\phi_{1}^{0}\approx
h$ decouples from the new CP-even Higgs ($\phi_{2}^{0}\approx H$). The masses
of physical scalar states in this limit are expressed as follows:

$\displaystyle
m^{2}_{h}=\lambda_{1}v^{2},\;m^{2}_{H}=\mu^{2}_{22}+\frac{v^{2}}{2}(\lambda_{3}+\lambda_{4}+\lambda_{5}),$
(6) $\displaystyle
m^{2}_{A}=m^{2}_{H}-v^{2}\lambda_{5},\;m^{2}_{H^{\pm}}=m^{2}_{H}-\frac{v^{2}}{2}(\lambda_{4}+\lambda_{5}),$
(7) $\displaystyle m_{S}^{2}=\mu_{S}^{2}+\frac{\kappa_{1}}{2}v^{2},$ (8)

where $\lambda_{i}$, $\kappa_{i}$, and $\mu_{22,S}$ are parameters in the
scalar potential (see Appendix-I). Here $m_{S}$ denotes the mass of the DM
candidate $S$. From the above mass relations, it is straightforward to see
that the BSM CP-even state $H$ can be made light without making the CP-odd
state $A$ and the charged $H^{\pm}$ light. The emergence of this light state
from the 2HDM is the key to realizing light thermal DM. However, having a
light $H$ puts an upper bound on the masses of $A$ and $H^{\pm}$ from EW
precision constraints which are discussed in detail later.

In our analysis, both for simplicity and possible connections to muon and
neutrino properties, we consider the second doublet to be leptophilic in
nature. The Yukawa part of the Lagrangian then reads,

$\displaystyle-$
$\displaystyle\mathcal{L}_{Y}\supset\widetilde{Y}_{l}\bar{\psi}_{L}H_{1}\psi_{R}+Y_{l}\bar{\psi}_{L}H_{2}\psi_{R}+h.c.$
(9)

In the alignment limit that we are working, the former Yukawa coupling is
responsible for generating masses of the charged leptons, i.e.,
$\widetilde{Y}_{l}=\mathrm{diag}(m_{e},m_{\mu},m_{\tau})/v$, while $Y_{l}$
determines the DM phenomenology. We focus on the minimal scalar DM scenario,
where the structure of $Y_{l}$ needs to ensure only kinematically forbidden
channels receive significant couplings. In particular, forbidden DM
annihilating to $\mu\mu$, $\mu\tau$ and $\tau\tau$ is phenomenologically
possible. The forbidden $ee$ channel is precluded by thermal DM of
$m_{\mathrm{DM}}\lesssim m_{e}$ being too light Boehm:2013jpa , while $e\mu$
or $e\tau$ are constrained by lepton flavour violation DAgnolo:2020mpt .

We also consider fermionic forbidden DM based on the light 2HDM mediated
scenario. In this case, the scalar mediator needs to have an admixture of an
additional light singlet scalar to couple to a pair of DM fermions. The full
model description is given in the Appendix-II. In the fermionic case,
annihilations are velocity-suppressed, and non-forbidden annihilation is no
longer precluded by CMB bounds, allowing in general for a wider range of DM
masses and Yukawa structures $Y_{l}$. For the purposes of this letter,
however, we restrict ourselves to forbidden mass spectra.

Figure 2: Theoretical and experimental constraints on the scalar (top) and
fermionic forbidden DM (bottom) for DM annihilations into $\mu^{+}\mu^{-}$
(left), $\mu+\tau$ (center), and $\tau^{+}\tau^{-}$ (right). The different
colored contours represent the DM relic density $\Omega h^{2}=0.12$ for
different values of relative mass spliting: $\Delta=0.1$ (blue), and
$\Delta=0.001$ (green). The green band indicates the $(g-2)_{\mu}$ $2\sigma$
preferred range. The other shaded regions regions are exclusion bounds:
supernovae cooling Kamiokande-II:1987idp ; Croon:2020lrf  (purple), SLAC beam
dump E137 Bjorken:1988as ; Batell:2017kty  (brown), $(g-2)_{\mu}$ at Fermilab
Muong-2:2021ojo  (gray),$(g-2)_{\tau}$ Beresford:2019gww  (gray), $\tau$ decay
width Tanabashi:2018oca  (light pink), $\tau\rightarrow\mu H$ at ARGUS
ARGUS:1995bjh  (orange), searches for $Z\rightarrow\bar{\tau}\tau+\text{MET}$
at LEP Tanabashi:2018oca ; Chen:2018vkr  (cyan), dark photon searches through
$e^{+}e^{-}\rightarrow\mu^{+}\mu^{-}H$ and $e^{+}e^{-}\rightarrow\gamma H$ at
BaBar TheBABAR:2016rlg ; BaBar:2017tiz  (light and dark yellow respectively).
We also show the constraints from Planck Planck:2018vyg ; Slatyer:2015jla  on
radiative DM annihilation into two photons (blue/green regions), as well as
the prospective reach of proposed MeV gamma-ray telescopes (blue/green
dashed). For the scalar (fermion) DM scenario, we set $\kappa_{ij}=10^{-3}$
($Y_{\chi}\cos{\alpha}=0.1$).

