# An AstroSat/UVIT study of galaxies in the cluster

Smriti Mahajan11footnotetext: Corresponding author Kulinder Pal Singh  Somak
Raychaudhury

###### Abstract

We present the newly acquired data for an AstroSat/UVIT field centered on a
face-on spiral starburst galaxy UGC 10420, located in the X-ray bright cluster
Abell 2199 ($z=0.031$). We have analysed the FUV BaF2 data for this field
along with the archival FUV and NUV data from the Galex mission, optical
photometric data from the SDSS, spectroscopic data from the literature, and
low-frequency radio data from the LoTSS survey, respectively. The stars were
separated from the galaxies using the SDSS photometric pipeline
classification, while the spectroscopic redshifts available for 35% of the
detected UVIT sources were used to identify member galaxies of the cluster .
We find that (a) the non-cluster galaxies are on average fainter than the
cluster galaxies at fixed magnitude, (b) stars and galaxies are
indistinguishable in the $r$ vs $NUV-r$ plane, and (c) bright stars are $\sim
1.5$ mag bluer than the galaxies in the $FUV-r$ vs $NUV-r$ colour-colour
plane. Besides UGC 10420 which is the only known cluster galaxy with an
extended-UV disk, we identify five more galaxies with asymmetric FUV
morphology and extended radio emission in this field. All the asymmetric
member galaxies of , lie within the virial boundaries of the cluster. This
observation, together with the fact that these asymmetric cluster galaxies
have low-frequency radio tails or FUV emission pointing away from the cluster
centre leads us to hypothesise that these galaxies are likely undergoing ram-
pressure stripping (RPS) under the influence of cluster-environment related
mechanisms. A comparison of optical and FUV star formation rate of UVIT
detected galaxies shows enhanced star formation in half of the RPS candidates,
suggesting that environment-related mechanisms may lead to a burst of star
formation in RPS galaxies.

Our analysis indicates the presence of at least two more groups or clusters at
$z\sim 0.077$ and $0.260$, coincident with along the line of sight of the
field of view studied here.

##  1 Introduction

Galaxy clusters are the largest gravitationally bound objects in the Universe.
They form at the intersection of large-scale filaments, therefore allowing for
sampling of a wide range of properties of galaxies such as colours,
luminosity, stellar mass, star formation rate (SFR), gas and dust properties
etc. This feature makes clusters of galaxies ideal laboratories to study the
evolution of galaxies over a continuous range of ‘environments’, quantified
either by the number density of galaxies, or the density of the intra-cluster
medium (ICM).

The ultraviolet imaging telescope [UVIT; 1, 2] aboard the multiwave Indian
satellite mission AstroSat [3], with its wide field of view of $\sim
28{{}^{\prime}}$ is the perfect choice for imaging clusters in the far
ultraviolet (FUV) waveband. The UVIT offers the best spatial resolution of
$1.3{{}^{\prime\prime}}-1.5{{}^{\prime\prime}}$ [2], relative to similar
missions, e.g. Galaxy evolution explorer (Galex), Swift-UVOT and XMM-OM,
observing in the FUV waveband. The unprecedented resolution and large field of
view together make UVIT a great tool for exploring the recent star formation
history of galaxies in and around clusters.

In this era of wide field surveys such as the two-degree Field Galaxy Redshift
Survey [2dFGRS; 4] and the Sloan Digital Sky Survey [SDSS; 5], the regions in
the outskirts of clusters have emerged as fields of great interest for
studying the evolution of galaxies. These regions offer three-fold advantage
for studying the evolution of galaxies:

  * •

The intermediate density environment is ideal for gravitational interactions
among galaxies comoving in the same velocity field under the gravitational
influence of the nearest massive cluster [e.g. 6, 7].

  * •

The density, and therefore the influence of ICM is expected to be weak on
galaxies beyond the virial radius (1-2$~{}R_{200}$). This offers an
opportunity to observe galaxies undergoing accelerated evolution in the
absence of cluster-specific environmental mechanisms.

  * •

These regions are bound by very dense cluster on one side and low density
field on the other, therefore offering a smooth transition in the parameter(s)
used to quantify environment.

The galaxies at the periphery of clusters experience a unique environment.
While the influence of the ICM may still be feeble at these distances from the
centre of the cluster, the unidirectional velocity fields pulling the galaxy
towards the centre of the cluster are strong [6]. The increased density of
galaxies on the periphery of the cluster due to the culmination of large-scale
filaments approaching from different directions provides better opportunities
for galaxies to interact gravitationally. Assuming that most of the galaxies
being assembled are young and gas-rich, this scenario may trigger an episode
of intense star formation in a small clustercentric region on the boundary of
the cluster [e.g. 7], consequently leading to exhaustion of gas in galaxies
even before they enter the cluster. This is an underrated, but important way
in which galaxies can be pre-processed prior to entering the clusters [e.g. 8,
7, 9, 10, 11].

The outskirts of clusters also provide an insight into the evolution of unique
population of galaxies which have crossed the cluster centre at least once,
yet have not had the time to virialize. These galaxies, mostly found between
1–2 $r_{virial}$, are called ‘backsplash’ galaxies [12]. The infalling and
backsplash galaxies are not only found at similar distance from the centre of
the cluster, but may also be alike in morphology, colour etc.. In the observed
data however, the backsplash galaxies can be differentiated from the infalling
ones based on their line-of-sight velocity, and by analysing the impact of the
cluster environment on their observed properties [13, 11].

