# Field-induced Topological Hall effect in antiferromagnetic axion insulator
candidate EuIn2As2

J. Yan<EMAIL_ADDRESS>The Institute for Solid State Physics, The
University of Tokyo, Kashiwa, 277-8581, Japan  Key Laboratory of Materials
Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences,
Hefei 230031, China  University of Science and Technology of China, Hefei,
230026, China  Z. Z. Jiang  Key Laboratory of Materials Physics, Institute of
Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China
University of Science and Technology of China, Hefei, 230026, China  R. C.
Xiao  Institutes of Physical Science and Information Technology, Anhui
University, Hefei, 230601, China  W. J. Lu  Key Laboratory of Materials
Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences,
Hefei 230031, China  W. H. Song  Key Laboratory of Materials Physics,
Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei
230031, China  X. B. Zhu  Key Laboratory of Materials Physics, Institute of
Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China
X. Luo  Key Laboratory of Materials Physics, Institute of Solid State Physics,
HFIPS, Chinese Academy of Sciences, Hefei 230031, China  Y. P. Sun
<EMAIL_ADDRESS>Anhui Province Key Laboratory of Condensed Matter Physics at
Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of
Sciences, Hefei 230031, China  Key Laboratory of Materials Physics, Institute
of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei 230031,
China  Collaborative Innovation Center of Microstructures, Nanjing University,
Nanjing 210093, China  M. Yamashita<EMAIL_ADDRESS>The Institute for
Solid State Physics, The University of Tokyo, Kashiwa, 277-8581, Japan

###### Abstract

The magnetic topological materials have attracted significant attention due to
their potential realization of variety of novel quantum phenomena. EuIn2As2
has recently been theoretically recognized as a long awaited intrinsic
antiferromagnetic bulk axion insulator. However, the experimental study on
transport properties arising from the topological states in this material is
scarce. In this paper, we perform the detailed magnetoresistance (MR) and Hall
measurements to study the magnetotransport properties of this material. We
find that the transport is strongly influenced by the spin configuration of
the Eu moments from the concomitant change in the field dependence of the MR
and that of the magnetization below the Néel temperature. Most importantly, an
anomalous Hall effect (AHE) and a large topological Hall effect (THE) are
observed. We suggest that the AHE is originated from a nonvanishing net Berry
curvature due to the helical spin structure and that the THE is attributed to
the formation of a noncoplanar spin texture with a finite scalar spin
chirality induced by the external magnetic field in EuIn2As2. Our studies
provide a platform to understand the influence of the interplay between the
topology of electronic bands and the field-induced magnetic structure on
magnetoelectric transport properties. In addition, our observations give a
hint to realize axion insulator states and high-order topological insulator
states through manipulating the magnetic state of EuIn2As2.

##  I Introduction

The success of the topological band theory places the studies of topological
quantum states at one of the frontier topics in condensed matter physics since
the last decades 1 ; 2 ; 3 ; 4 . After a well-understanding on nonmagnetic
topological states, breaking the time-reversal symmetry by introducing
magnetism in topological materials provides a more fertile playground to give
rise to nontrivial topological phases, such as a quantum anomalous Hall effect
and axion insulator states 5 ; 6 ; 7 ; 8 . In magnetic topological materials,
the interplay between magnetism and non-trivial band topology can generate new
exotic quantum states and will give rise to novel transport phenomena. For
instance, magnetic Weyl semimetals Co3Sn2S2 9 , Mn3Sn 10  and GdPtBi 11  have
been reported to show a large intrinsic anomalous Hall effect (AHE) originated
from the net Berry curvature around the Weyl nodes. On the other hand, a real-
space Berry phase arising from a skyrmion phase or a noncollinear spin texture
with nonzero scalar spin chirality
[$\chi_{\textrm{s}}=\bm{S}_{i}\cdot(\bm{S}_{j}\times\bm{S}_{k})\neq 0$, where
$\bm{S}_{i}$, $\bm{S}_{j}$, and $\bm{S}_{k}$ are three nearest spins] can act
as a fictitious magnetic field on the conduction electrons, giving rise to
topological Hall effect (THE) 12 ; 13 ; 14 ; 15 . For example, an intrinsic
THE arising from a noncollinear spin structure under a magnetic field has been
established in the bulk antiferromagnetic (AFM) topological insulator MnBi2Te4
16 . However, in contrast to the topology in momentum space, electromagnetic
responses caused by the noncollinear spin texture in real space need further
study.

Rare-earth Zintl compound EuIn2As2 is a new promising candidate of the AFM
topological materials. EuIn2As2 crystallizes in hexagonal $P$63$/mmc$ space
group with the alternating stacking of Eu and In2As2 layers 17  as shown in
Fig. 1(a) and (b), realizing a topological transport of conducting electrons
in In2As2 layers affected by the magnetic moments of Eu2+ ions. In fact, a
bulk axion insulator phase has been predicted when the Eu moments exhibit the
A-type AFM order, in which the ordered Eu moments are ferromagnetically
aligned in the $ab$ plane but antiferromagnetically aligned in adjacent layers
along the $c$ axis 17 . Furthermore, different topological states are
suggested to be realized depending on the direction of the magnetic moments. A
topological crystalline insulator phase with gapless surface states on the
(100), (010), (001) surfaces is expected in EuIn2As2 for in-plane oriented Eu
magnetic moments. On the other hand, a high-order topological insulator phase
with chiral hinge states is predicted with out-of-plane magnetic order 17 .
These different topological states expected in the different orientation of
the Eu moments provide a promising way to control the topological state by
external magnetic field. Angle-resolved photoemission spectroscopy (ARPES)
results show an inversion of the bulk band as entering to the AFM state,
suggesting that there is a topological phase transition accomplished with the
magnetic transition 18 ; 19 . Although, recent neutron diffraction experiments
show that EuIn2As2 has a low-symmetry helical AFM order, not an A-type AFM
order, it has also been predicted that the direction of a modest applied
magnetic field of $B\approx 1$–2 T can tune between gapless and gapped surface
states 20 . Thus, the fruitful topological nature and easily magnetic field
tunability of this system will be a promising platform to realize “clean”
topological quantum effect and many novel transport phenomena.

In this paper, we perform a systematic study of single-crystal samples of
EuIn2As2, focusing on the interplay between the topological transport
phenomena and the magnetic state. The non-monotonic field dependence of the
magnetoresistance (MR) reveals that the transport phenomena is strongly
influenced by the spin configuration in EuIn2As2 system. Most importantly, we
observe an AHE and a large THE in the AFM state. From the dependence of the
AHE on the longitudinal conductivity and the temperature, we find that the AHE
is dominated by the intrinsic mechanism. In addition, from the field and the
angle dependence of the THE, we suggest that the THE is attributed to a finite
$\chi_{\textrm{s}}$ caused by the noncoplanar spin texture formed under out-
of-plane magnetic field.

Figure 1: The crystal structure of EuIn2As2, viewed along the $a$ axis(a) and
the $c$ axis(b). (c) The temperature dependence of the magnetic susceptibility
($\chi$($T$), left) and that of the inverse magnetic susceptibility
($1/\chi(T)$, right) under a magnetic field $B$ = 0.1 T applied parallel to
the $c$ axis (black) and the $ab$ plane (red). The blue lines show a Curie-
Weiss fit for the data. The inset shows the field dependence of the
magnetization $M(B)$ at 5 K and at $B\parallel c$ (black) and $B\parallel ab$
(red). (d) The temperature dependence of the resistivity with the current
applied along the $ab$ plane at 0 T and 5 T ($B\parallel c$). (e) The field
dependence of the magnetoresistance (MR) at various temperatures with
$B\parallel c$ (left panel) and $B\parallel ab$ (right panel). (f) The field
dependence of MR in different tilted angles from the $c$ axis to the $ab$
plane at 5 K.

##  II Experimental details

EuIn2As2 single crystals were grown by the self-flux method. Eu, In and As
with a mole ratio 1:12:3 were weighted and ground into alumina crucible in an
Ar-filled glove box, which was sealed in a quartz ampoule under high vacuum.
The sealed quartz ampoule was heated to 1323 K and maintained for 12 hours,
then cooled down to 873 K over 100 hours. At this temperature, the quartz
ampoule was quickly taken out from the furnace and decanted with a centrifuge
to separate EuIn2As2 single crystals. As shown in Fig. S1 in the Supplementary
Material 21 , the crystal was grown like a hexagonal piece, with dimensions of
2$\times$2$\times$0.1 mm3. The X-ray diffraction shows sharp peaks on the
pattern of (00$l$) plane, indicating the high-quality single crystallinity of
the samples.

Magnetization and electrical transport measurements were carried out by using
a Quantum Design Magnetic Property Measurement System (MPMS-XL5), a Physical
Properties Measurement System (PPMS-9 T) for 5 K $<T<400$ K and $B<9$ T, and a
dilution refrigerator (DR) for 0.1 K $<T<30$ K and $B<14$ T. Standard four-
probe and five-probe methods were used for the longitudinal resistivity and
the Hall measurements with a current in the $ab$ plane, respectively. All the
Hall resistivity were obtained by
$\rho_{yx}(B)=(\rho_{yx}(+B)-\rho_{yx}(-B))/2$ to remove the influence of
misalignment of the contacts. The reproducibility of our results were
confirmed by the measurements done for other samples from different batches as
shown in Fig. S2 and S3 in the Supplementary Material 21 .

##  III Results and discussion

Figure 1(c) shows the temperature dependence of the magnetic susceptibility
($\chi$) under a magnetic field ($B$) of 0.1 T applied along the $c$ axis
($\chi_{c}$) and the $ab$ plane ($\chi_{ab}$). As shown in Fig. 1(c),
$\chi_{ab}$ is larger than $\chi_{c}$ in the whole temperature range we
measured, showing the easy axis is in the $ab$ plane. The AFM transition at
Néel temperature $T_{\textrm{N}}=17$ K is clearly seen by the peak in
$\chi$($T$) for both $B\parallel c$ and $B\parallel ab$. The temperature
dependence of $\chi^{-1}$ above $T_{\textrm{N}}$ follows the Curie-Weiss law
with a positive Weiss temperature of 16.9 K and 18.5 K for $\chi_{c}$ and
$\chi_{ab}$, respectively, showing a dominant ferromagnetic (FM) interaction
in EuIn2As2. This dominant FM interaction is suggested to be caused by the
magnetic polarons in this material 22 ; 23 , which reflects the strong
exchange interaction between the spins of conduction electrons and the
localized Eu moments in EuIn2As2. The effective magnetic moment obtained by
the Curie-Weiss fit ($8.0\mu_{B}$ and 8.7$\mu$B for $\chi_{c}$ and
$\chi_{ab}$, respectively) agrees well with that expected for the highest spin
state of a Eu2+(7.94$\mu_{B}$). The field dependence of the magnetization
($M$) at 5 K (inset of Fig. 1(c)) shows a saturation at $B_{\textrm{sat}}$
$\sim$ 1.7 T for $B\parallel c$, which becomes smaller ($\sim 0.5$ T) for
$B\parallel ab$ at 5 K.