_Results and phenomenological implications_.– Our model incorporates new
physics below the electroweak scale, which has a myriad of phenomenological
implications and makes it very predictive. This section analyzes and discusses
the major results and the implications. Figure 2 shows relic abundance
predictions, contrasted with constraints from laboratory experiments and late
time DM annihilation. The panels show the values of the Yukawa couplings
$Y_{\mu\mu,\mu\tau,\tau\tau}$ required to reproduce the observed relic
abundance in the three leptophilic forbidden DM regimes
$m_{\mathrm{DM}}\lesssim\\{m_{\mu},(m_{\mu}+m_{\tau})/2,m_{\tau}\\}$ (left to
right) for both the scalar (top row) and fermionic (bottom row) DM scenarios
and different mass splittings, as function of the mediator mass. The
$\Delta=10^{-3}\sim 0$ line (green) indicates the lowest achievable couplings
in the forbidden DM scenario. Larger $\Delta=0.1$ (blue) results in a larger
Boltzmann suppression, implying larger couplings. The smallest couplings
$y\sim 10^{-5}$ are reached close to the $s$-channel resonance for
$m_{H}\gtrsim 2m_{\mathrm{DM}}$. Towards low $m_{H}$, ‘secluded’ annihilation
Pospelov:2007mp  into mediator pairs determines the relic abundance, which
becomes independent of the coupling to leptons 444The secluded parameter space
is ruled out by indirect detection constraints on $SS\to HH\to 4\gamma$ in the
case of scalar DM annihilating to $\tau\tau$ (drawn with solid gray vertical
lines in the plot). In the other cases shown, the correct relic abundance is
reached in the forbidden secluded regime..

DM indirect detection constraints on tree-level DM annihilation are avoided in
the forbidden DM scenario. We point out that loop-level annihilation into two
photons is a generic probe of forbidden DM coupled to SM fermions. Planck
bounds Planck:2018vyg ; Slatyer:2015jla  on ${\langle\sigma
v\rangle}_{SS\to\gamma\gamma}$(see eqn. 17 in the Appendix) during CMB
decoupling are shown in Fig. 2 as blue and green shaded regions. Galactic
gamma ray lines at energies just below the lepton masses are a specific
prediction of the present scenario, which could be probed at future MeV gamma
ray missions like the AMEGO and e-ASTROGAM proposals AMEGO:2019gny ;
e-ASTROGAM:2017pxr ; Bartels:2017dpb  (dashed lines). In the fermionic DM
scenario, annihilation is velocity suppressed, rendering this detection
channel ineffective.

Due to the requirement of a light mediator, there are non-trivial consequences
on the scalar mass-spectrum; moreover, to be consistent with all experimental
constraints, we consider the possibility of leptophilic 2HDM, for which we
assume the second Higgs doublet to have zero/negligible coupling with the
quarks. A lower bound on the mass of the CP-odd scalar $A$ is obtained from
$Z$ decay width measurements, $m_{A}\geq m_{Z}-m_{H}\simeq 90$ GeV
Electroweak:2003ram ; Tanabashi:2018oca , where $m_{Z}$ is mass of the $Z$
boson. In addition, the LEP experiment set a lower bound on the charged scalar
mass, $m_{H^{+}}\simeq 100$ GeV Babu:2019mfe . Additionally, there will be
bounds from slepton searches at the LHC CMS:2018yan ; ATLAS:2014hep ;
CMS:2018eqb , which are less stringent for this sort of light leptophilic
charged scalars (For details, see discussion in Ref. Babu:2019mfe ). These
lead to the mass hierarchy $m_{H}\ll m_{A},m_{H^{+}}$. A mass splitting of
this type is strongly constrained from the electroweak precision observables.
The choice $m_{H}\ll m_{A}\simeq m_{H^{+}}$ with $\mathcal{O}(100)$ GeV mass
splitting between $m_{H}$ and $m_{H^{+}}$ is however allowed Jana:2020pxx
from the $T$ parameter constraints, presenting no obstacles to the role of $H$
as a light mediator. Due to the alignment limit (no mixing of the SM Higgs $h$
and CP-even scalar $H$) and the absence of massive cubic scalar couplings
involving the SM Higgs, the predictions for Higgs observables do not deviate
from the SM predictions and are hence unconstrained by the LHC Higgs searches.
For the rest of our analysis, we set $m_{A},m_{H^{+}}\simeq$110 GeV and vary
the light CP-even scalar mass from the $\mathcal{O}$(MeV) to the
$\mathcal{O}$(GeV) range. This unrestricted parametric space of the 2HDM has
received little attention in the literature.

The light leptophilic charged scalar $\mathcal{O}(100)$ GeV can result in
large non-standard neutrino interactions Babu:2019mfe  and generate Glashow-
like resonance features in the ultrahigh energy neutrino event spectrum of
future neutrino telescopes Babu:2019vff ; Huang:2021mki ; Babu:2022fje . This
form of hierarchical scalar mass spectrum predicts the novel same-sign di-
lepton signature $pp\to H^{\pm}H^{\pm}jj\to
l_{\alpha}^{\pm}l_{\beta}^{\pm}jj+{E\\!\\!\\!\\!/}_{T}$ through same-sign pair
production of charged scalars at the LHC Jana:2020pxx . This can be a good
test of our model, but the detailed exploration is beyond the scope of this
study.

In the following, we discuss other phenomenological implications of a light
scalar coupling to SM leptons and DM. Constraints are shown as bordered shaded
regions in Fig. 2. Light scalars coupled to charged leptons contribute to the
lepton anomalous magnetic moments. For coupling to the muon or muon and tauon,
the loop corrections mediated by the light CP-even scalar $H$ always
contribute positively to the muon anomalous magnetic moment. In Fig. 2, we
show the parameter space consistent with the observed muon anomalous magnetic
moment measurement at Fermilab Muong-2:2021ojo  as green band. The grey shaded
regions above this band indicate the parameter space where the $(g-2)_{\mu}$
discrepancy is larger than $5\sigma$, or $(g-2)_{\tau}$ is larger than the
$2\sigma$ constraint determined by Beresford:2019gww .