Literature based on observations suggests that backsplash galaxies are older,
have lower star formation rate and higher fraction of quiescent galaxies
relative to the new entrants to the cluster [13, 9, 14]. In fact, [13] used
optical data for more than 260 galaxy clusters from the SDSS, together with
dark matter simulations to show that the star formation in a galaxy is likely
to be completely quenched in a single passage through the cluster centre. Even
the ultraviolet SFR of galaxies on the outskirts of the Coma cluster ($\sim
100h^{-1}$ Mpc) is found to be in between that of the field and the cluster
interiors [15]. These observations highlight the importance of studying the
transitional populations of galaxies on the cluster outskirts to further our
understanding of the evolution of galaxies, and assembly of the cosmic-web.

With this in mind, we initiated a campaign to explore the outskirts of nearby
clusters in the FUV waveband. We centred the $28{{}^{\prime}}$ UVIT field of
view on galaxies known to have higher than average SFR (as estimated using the
SDSS spectroscopic data) in [7]. Aided by ancillary data in other wavebands,
these newly acquired AstroSat/UVIT data are furthering our understanding of
the properties and evolution of the targeted galaxies [16]. These data have
also provided an opportunity to study the properties of a variety of galactic
and extragalactic sources detected by the UVIT [17], thereby creating a
benchmark for other similar studies.

In this paper, we study a field in the cluster ($z=0.031$). is an X-ray bright
cluster, with a massive radio-loud galaxy NGC 6166 at its core. Together with
its neighbouring cluster Abell 2197 ($z=0.030$), and several other groups of
galaxies, forms a large supercluster [18, 19]. A field centred around $0.45$
rvirial of this dynamic cluster provides a golden opportunity to study
plethora of interesting galaxies, many of which are in a transition phase.
Throughout this work we use concordance $\Lambda$ cold dark matter
cosmological model with $H_{0}=70$ km s-1 Mpc-1, $\Omega_{\Lambda}=0.7$ and
$\Omega_{m}=0.3$ to calculate distances and magnitudes.

Figure 1: The UVIT field of view with the red circular region centred at
$\alpha=247.468^{\circ}$ and $\delta=+39.802^{\circ}$, having a radius of
$14.15{{}^{\prime}}$ analysed in this work. The blue ‘X’ symbol shows the
x-ray centre of Abell 2199 [19]. The image is orientated such that north is up
and east is on the left.

##  2 Data

###  2.1 Ultraviolet imaging and data processing

We observed a field centred on the spiral galaxy UGC 10420
[$\alpha=247.463^{\circ}~{}{\rm and}~{}\delta=39.766^{\circ}$; 16], in
($z=0.031$) with the AstroSat/UVIT [20, 3, 1]. This field (observation ID:
A05_063T03_9000003066; PI: Smriti Mahajan; observation date: 30-July-2019) was
observed by the UVIT simultaneously in the broadband BaF2 FUV filter [mean
$\lambda=1541~{}\AA$; $\Delta\lambda=380~{}\AA$; 1, 2], and visible wavebands
($3040-5500~{}\AA$). The latter data however, are only used for data
reduction. The raw data from the mission are processed by the Indian Space
Science Data Centre (ISSDC), and the Level 1 (L1) data from all instruments
are provided to the users. The L1 data were processed using the CCDLAB
software [21], following the procedure described in [22]. A detailed account
of the steps followed for the reduction of data are well described in [17],
but a very brief description is given below for completeness.

The CCDLAB software pipeline takes the L1 zip file as input and performs
various corrections on individual images before performing the astrometric
correction to coalign and stack them together to create a deep field image.
The automatic procedure for optimising the point source function was then
initiated to remove the residual drift effect, and yielding a full width half
maximum of $<1.2{{}^{\prime\prime}}$ for this image. Following this, the world
coordinate system (WCS) solution was applied by mapping the pixel coordinates
of the sources in the image to the GAIA catalogue using the Astroquery utility
[23], through CCDLAB [24]. The image was finally derotated to match the sky
coordinates, and used for further scientific analysis. The UVIT data for have
a useful exposure time of 9600.3 seconds and resolution
$<1.2{{}^{\prime\prime}}$. The final image is shown in Figure 1, with the UVIT
field of view and the centre of marked for reference.

The FUV sources were detected using the sextractor software [SE henceforth;
25]. Sources were detected on a convolved version of the image (Gaussian
kernel of FWHM $=4.0$ pixels) in order to prevent shredding of larger
galaxies. Other de-blending and detection parameters used by sextractor were
chosen after extensively testing a wide range of values and visually testing
the processed image, and are similar to the ones mentioned in [17]. The
background was detected by sextractor in the ‘AUTO’ mode.

A deeper analysis of the generated catalogue showed that four of the larger
galaxies in the field were broken into multiple components. For two of these
galaxies (LEDA222Lyon-Meudon Extragalactic Database (LEDA), [26] 58382 and
LEDA 2153801), which were split into two components each, the total counts
estimated by the SE were summed up to get the total flux. For the other two
(UGC 10420 and UGC 10429), we used the SAOImageDS9 software package [27] to
get the total counts using the method described in [16]. To do so, we chose an
aperture size of $1.5{{}^{\prime}}$ centred at the optical nucleus for UGC
10420, and of $0.8{{}^{\prime}}$ for UGC 10429, respectively.