Figure 1(d) shows the temperature dependence of the longitudinal resistivity
($\rho$xx) at 0 and 5 T applied along the $c$ axis. As shown in Fig. 1(d),
$\rho$xx at 0 T starts to increase below $\sim$ 60 K as lowering temperature,
which is followed by a sharp peak at $T_{\textrm{N}}$. This peak in $\rho$xx
shows a strong scattering effect on conduction electrons by magnetic
fluctuations at 0 T, as it completely disappears at 5 T ($>B_{\textrm{sat}}$).
The high onset temperature of the magnetic scattering, which is far above
$T_{\textrm{N}}$, shows the presence of a strong magnetic fluctuation above
$T_{\textrm{N}}$ enhanced by the two-dimensional nature of the material.
Figure 1(e) shows the field dependence of the longitudinal resistivity
$\rho$xx at different temperatures under the magnetic field applied along the
$c$ axis and the $ab$ plane. In the paramagnetic state ($T>T_{\textrm{N}}$), a
negative MR is observed up to the highest field, which reaches a maximum of
60$\%$ at $T_{\textrm{N}}$. Below $T_{\textrm{N}}$, a positive MR appears
below $B_{\textrm{sat}}$, which is followed by a negative MR above
$B_{\textrm{sat}}$. This crossover from the positive MR to the negative one
becomes lower as the magnetic field is tilted to the $ab$ plane in accordance
with the decrease of $B_{\textrm{sat}}$ as shown in Fig. 1(f), indicating that
the positive-to-negative crossover behavior in MR is caused by the magnetic
scattering effects enhanced by suppressing the AFM order. Therefore, it
confirms that the transport phenomena are strongly influenced by the spin
configuration. Effects of magnetic polarons formed by the FM interaction and a
crossover from weak antilocalization to weak localization above
$B_{\textrm{sat}}$ have been put forward for the increase of $\rho$xx near
$T_{\textrm{N}}$ and the field dependence of MR below $T_{\textrm{N}}$ 22 ; 23
.

Next, we estimate the AHE in EuIn2As2 system. Figure 2(a) shows the field
dependence of the Hall resistivity ($\rho$yx) at 5 K (the data of different
samples at different temperatures are shown Fig. S3 in Supplementary Materials
21 ). As shown in Fig. 2(a), $\rho$yx shows a non-linear field dependence near
1.5 T (see the inset of Fig. 2(a)), showing an anomalous contribution in
$\rho$yx. To determine the field dependence of the anomalous part, $\rho$yx is
decomposed to the normal part $\rho^{\textrm{N}}_{yx}=R_{0}B$ and the
anomalous part $\Delta\rho_{yx}$ as

$\rho_{yx}=\rho^{\textrm{N}}_{yx}+\Delta\rho_{yx}=R_{0}B+\Delta\rho_{yx},$

where $R$0 is the Hall coefficient. First, we estimate $R$0 by a linear
fitting of the field dependence of $\rho$yx above $B_{\textrm{sat}}$ (the red
dashed line) and subtract $\rho^{\textrm{N}}_{yx}$ from $\rho$yx to obtain the
field dependence of $\Delta$$\rho$yx (the bule line in Fig. 2(a)). For the AHE
in this material, we estimate that the anomalous Hall resistivity
$\rho^{\textrm{A}}_{yx}$ linearly scales with $M$, which arises from both
extrinsic and intrinsic contributions 16 . The temperature dependence of
$\rho^{\textrm{A}}_{yx}$ shows a peak at around $T_{\textrm{N}}$ and decreases
as lowering the temperature (the black squares in Fig. 2(d)). This decrease of
$\rho^{\textrm{A}}_{yx}$ at lower temperatures continues down to 0.2 K as
shown by the data obtained in a different sample by using DR (the grey squares
in Fig. 2(d)).

As shown in Fig. 2(b), whereas the relation of $\Delta\rho_{yx}\propto M$
holds above $B_{\textrm{sat}}$, $\Delta$$\rho$yx considerably deviates from
$\rho^{\textrm{A}}_{yx}$ below $B_{\textrm{sat}}$. This deviation demonstrates
an additional component in $\Delta$$\rho$yx, named as a topological part
$\rho^{\textrm{T}}_{yx}$. We estimate $\rho^{\textrm{T}}_{yx}$ by subtracting
$R$A$\mu$0$M$ from $\Delta$$\rho$yx, where $R$A is the modified anomalous Hall
coefficient and plot the field dependence of $\rho^{\textrm{T}}_{yx}$ in Fig.
2(c). The magnetic field dependence of $\rho^{\textrm{T}}_{yx}$ at various
temperatures below $T_{\textrm{N}}$ (Fig. 2(c)) shows the negative peak at
$\sim$ $B_{\textrm{sat}}$/2. The magnitude of the peak of
$\rho^{\textrm{T}}_{yx}$ ($\rho^{\textrm{Tmax}}_{yx}$) is almost temperature
independent around 1 $\mu\Omega$ cm, and quickly disappears above
$T_{\textrm{N}}$ (orange circles of Fig. 2(d)).

Figure 2: Anomalous Hall effect (AHE) and topological Hall effect (THE). (a)
The magnetic field dependence of the Hall resistivity ($\rho$yx) at 5 K. The
red dashed-dotted line is a fitting curve to estimate the Hall coefficient
$R$0, which is used to extract anomalous Hall part
$\Delta\rho_{yx}=\rho_{yx}-R_{0}B$ (blue line). The inset shows an enlarged
view of $\rho$yx for 1–2 T. (b) The magnetic field dependence of
$\Delta$$\rho$yx at different temperatures, obtained after subtracting the
normal Hall resistivity. Each solid line shows a fit of the anomalous Hall
resistivity $\rho^{\textrm{A}}_{yx}$ by
$\rho^{\textrm{A}}_{yx}=R_{\textrm{A}}\mu_{0}M$. (c) The magnetic field
dependence of the topological Hall resistivity $\rho^{\textrm{T}}_{yx}$ at
various temperatures, the arrows indicate the position of the peak of
$\rho^{\textrm{T}}_{yx}$ ($\rho^{\textrm{Tmax}}_{yx}$). (d) The temperature
dependence of $\rho^{\textrm{A}}_{yx}$ (black and grey squares for different
samples respectively, left axis), $\rho^{\textrm{Tmax}}_{yx}$ (orange circles,
left axis), the anomalous Hall conductivity $\sigma^{\textrm{A}}_{yx}$ (red
circles, 1st right axis), and the magnetization at 2 T above
$B_{\textrm{sat}}$ (blue dashed line, 2nd right axis). Figure 3: (a) Anomalous
Hall conductivity $\sigma^{\textrm{A}}_{yx}$ in the low temperature range
plotted against $\sigma_{xx}$ for EuIn2As2 and other materials in a log-log
graph. The “bad metal regime”, “intrinsic regime”, and “extrinsic regime” of
$\sigma_{xx}$ are denoted with different background colors. The reported data
for other materials are obtained from refs. 9 ; 10 ; 11 ; 31 ; 32 ; 33 ; 34 ;
35 ; 36 ; 37 . (b–d) The spin configurations of Eu with out-of-plane magnetic
field. The in-plane helical structure at 0 T (b) is modified to a noncoplanar
structure for $0<B<B_{\textrm{sat}}$ (c) and a polarized one for
$B_{\textrm{sat}}<B$ (d).

We first discuss the origin of $\rho^{\textrm{A}}_{yx}$ in this compound. As
current knowledge, it has been well established that an AHE emerges from the
two mechanisms: the intrinsic one caused by a Berry curvature effect 24 ; 25
and the extrinsic one by either skew or side-jump scattering effects 26 ; 27 .
The former is observed in a moderately dirty metal in which the anomalous Hall
conductivity
$\sigma^{\textrm{A}}_{yx}=\rho^{\textrm{A}}_{yx}/({\rho^{\textrm{A}}_{yx}}^{2}+{\rho_{xx}}^{2})$
becomes independent on $\sigma_{xx}$, whereas the latter in a clean one in
which $\sigma^{\textrm{A}}_{yx}\propto\sigma_{xx}$ 28 . In addition,
$\sigma^{\textrm{A}}_{yx}$ of the intrinsic AHE is known to linearly scale to
$M$ 24 ; 28 .

We find that the AHE in EuIn2As2 fulfills these features of the intrinsic AHE.
We plot the anomalous Hall conductivity $\sigma^{\textrm{A}}_{yx}$ against the
longitudinal conductivity $\sigma_{xx}$ with other FM and AFM systems in Fig.
3(a). First, we find that the $\sigma_{xx}$ is in the range around
6$\times$103 $\Omega^{-1}$cm-1 and the $\sigma^{\textrm{A}}_{yx}$ does not
depend on $\sigma_{xx}$. Both features indicate that EuIn2As2 is located at
the “intrinsic regime”, where the intrinsic mechanism is suggested to be
dominant. In addition, as shown in Fig. 2(d), we find that the temperature
dependence of $\sigma^{\textrm{A}}_{yx}$ almost follows that of $M$ (i.e.
$\rho^{\textrm{A}}_{yx}\propto\rho_{xx}^{2}M$), supporting the dominant
intrinsic AHE in $\rho^{\textrm{A}}_{yx}$. In fact, in the time-reversal-
symmetry-broken systems, a band crossing near the Fermi energy
$E_{\textrm{F}}$ with a strong spin-orbit coupling (SOC) can lift the spin
degeneracy. The energy gap induced by the SOC produces a large Berry
curvature, contributing to the intrinsic AHE. It has been verified that
noncollinear antiferromagnets with zero net magnetization can produce a large
AHE when their electronic structure exhibits a nonvanishing Berry curvature
that acts like a large fictitious magnetic field 10 ; 29 ; 30 . According to
the recent neutron diffraction experiment, EuIn2As2 has a helical magnetic
structure 20 , in which the magnetic moment ferromagnetically aligning in the
$ab$ plane rotates antiferromagnetically along the $c$ axis with the magnetic
space group of $P$612’2’/$C$2’2’21 (Fig. 3(b)). These symmetries break both
the space and time reversal symmetries, giving rise to local nonzero Berry
curvature. In fact, the unitary operators (space symmetry, such as the 61) and
the anti-unitary operators (such as $T$$\cdot$2x) can own a finite Berry
curvature in the reciprocal space, ensuring that AHE can emerge in the helical
AFM of EuIn2As2.