New scalars lighter than a few hundred MeV can be produced in astrophysical
settings such as supernovae. Their possible contribution to supernova cooling
is constrained by the neutrino observation of SN1987A Kamiokande-II:1987idp .
Recently Ref. Croon:2020lrf  studied the impact of new light particles
interacting with muons on SN1987A, which we recast to the purple-shaded region
in Fig. 2.

At collider or beam dump experiments, the light scalar can be produced in
association with the leptons it couples to. The null results from the electron
beam dump experiment E137 Bjorken:1988as  constrain the $H\mu^{+}\mu^{-}$
coupling Batell:2017kty  (brown in Fig. 2). Dark photon searches at BaBar
TheBABAR:2016rlg  provide a stringent constraint on a light scalar with
coupling to the muons through the $e^{+}e^{-}\rightarrow\mu^{+}\mu^{-}H$
process Batell:2016ove ; Batell:2017kty , with $H\rightarrow\mu^{+}\mu^{-}$.
We recast this result for the case $\text{BR}(H\rightarrow\mu^{+}\mu^{-})<1$
(light-yellow in Fig. 2). The BaBar collaboration also searches for events
with a high energy monophoton and large missing energy BaBar:2017tiz , which
puts limits on the $H\tau^{+}\tau^{-}$ coupling DAgnolo:2020mpt ; Chen:2018vkr
; Dolan:2017osp  (yellow in Fig. 2). The dashed yellow line below this region
indicates the projected sensitivity on the same process from the Belle-II
experiment DAgnolo:2020mpt ; Dolan:2017osp ; Belle-II:2010dht .

The $Y_{\tau\tau}$ coupling is also constrained from the $Z$ decay width
measurement Chen:2018vkr ; DAgnolo:2020mpt , where the associated production
and subsequent dark decay of $H$ can contribute to the measured
$Z\rightarrow\tau^{+}\tau^{-}$ width Tanabashi:2018oca  (cyan in Fig. 2).
Finally, $\tau$ decays are modified in the $\mu\tau$-coupled case. The search
for lepton flavour violating two-body $\tau$ decay at ARGUS ARGUS:1995bjh
requires $m_{H}>m_{\tau}-m_{\mu}$ to forbid $\tau\to\mu H$ decay (orange in
Fig. 2). Similarly, the decay $\tau\to\mu SS$ would contribute to the measured
width $\Gamma(\tau\rightarrow\mu\bar{\nu}_{\mu}\nu_{\tau})$ Tanabashi:2018oca
, requiring $m_{\rm DM}>(m_{\tau}-m_{\mu})/2$ or equivalently $\Delta<0.126$
(light pink in Fig. 2).

In Fig. 2, we also show the projected sensitivities from various experiments.
Muon beam dump experiments can be used to probe for a light scalar that has
couplings to muons and DM by performing a muon missing energy search. The
corresponding projected sensitivity from the muon beam experiment NA64-$\mu$
DAgnolo:2020mpt ; Chen:2018vkr ; Gninenko:2014pea  is shown in Fig. 2 as a
brown-dashed line. Future $Z$ factories based on $e^{+}e^{-}$ colliders look
for exotic decay modes of $Z$ bosons. The projected sensitivity from these
experiments DAgnolo:2020mpt ; Liu:2017zdh ;
TLEPDesignStudyWorkingGroup:2013myl ; dEnterria:2016fpc ; dEnterria:2016sca
is shown in Fig. 2 as a cyan-dashed line.

Overall, the light 2HDM-mediated forbidden DM scenario shares many
implications with previous phenomenological models DAgnolo:2020mpt , but makes
further predictions for the scalar sector around the electroweak scale. From
the DM side, radiative annihilation is a very informative probe of forbidden
DM annihilating into SM particles, which in particular could identify
$\mu\mu$-coupled scalar DM in the $(g-2)_{\mu}$-favoured part of parameter
space in the future.

_Neutrino mass_.– The simplest radiative neutrino mass model, namely, the Zee
model Zee:1980ai ; Zee:1985id , utilizes two-Higgs-doublets. Hence neutrino
masses can arise naturally by embedding our setup within the Zee model. A
singly charged scalar needs to be added to our setup to complete the loop
diagram that provides neutrino mass. We consider such a possibility and show
that the same Yukawa couplings responsible for providing the correct DM relic
abundance give rise to non-zero neutrino masses.

In addition to the Yukawa couplings given in Eq. (9), the Zee model contains
one more term, which is

$\displaystyle-\mathcal{L}_{Y}\supset f_{ij}L_{i}\epsilon L_{j}\eta^{+}+h.c.,$
(10)

where $\epsilon$ is the Levi-Civita tensor and $\eta^{+}\sim(1,1,1)$ is a
singly charged scalar. The Yukawa coupling $f_{ij}$ is antisymmetric in flavor
indices. Eqs. (9) and (10), together with the following cubic term in the
scalar potential,

$\displaystyle-V\supset\mu H_{1}\epsilon H_{2}\eta^{-}+h.c.,$ (11)

lead to non-zero neutrino mass given by,

$\displaystyle M_{\nu}=a_{0}\left(fm_{E}Y_{l}-Y_{l}^{T}m_{E}f\right),$ (12)
$\displaystyle a_{0}=\frac{\sin
2\omega}{16\pi^{2}}\ln\left(\frac{m^{2}_{h^{+}}}{m^{2}_{H^{+}}}\right);\;\;\sin
2\omega=\frac{\sqrt{2}v\mu}{m^{2}_{h^{+}}-m^{2}_{H^{+}}},$ (13)

where, $m_{E}$ is the diagonal charged lepton mass matrix, $\omega$ is the
mixing angle between the singly charged scalars, and $h^{+}$ and $H^{+}$
represent the mass eigenstates 555For small mixing angle, which is typically
required to provide tiny masses to neutrinos, to a good approximation, the
$H^{+}$-state can be identified with the charged guy coming from 2HDM..