Following this methodology, we detected 352 unique sources in the UVIT BaF2
filter, which form the primary sample for this paper. The integrated counts
for all the sources were then normalised by the total integration time, and
converted to fluxes using the conversion factors provided by [2]. These fluxes
were corrected for the extinction due to the dust in our galaxy by assuming a
Milkyway-like extinction curve [28]. We assume $A_{FUV}=8.06E(B-V)$ [29],
where the $E(B-V)$ estimates of [30] for all the identified sources were
obtained from https://irsa.pac.caltech.edu/applications/DUST/. The mean
reddening excess, $E(B-V)=0.0087\pm 0.0012$ for our sample. Figure 2 shows the
distribution of the extinction corrected fluxes and the corresponding
magnitudes for all the detected sources.

Figure 2: The distribution of UVIT FUV flux corrected for the Milkyway
extinction for all the 352 sources analysed in this work. The top axis shows
the AB magnitudes for the same.

###  2.2 Optical data

We found optical counterparts for 337/352 sources in the Sloan Digital Sky
Survey [SDSS, data release 16; 31] photometric catalogue. The optical
counterparts were found by searching for an analogue within
$5{{}^{\prime\prime}}$ of each FUV source, and having $r<22.7$ mag333The
median $5\sigma$ depth for SDSS photometric observations is $r=22.7$ mag..
More than 95% of the matches were found within a radius of
$1.4{{}^{\prime\prime}}$. 281 of these sources are identified as galaxies,
while the rest of the 56 are stars in the Milkyway according to the SDSS
photometric pipeline. It is noteworthy that on visual inspection many of the
‘stars’ appear to be faint distant galaxies, or compact sources on the
outskirts of large nearby galaxies [e.g. 32] in the multi-band SDSS images. A
confirmation of the same however, would require higher resolution images and
spectroscopic data for these sources, and in this work we continue to consider
them as stars.

An extensive spectroscopic survey of the cluster has been performed by [33].
They combined 775 new redshifts from the MMT/Hectospec observations with the
existing ones in the literature to construct a large catalogue of 1624 objects
in the field of . Their catalogue is spectroscopically 77% complete to
$r_{petro,0}<20.5$ mag. By searching for an optical counterpart for each of
our confirmed FUV source within a radius of $5{{}^{\prime\prime}}$, we found
spectroscopic redshifts for 123 UVIT sources, more than 96% of which are
matched within $\leq 2.0{{}^{\prime\prime}}$. Of these, 42 redshifts were
taken from [34], 32 from SDSS (DR 12), 48 were added by the MMT/Hectospec
observations of [33], and one was taken from [35], respectively. Amongst these
123 sources, 57 are classified as extended sources while 66 are point sources
according to the SDSS pipeline. A few rows from the complete catalogue of 352
sources detected in this UVIT image are presented in Table 1. The complete
catalogue is available online.

Table 1: The object ID, sky coordinates, UVIT flux and the uncertainty in the flux, object type (1: QSO; 3: galaxy; 6: star), $r$-band magnitude and redshift for all the 352 sources detected in the FUV  image used in this paper. (A complete version of this table is available online here (Supplementary materials)). ID | $\alpha$ | $\delta$ | Flux ($10^{-15}$ |  $\Delta$(Flux) ($10^{-15}$ | Object | $m_{r}$ | Redshift
---|---|---|---|---|---|---|---
| (J2000) | (J2000) | ergs/s/cm2/Å) | ergs/s/cm2/Å) | type | mag | $(z)$
1 | 247.443 | 40.034 | 0.0173 | 0.0028 | 3 | 20.82 | -
2 | 247.389 | 40.028 | 0.0835 | 0.0061 | 3 | 19.25 | -
3 | 247.542 | 40.028 | 0.0356 | 0.0040 | 3 | 20.78 | -
4 | 247.416 | 40.023 | 0.0178 | 0.0028 | 3 | 19.91 | -
5 | 247.461 | 40.022 | 0.0195 | 0.0030 | 3 | 20.56 | -
6 | 247.473 | 40.016 | 0.5242 | 0.0147 | 3 | 17.46 | 0.048
7 | 247.567 | 40.018 | 0.0960 | 0.0064 | 3 | 19.10 | -
8 | 247.400 | 40.011 | 0.4432 | 0.0137 | 3 | 18.31 | 0.075
9 | 247.590 | 40.013 | 0.0415 | 0.0043 | 3 | 20.66 | -
10 | 247.393 | 40.011 | 0.0244 | 0.0033 | 3 | 19.92 | -
Figure 3: The distribution of 50% Petrosian radius as a function of extinction
corrected $r$-band magnitude for the optical counterparts of our UVIT sources.
The sources are separated into stars (grey asteriks) and galaxies (red points)
by using the SDSS classification. The member galaxies of are highlighted as
blue triangles. The dot-dashed line represents the completeness limit for the
SDSS photometric catalogue.