Figure 4: (a) The field dependence of the Hall resistivity $\rho_{yx}$ of
EuIn2As2 at various tilted angles at 5 K. (b) The field dependence of the
magnetization $M$ at the same angles of (a). (c) The magnetic field dependence
of the anomalous Hall resistivity $\Delta$$\rho$yx under various field
orientations. Each solid line shows a fitting of $\rho^{\textrm{A}}_{yx}$
using the relation $\rho^{\textrm{A}}_{yx}=R_{\textrm{A}}\mu_{0}M$. (d) The
magnetic field dependence of the topological Hall resistivity
$\rho^{\textrm{T}}_{yx}$ at various field tilted angles. The arrows in (b),
(c) and (d) indicate the saturation field in different tilted angles.

Having established the origin of the AHE, we now discuss the origin of
$\rho^{\textrm{T}}_{yx}$. As shown in Fig. 2(d), $\rho^{\textrm{Tmax}}_{yx}$
emerges below $T_{\textrm{N}}$ and stays a constant at lower temperatures.
This temperature dependence is in sharp contrast to $\rho^{\textrm{A}}_{yx}$
that decreases below 20 K, suggesting a different origin of
$\rho^{\textrm{T}}_{yx}$. The field dependence of $\rho^{\textrm{T}}_{yx}$
(Fig. 2(c)) shows that $\rho^{\textrm{T}}_{yx}$ is caused by a deformation of
the magnetic structure from either the zero-field state and the fully
polarized state. Since no magnetic transition is observed for
$B<B_{\textrm{sat}}$, the helical magnetic structure at $B=0$ (Fig. 3(b)) is
continuously deformed to a noncoplanar structure (Fig. 3(c)) under a magnetic
field applied along the $c$ axis, which is followed by the polarized one above
$B_{\textrm{sat}}$ (Fig. 3(d)). Although it remains as a future work to
confirm the actual magnetic structure under the magnetic field, this
noncoplanar magnetic structure gives rise to a finite $\chi_{\textrm{s}}$
which eventually vanishes in the fully polarized state above
$B_{\textrm{sat}}$. Therefore, the field dependence of
$\rho^{\textrm{T}}_{yx}$ is well explained by that of $\chi_{\textrm{s}}$ that
develops in the helical magnetic structure under $B\parallel c$ 31 ; 38 ; 39 .
A similar THE is observed in the kagome AFM YMn6Sn6 with the helical magnetic
ground state, where the formation of double-fan spin structure under magnetic
field contributes to the THE 40 . We note that a possibility of a field-
induced band structure changing, as observed in EuO 41 , can be safely
excluded as the origin of THE in this material. The band structure calculation
of EuIn2As2 predicts that the energy shift of the unoccupied band closes the
inverted band gap near the $\Gamma$ point when the magnetic order is changed
from helical to FM, suggesting a possibility of the band-structure control by
applying a magnetic field 20 . However, in contrast to these band calculations
predicting a semiconducting state for EuIn2As2, this compound is a naturally
hole-doped metal as shown by our Hall measurements. In fact, the previous
ARPES measurements 18  show that the actual Fermi energy is far below the
energy gap ($\sim-0.3$ eV), indicating that the slight energy shift of the
unoccupied band does not affect the electric transport of this material.

To confirm this topological transport caused by $\chi_{\textrm{s}}$ of the
noncoplanar magnetic structure in EuIn2As2, we investigate the angle
dependence of $\rho^{\textrm{T}}_{yx}$ by tilting the magnetic field from the
$c$ axis to the $ab$ plane. Figure 4(a) shows the field dependence of $\rho$yx
at different angles at 5 K. Simultaneously, we also take the magnetization
data at the same tilted angle of the magnetic field, displayed in Fig. 4(b).
First, we extract the field dependence of $\Delta$$\rho$yx(Fig. 4(c)) by
subtracting the normal part. As shown in Fig. 4(c), $\Delta$$\rho$yx is
gradually suppressed by tilting the magnetic field to the $ab$ plane. Then we
focus on the THE below the saturation field in different tilted angle, we
obtain $\rho^{\textrm{T}}_{yx}$ in the tilted magnetic field by subtracting
the $M$-linear component from $\Delta$$\rho$yx. As shown in Fig. 4(d),
$\rho^{\textrm{T}}_{yx}$ decreases as the magnetic field is tilted to the $ab$
plane. This angle dependence indicates that $\chi_{\textrm{s}}$ caused by the
$c$-axis component of the applied field is directly linked to the THE.

Similar AHEs are also observed in the related Eu-based compounds EuCd2Sb2 42
and EuCd2As2 43 . In these compounds, the Weyl points near the Fermi energy or
a dynamical Weyl semimetal state are suggested to contribute the AHEs. It
should be noted that, although a similar THE might be observed in these
compounds below the saturation field, the origin of the THE is not discussed
in these previous works 42 ; 43 . Given the different collinear AFM state
suggested in EuCd2Sb2 and EuCd2As2 and the different crystal structure of
these compounds, the origin of the THE in EuCd2Sb2 and EuCd2As2 may be
different from that in EuIn2As2.

##  IV Summary

In conclusion, our detailed transport measurements on bulk EuIn2As2 single
crystals reveal that the transport properties in this compound are strongly
influenced by the spin texture formed below $T_{\textrm{N}}$. Most
importantly, we find an AHE and a THE emerge in the AFM state. We suggest that
the AHE is originated from a nonvanishing net Berry curvature in the momentum
space due to the helical spin structure and that the THE is attributed to the
scalar spin chirality of the noncoplanar spin structure caused by the external
field. These observations and analysis in EuIn2As2 provide a fertile ground to
understand the influence of the interplay between the topology of electronic
bands and field-induced novel magnetic structure on unconventional
magnetoelectric response. Our findings may push the advanced experiments to
understand the nature of this material and other magnetic topological
materials.

##  V Acknowledgements

This work was supported by the National Nature Science Foundation of China
under Contract Nos. 11674326, 11874357, the Joint Funds of the National
Natural Science Foundation of China, the Chinese Academy of Sciences’ Large-
Scale Scientific Facility under Contract Nos. U1832141, U1932217, and
U2032215, the Key Research Program of Frontier Sciences, CAS (No. QYZDB-SSW-
SLH015), the uses with Excellence and Scientific Research Grant of Hefei
Science Center of CAS (No.2018HSC-UE011). The work in Japan was supported by
KAKENHI (Grants-in-Aid for Scientific Research) Grants No. JP19H01848 and No.
JP19K21842.

## References

  * (1) M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
  * (2) F. D. M. Haldane, Rev. Mod. Phys. 89, 040502 (2017).
  * (3) B. Yan and C. Felser, Annu. Rev. Condens. Matter Phys. 8, 337 (2017).
  * (4) N. Armitage, E. Mele, and A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018).
  * (5) A. M. Essin, J. E. Moore, and D. Vanderbilt, Phys. Rev. Lett. 102, 146805 (2009).
  * (6) R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, and Z. Fang, Science 329, 61 (2010).
  * (7) Y. Tokura, K. Yasuda, and A. Tsukazaki, Nat. Rev. Phys. 1, 126 (2019).
  * (8) D. Xiao, J. Jiang, J.-H. Shin, W. Wang, F. Wang, Y.-F. Zhao, C. Liu, W. Wu, M. H. W. Chan, N. Samarth et al., Phys. Rev. Lett. 120, 056801 (2018).
  * (9) E. Liu, Y. Sun, N. Kumar, L. Muechler, A. Sun, L. Jiao, S.-Y. Yang, D. Liu, A. Liang, Q. Xu et al., Nat. Phys. 14, 1125 (2018).
  * (10) S. Nakatsuji, N. Kiyohara, and T. Higo, Nature (London) 527, 212 (2015).
  * (11) T. Suzuki, R. Chisnell, A. Devarakonda, Y. T. Liu, W. Feng, D. Xiao, J. W. Lynn, and J. G. Checkelsky, Nat. Phys. 12, 1119 (2016).
  * (12) K. Ueda, S. Iguchi, T. Suzuki, S. Ishiwata, Y. Taguchi, and Y. Tokura, Phys. Rev. Lett. 108, 156601 (2012).
  * (13) B. G. Ueland, C. F. Miclea, Y. Kato, O. Ayala-Valenzuela, R. D. McDonald, R. Okazaki, P. H. Tobash, M. A. Torrez, F. Ronning, R. Movshovich et al., Nat. Commun. 3, 1067 (2012).
  * (14) N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013).
  * (15) K. S. Denisov, I. V. Rozhansky, N. S. Averkiev, and E. Lähderanta, Phys. Rev. B 98, 195439 (2018).
  * (16) S. H. Lee, Y. Zhu, Y. Wang, L. Miao, T. Pillsbury, H. Yi, S. Kempinger, J. Hu, C. A. Heikes, P. Quarterman et al., Phys. Rev. Res. 1, 012011(R) (2019).
  * (17) Y. Xu, Z. Song, Z. Wang, H. Weng, and X. Dai, Phys. Rev. Lett. 122, 256402 (2019).
  * (18) S. Regmi, M. M. Hosen, B. Ghosh, B. Singh, G. Dhakal, C. Sims, B. Wang, F. Kabir, K. Dimitri, and Y. Liu et al., Phys. Rev. B 102, 165153 (2020).
  * (19) T. Sato, Z. Wang, D. Takane, S. Souma, C. Cui, Y. Li, K. Nakayama, T. Kawakami, Y. Kubota, and C. Cacho et al., Phys. Rev. Res. 2, 033342 (2020).
  * (20) S. X. Riberolles, T. V. Trevisan, B. Kuthanazhi, T. Heitmann, F. Ye, D. C. Johnston, S. L. Bud’ko, D. Ryan, P. C. Canfield, and A. Kreyssig et al., Nat. Commun. 12, 999 (2021).
  * (21) See Supplementary Materials for X-ray dispersion characterization and extended Hall data at different temperaures and different samples.
  * (22) W. Shon, J.-S. Rhyee, Y. Jin, and S.-J. Kim, Phys. Rev. B 100, 024433 (2019).
  * (23) Y. Zhang, K. Deng, X. Zhang, M. Wang, Y. Wang, C. Liu, J.-W. Mei, S. Kumar, E. F. Schwier, K. Shimada et al., Phys. Rev. B 101, 205126 (2020).
  * (24) R. Karplus and J. M. Luttinger, Phys. Rev. 95, 1154 (1954).
  * (25) T. Jungwirth, Q. Niu, and A. H. MacDonald, Phys. Rev. Lett. 88, 207208 (2002).
  * (26) J. Smit, Physica 24, 39 (1958).
  * (27) L. Berger, Phys. Rev. B 2, 4559 (1970).
  * (28) N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Rev. Mod. Phys. 82, 1539 (2010).
  * (29) J. Kübler and C. Felser, Europhys. Lett. 108, 67001 (2014).
  * (30) H. Chen, Q. Niu, and A. H. MacDonald, Phys. Rev. Lett. 112, 017205 (2014).
  * (31) N. Kanazawa, Y. Onose, T. Arima, D. Okuyama, K. Ohoyama, S. Wakimoto, K. Kakurai, S. Ishiwata, and Y. Tokura, Phys. Rev. Lett. 106, 156603 (2011).
  * (32) S.-Y. Yang, Y. Wang, B. R. Ortiz, D. Liu, J. Gayles, E. Derunova, R. Gonzalez-Hernandez, L. Šmejkal, Y. Chen, S. S. P. Parkin et al., Sci. Adv. 6, eabb6003 (2020).
  * (33) T. Miyasato, N. Abe, T. Fujii, A. Asamitsu, S. Onoda, Y. Onose, N. Nagaosa, and Y. Tokura, Phys. Rev. Lett. 99, 086602 (2007).
  * (34) S. Onoda, N. Sugimoto, and N. Nagaosa, Phys. Rev. B 77, 165103 (2008).
  * (35) Y. Shiomi, Y. Onose, and Y. Tokura, Phys. Rev. B 79, 100404 (2009).
  * (36) N. Manyala, Y. Sidis, J. F. DiTusa, G. Aeppli, D. P. Young, and Z. Fisk, Nat. Mater. 3, 255 (2004).
  * (37) K. S. Takahashi, H. Ishizuka, T. Murata, Q. Y. Wang, Y. Tokura, N. Nagaosa, and M. Kawasaki, Sci. Adv. 4, eaar7880 (2018).
  * (38) P. Bruno, V. K. Dugaev, and M. Taillefumier, Phys. Rev. Lett. 93, 096806 (2004).
  * (39) J. Ye, Y. B. Kim, A. J. Millis, B. I. Shraiman, P. Majumdar, and Z. Tešanović, Phys. Rev. Lett. 83, 3737 (1999).
  * (40) Q. Wang, K. J. Neubauer, C. Duan, Q. Yin, S. Fujitsu, H. Hosono, F. Ye, R. Zhang, S. Chi, K. Krycka et al., Phys. Rev. B 103, 014416 (2021).
  * (41) P. G. Steeneken, L. H. Tjeng, I. Elfimov, G. A. Sawatzky, G. Ghiringhelli, N. B. Brookes, and D.-J. Huang, Phys. Rev. Lett. 88, 047201 (2002).
  * (42) H. Su, B. Gong, W. Shi, H. Yang, H. Wang, W. Xia, Z. Yu, P.-J. Guo, J. Wang, L. Ding et al., APL Mater. 8, 011109 (2020).
  * (43) J. Z. Ma, S. M. Nie, C. J. Yi, J. Jandke, T. Shang, M. Y. Yao, M. Naamneh, L. Q. Yan, Y. Sun, A. Chikina et al., Sci. Adv. 5, eaaw4718 (2019).