DM annihilation into SM particles occurs through the Yukawa coupling $Y_{l}$;
hence its texture is highly restricted from DM phenomenology. Moreover, lepton
flavor violating (LFV) processes put stringent limits on its off-diagonal
entries required to satisfy neutrino oscillation data. In the $\mu\mu$-coupled
forbidden DM scenario, the mediator mass must be close to twice the muon mass.
In this case, the ARGUS experiment rules out any sizable non-zero entry with
the tau-lepton due to null observation of $\tau\to\ell H$ processes, where
$\ell=e,\mu$. To generate viable neutrino masses and mixings, we hence
consider a Yukawa texture with zero $2\times 2$ block in the 1-2 sector.

Now, to be consistent with DM phenomenology, we fix $y_{\mu\tau}=5\times
10^{-4}$. As can be seen from Fig. 2 (upper-middle plot), a coupling of this
order correctly reproduces the DM relic abundance with the mediator mass close
to 2 GeV. Since the upper $2\times 2$-block is set to zero, reproducing the
neutrino oscillation data requires the rest of the entries to be non-zero.
However, each non-vanishing entry causes LFV and is required to be small.
Since the charged scalars are heavier than 110 GeV, LFV is entirely dominated
by the light scalar $H$ in this theory. The most dangerous LFV processes are
light scalar mediated $\mu\to e\gamma,\tau\to e\gamma,$ and $\tau\to\mu\gamma$
at one-loop, which we compute following Dutta:2020scq .

Following the discussion above, we perform a fit to the neutrino sector, which
is simultaneously consistent with the DM relic abundance and provide a
benchmark,

$\displaystyle Y_{l}=10^{-4}\begin{pmatrix}0&0&3.494\times 10^{-4}\\\ 0&0&5\\\
-10^{-3}&-0.382&0.542\end{pmatrix},$ (14) $\displaystyle a_{0}\cdot
f=10^{-7}\begin{pmatrix}0&2.135&0\\\ -2.135&0&2.266\\\
0&-2.266&0\end{pmatrix}.$ (15)

Neutrino observables associated with this fit yield,

$\displaystyle\Delta m^{2}_{21}=7.486\times 10^{-5}eV^{2},\;\Delta
m^{2}_{31}=2.511\times 10^{-3}eV^{2},$
$\displaystyle\theta_{12}=34.551^{\circ},\;\theta_{23}=47.830^{\circ},\;\theta_{13}=8.545^{\circ}.$

These predictions are in good agreement with the current neutrino oscillation
data Esteban:2020cvm . While the rates of $\tau\to e\gamma$ and
$\tau\to\mu\gamma$ can be easily suppressed, the branching ratio of $\mu\to
e\gamma$ is typically close to the current limit 666Current experimental
limits on these LFV processes are ParticleDataGroup:2020ssz :  $\displaystyle
BR(\mu\to e\gamma)<4.2\times 10^{-13},$ $\displaystyle BR(\tau\to
e\gamma)<3.3\times 10^{-8},$ $\displaystyle BR(\tau\to\mu\gamma)<4.4\times
10^{-8}.$ or within one order of magnitude smaller; therefore, future
experiments such as MEG-II collaboration MEG:2016leq  will be able to test
this theory.

_Conclusions_.– This work proposes a minimal realization of light Dark Matter,
enabled by a light scalar mediator that can arise in the 2HDM. We focus on
forbidden DM annihilating to SM leptons, which predicts the DM mass to be
close to the $\mu$ or $\tau$ masses. Stringent CMB constraints on sub-GeV DM
are avoided, while we have identified Galactic gamma ray lines from radiative
annihiation as a specific probe. A distinctive trademark is that all new
physics states appear at or below the EW scale; in particular, a CP-odd and
charged scalars are predicted to have masses of order 100 GeV. Furthermore, a
leptophilic-like 2HDM of this type can shed light on the $(g-2)_{\mu}$
anomaly, and –when embedded within the Zee model– the couplings that determine
the relic abundance become intimately linked to neutrino oscillations. This
minimal kinematically forbidden scenario is very predictive and in particular
testable at future beam-dump experiments, colliders and sub-GeV gamma-ray
telescopes. However, the light 2HDM portal to Dark Matter is rather general
and provides a simple way of linking light dark sectors to the Standard Model
that may well have wider application.

###### Acknowledgements.

Acknowledgments.– The work of VPK is in part supported by US Department of
Energy Grant Number DE-SC 0016013. The work of S.S. has been supported by the
Swiss National Science Foundation. We acknowledge the use of the FeynCalc
package Shtabovenko:2016sxi .