We identified the member galaxies of based on the cluster properties derived
by [36]. These authors found that ($z=0.031$) has a velocity dispersion,
$\sigma_{v}=676^{+37}_{-32}$ km s-1, and mass $M_{200}=(2.39\pm 0.77)\times
10^{14}$ M⊙. In this paper, we define all galaxies within $\pm 3\sigma_{v}$ of
the cluster’s mean redshift as the members of the cluster Abell 2199. All
other galaxies, with or without redshift are henceforth referred to as the
‘other’ galaxies, although some of them, especially the ones close to the
faint-end limit of SDSS (e.g. Figure 3), might be members of the cluster as
well.

In Figure 3 we plot the Petrosian radius containing 50% of the total flux in
the $r$-band ($R_{50}$) as a function of the extinction-corrected $r$-band
magnitude for all the optical counterparts of the UVIT sources sub-classified
into stars, cluster galaxies and other galaxies, respectively. Figure 3 shows
that most of the galaxies brighter than $r\sim 19$ mag, detected in the UVIT
image are members of the cluster . The bright stars ($r\lesssim 20$ mag) on
the other hand, are well separated from the galaxies in this magnitude-radius
space. We note that the faint stars within $\sim 2$ magnitudes from the
completeness limit of the SDSS, might be high redshift or faint galaxies,
misclassified as stars by the automated SDSS pipeline. Spectroscopic data or
high resolution, deeper imaging of this field can help clarify the status of
these sources.

##  3 The FUV sources detected by UVIT

Figure 4: All 352 UVIT FUV sources (black points) are shown, along with those
detected by the Galex mission. The blue squares and red triangles represent
the sources detected in the deeper FUV and NUV MIS Galex image, while the blue
circles and green triangles depict the FUV and NUV sources detected in the AIS
Galex images, respectively.

Prior to UVIT/AstroSat, has been observed by the Galex mission. However, two
sets of Galex images overlap with different parts of the UVIT field of view.
So in order to compare UVIT and Galex data, and make use of the NUV images in
this work, we employ all the Galex images. The Galex mission provides two sets
of images with one image each in the far ultraviolet (FUV) and near
ultraviolet (NUV) bands. One set of images belonging to the all-sky imaging
survey (AIS) have an exposure time of 239 seconds (FUV) and 319 seconds (NUV),
respectively, while the medium imaging surveys (MIS) of the Galex mission were
exposed for 1649 seconds in both the filters. sextractor was used to identify
sources on each of the Galex images individually. We then searched for a Galex
counterpart within $3^{\prime\prime}$ of each of the UVIT sources
independently, prioritising the deeper Galex image in regions of overlap. This
exercise yielded 99 FUV and 140 NUV sources matched between the Galex and UVIT
images.

All the UVIT sources, overplotted with symbols representing different Galex
images are shown in Fig. 4. A little less than the top half of the UVIT field
of view overlaps with the shallow AIS images, as a consequence of which many
of the UVIT sources were not detected in the Galex images. On the other hand,
the bottom half of the UVIT field of view is well covered by the Galex MIS
images, although there still remain a non-negligible number of sources which
have been observed in the FUV band by the UVIT for the first time. This
analysis shows the power of UVIT’s unprecedented resolution in discovering new
FUV sources.

Figure 5: The distribution of magnitude of (a) Galex NUV , and (b) Galex FUV
sources plotted as a function of the UVIT FUV magnitude for all the sources
detected by both the instruments. All magnitudes are corrected for extinction
due to Milkyway. The red points denote galaxies and grey asterisks represent
the stars, respectively. The dot-dashed line in both panels represents equal
magnitudes from both the instruments, while the dashed lines represent the
least square fit to the data, along with $1\sigma$ deviation (dotted lines) in
it. Typical uncertainty along each axis is shown in the bottom right corner of
the panels. This figure therefore shows that the FUV fluxes of the matched
sources are consistent between the UVIT BaF2 band and both the wavebands of
the Galex mission.

The Galex FUV and NUV magnitudes of all the matched galaxies and stars are
shown as a function of their UVIT FUV magnitude in Figure 5. The magnitudes
for the sources are well matched, with many of the stars forming a separate
sequence in the FUVUVIT-NUVGalex plane. As expected, the scatter at the faint
end is higher than the bright end for both the distributions. In fact, the
standard deviation of the correlation is clearly dictated by the faint-end
scatter, especially in the FUVUVIT-NUVGalex plane. The typical uncertainty in
the Galex FUV and NUV filters are $\sim 0.3$ and $0.6$ mag, respectively,
which is more than an order of magnitude higher than the uncertainty of $\sim
0.02$ mag found for the UVIT BaF2 magnitudes reported here.

Figure 6: The distributions for all UVIT sources along with their optical and
Galex counterparts in different colour–colour and colour–magnitude planes.
Clockwise from top left, we have shown (a) $NUV-r$ vs $r$-band magnitude, (b)
$NUV-r$ vs $FUV-r$, (c) $FUV-r$ vs $g-r$, and (d) $g-r$ vs $r$-band magnitude
plane, respectively. The symbols are same as in Fig. 3. The $FUV$ magnitudes
are from UVIT, while the NUV magnitudes are from the Galex mission. The number
of data points in each quadrant will vary as mentioned in Sec. 2. While the
cluster galaxies span the entire range of colours and magnitudes available,
the other galaxies are relatively fainter and bluer in comparison. It is
notable that galaxies and stars are not easily distinguishable in these
planes, except for one exception. A handful of stars redder than $NUV-r\sim 2$
mag and $FUV-r\sim 5$ mag, seem to form a separate sequence parallel to the
galaxies in the FUV-r vs NUV-r plane.