# Monitoring the evolution of antisemitic discourse on extremist social media
using BERT††thanks: Acknowledgements: Research supported by American
University’s Signature Research Initiative program. We also thank Matan
Schwartz for his initial help with this project.

Raza Ul Mustafa, Nathalie Japkowicz  American University, 4400 Massachusetts
Ave NW, Washington, DC 20016, USA
<EMAIL_ADDRESS>
###### Abstract

Racism and intolerance on social media contribute to a toxic online
environment which may spill offline to foster hatred, and eventually lead to
physical violence. That is the case with online antisemitism, the specific
category of hatred considered in this study. Tracking antisemitic themes and
their associated terminology over time in online discussions could help
monitor the sentiments of their participants and their evolution, and possibly
offer avenues for intervention that may prevent the escalation of hatred. Due
to the large volume and constant evolution of online traffic, monitoring
conversations manually is impractical. Instead, we propose an automated method
that extracts antisemitic themes and terminology from extremist social media
over time and captures their evolution. Since supervised learning would be too
limited for such a task, we created an unsupervised online machine learning
approach that uses large language models to assess the contextual similarity
of posts. The method clusters similar posts together, dividing, and creating
additional clusters over time when sub-themes emerge from existing ones or new
themes appear. The antisemitic terminology used within each theme is extracted
from the posts in each cluster. Our experiments show that our methodology
outperforms existing baselines and demonstrates the kind of themes and sub-
themes it discovers within antisemitic discourse along with their associated
terminology. We believe that our approach will be useful for monitoring the
evolution of all kinds of hatred beyond antisemitism on social platforms.

###### Index Terms:

hate speech, concept formation, monitoring, antisemitic speech, large language
model, NLP, social media, BERT, transfer learning

##  I Introduction

Social111Warning: This paper contains examples of racist and antisemitic
statements that may be disturbing to the reader. media has played a crucial
role in simplifying the human process of joining communities of like-minded
individuals. People use these platforms to engage with others by way of
expressing their opinions and commenting on those of others. While technology
has had a positive impact on many people’s lives, it has also brought serious
negative consequences onto society, including an acceleration of the spread of
hatred.

In the past few years, a large number of studies have been devoted to
automatic hate speech detection [1, 2, 3, 4]. The more difficult task of
understanding the nature of online discussions automatically has been
considered, though only rarely. On those few occasions, the task was
considered in a static fashion, ignoring the fact that online discussions
evolve quickly. Though these attempts constitute a good start, they are not
sufficient since organizations that seek to promote social peace need to be
informed of changes in discussion themes as they occur rather than on, say, a
monthly basis, when the software is run on a new batch of posts. The purpose
of our work is to explore the ability of machine learning (ML) and natural
language processing (NLP) tools to extract a continuously evolving map of the
semantic themes represented in social media posts, automatically. To provide
continuity and avoid catastrophic forgetting, it is of utmost importance that
past knowledge be preserved and only updated when necessary.

We develop a method to continuously monitor antisemitic themes from
discussions taking place on extremist social media. Many antisemitic themes
have emerged throughout the years, making antisemitism an unfortunately good
testbed for our approach. Indeed, Jews have been victims of discrimination for
centuries, sometimes accused of having too much power, controlling the world
economy, or being disloyal. Discussions and conspiracy theories about the
Holocaust abound. Other historical tropes include: “Jews killed Jesus” and
“Jews are greedy”. These conspiracy theories evolve continuously developing
new themes, such as linking Jews to the COVID-19 pandemic [5]. The purpose of
our endeavor is to stay ahead of the ”mood” in extremist social media
communities where antisemitic posts are frequent, so as to be aware of
emerging new themes or recurring old ones in the same or altered form. To be
practical, given the exploratory and continuous nature of the task, the method
we devised is unsupervised and works in a continual and, thus, stable fashion
using state-of-the-art ML and NLP techniques such as Large Language Models
(LLMs). Though antisemitism was used in this work as a case study, the methods
we propose will apply to any other kinds of hatred, such as Islamophobia,
anti-Black or anti-Asian racism, anti-LGBTQ+ discourse, etc.

Our proposed approach begins by considering posts collected in a first time-
window and groups together semantically related themes (i.e., concepts,
topics). It then proceeds with the next time-window, adding new posts to the
previously discovered themes and discovering new themes in the data if the
discourse they represent stands semantically apart from the themes already
present in memory and sub-themes, if they share enough commonality with
existing ones. The system then considers the posts collected in the next time-
window and repeats the same steps over and over.

The remainder of the paper is organized as follows. In Section II, we discuss
the philosophical basis for our work along with related studies from the
fields of Computer Science, Psychology and Business. We then review ML and NLP
techniques previously used for combating online hate speech and antisemitism
in Section III. Section IV describes our methodology. We present and discuss
our results in Section V and conclude our paper in Section VI.

##  II General Background

In this section, we consider related work from four different disciplines:
Philosophy, Computer Science, Psychology, Business.

#### Philosophical Concept Theory

Our work is based on Philosophical Concept Theory [6] used extensively in the
fields of Psychology and Cognitive Science. In a nutshell, we take the view
that concepts are representations of the mind and that complex concepts are
composed of sub-concepts. Furthermore, we subscribe to the Prototype Theory
rooted in Wittgenstein [7] and Rosch [8]’s thought where a concept is defined
by its most central, or prototypical, instance and the association of a
separate instance to that concept depends on its distance to the prototype. We
illustrate these ideas with the following example. A common concept is that
flowers are beautiful and fragrant. However, the reality is more complex:
while most flowers fit the common concept, some flowers are odorless, and some
are even pungent and cause allergies. Therefore, beauty and fragrance, while
brought together in the common concept of a flower, can also be taken apart.
That is the case for the concept of flowers that are beautiful but pungent (or
odorless). Such flowers remain semantically close to the prototypical instance
(a rose, for example) of beautiful and fragrant flowers because of their many
shared features, but they must be represented by a different sub-concept
since, while still beautiful, they are not fragrant. Similarly, flowers that
cause allergies must be represented by yet a new sub-concept that intersects
with the concepts of beautiful and fragrant flowers and beautiful but pungent
(or odorless) ones. Our work equates clusters of posts to concepts and
subconcepts and assesses the relations between them by means of their distance
in LLM embedded space.

#### Lifelong Unsupervised Learning

The method designed in this paper is inspired by a recent approach for
lifelong anomaly detection presented in [9, 10]. The main purpose of that
approach was to build an evolving representation and organization of memory to
ensure that new concepts could be coherently added to the organized structure
while older pieces of knowledge could be retrieved efficiently in a lifelong
learning regimen. The stability of the method ensured that catastrophic
forgetting was avoided. Anomaly detection was performed on a continual basis
by checking whether the new data fell into one of the categories present in
memory. If not, a decision was made as to whether the new data was anomalous
or not. If it was deemed anomalous, an alert was issued and the data not
saved. Otherwise, the new data was introduced into the memory structure as
either a sub-concept or a new concept altogether. Decisions were made based on
distance in an autoencoder-based embedding space. The approach was tested and
validated on tabular data representing fairly straightforward hierarchically
organized categories of data. One of the challenges of the present study is to
see to what extent the principles used in the earlier work can apply to text
data and imprecise concepts that are not always hierarchically organized.

#### Psychological Studies on Hate Speech

To underline the importance of the task we address with our method, we review
two related psychological studies on hate speech that seek to extract similar
types of information as ours from their analysis, albeit manually. In the
first study, closest to our proposed one, [11] extracted four semantic themes
from a series of comments responding to a Youtube video that displayed a white
British woman abusing black passengers on the Tube (subway). The four themes
they organized the posts around are: 1) posts that explain the abuser’s
behavior; 2) posts that counter the abuser’s behavior with aggressive and
hateful language; 3) posts that categorize other posters into racist or non
racist people; 4) posts that discuss what it means to be British. The authors’
analysis led them to conclude that online hate speech does not necessarily
generate more hate speech, a potentially useful conclusion for this specific
content and platform. In a second study, [12] analyzed the behavioral roles
taken by online users responding to hate speech posts in Ethiopia. They
identified five major roles—trolling, pace-making, peace-making, informing,
and guarding—and used their conclusions to make recommendations on how to
counter online hatred. Though like in our work, both studies support the need
for a deeper semantic analysis of posts rather than their mere classification
as hateful or not, it is important to note that both were conducted through
human analysis of a relatively small and static number of posts. Our work, in
contrast, seeks to perform the same type of analysis automatically and
dynamically.