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## Appendix-I

Scalar potential: The most general scalar potential (2HDM $+$ real scalar
singlet) in the Higgs basis is given by

$\displaystyle
V(H_{1},H_{2},S)=\mu_{1}^{2}H_{1}^{\dagger}H_{1}+\mu_{2}^{2}H_{2}^{\dagger}H_{2}-\\{\mu_{12}^{2}H_{1}^{\dagger}H_{2}+{\rm
h.c.}\\}+\frac{\lambda_{1}}{2}(H_{1}^{\dagger}H_{1})^{2}+\frac{\lambda_{2}}{2}(H_{2}^{\dagger}H_{2})^{2}+\lambda_{3}(H_{1}^{\dagger}H_{1})(H_{2}^{\dagger}H_{2})$
$\displaystyle\quad+\lambda_{4}(H_{1}^{\dagger}H_{2})(H_{2}^{\dagger}H_{1})+\left\\{\frac{\lambda_{5}}{2}(H_{1}^{\dagger}H_{2})^{2}+{\rm
h.c.}\right\\}+\left\\{\big{[}\lambda_{6}(H_{1}^{\dagger}H_{1})+\lambda_{7}(H_{2}^{\dagger}H_{2})\big{]}H_{1}^{\dagger}H_{2}+{\rm
h.c.}\right\\}$
$\displaystyle\quad+\frac{\mu_{S}^{2}}{2}S^{2}+\frac{\lambda_{S}}{4!}S^{4}+\frac{\kappa_{1}}{2}S^{2}(H_{1}^{\dagger}H_{1})+\frac{\kappa_{2}}{2}S^{2}(H_{2}^{\dagger}H_{2})+\left\\{\frac{\kappa_{12}}{2}S^{2}(H_{1}^{\dagger}H_{2})+h.c.\right\\}.$
(16)

Cross section $SS\to\gamma\gamma$: The velocity averaged $s$-wave annihilation
cross section of scalar DM into two photons is given by (using Resnick:1973vg
):

$\langle\sigma
v\rangle_{SS\to\gamma\gamma}^{s\mathrm{-wave}}=\frac{e^{4}\kappa_{12}^{2}v^{2}m_{S}^{2}Y_{ll}^{2}\left|\mathcal{I}[(2m_{S})/m_{l}]\right|^{2}}{64\pi^{5}m_{l}^{2}((4m_{S}^{2}-m_{H}^{2})^{2}-\Gamma_{H}^{2}m_{H}^{2})}\,,$
(17)

where

$\mathcal{I}[r]=\int_{0}^{1}\mathop{dx}\int_{0}^{1-x}\mathop{dy}\frac{1-4xy}{1-xyr^{2}}\,.$
(18)

## Appendix-II

Fermionic DM scenario: Fermionic DM candidates can be either Dirac or Majorana
in nature. In this work, we consider both these possibilities. As usual, the
stability of the DM is ensured by a $\mathcal{Z}_{2}$ symmetry. Similar to the
scalar DM setup discussed in the main text, the 2HDM-portal is needed to
implement the forbidden fermionic DM scenario. Since a singlet fermion $\chi$
cannot directly couple to the 2HDM sector, the presence of a scalar singlet
$S=v_{S}+\omega$ is required. Then the relevant Yukawa couplings are given by,

$\displaystyle-\mathcal{L}_{Y}$
$\displaystyle\supset\widetilde{Y}_{l}\bar{\psi}_{L}H_{1}\psi_{R}+Y_{l}\bar{\psi}_{L}H_{2}\psi_{R}+b\;Y_{\chi}S\bar{\chi}\chi+b\;m_{\chi}\bar{\chi}\chi+h.c.,$
(19)

with $b=1(1/2)$ for Dirac (Majorana) fermion. The mass of the DM candidate
$\chi$ can be written as,

$\displaystyle m_{\rm DM}=m_{\chi}+Y_{\chi}v_{S}.$ (20)

Like in the previous case, it is convenient to rotate the doublet scalars to
the Higgs basis Eq. 5, then the full scalar potential can be written as,

$\displaystyle V(H_{1},H_{2},S)$
$\displaystyle=\mu_{1}^{2}H_{1}^{\dagger}H_{1}+\mu_{2}^{2}H_{2}^{\dagger}H_{2}-\\{\mu_{12}^{2}H_{1}^{\dagger}H_{2}+{\rm
h.c.}\\}+\frac{\lambda_{1}}{2}(H_{1}^{\dagger}H_{1})^{2}+\frac{\lambda_{2}}{2}(H_{2}^{\dagger}H_{2})^{2}+\lambda_{3}(H_{1}^{\dagger}H_{1})(H_{2}^{\dagger}H_{2})$
$\displaystyle\quad+\lambda_{4}(H_{1}^{\dagger}H_{2})(H_{2}^{\dagger}H_{1})+\left\\{\frac{\lambda_{5}}{2}(H_{1}^{\dagger}H_{2})^{2}+{\rm
h.c.}\right\\}+\left\\{\big{[}\lambda_{6}(H_{1}^{\dagger}H_{1})+\lambda_{7}(H_{2}^{\dagger}H_{2})\big{]}H_{1}^{\dagger}H_{2}+{\rm
h.c.}\right\\}$
$\displaystyle\quad+\frac{\mu_{S}^{2}}{2}S^{2}+\frac{\mu_{SS}}{3!}S^{3}+\frac{\lambda_{S}}{4!}S^{4}+\mu_{1S}S(H_{1}^{\dagger}H_{1})+\mu_{2S}S(H_{2}^{\dagger}H_{2})+\left\\{\mu_{12S}S(H_{1}^{\dagger}H_{2})+h.c.\right\\}$
$\displaystyle\quad+\frac{\kappa_{1}}{2}S^{2}(H_{1}^{\dagger}H_{1})+\frac{\kappa_{2}}{2}S^{2}(H_{2}^{\dagger}H_{2})+\left\\{\frac{\kappa_{12}}{2}S^{2}(H_{1}^{\dagger}H_{2})+h.c.\right\\}.$
(21)