All the stars and galaxies observed in the UVIT image are plotted in planes
mapped by various colours and magnitudes in Figure 6. Note that the different
panels comprise different number of data points as per the availability. The
cluster galaxies span the entire range covered by the $r$-band magnitude and
the NUV-r colour (Figure 6 (a)). It is interesting to note that even the stars
occupy the entire range of $r$-band magnitude, making it impossible to
distinguish them from galaxies. The other galaxies coincide with the cluster
galaxies, but are on average fainter than their counterparts in the cluster.
It is interesting to note that these results are in contrast with a similar
analysis performed for the Coma cluster [Abell 1656, $z=0.023$; 17]. In figure
7 of [17], the bright galaxies in the Coma cluster clearly separated from the
other galaxies. This discrepancy may be due to the fact that: (i) higher
number of sources detected in the Coma field improved the statistics, (ii) the
brightest Coma galaxies are $M_{r}\sim 3$ mag brighter than the ones detected
in , providing for a better contrast than available in the sample used here,
(iii) Coma is a more evolved cluster relative to , (iv) a combination of the
above.

All galaxies form a rather narrow sequence in the FUV-r vs NUV-r colour-colour
plane (Figure 6 (b)). In this case however, the stars redder than $NUV-r\sim
2$ mag and $FUV-r\sim 5$ mag, form a separate sequence parallel to the
galaxies, similar to what was observed for the Coma field [17].

The FUV-r vs g-r colour-colour plane (Figure 6 (c)) shows that the bright red
cluster galaxies are somewhat separated from their fainter counterparts, which
coincide well with the other galaxies. The stars on the other hand, do not
show any trend, and are scattered everywhere in this plane.

In the optical colour-magnitude plane (Figure 6 (d)) the cluster galaxies form
the expected red sequence, while the other galaxies show considerable scatter
in colour at fixed magnitude. We note that the observed cluster galaxies form
a red sequence overlapping the one observed using optical data alone [33, see
their figure 1 for comparison]. Also, most of the other galaxies are fainter
than the cluster galaxies, such that the brightest galaxies observed in the
UVIT field are invariably classified as members of the cluster .

Figure 7: The distribution of all the UVIT sources having optical and Galex
counterparts in the (a) FUV-NUV vs $r$-band and (b) FUV-NUV vs g-r colour-
colour plane, respectively. The symbols are same as in Fig. 3. With the
exception of three outliers, the cluster galaxies form a sequence, such that
the fainter galaxies have bluer UV colour, the other galaxies and handful of
stars making an appearance in these planes do not show any trend.

In Figure 7 we show the distribution of the FUV-NUV colour of the cluster
galaxies, other galaxies and stars as a function of their $r$-band magnitude
and the optical g-r colour, respectively. It is interesting to note that while
most of the cluster galaxies do seem to form a sequence such that the fainter
galaxies have bluer UV colour, the other galaxies are very scattered in this
space. This observation is in contrast to a similar diagnostic for the Coma
cluster [see figure 8 of 17], where the cluster galaxies were found to occupy
well defined regions in this plane. This discrepancy is partly due to the
lower number density of sources observed in the image used in this work,
relative to the Coma field.

##  4 Multi-wavelength observations of distorted candidates in

Table 2: UVIT sources with LoTSS (144 MHz) radio counterparts. Galaxy | Right Ascension | Declination | Redshift | 144 MHz flux | Source of flux
---|---|---|---|---|---
| (J2000) | (J2000) | ($z$) | (mJy) |
UGC 10420 | 247.4627 | 39.766 | 0.0306 | $74.67$ | [16]
UGC 10429 | 247.6387 | 39.831 | 0.0246 | $26.40$ | [37]
Z224-44 | 247.2091 | 39.835 | 0.0359 | $20.40$ | [37]
Z 224-55 | 247.6200 | 39.626 | 0.0304 | $8.50$ | [38]
Z 224-65 | 247.7642 | 39.838 | 0.0305 | $6.10$ | [38]
SDSS J163017.01$+$394924.3 | 247.5709 | 39.823 | 0.0701 | $3.20$ | [38]
Figure 8: A multi-wavelength view of galaxies UGC 10420 and UGC 10429 in . The
rgb colours represent 144 MHz emission (red), SDSS $r$-band (green) and the
UVIT FUV (blue), respectively.

Figure 9: Multi-wavelength view of RPS candidate galaxies in . (left to
right:) UGC 10429, Z224-65 and Z224-55, respectively. The yellow arrow points
in the direction of the cluster centre. While the radio tail of Z224-55 points
opposite the cluster centre, the FUV emission in the other two galaxies follow
suit, suggesting an outburst of star formation as a consequence of interaction
with the intra-cluster medium.

We searched the literature for existing observations of galaxies in our UVIT
image, and found radio counterparts for six galaxies in the LOw-Frequency
ARray (LOFAR) Two-metre Sky Survey (LoTSS) data [120-168 MHz; 39, 38]. The
positions, redshift and LOFAR (144 MHz) fluxes for these galaxies are listed
in Table 2.