#### Information Extraction from Customer Surveys

Although the aim of our study is new in the context of automated hate speech
analysis, the business community has understood the value of extracting
information from product reviews for some time. As a matter of fact, it has
already seized upon the power of AI to learn how to extract automatically the
areas of satisfaction and concern about its products expressed by customers.
This is shown in both academic research papers [13, 14] and commercial
products available to businesses. It is important to note, however, that the
domain explored by such business tools is much simpler than the hate speech
domain. Indeed, human beings typically have many conflicting and hard-to-
express resentments about other human beings, and these feelings may fluctuate
as a result of national or international news items or personal experiences.
On the other hand, feelings about purchased goods are rather straightforward
and limited since they are non-conflictual and pertain to simple and finite
properties such as the product’s price, functionality, or looks. In addition,
the approaches considered in these works take a static rather than a dynamic
view of the problem. For these reasons, the techniques used by the business
community, though relevant, are not sufficient, and new methods must be
developed to handle the monitoring of complex themes that also evolve over
time.

##  III Background on Computer-Based Hate Speech Analysis

As previously mentioned, hate-speech detection has become an important area of
study in NLP as reported by a number of surveys on the topic [1, 2, 3, 4].
Recently, many of these studies have employed deep learning techniques [15].
In [16], the authors proposed a Recurrent Neural Networks (RNNs) based
framework for the classification of racism & sexism, offensive speech, and
cyberbullying using text and metadata. In [17], the LSTM (Long Short-Term
Memory) architecture is used for the classification of abusive content on
social media while [18] uses more advanced recurrent neural network techniques
to classify sexism and misogyny. In another study, [19] compared multiple deep
learning techniques to classify tweets into three categories: racism, sexism,
or neither.

There have been a few studies devoted to the particular issue of online
antisemitism. [20] used a transformer architecture (RoBERTA) to classify
antisemitic content into four categories: political, economic, religious, or
racial. In [5] the authors used Latent Dirichlet Allocation (LDA) to find
topics particularly related to the coronavirus and antisemitism in the
Hungarian language. [21] describes a large study with several outcomes. In
that work, the authors collected 7 million images and comments from 4chan and
Gab to study the spread of antisemitic memes. They provide a framework to
better understand antisemitic memes and content and their relation to
political events. In one part of the study, they used Word2Vec to discover
words closely associated with the term ”Jew” and used network analysis tools
such as community discovery in an attempt to uncover the themes represented by
these terms. The themes they uncovered are: Jewish moral corruptness, Jews as
geopolitical conspirators, ethnic Jewish identities, Kabbalistic and cryptic
themes, and religious or theological topics. Following this study, [22]
considers both antisemitism and Islamophobia. In that work, the authors
constructed two lexicons: a lexicon of 48 Antisemitic terms and another of 135
Islamophobic terms. The lexicons were built using pre-existing knowledge
graphs, pre-trained word embedding models, and manual annotations. Using their
lexicons, they extracted posts from 4Chan and analyzed them using sentence
embeddings by BERT and clustering using HDBSCAN. They subsequently analyzed
the groupings qualitatively.

We summarize the previous work in Table I. Our proposed approach is summarized
at the bottom of the table. As can be seen, our work is most similar to [5],
[21] and [22]. The main difference between these three works and ours is that
they consider a static situation whereas our approach is an online machine
learning approach that provides self-adaptation mechanisms in a dynamic
setting, making sure that the knowledge base induced in previous steps is not
compromised by a new influx of information. Self-adaptation, dynamism, and
stability aside, of the three methods closest to ours, [22] is the one that
uses the closest methodology since [5] performs topic extraction using LDA,
and [21] does so using Word2Vec. These two methodologies are less recent and
typically obtain lower performance than the one used by both [22] and our
work: transformers. In particular, both works use BERT, though while [22] rely
on pre-trained language models, we fine-tuned our model to the particular type
of data we analyze. Like in our study, [22] uses clustering on the language
representations learned and, in particular, HDBSCAN. Rather than using an off-
the-shelf static clustering approach, however, we design our own approach that
works in a dynamic environment without causing catastrophic forgetting.

TABLE I: Comparison to traditional work and techniques used in hate speech
detection.

Ref Unsupervised Online Term Extraction Topic Extraction ML Tools Hate Type
[16] $\times$ $\times$ $\times$ $\times$ RNNs racism & sexism, offensive
speech, and cyberbullying [17] $\times$ $\times$ $\times$ $\times$ LSTMs
abusive content [18] $\times$ $\times$ $\times$ $\times$ LSTMs, CNNs sexism
and misogyny [19] $\times$ $\times$ $\times$ $\times$ LSTMs, CNNs, GloVe
racism, sexism, or neither [20] $\times$ $\times$ $\times$ $\times$ RoBERTa
antisemitism [5] ✓ $\times$ $\times$ ✓ LDA coronavirus related antisemitism
[21] ✓ $\times$ ✓ ✓ Word2Vec, network analysis antisemitism [22] ✓ $\times$ ✓
✓ BERT, HDBSCAN antisemitism and islamophobia This work ✓ ✓ ✓ ✓ BERT, novel
algorithm antisemitism

Figure 1: Overview of the methodology.

##  IV Methodology

Our antisemitic discourse monitoring approach takes as input continuously
arriving batches of posts and organizes them into a knowledge base containing
the antisemitic themes they convey in an unsupervised way. In more detail, we
designed a repeating two step-method that takes the following actions for each
batch of incoming posts: 1) it generates contextual embeddings from the posts
using a fine-tuned BERT model; 2) it inputs these embeddings into our newly
proposed divisive clustering approach which adaptively updates the last
clustering to integrate the new batch of embeddings into the existing
knowledge base using local or global updates. Decisions are made based on the
distance in embedding space between the new posts and the existing cluster
centers. The two main mechanisms used in the process are illustrated in Figure
1. Each step of the process will be described in more detail below.

###  IV-A Dataset and Pre-Processing

####  IV-A1 Data Collection and Labeling

This work is part of a larger project entitled unmasking antisemitism that our
organization has undertaken to control anti-Jewish hatred. Under this project,
a data team collected and labeled the data set using third-party software
Pyrra222https://www.pyrratech.com/. A baseline was set for data selection
under which currently known antisemitic seed words from the American Jewish
Committee (AJC) and other sources were used (e.g., cabal, new world order).
During labeling, the data team carefully examined word selection in posts as
well as other pieces of information such as i) does the post demonstrate an
applied understanding of particular antisemitic tropes? ii) does the post
express themes of control over media, politics, academia, economy, or culture
at large? and so on. It then classified the data into different pre-defined
historic tropes or generated variations on them when the post was found to be
antisemitic. The labels generated by the data team are used in this work to
evaluate our approach and the baselines we will be comparing it to.333The
coding statement used by the data team is available upon request.

####  IV-A2 Data Pre-Processing

The initial step of our approach, not shown in Figure 1, involves preparing
the dataset using different techniques. We first normalize the text documents
by converting uppercase to lowercase and replacing references. Next, we remove
links from the text. However, we replace the links with the titles of the
posts they lead to. Finally, we remove all special characters, white spaces,
and line breaks using regular expressions. The cleaned-up texts are then fed
into BERT for tokenization into small units (words or word parts) and
contextual embeddings are generated to facilitate the discovery of underlying
concepts in the text. The details of the contextual embedding method used here
are described in the next section.

Figure 2: BERT layers to extract contextual embedding.

###  IV-B Contextual Embedding

To convert our extremist cleaned-up dataset into embeddings, we use embedding
techniques derived from large language models to extract a structural
representation that captures semantic relationships and contextual meanings.
This approach facilitates the categorization of information to uncover hidden
patterns [20]. Since BERT doesn’t possess vocabulary specific to our domain,
we first added Out of Vocabulary (OOV) tokens and fine-tuned the BERT uncased
model as in [23]. During concept extraction, we consider different types of
combinations to extract contextual embedding from the BERT (see Figure 2). To
this end, we first explored the summation of the last four layers, followed by
the concatenation of the last four layers. We also considered the pooled
layer, which provides 768-dimensional sentence-level embeddings. In our case,
the last hidden layer, after taking the mean of tokens level embedding,
produces the best results and was therefore the embedding technique we
retained. These variations allowed us to evaluate the impact of different
feature representations, contributing to a deeper understanding of the model’s
capabilities and suitability for our specific NLP task.

###  IV-C Antisemitic Themes discovery

We now describe the approach we designed to extract concepts from extremist
posts. To simulate a streaming situation, we divide the dataset into batches
of vectors $\vec{v}$ (each containing instances of posts embeddings) and feed
each batch into algorithm 1. Algorithm 1 uses distances in the embedding space
along with several thresholds to capture the antisemitic themes expressed in
our extremist dataset. Several parameters need to be set prior to running the
algorithm: $k,lo,hi,$ and thresholds $\lambda$ and $\delta$. $k$ represents
the number of initial concepts considered in the first batch of data
$\vec{v_{1}}$. In our work, we set $k=2$, assuming that the posts in
$\vec{v_{1}}$ align along two main themes. $lo$ and $hi$ represent the lower
and higher percentile marks used in our computations to consider whether a
post is within the vicinity of a concept or not. We set them to $lo=40$ and
$hi=60$, here. $\lambda$ is the multiplier used (combined with $lo$ and $hi$)
to calculate the percentile distribution ranges that will help determine
whether instances from a given batch are outliers with respect to the concept
considered. Finally, $\delta$, determines the minimum number of outlying
instances required to justify the need for an additional concept in memory
(i.e., an increase in $k$). In our work, we choose a $\lambda$ value of 0.25,
and $\delta$ is set to 15% of the batch size.

A crucial aspect of the algorithm is its stability. Indeed, given its
continual learning nature, it is imperative that when new information comes
in, previous knowledge is preserved to the greatest extent possible. To
implement this requirement, we only allow for two kinds of updates: a local
update and a global one, each with the following allowances and limitations.
The local adjustment phase may be drastic, but it can involve only one
concept. The global adjustment phase is much lighter but it may affect all the
concepts in memory. The two adjustments are shown in Figure 3 where the top
figure illustrates a local adjustment while the bottom one illustrates a
global one. The leftmost pictures show the “before” situation with black dots
on the top figure and green ones on the bottom representing data that has
arrived in a new batch, but has not yet been processed. The rightmost pictures
show the “after” situation, i.e., the result of the processing in each case.
What is important to note in the top figure is that while the original C0
concept gets split into two new concepts C0 and C2, concept C1 is not affected
by this change. That is an instance of a local adjustment. In the bottom
figure, an example of a global adjustment, no new concept is created, but both
C1 and C2 are slightly modified (their center and/or spread change from the
picture on the left to that on the right) to accommodate the new data. C0
could have accommodated new data as well, but in our particular illustration,
no new data affected it.