In the alignment limit, $\phi_{1}^{0}\approx h$ is the SM Higgs, which
decouples from the other two CP-even scalars $\phi_{2}^{0}$ and $\omega$. The
latter two mix with each other, and the corresponding mass eigenstates are
denoted as $H$ (with mass $m^{2}_{H}$) and $H^{\prime}$ (with mass
$m^{2}_{H^{\prime}}$) and are given by,

$\displaystyle H=\cos{\alpha}\;\omega+\sin{\alpha}\;\phi_{2}^{0},$
$\displaystyle H^{\prime}=-\sin{\alpha}\;\omega+\cos{\alpha}\;\phi_{2}^{0},$
(22)

where the mixing angle $\alpha$ is defined as

$\displaystyle\sin
2\alpha=\frac{2v(\mu_{12S}+k_{12}v_{S})}{m_{H}^{2}-m_{H^{\prime}}^{2}}.$ (23)

This mixing is essential for DM phenomenology since it allows the DM to
annihilate into SM leptons.


# Attention at SemEval-2023 Task 10: Explainable Detection of Online Sexism
(EDOS)

Debashish Roy, Manish Shrivastava
IIIT Hyderabad, India
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>

###### Abstract

In this paper, we have worked on interpretability, trust, and understanding of
the decisions made by models in the form of classification tasks. The task is
divided into 3 subtasks. The first task consists of determining Binary Sexism
Detection. The second task describes the Category of Sexism. The third task
describes a more Fine-grained Category of Sexism. Our work explores solving
these tasks as a classification problem by fine-tuning transformer-based
architecture. We have performed several experiments with our architecture,
including combining multiple transformers, using domain adaptive pretraining
on the unlabelled dataset provided by Reddit and Gab, Joint learning, and
taking different layers of transformers as input to a classification head. Our
system (with team name ‘Attention’) was able to achieve a macro F1 score of
0.839 for task A, 0.5835 macro F1 score for task B and 0.3356 macro F1 score
for task C at the Codalab SemEval Competition. Later we improved the accuracy
of Task B to 0.6228 and Task C to 0.3693 in the test set.

##  1 Introduction

Online sexism is a growing problem in this era, considering the large scale of
online texts. Detecting online Sexism is an important NLP task, and has a lot
of social impacts related to it. Sexism is defined as any abuse or negative
sentiment that is directed towards women based on their gender or based on
their gender combined with one or more other identity attributes (e.g. black
women, trans women).

Automated tools are widely available to detect sexism but mostly don’t work
with the issue of explaining why the text is sexist. Flagging what is sexist
content and also explaining why it is sexist is very important aspects of
these automated tools. We tried to focus on interpretability, trust, and
understanding of the decisions made by models. Having an automated system that
is capable of understanding, interpreting, and classifying sexist text will be
a major step to make online sites safe.

Explainable Detection of Online Sexism (EDOS) at SemEval 2023 Kirk et al.
(2023), tries to solve this problem by exploring different systems that can
categorize the dataset created with texts from Reddit and Gab.

The problem is divided into 3 subtasks. The first task is formulated as Binary
Sexism Detection, where the main idea is to detect whether a text is sexist or
not.

The second task describes the Category of Sexism. So, if the text is sexist,
under which category it belongs? The categories are threats, derogation
(treating someone as little worthy), animosity (a strong dislike or unfriendly
feeling), and prejudiced discussions (an unfair feeling of dislike for a
person or group because of race, sex, religion, etc). This makes this task a
four-class classification problem given the text is sexist.

The third task describes the Fine-grained Vector of Sexist text. For posts
that are sexist, systems were supposed to predict more fine-grained aspects of
the category of sexism. Which can help in interpretability and understanding
why the post is sexist on a much deeper level. The sexist posts are classified
into an 11-class classification problem, given the text is sexist. The 11
classes are Descriptive attacks, Aggressive and emotive attacks, Casual use of
gendered slurs, Profanities, and insults, Immutable gender differences and
gender stereotypes, Supporting systemic discrimination against women as a
group, Incitement, and encouragement of harm, Dehumanising attacks & overt
sexual objectification, Supporting mistreatment of individual women,
Backhanded gendered compliments, Threats of harm, Condescending explanations
or unwelcome advice.

To solve this problem, we have fine-tuned transformer-based architecture. Our
final submission is made up of two models: RoBERTa Zhuang et al. (2021) and
DeBERTa He et al. (2020). The last layer is then passed to the MLP. At the
last layer, we have the number of classes. We have also explored Domain
Adaptive Pre Training using masked language modeling on both of these
transformers and used their weights for the classification task. The models
remain the same for all the tasks except the last layer changes based on the
number of classes.

Our system ranked 35th in sub-task 1, 50th in sub-task 2, and 44th in sub-task
3, out of 583 participants.

All of our code is made publicly available on
Github111https://github.com/debashish05/Explainable_Detection_of_Online_Sexism.
The domain adaptive pretrained versions of RoBERTa and DeBERTa are also made
publicly available at Huggingface 222https://huggingface.co/debashish-roy/

##  2 Background

Transformer-based models such as RoBERTa and DeBERTa has shown outstanding
performance on wide domains of NLP, including text classification. These
models can capture a sort of structure in the hateful speech as well Basile et
al. (2019).

Domain Adaptive Pre Training is used in many domains of NLP, to make the model
focus on the specific domain rather than a large variety of text it is trained
on. Don’t Stop Pre Training: Adapt Language Models to Domains and Tasks
Gururangan et al. (2020) talk about the increase in the performance of a model
if it is pretrained on similar types of data.