###  4.1 UGC 10420 and 10429

UGC 10420 is a face-on spiral galaxy undergoing ram-pressure stripping in
(Figure 8). We have presented detailed multi-wavelength analysis of UGC 10420
in [16], where we showed that it is not only an RPS candidate, but the only
known cluster galaxy with an extended UV disk.

[37] have recently presented radio data, taken from LoTSS for nearby
($z<0.05$) jellyfish444In the context of this paper, the term ‘jellyfish’ is
used for galaxies with unambiguous tail(s) of material stripped from their
disc. These galaxies are believed to be a product of RPS in clusters.
galaxies. One of the cluster galaxies from their sample observed by the UVIT
is UGC 10429 (Figures 8 and 9(left)). UGC 10429 having
$M^{*}=10^{10.5}M_{\odot}$ [40], is $\sim 2100$ km s-1 away from the nearest
large galaxy UGC 10420 in redshift space (Figure 8). The projected distance
between UGC 10429 and UGC 10420 is $\sim 347~{}h^{-1}$ kpc, which diminishes a
chance of ongoing interaction between them. These two galaxies however, may
have had a close flyby interaction in the past.

UGC 10429 is a low-ionization nuclear emission region galaxy [LINER; 41, 42].
Interestingly, while the low-frequency radio emission in UGC 10420 appears
behind the galaxy relative to the optical disc [see, 16, for a detailed
discussion], in UGC 10429 the radio emission is observed at the edge of the
optical disc facing the cluster centre (Figure 9(left)). On the other hand,
the FUV emission is more intense on the side of the disc away from the cluster
centre.

Figure 10: left: The Sd spiral galaxy Z224-44, with large-scale radio emission
associated with it is classified as a jellyfish galaxy by [37]. right: Spiral
galaxy SDSS J163017.01$+$394924.3, which is not a member of , but could be
part of another large-scale structure (see Sec. 6). The rgb colour scheme for
both images is the same as in Figure 8.

###  4.2 Z224-65

Z224-65 (Figure 9(centre)) is a barred Seyfert type II galaxy [41]. [43] have
classified Z224-65 as a mid-infrared (MIR) green valley555Galaxies lying
between the red sequence and blue cloud in a colour-magnitude diagram are
popularly known as ‘green valley’ galaxies in the literature. [43] classified
MIR green valley galaxies using a $\nu L_{\nu}/L_{\odot}~{}(12\mu{\rm m})$ vs
$[3.4]-[12]$ WISE colour (see their fig. 3).  galaxy based on its Wide-field
Infrared Survey Explorer (WISE) data. These authors find that most of the MIR
green valley galaxies belong to the optical red sequence. Their analysis
suggests that the morphological transition of galaxies from early to late type
occurs in the MIR green valley phase. [43] also find that the galaxies
entering the MIR green valley phase have already been quenched.

The UVIT FUV emission from Z224-65 is mostly constrained in an arch around the
central bulge, in a direction opposite to the cluster centre. The low-
frequency radio emission shows no preference, and is scattered around the
optical disc. It would be interesting to obtain a high-frequency radio image
of Z224-65 to throw more light on the interaction between the intra-cluster
and the interstellar mediums, and confirm if the FUV emission is linked to the
turbulence caused by an environment related mechanism.

###  4.3 Z224-55

Z224-55 ($z=0.030$; Figure 9(right)) is classified as a LINER galaxy [41] in .
[42] classified this galaxy as a Type I AGN based on the broad EW(H$\alpha$)
and other emission lines present in the spectra. Z224-55 shows an
$80{{}^{\prime\prime}}$ long low-frequency radio tail in the direction
opposite to the cluster centre. These multi-wavelength data suggests that
Z224-55 may be undergoing ram-pressure stripping under the influence of the
cluster’s potential well, at a distance of $\sim 0.8h^{-1}$ Mpc (almost
$0.5R_{200}$) from the cluster centre.

###  4.4 Z224-44

The second galaxy in common with the sample of [37], Z224-44, is an Sd-type
spiral galaxy with large-scale radio emission associated with it (Figure 10).
This galaxy with $M^{*}=10^{10.7}M_{\odot}$, and SFR $\sim
3.16~{}M_{\odot}{\rm yr^{-1}}$ [44] is also classified as a jellyfish galaxy
[37]. The SDSS spectra for Z224-44 reveals large equivalent width,
EW(H$\alpha$), but negligible emission in [OIII], suggesting that this galaxy
is not an optical AGN. We also did not find any X-ray emission associated with
this object. Therefore, the low-frequency radio emission seems to be
associated with the ongoing star formation in the galaxy: either feeding it,
or a consequence of a stellar feedback from massive stars, or a combination of
both.

###  4.5 SDSS J163017.01$+$394924.3

At redshift $z=0.0701$, SDSS J163017.01$+$394924.3 is not be a member of . The
bright spot seen northward of the core in the optical image of this spiral
galaxy is a foreground star with no FUV emission associated with it (Figure
10). The low frequency radio emission outside the optical disk is faint, but
assumes a tail-like morphology extending in the north-east direction. It is
interesting to note that this galaxy will be close in redshift space ($\sim
2000$ km s-1) to the large-scale structure which may be present in this field
of view at a higher redshift (see Sec. 6 and Fig. 12 below).