We now describe Algorithm 1 line by line. It begins on line 1 where the batch
number $b$ is set to 1. On line 2, a model is built by clustering the data in
$\vec{v_{1}}$ using the k-means algorithm (we chose an initial value of
$k=2$). Next, on lines 3-4, we store the initial centroid values in $cc$ and
initialize the semantic similarity structure, $ss$, that associates the two
concepts most closely related to one another. Specifically, $ss$ is a list of
$[r,l]$’s, where $r$ refers to the root concept that already existed in
memory, and $l$, the concept derived from $r$ during local updating. $l$ has
some degree of similarity with $r$ though the majority of the data in $l$
represents a new concept. On line 4, we have $r_{1}=r_{2}=0$ since these are
the initial concepts with no root from which tehy derived. During our
continual learning process, new concepts are created or old ones modified
based on percentile distributions and numbers of outlying instances, as
illustrated in Figure 3. On line 5, we increment the batch number and on line
6, we assign the next batch of posts to $\vec{curr}$. Line 7 is the while loop
that drives the continual consideration of new batches of posts. Inside the
loop, line 8 calculates the size of the batch and assigns it to $s$. Line 9 is
another loop that considers each of the concepts currently present in memory,
in turn. The purpose of that loop is to implement the local updates of the
type shown on the top of Figure 3. In more detail, lines 10-22 are repeated
for each concept in memory with respect to the current batch, $\vec{curr}$.
The purpose of the loop is to estimate whether the data in the batch fits the
current concept well or whether it would be beneficial to split it. This
question is repeated for each of the current concepts in memory and in every
case, if the answer is yes, $k$ gets incremented. The decision of whether to
increment $k$ or not for a given concept is done by first, determining the
lower and upper percentiles of the distance distribution to find out whether a
particular post belongs to concept c and falls within the outlier category,
and second, seeing whether the number of instances from the batch to be
considered outliers by these percentiles exceeds a specific threshold. In more
detail, on line 10, a vector is calculated that stores the distance of each
instance in the batch to the concept’s centroid. Lines 11-12 calculate the
lower and upper distance values representing the $lo^{th}$ (40) and $hi^{th}$
(60)’s percentiles. These correspond to the limits within which a post is
considered the purview of concept c. These values are used on lines 13-14,
along with threshold $\lambda$ (.25) to determine the lower and upper
percentile distribution ranges used to establish whether an instance in the
batch is an outlier or not. On line 15, $\vec{out}$ is assigned all the
instances from the current batch that are the purview of concept c and yet
deviate too much from its centroid (either from the lower or from the upper
end). On line 16, the number of instances in $\vec{out}$ is pitted against
threshold $\delta$. If that number exceeds $\delta$ (15%), k-means is run with
k=2 on all instances of concept c ($\vec{c}$) and all instances contained in
$\vec{out}$ on line 17 to split the concept and its outliers appropriately
(see top of Figure 3). On lines 18-20, the centroids cc are updated, the
number of concepts present in memory, $k$, is incremented, and the cluster
pair is added to the semantic similarity list, $ss$. For example, in the top
situation of Figure 3, C2 is created and was derived from C0 (which itself was
shifted), so we add $[C0,C2]$ to $ss$. Line 21 ends the “if statement” that
causes a local update to occur, while line 22 terminates the inner loop that
considers each concept in memory one after the other. Lines 23-24 implement
the second type of adjustment, the global adjustment, that takes place in our
algorithm. This consists of simply running k-means on the union of all batches
of data seen so far with the updated value of $k$. Since $k$ fits the data
perfectly thanks to our carefully crafted local adjustment approach and since
k-means has theoretical guarantees of stability [24], line 23 will have the
minimum effect of adjusting the centroids as shown at the bottom of Figure 3,
thus adjusting the knowledge in a stable manner, as required. Lines 25-26
increment the batch number and assign the next batch to $\vec{curr}$ prior to
looping back to line 7. The algorithm terminates if no new batch is present.
It is important to note that this process is a continual learning process.
However, though our approach has focused on the stability of the memory-
building process, it has left out a number of features necessary in lifelong
learning. To ensure our system’s long-term viability, we will outfit it, in
the future, with lifelong learning features such as those proposed in [10]
including knowledge distillation and experience replay.

Figure 3: Local and Global Updates.

3

$b\leftarrow 1$ ;

/* initial batch number*/

$m\leftarrow kmeans(\vec{v_{b}},k)$ ;

/* build initial model*/

$cc\leftarrow m(k)$ ;

/* $cc$ contains centroids $c_{1},...,c_{k}$*/

$ss\leftarrow[(r_{1},l_{1}),...,(r_{k},l_{k})]$ ;

/* initialize semantic similarity structure*/

$b\leftarrow b+1$;

/* increment batch number*/

$\vec{curr}\leftarrow\vec{v_{b}}$ ;

/* Consider next batch*/

4 while  _$\vec{curr}$ != Empty_ do

$s\leftarrow len(\vec{curr})$ ;

/* numb. of instances in $\vec{curr}$*/

5 foreach  _$concept$ $c=1$ to $k$ in $memory,m$_ do

$\hat{d^{c}}\leftarrow\begin{bmatrix}\hat{d_{1}^{c}},\hat{d_{2}^{c}},...,\hat{d_{s}^{c}}\end{bmatrix}$
;

/* pred. dist. to c*/

$l\leftarrow percentile(\hat{d^{c}},lo)$ ;

/* $lo^{th}$ perc. in $\hat{d^{c}}$*/

$u\leftarrow percentile(\hat{d^{c}},hi)$ ;

/* $hi^{th}$ perc. in $\hat{d^{c}}$*/

$lower\leftarrow l-\lambda*(u-l)$ ;

/* lower percentile*/

$upper\leftarrow u+\lambda*(u-l)$ ;

/* upper percentile*/

6

$\vec{out}\leftarrow(l<\vec{curr}<\textit{lower})+(u>\vec{curr}>\textit{upper})$
;

/* set of outliers*/

7 if  _$len(\vec{out}) >\delta$_ then

$kmeans([\vec{c},\vec{out}],2)$ ;

/* local adjustment*/

$update$ $cc$ ;

/* add new centroid to cc*/

$k+=1$ ;

/* increment numb. of k*/

$ss\leftarrow(r_{c},l_{c})$ ;

/* root and child concept*/

8

9 end if

10

11 end foreach

$m\leftarrow kmeans([\vec{v_{1}},...,\vec{v_{b}}],k)$ ;

/* global adjustment*/

$cc\leftarrow m(k)$ ;

/* update all centroids*/

$b\leftarrow b+1$;

/* increment batch number*/

$\vec{curr}\leftarrow\vec{v_{b}}$ ;

/* Consider next batch*/

12

13 end while

14

Input:
$\vec{v}=\begin{bmatrix}\vec{v_{1}},\vec{v_{2}},...,\vec{v_{n}}\end{bmatrix}$
; Parameters: $k$, $\delta$ , $\lambda$, $lo$, $hi$

Algorithm 1 Antisemitic concepts extraction

Input:
$\vec{v}=\begin{bmatrix}\vec{v_{1}},\vec{v_{2}},...,\vec{v_{n}}\end{bmatrix}$
; Parameters: $k$, $\delta$ , $\lambda$, $lo$, $hi$

##  V Results and Discussion

We now discuss both the quantitative and qualitative ways in which we tested
our trope discovery approach. We recall that our approach is dynamic and
creates clusterings over time. Unfortunately, there are no clear baselines for
comparing the performance of our approach over others in that fashion.
Therefore, we consider the final clustering output by our approach and compare
it quantitatively to those of state-of-the-art static clustering methods,
along with qualitative considerations. The section starts with a quantitative
analysis, followed by a qualitative one. Using specific information from the
qualitative analysis, we then return to the quantitative analysis focusing on
particular regions of the clustering.

###  V-A Quantitative Analysis

We compared the final clustering obtained by our method to the following five
state-of-the-art clustering approaches.
Affinity Propagation: Affinity Propagation groups data points together relying
on a message-passing process between points that assesses their similarity to
the different groupings. The algorithm doesn’t require pre-defining the number
of clusters [25].
Birch: Birch begins by producing a brief summary tree structure that preserves
the maximum amount of information in the dataset. In the next step, this
summary is classified into different numbers of clusters. Birch can be used
with or without specifying the desired number of clusters, $k$. We ran it
without specifying, $k$ and obtained over 300 clusters. We then searched for
the $k$ that optimized the results and settled on $k=9$
Spectral Clustering: Spectral Clustering is derived from spectral graph
theory. It involves analyzing the eigenvalues and eigenvectors of a similarity
matrix derived from the data. The number of desired clusters, $k$, must be
fixed prior to running the algorithm. We considered different combinations of
parameters, but none of the combinations clearly differentiated between the
antisemitic themes. For comparison purposes, we settled on $k=9$.
Gaussian Mixture: In Gaussian Mixture (GM), each cluster is represented as a
Gaussian distribution, and data points are assigned to clusters based on their
likelihood of belonging to each component. GM requires a pre-defined number of
clusters, $k$. Here again, after evaluating different combinations to look at
the distributions of clusters, we use $k=9$ to compare the results to our
method.
Mean Shift: Mean Shift is a centroid-based algorithm that updates the centroid
with each new point. Mean Shift works in high-dimensional spaces and uses the
mean as the centroid [26]. It does not require a predefined number of
clusters.

The results of our comparison are shown in Table II. In this discussion, we
focus on columns 1-4 of the table. The last two columns will be discussed in
Section V-C. We use three well-known metrics devised for unsupervised
learning: the Davies-Bouldin Index (DBI), the Silhouette Coefficient (SC), and
the Calinski-Harabasz Index (CHI). The first metric, DBI, computes the average
similarity between each cluster and its most similar one. In contrast to the
next metrics, a clear separation is indicated by a lower score. The second
metric, SC, measures the similarity of each point within a cluster to its
similarity to the nearest cluster. It then averages all the results. It
returns a value between -1 and 1, where 1 represents an ideal clustering. The
third metric, CHI, also determines the quality of clustering by measuring the
ratio of between- to within-cluster dispersion, however, it does so at a more
abstract level than SC. Here again, the higher the value of CHI, the clearer
the separation of the data points; however, there is no upper bound. Table II
also shows the number of clusters discovered by each clustering method on its
own when possible (underlined), or assigned to it. Figure 4 in the appendix
gives a visual illustration of each approach’s results by displaying their
T-SNE projections.