SemEval-2021 Task 7: HaHackathon, Detecting and Rating Humor and Offense
Meaney et al. (2021) talks about the importance of pretraining and using
ensembling methods to achieve high accuracy. It also described the importance
of lexical features.

This SemEval task itself provided the dataset. The dataset contains text in
English. The dataset contains 20,000 texts. Half of the text was taken from
Gab and the other half from Reddit. The entries are then manually annotated by
three trained annotator women. For each text, we have (a) label-sexist,
describing whether the label is sexist or not, (b) label-category: given the
text is sexist what is the category of sexism, in the case of non-sexist text
it is none. (c) label-vector: it is more fine-grained details about the
category of sexism.

The data is divided into 70% as training data, 10% as validation data, and 20%
as test data. The distribution of labels for all three tasks is described in
Table 1, Table 2, and Table 3. The major issue with the dataset for task C is
less number of samples. All of the text is less than 64 words, so while
generating tokens for transformers we have kept the max length to 64.

Classes | Instances
---|---
Sexist Text | 3398
Non-Sexist Text | 10602
Table 1: Class distribution for sub-task 1 train dataset. Classes | Instances
---|---
Threats plan to harm, and incitement | 310
Derogation | 1590
Animosity | 1165
Prejudiced discussions | 333
Table 2: Class distribution for sub-task 2 train dataset. Classes | Instances
---|---
Threats of harm | 56
Incitement and encouragement of harm | 254
Descriptive attacks | 717
Aggressive and emotive attacks | 673
Dehumanising attacks & overt sexual objectification | 200
Casual use of gendered slurs, profanities, and insults | 637
Immutable gender differences and gender stereotypes | 417
Backhanded gendered compliments | 64
Condescending explanations or unwelcome advice | 47
Supporting mistreatment of individual women | 75
Supporting systemic discrimination against women as a group | 258
Table 3: Class distribution for sub-task 3 train dataset.

##  3 System Overview

We have used Transformers with several variations. Based on this variation we
try to come up with the best model.

Figure 1: Architecture of our system.

  * •

RoBERTa: It is built on BERT masked language strategy, but excludes BERT’s
next-sentence pretraining objective, and training with much larger mini-
batches and learning rates. RoBERTa BASE model consists of 12 transformer
layers, 12 self-attention heads per layer, and a hidden size of 768.

  * •

DeBERTa: We have used the BASE model which consists of 12 transformer layers,
12 self-attention heads per layer, and a hidden size of 768. It tries to
improve RoBERTa by using two techniques: a disentangled attention mechanism
and an enhanced mask decoder.

  * •

Domain Adaptive Pretraining: We try to tailor a pretrained model to the domain
of a target task. To do so we do masked language modeling over the text
related to the domain.

With these two transformers, we have experimented with the architecture. The
different architecture is as follows:

  1. 1.

RoBERTa/DeBERTa (last layer) + MLP: We have taken the last layer of the
RoBERTa the base model followed by some MLP layers and fine-tuned over the
training data. The same setup has been used with DeBERTa as well.

  2. 2.

RoBERTa/DeBERTa (average of all layers) + MLP: Instead of taking the last
layer only, here we have taken the average of all the layers in the RoBERTa
base model. Which are then followed by some MLP layers and fine-tuned over the
training data. The same setup has been used with DeBERTa as well.

  3. 3.

RoBERTa and DeBERTa concatenation of the last layer + MLP: Output from the
last layers of RoBERTa and DeBERTa were concatenated. Then this is followed by
some fully connected layers of MLP. The last layer consists of neurons with a
number of classes.

  4. 4.

RoBERTa and DeBERTa combined (before concatenation of two transformers they
are passed through MLP): Output from the last layers of RoBERTa and DeBERTa
were passed through different MLP layers and then concatenated with each
other. Then this is followed by some more fully connected layers. The last
layer consists of neurons with a number of classes. The model is presented in
Fig 1.

  5. 5.

Joint Learning for Task B: For task B, earlier we were only taking the text
that is only sexist. But now we will use all the data. And instead of treating
the label category which is class, we are adding another class which implies
the text is non-sexist. This makes the problem a 5-class classification
problem, rather than a 4-class with the increase in a large amount of data. At
the inference time since we are supposed to output only from the 4 classes, we
will give the class with the largest probability as output. But if the class
is not sexist text, then return the second largest probability class.

  6. 6.

Experiment 4 with Domain Adaptive Pretraining: This model is the same as
experiment 4 with the exception that we are using Domain Adaptive Pretrained
RoBERTa and DeBERTa. The transformers are trained on the 2M unlabelled texts
provided in the task itself.

All these models are used for all the tasks with a change in the last layer
with the number of classes.