To summarise this section, the data suggests that all five member galaxies are
undergoing transformation lead by environment-driven processes in the cluster
. SDSS J163017.01$+$394924.3 also shows a low-frequency radio tail and could
be a RPS candidate in a higher redshift group. The fact that all the members
lie within the virial radius [$r_{vir}=1.6h^{-1}$ Mpc; 19], further supports
our speculations. Amongst these, Z224-44 $\sim 0.72h^{-1}$ Mpc from the centre
of the cluster is the closest, while Z224-65 at $\sim 1.26h^{-1}$ Mpc is the
farthest, respectively.

##  5 Star formation rates of FUV detected galaxies

Figure 11: SFR of galaxies estimated using FUV data plotted as a function of
the SFR estimated using the SDSS optical data. 20 out of 28 galaxies plotted
here are members of the cluster (black circles). The RPS candidate galaxies
are marked by red squares, while the BPT classification is represented as: AGN
or LINER (green triangles), star-forming (blue stars) and composite (purple
diamond), respectively.

We find 28 galaxies in common with the UVIT data presented here and the MPA-
JHU star formation rate (SFR) catalogues666The MPA-JHU catalogues are produced
by a group of researchers currently or formerly at the Max Planck Institute
for Astrophysics and thr John Hopkins University. https://wwwmpa.mpa-
garching.mpg.de/SDSS/. Of these, 20 galaxies are members of the cluster .
Figure 11 shows 27 of these galaxies (one galaxy at [$10^{-3.52},10^{-6.89}$]
is omitted for clarity), including six RPS candidate galaxies discussed above
marked explicitly. The FUV SFR is estimated using the calibration provided by
[45]. We have not changed the formula to compensate for the UVIT wavebands
instead of Galex used by them because both the missions have FUV broadbands
similar to each other. We have also not applied any extinction correction to
the FUV fluxes other than that mentioned in Sec. 2.1, because the required far
infrared data are not available for these galaxies [see, 46, for a detailed
discussion on multi-wavelength SFRs].

As expected, the attenuated SFRFUV underestimates the SFR for all galaxies by
$\sim 2$ orders of magnitude, except three RPS candidates in , namely UGC
10420, UGC 10429 and Z224-65. On the other hand, Z224-55, Z224-44 and the non-
member RPS candidate SDSS J163017.01$+$394924.3 seem to follow the sequence
formed by the other galaxies in this SFRoptical vs SFRFUV plane. This analysis
therefore suggests that environment-related processes such as RPS may enhance
star formation in some of the cluster galaxies.

##  6 Background group(s) in the field of view

Figure 12: (a) The redshift distribution of sources with spectroscopic
redshift $\geq 0.02$ in the field of view. The first set of lines represent
the redshift slice for the cluster ($z_{A2199}\pm 3\sigma_{v}$). The compact
group SDSSCGA 00777 ($z=0.0769$), on the other hand is likely an embedded
substructure in a larger cluster or group (see text for discussion). There are
22 galaxies in a redshift slice of $\pm 2000$ km s-1 (dotted lines) around
this group. Another prominent peak in the redshift distribution is also
observed $\sim 0.28$, although no documented groups or clusters were
identified at this position. (b) Position of all the observed galaxies in the
UVIT field of view for . The galaxies highlighted as blue squares are cluster
members, while the ones marked by red circles represent the galaxies within
$\pm 2000$ km s-1 of the compact group SDSSCGA 00777 (large red circle).

Figure 13: The SDSS u,g,r,i,z image of the compact group SDSSCGA 00777. The
coordinates for LEDA 2158671, the only galaxy with redshift, are marked
explicitly. While this galaxy is not seen by the UVIT, very faint emission
from the other two interacting galaxies can be observed in the UVIT image.

We noticed several interesting galaxies further away in redshift space from .
This observation led us to explore the chance alignment of background
structures behind , in this field of view. Figure 12(a) shows the distribution
of redshift for 122 sources with $z\geq 0.02$. The redshift distribution
evidently peaks at $z\sim 0.03$, for , but shows two other peaks at redshift
$\sim 0.077$ and 0.260, respectively.

Further investigation revealed the presence of a photometrically-selected
compact group SDSSCGA 00777
[$\alpha:247.402^{\circ},\delta:39.980^{\circ},z=0.0769$; 47], having four
members in the UVIT field of view (Figure 13). The group redshift is assigned
based on the spectroscopic redshift of one of the four galaxies, LEDA 2158671
(which is not detected by UVIT). It is noticed, however, that a set of 22 UVIT
sources with spectroscopic redshifts were observed within a redshift slice of
$\pm 2000$ km s-1 around this compact group. The position of these galaxies,
along with the centre of SDSSCGA 00777 group are shown in Figure 12(b). It is
likely that these galaxies and group are embedded within another large-scale
structure behind along the line of sight of this field. The fact that most of
these galaxies are confined to the right hand side of the image, of which
16/22 sources are found only within the top right quadrant of the UVIT field
of view, further adds to our speculation.