TABLE II: Comparison of our approach with five baselines. Approach | Davies-Bouldin | Silhouette Coefficient | Calinski-Harabasz | Clusters | C2 Coverage | C7 Coverage
---|---|---|---|---|---|---
Affinity | 0.85 | 0.34 | 407.22 | 31 | 30.50 & 23.72% | 100%
Birch | 0.86 | 0.35 | 384.60 | 9 and 300+ | 67.79% and ¡5% | 100% and ¡5%
Spectral | 0.64 | -0.01 | 67.76 | 9 | Not Applicable | Not Applicable
Gaussian | 0.81 | 0.30 | 283.65 | 9 | 33.89% | 100%
MeanShift | 0.76 | 0.45 | 394.10 | 2 | Not Applicable | Not Applicable
Our approach | 0.86 | 0.33 | 340.38 | 9 | 75.50% | 100%

Putting aside the dynamic element of our approach not present in any of the
methods we compared it to, these results suggest that our approach is the only
one able to estimate a reasonable number of clusters while also performing
near the top. Indeed, none of the methods that discover $k$ on their own did a
reasonable job: Affinity discovered 31 clusters, Birch, over 300, and
MeanShift, only two. In all these cases, the results are not very practical
and disqualify Affinity and MeanShift. Birch, on the other hand, remains in
the game since it allows the user to provide a predefined number of clusters.
Our approach settled on 9 clusters which we use going forward. Once provided
with the number of clusters ($k=9$), Birch, Gaussian, and our method perform
reasonably well according to two of the metrics considered (SC and CHI) with
Birch leading the pack, whereas Spectral does well on DBI and poorly on the
other two metrics. A look at the T-SNE plot for Spectral reveals that the
algorithm learns one very large cluster and eight very small ones, therefore,
not capturing the essence of the dataset. This observation along with
Spectral’s very low scores on SC and CHI disqualify it from further
consideration. We, thus, conclude that Birch, Gaussian, and our method are
competitive for this domain with Birch possibly learning slightly better
clusters as seen by its slightly better results on SC and CHI (Gaussian does
poorly on CHI, a little worse than Birch and our method on SC though a little
better than both methods on DBI). Nonetheless, we recall that our method has
two advantages over Birch (and Gaussian): 1) it is a continual and stable
self-adjusting algorithm; 2) it does not require a pre-defined number of
clusters.

###  V-B Qualitative Analysis

TABLE III: Trending Terms present in the extracted concepts

Concepts Unigrams Bigrams/Trigrams C1: Control (Economic) world, new, order,
evil, need, state, zionist, globalists, economic, forum new world order, world
economic forum, deep state, banking cabal, state cabal C2: Control (Economic &
Political) goyim, know, shut, jew, oy, well, kike, cope, oey, kek goyim know,
know shut, many kike, low birthrates, cunning plan, know fire C3: Control
(Cultural) jewish, cultural, war, marxism, frankfurt, school, political,
group, white, lobby frankfurt school, political correctness, central bank,
white reproduction, holy war, correct coalition C4: Control (Political)
jewish, war, military, nation, money, control, Ukraine, russia, communist mel
gibson, zionist partners, zionist agent, ethnic foods , interest group, jewish
community, moon landing, deception mentality, communist coup, color revolution
C5: Religion zionist, type, Jesus, reptilian, blood, time, know, f**k, people
blood type, zionist reptilians, jews bible, real jew, fearsome warrior,
rabbinical jew C6: Control (Western World) government, shabbos, biden,
occupational, enslavement, american, goy, fake zog/zionist, shabbos goy,
ashkenazi jewish, enslavement agenda, mind control, terrorist cabinet, kosher
sandwich C7: Dystopia slaughtering, zionist, partner, rock, agent, stone,
time, information, domain online domain, zionist reptilian, zionist partners,
black stone, latin brown, black rocks C8: ZOG Jewish, communist, zionist, zog,
capitalist, like ZOG, scott greer, elephant room, capitalist subhuman, machine
Georgia, bloodline conglomeration, diana spencer, gay jewish C9: Jewish Mafia
Jewish, rothschild, world, f**k, people, need, soros jacob rothschild,
khazarian mafia, klaus schwab, mafia minion, george soros, trillionaire jacob

We now present a qualitative analysis of the results obtained by our method
and reported in Tables III and IV. The tables show samples of prototypical
terminology and posts per extracted concept. The results of Table III were
obtained using aspects444[23] focuses on coded terminology. This work doesn’t
so we disabled the filtering of non-coded terminology. We also return unigrams
in addition to bi- and tri- grams. of the term extraction methodology
described in [23] on each of the concepts extracted by our method. Due to
space limitations, Table IV can be found in the Appendix. We conducted a
qualitative analysis of these tables as follows. The majority of posts in C1
is about Jews controlling the world. Indeed, we frequently observe the term
New world order which, according to the AJC Translate Hate Glossary (AJC)
conveys, in its antisemitic use, the belief that Jews have created a power
structure that they fully control at the economic, media and political levels.
Some frequent unigrams appearing in C1 are evil, need, state, zionist,
globalists, economic while bigrams and trigrams include new world order, world
economic forum, deep state, banking cabal, state cabal. As discussed in AJC,
the term “cabal” refers to a powerful group of (Jewish) individuals whose goal
is to establish control while “globalists”, which also introduces the idea of
dual loyalty, can refer to a Jewish elite bent on destroying the western world
order. Based on the terms extracted for C1 (Table III) and on the typical
posts belonging to this category (Table IV), we concluded that while the
concept presents a mixture of control types, the dominant one was economic,
and we thus label it C1: accusation of economic control. In C2, our approach
grouped posts referring to the meme Shut it down; The goyim know into a single
concept, which we labeled C2: The goyim know. This meme portrays, in a
satirical way, Jews panicking because their “secret plot to control the world”
has been discovered (AJC). Our algorithm’s ss-structure shows that C2 was
derived from C1 along with C3 and C4 described next. In C3, we observe the
terms cultural, marxism, frankfurt, school as well as frankfurt school, white
reproduction, political correctness, etc. According to a report by the
Southern Poverty Law Center (SPLC), these expressions refer to an antisemitic
conspiracy theory that suggests that Cultural Marxism rooted in the Frankfurt
School, a group of self-interested Jews, is responsible for progressive causes
such as LGPTQ+, identity politics, and political correctness which are meant
to destroy American values.555https://www.splcenter.org/fighting-
hate/intelligence-report/2003/cultural-marxism-catching We labeled that
concept C3: accusation of cultural control. C4 is mostly centered around wars
and historical events. The themes revolve around history including USSR,
Russia, Ukraine, Britain, WWII and the current war between Russia and Ukraine.
Holocaust denial is also present. We labeled this concept C4: accusation of
political control. Two seemingly unrelated expressions appear in C4 including
Mel Gibson and Moon Landing. Our Web investigation revealed that Mel Gibson,
upon receiving probation for DUI in 2006, remarked to the policeman arresting
him that “the Jews are responsible for all the wars in the
world.”666https://shorturl.at/dqyDH. This comment (about wars) is what must
have landed him into C4. Moon landing refers to the conspiracy theory that
claims that the 1969 moon landing never happened (the footage was, supposedly,
fake).777https://en.wikipedia.org/wiki/Moon_landing_conspiracy_theories Moon
landing landed in C4 most probably because of its role in the Cold War. Though
the conspiracy theories revolving around it are not antisemitic in nature, it
is worth noting that many proponents of these theories also support
antisemitic ones and that some cross-overs sometimes take place.888E.g.,
https://www.memri.org/tv/french-author-guyenot-moon-landing-hoax-proves-
america-is-empire-of-lies In C5, we observe religious themes represented by
terms such as Jesus, Jews bible, Jews commit, deicide, rabbinical tradition.
These terms and the text they center around them fit in with the historical
antisemitic trope Jews Killed Jesus Christ. They are mixed with other terms
such as reptilian, Zionist reptilians which refer to the reptilian conspiracy
theory that suggests that reptilian aliens take the form of politicians in
order to control the
world.999https://en.wikipedia.org/wiki/Reptilian_conspiracy_theory This, of
course, gets back to the trope claiming that Jews control the world and is
clearly antisemitic.101010https://shorturl.at/cfvEQ We labeled this concept
C5: rejection of Christianity as we felt that despite the spread of this
concept, that was the most representative theme. Next, in C6, the theme seems
to revolve around the Zionist Occupation Government conspiracy theory that
claims, once again, that Jews control the government of Western
States.111111https://en.wikipedia.org/wiki/Zionist_Occupation_Government_conspiracy_theory
This concept, which we labeled C6: accusation of control of the Western States
is shown to be derived from C4 from the algorithm’s ss-structure. Finally, C7
directly advocates for the slaughter of “Zionists” using language rife in
conspiratorial metaphors about, once again, reptilians, but other dystopian
types of themes such as online domains, time, information. We labeled this
concept C7: Dystopian Antisemitism. C8, which we labeled C8:Zionist Occupation
Government (ZOG) is derived from C6 (itself derived from C4). Finally, C9,
labeled C9: Jewish Mafia lists names of Jewish millionaires or purported
Jewish millionaires (e.g., Klaus Schwab) and is directly related to C8.

###  V-C Quantitative Analysis (cont’d)

Having described the concepts derived by our approach, we can now get back to
the last two columns of Table II that present the coverage by each approach of
concepts C2 and C7 representing 15.90% and 5% of the entire data set,
respectively. C2 and C7 were chosen for a detailed analysis because they are
the most compact and unambiguous concepts in the entire set of posts. We
discuss their treatment by each of the clustering methods discussed in Section
V-A. Using our own approach described in Algorithm 1, coverage of concepts C2
and C7 are 75.5% and 100%, respectively. We note that for C7, three other
methods obtain 100% coverage: Affinity, Birch, and Gaussian. Of these,
Affinity is the only one that determines $k$, the number of clusters, on its
own. The other two methods: Spectral and MeanShift receive the results “Not
Applicable” because, as seen in Figure 4, MeanShift learns only two concepts
and, therefore, does not discriminate enough to learn small concepts and, in
the case of Spectral, even though small concepts are learned, our analysis
revealed that C7 was merged with C4, with no clear separation between them. C2
is more difficult to cover as seen in Table II. Affinity splits C2 into two
clusters covering 30.50% and 23.72%, respectively, of C2 or 54.22% when
considered together. When Birch is run with $k=9$, it does pretty well,
covering 67.69% of C2. That is less than the 75.5% obtained by our method, but
it is close. Gaussian, on the other hand, only covers 33.89% of C2. Once
again, Spectral received the ”Not Applicable” mention because C2 was
distributed into more than one concept. Conversely, C2 was one of many
amalgamated concepts in MeanShift. This analysis confirms that Birch works
quite well on this domain, but that, based on this detailed analysis as well
as the previously mentioned strength of our approach, it is preferable given
our practical goals.