|  | Task A Macro F1 | Task B Macro F1 | Task C Macro F1
---|---|---|---|---
S.No |  Experiment | Val | Test | Val | Test | Val | Test
1 |  RoBERTa last layer + MLP | 82.90 | 81.47 | 59.74 | 58.29 | 59.70 | 33.48
2 |  DeBERTa last layer + MLP | 83.24 | 81.99 | 61.05 | 59.07 | 29.85 | 30.09
3 |  RoBERTa avg of all layers + MLP | 79.85 | 78.65 | 34.83 | 45.71 | 26.76 | 21.58
4 |  DeBERTa avg of all layer + MLP | 80.40 | 78.62 | 59.79 | 55.15 | 22.11 | 21.61
5 |  RoBERTa+DeBERTa+ (Embeddings of these two are concatenated before concatenating these are passed through MLP) + MLP | 82.96 | 82.26 | 62.47 | 62.28 | 33.99 | 31.61
6 |  Experiment 5 + Domain Adaptive Pre Training with unlabelled text | 84.27 | 82.66 | 63.48 | 60.85 | 35.30 | 36.93
7 |  Joint Learning for task B using task (A and B’s data), the last layer is of 5 neurons with labels from task B and one non-sexist text | NA | NA | 54.57 | 53.29 | NA | NA
8 |  RoBERTa+DeBERTa+ (Embedding of RoBERTa and DeBERTa are concatenated and passed through MLP) + Domain Adaptive Pretraining | 84.13 | 83.9 | 67.00 | 58.35 | 34.33 | 33.56
Table 4: Results of experiments. Predicted -> | Threats, plans to harm and incitement | Derogation | Animosity | Prejudiced
---|---|---|---|---
Threats, plans to harm and incitement (Actual) | 62 | 11 | 12 | 4
Derogation (Actual) | 16 | 303 | 107 | 28
Animosity (Actual) | 11 | 112 | 199 | 11
Prejudiced discussions (Actual) | 9 | 27 | 12 | 46
Table 5: Confusion Matrix for Task B

##  4 Experimental setup

The dataset provided was already divided into train, dev, and test. We have
done some preprocessing of the text, which includes converting emoji to text,
converting all the characters to lowercase, converting the link to <link> tag,
removing punctuations, removing words with numbers, removing stop words, and
using WordNet Lemmatizer. But after the cleaning step accuracy was low
compared to the non-cleaned text. A probable reason is with transformer
tokenization, subword tokenization can perform better than normal
tokenization.

The hyperparameter used in this experiment are

epoch = 20, Learning Rate = 1e-5, Loss = Cross Entropy loss, Optimizer =
AdamW.

We have used the Macro F1 score as a measure of evaluation for all three
tasks.

##  5 Results

Results for different experiments are mentioned in Table 4. Our official
submission is experiment number 8. Later we experimented with 5 and 6 after
the deadline. We have achieved a rank of 35th in task A, 50th in task B and
44th in task C.

With Domain Adaptive Pretraining the evaluation loss of Roberta changes from
2.49 to 1.98. For Deberta it changes from 11.52 to 2.27. We have also seen
reduced perplexity scores, which measure the amount of randomness in our model
or how confused the model is, so the less the better.

##  6 Error Analysis

These error analyses are performed on experiment no 6.

###  6.1 Task A

Predicted-> | Not sexist | Sexist
---|---|---
Not sexist (Actual) | 2909 | 121
Sexist (Actual) | 346 | 624
Table 6: Confusion Matrix for Task A

With the given confusion matrix in Table 6 test data, we can infer that the
model will predict the right label 96% of the time if the text is not sexist.
Issues come when the tweet is sexist. Which is a major problem. Approximately
35% of the time the model is classifying sexist text as non-sexist, which is a
dangerous thing.

For example, this text: “Don’t run away like a little jewish girl.” and “woman
here Opinion discarded.” are treated as not sexist., but they are sexist.

Out of the 346 texts that are sexist but classified as not sexist. Applying
some sort of rule-based system where if this word comes then it will be sexist
will not work. Because we need to understand the whole context. Most of the
time there is no hidden meaning in the sentence.

One of the main reasons for poor performance in predicting text is sexist,
which is less number of samples that are sexist. If we can get more samples
that are sexist, our model can try to learn the pattern among them and perform
better. We should have tried using distil version of these transformers, as
they have less number of weights, which can be trained with fewer samples. And
the different distil versions of the transformer can be used, as the number of
samples to train on keeps on getting smaller.

###  6.2 Task B

The confusion matrix for task B is provided in Table 5. The model is confused
many times between Derogation and Animosity. Approximately 25% of the time
when the text is derogation it is predicting animosity. And nearly 33% time
when the text is animosity it is treating it as derogation. So the model is
not able to clearly distinguish between these classes. Adding more data can
help us solve this issue.

##  7 Conclusion

Domain Adaptive Pre-Training helps us get some extra accuracy numbers in all
three sub-tasks. Combining RoBERTa and DeBERTa makes the model big but also
brings more variety of aspects to the model.

Although the macro F1 accuracy is quite good, the data instances where it is
failing are very costly in the case of task A. Taking a text down from social
media for some time even if it is not sexist is less harmful than keeping a
sexist text on social platforms. The model is failing to predict sexist texts.
A manual inspection of the failed text of this type suggested that there is a
large scope for improvement in the model.

Despite that, the model shows very promising results, where the number of
samples to train on is large. To further improve the accuracy we can use more
annotated data from people. Although this will be costly, it will be a one-
time effort.

The model that we submitted for Task B was not able to generalize well. The
macro F1 dropped from 67% to 58.35%. This can be due to over-fitting or
dissimilarity between the distribution of the test and train set.

One of the ideas that we look forward to working with is to predict pseudo
labels for unlabelled tasks. For example, if our best model is sure that the
label belongs to a particular task with more than 99% probability then use
that data instance as training data for the model. In this way, we can
increase the data to train for our model.

Another idea that can be looked for is to generate text of a similar type
Bhatt and Shrivastava (2022) using decoder-based transformers. For example, we
can take text which is less in number and can train on causal language
objectives over the labeled samples. This results in more data samples to
train on.

##  8 Acknowledgments

I want to thank Sagar Joshi for helping me understand the task. I would also
like to thank Tathagata Raha and Vijayasaradhi Indurthi for giving possible
directions to explore the problem. We also want to thank the organizers of
this task

## References

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