##  VI Conclusion

This work proposes a completely unsupervised machine learning method for
monitoring the evolution of antisemitic discourse in a continual manner. As
new posts arrive, they are presented to the system in a mini-batch fashion.
Concepts representing new themes discussed in the posts are formed and added
to the existing knowledge base while existing concepts are updated in
accordance with the new information contained in the posts. Our quantitative
and qualitative analyses reveal that our approach accurately describes the
themes discussed in the posts, thus providing a useful monitoring tool for
social media content. Our future work will add lifelong learning features to
ensure that our method is robust enough to sustain long periods of online use.
Our future work will also involve working in tandem with social scientists to
assess how useful our tool is in answering their research questions. This will
allow us to refine our method to make it more focused on its users’ needs. In
addition, we will add information visualization features to make the approach
more user-friendly. Finally, we will apply our work to other kinds of hatred
in social media.

## References

  * [1] A. Schmidt and M. Wiegand, “A survey on hate speech detection using natural language processing,” in SocialNLP@EACL, 2017.
  * [2] P. Fortuna and S. Nunes, “A survey on automatic detection of hate speech in text,” ACM Computing Surveys (CSUR), vol. 51, pp. 1 – 30, 2018.
  * [3] F. Poletto, V. Basile, M. Sanguinetti, C. Bosco, and V. Patti, “Resources and benchmark corpora for hate speech detection: a systematic review,” Language Resources and Evaluation, vol. 55, pp. 477 – 523, 2020.
  * [4] M. S. Jahan and M. Oussalah, “A systematic review of hate speech automatic detection using natural language processing,” Neurocomputing, vol. 546, p. 126232, 2021.
  * [5] I. Barna and Á. Knap, “An exploration of coronavirus-related online antisemitism in hungary using quantitative topic model and qualitative discourse analysis,” Intersections. East European Journal of Society and Politics, vol. 7, no. 3, pp. 80–100, 2021.
  * [6] C. Allen, U. Nodelman, and E. N. Zalta, “Stanford encyclopedia of philosophy: a dynamic reference work,” 2003 Joint Conference on Digital Libraries, 2003. Proceedings., pp. 383–, 2003.
  * [7] L. Wittgenstein, “Philosophical investigations = philosophische untersuchungen,” in PHILOSOPHICAL INVESTIGATIONS, 1958.
  * [8] E. Rosch, “Principles of categorization,” in Cognitive Science, 1978.
  * [9] R. Corizzo, M. I. Baron, and N. Japkowicz, “Cpdga: Change point driven growing auto-encoder for lifelong anomaly detection,” Knowl. Based Syst., vol. 247, p. 108756, 2022.
  * [10] K. Faber, R. Corizzo, B. Sniezynski, and N. Japkowicz, “Vlad: Task-agnostic vae-based lifelong anomaly detection,” Neural networks : the official journal of the International Neural Network Society, vol. 165, pp. 248–273, 2023.
  * [11] S. Rohlfing and S. J. Sonnenberg, ““who is really british anyway?”: A thematic analysis of responses to online hate materials,” Journal of psychosocial research, vol. 10, p. 2, 2016.
  * [12] T. Megersa and A. M. Gezie, “Social media users’ online behavior with regard to the circulation of hate speech,” Frontiers in Communication, 2023.
  * [13] S. Ramaswamy and N. DeClerck, “Customer perception analysis using deep learning and nlp,” Procedia Computer Science, vol. 140, pp. 170–178, 2018.
  * [14] Á. Aldunate, S. Maldonado, C. Vairetti, and G. Armelini, “Understanding customer satisfaction via deep learning and natural language processing,” Expert Syst. Appl., vol. 209, p. 118309, 2022.
  * [15] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, “Attention is all you need,” Advances in neural information processing systems, vol. 30, 2017.
  * [16] A. M. Founta, D. Chatzakou, N. Kourtellis, J. Blackburn, A. Vakali, and I. Leontiadis, “A unified deep learning architecture for abuse detection,” in Proceedings of the 10th ACM conference on web science, pp. 105–114, 2019.
  * [17] J. Serra, I. Leontiadis, D. Spathis, G. Stringhini, J. Blackburn, and A. Vakali, “Class-based prediction errors to detect hate speech with out-of-vocabulary words,” in Proceedings of the first workshop on abusive language online, pp. 36–40, 2017.
  * [18] P. Parikh, H. Abburi, N. Chhaya, M. Gupta, and V. Varma, “Categorizing sexism and misogyny through neural approaches,” ACM Transactions on the Web (TWEB), vol. 15, no. 4, pp. 1–31, 2021.
  * [19] P. Badjatiya, S. Gupta, M. Gupta, and V. Varma, “Deep learning for hate speech detection in tweets,” in Proceedings of the 26th international conference on World Wide Web companion, pp. 759–760, 2017.
  * [20] M. Chandra, D. Pailla, H. Bhatia, A. Sanchawala, M. Gupta, M. Shrivastava, and P. Kumaraguru, ““subverting the jewtocracy”: Online antisemitism detection using multimodal deep learning,” in Proceedings of the 13th ACM Web Science Conference 2021, pp. 148–157, 2021.
  * [21] S. Zannettou, J. Finkelstein, B. Bradlyn, and J. Blackburn, “A quantitative approach to understanding online antisemitism,” in Proceedings of the International AAAI conference on Web and Social Media, vol. 14, pp. 786–797, 2020.
  * [22] M. Ali and S. Zannettou, “Analyzing antisemitism and islamophobia using a lexicon-based approach,” in Workshop Proceedings of the 16th International AAAI Conference on Web and Social Media. Retrieved from https://doi. org/10.36190, 2022.
  * [23] D. Kikkisetti, R. Ul-Mustafa, W. Melillo, R. Corizzo, Z. Boukouvalas, J. Gill, and N. Japkowicz, “Using llms to discover emerging coded antisemitic hate-speech in extremist social media,” ArXiv, vol. abs/2401.10841, 2024.
  * [24] S. Ben-David, D. Pál, and H. U. Simon, “Stability of k -means clustering,” in Annual Conference Computational Learning Theory, 2007.
  * [25] D. Dueck and B. J. Frey, “Non-metric affinity propagation for unsupervised image categorization,” in 2007 IEEE 11th international conference on computer vision, pp. 1–8, IEEE, 2007.
  * [26] K. G. Derpanis, “Mean shift clustering,” Lecture Notes, vol. 32, pp. 1–4, 2005.

##  VII Appendix

(a) Affinity Propagation (b) Birch (c) Birch (with K) (d) Spectral (e)
Gaussian (f) MeanShift

(g) Our Approach

Figure 4: T-SNE projections of the clustering obtained by our approach and baseline clustering methods TABLE IV: Examples from our data set of posts found on extreme social platforms along with the concept they belong to and the terminology they use as extracted by the approach in [23] Posts |  Concepts
---|---
these poor souls were murdered by the cabal world economic forum evil mad scientists elites. they should all be in front of a patriot firing squad |  C1
the illegal us corp of american government must be eradicated closed permanently all the cabal ,illuminate, world economic forum, world health organization, united nation, north atlantic treaty organization, new world order and its sub cults all must be arrested and fully prosecuted world wide door to door |  C1
the goyim know about isis. |  C2
shut it down, the goyim know |  C2
advertising should be banned. it has been used as a social manipulation tool for decades. just watch mad men. it started with the frankfurt school. the birth of cultural marxism. how the frankfurt school changed america |  C3
we are in a war with frankfurt school cultural marxism . harris is an apostle of that woke cult. please stop conflating liberalism with left wing marxism when we need to divide them starting with the difficult task of convincing boomer liberals they have been fooled since teenage hood. |  C3
you also need to provide all zionist agents embedded in the media organizations, zionist codenames, zionist handlers, zionist caves they report to, zionist time travellers giving them information, space time information about zionists, zionist ”partner/s”, zionist alliances, zionist sponsored businesses, zionist media organizations, zionist agents embedded in the national security apparatuses, zionist agents’ names censoring news and content, etc., etc. … |  C4
the united states government is controlled by interest groups that are only seeking to enlarge their own power. the us government does not represent the will of the citizenry, and condemning it is not a condemnation on the principles of freedom, democracy, etc.the usa is being set up to fail.the rootless cosmopolitan elite have been constructing elaborate safehouses for decades in preparation for this… |  C4
did jesus came to his own? yes but his own did not receive him? that is correct. so jews killed jesus? yes. so jesus was jewish? no, jews are not the jews of the bible so how did jews commit deicide if they are not the jews from the bible? hurr durr |  C5
he was but the definition of jew changed entirely after the fulfilment of the prophecy those who calls themselves jews now are not the real jews they are the rabbinical tradition that rejected christ |  C5
meet the new shabbos, same as the old shabbos stop eating the kosher sandwich goy zionist occupied government. |  C6
zog, zionist occupied government. secretary of state=zog. attorney general=zog. senate majority leader=zog. head of dhs=zog 98 percent of americans are non jews. |  C6
are the jews of belgium, providing the zionist codenames, zionist agent names, names of the zionist reptilians, names of the zionist ”partner/s”, zionist caves, space time information about zionist, etc need full disclosure from the zionists, zionist reptilians, zionist agents, zionist ”partner/s”, and reptilian ”partner/s”, etc. afterwards, i will slaughter them all, including their women, and their children. i will spare no one.but then again, i prefer genocides, mass erasures, etc., rather than patches. |  C7
i also need the names of all zionist partner/s, all zionist agents, zionist caves, zionist time travel agents, zionist time portal technology, zionist advanced technology, and zionist reptilian ”partner/s”.and all zionist reptilians embedded in albania, and zionist reptilian ”partner/s” embedded in albania.all can be published in the online domain, on the internet, available for all to dissect such information.afterwards, i will slaughter them all. including zionist women, and zionist children, zionist ”partner/s”, and those that interfere on behalf of zionists. |  C7
you can post about the gae all you want and not get banned on any platform, like scott greer for example. start tweeting about the zionist occupied government and expect to be censored and banned. lesson there. |  C8
you got a gay jewish communist takeover that is as communist as the chinese, without putting communist in the name.enjoy being spied, subverted, and psyoped. |  C8
klaus schwab is a rothschild on his mother side. he answers to the trillionaire, jacob rothschild and his khazarian mafia minions |  C9
radical soros backed group boosts warnock campaign funding ahead of run off billionaire radical george soros has worked his entire life to control the democrat party and destroy the united states. he has a deep seated hatred of the west and promotes its collapse, pouring millions of dollars into campaigns and causes that further his radical agenda. |  C9