We could not find any documented group or cluster corresponding to the second
peak at $z\sim 0.260$. It is, however, worth mentioning that seven UVIT
galaxies are found within a redshift slice of $\pm 2000$ km s-1 around
$z=0.2794$. Based on the distribution of redshifts, it is also possible that a
large-scale filament extending in the redshift space with its axis close to
the line of sight is observed projected in this field of view. Further
investigation along these lines are however, out of the scope of this work.

##  7 Summary and results

In this paper, we have studied an AstroSat/UVIT field located in the X-ray
bright cluster ($z=0.031$). We have used optical photometric data from the
SDSS, spectroscopic data compiled by [33] and low-frequency radio data from
the LoTSS (DR2) to study properties of objects detected by the UVIT in the
BaF2 FUV filter ($\lambda_{mean}=1541~{}\AA;~{}\Delta\lambda=380~{}\AA$). A
complete catalogue of 352 sources detected in this UVIT field, along with the
optical data sourced from the literature is presented. We find that 35% of the
UVIT sources have spectroscopic redshifts, based on which they have been
classified into member and non-member galaxies. The source type identification
for the rest of the data are based on the classification provided by the SDSS
pipeline, which determines if the source detected in the 5-band SDSS image is
resolved (extended) or unresolved (point-like). The pipeline also folds in the
information about colours to distinguish stars from quasars. It is noteworthy
that some of the non-member galaxies may be cluster galaxies, and, some of the
stars identified by the SDSS photometric pipeline may be faint galaxies.
However, deeper spectroscopic and better imaging data are required to confirm
the status of these objects.

We summarise the main results from our analysis below.

  * •

Galaxies other than the members of are on average fainter than the cluster
galaxies. However, all stars and galaxies occupy the same range of colour and
magnitude in the r vs NUV-r plane, making them indistinguishable.

  * •

Some of the bright stars form a distinct sequence separated from the galaxies
by $\sim 1.5$ mag in the FUV-r vs NUV-r colour-colour plane.

  * •

Besides UGC 10420 discussed in [16], five new candidates have been identified
in the newly acquired UVIT data as galaxies undergoing environment-related gas
stripping. Our hypothesis is based on the asymmetric morphology of these
galaxies in the UVIT FUV and low-frequency radio images, and the fact that all
member galaxies lie within the virial radius of , where they are more likely
to experience the wrath of the cluster environment. Two of these galaxies are
LINERS (UGC 10429 and Z224-55), while one (Z224-65) is a known Seyfert galaxy.
SDSS J163017.01$+$394924.3, which is also an RPS candidate does not belong to
, but could be a member of the large-scale structure behind in this field of
view.

  * •

A comparison between optical and FUV SFR of UVIT detected galaxies shows that
the attenuated SFRFUV for most of the galaxies are underestimated relative to
the optical estimate by $\sim 2$ orders of magnitude. Moreover, while SFRFUV
of three RPS candidate galaxies in are comparable to their SFRoptical, the
remaining three follow the same trend as other galaxies in the SFRFUV vs
SFRoptical plane.

  * •

Our analysis suggests the presence of large-scale structures other than in the
UVIT field of view. One of these is a larger cluster or group in which the
compact group SDSSCGA 00777 is embedded ($z\sim 0.077$). There may also be
another system present around $z\sim 0.260$, but no corresponding documented
structure could be confirmed.

Further spectroscopic investigation and deeper multi-wavelength imagery can
throw more light on our results. In particular, it would be very interesting
to explore a wider field covering this region to confirm the presence of a
group or cluster around $z\sim 0.077$ and $0.260$.

## Acknowledgments

S. Mahajan was funded by the SERB Research Scientist (SRS) award (SB-
SRS/2020-21/56/PS), Department of Science and Technology (DST), Government of
India. Prof. K. P. Singh thanks the Indian National Science Academy for
support under the INSA Senior Scientist Programme.

This publication uses data from the AstroSat mission of the Indian Space
Research Organisation (ISRO), archived at the Indian Space Science Data Centre
(ISSDC). UVIT project is a result of collaboration between IIA (Bengaluru),
IUCAA (Pune), TIFR (Mumbai), several centres of ISRO, and the Canadian Space
Agency (CSA). This research has made use of the NASA/IPAC Infrared Science
Archive, which is funded by the National Aeronautics and Space Administration
and operated by the California Institute of Technology. The topcat software
[48] was used for some of the analysis presented in this paper. We acknowledge
the use of LOFAR data in accordance with the credits given on https://lofar-
surveys.org/credits.html, and SDSS data given on
https://www.sdss.org/collaboration/citing-sdss/.

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# Contrastive Representation Learning for Exemplar-Guided Paraphrase
Generation 111The work described in this paper is substantially supported by a
grant from the Research Grant Council of the Hong Kong Special Administrative
Region, China (Project Code: 14200620).

Haoran Yang1 , Wai Lam1 , Piji Li2
1The Chinese University of Hong Kong
2Tencent AI Lab
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>

###### Abstract

Exemplar-Guided Paraphrase Generation (EGPG) aims to generate a target
sentence which conforms to the style of the given exemplar while encapsulating
the content information of the source sentence. In this paper, we propose a
new method with the goal of learning a better representation of the style and
the content. This method is mainly motivated by the recent success of
contrastive learning which has demonstrated its power in unsupervised feature
extraction tasks. The idea is to design two contrastive losses with respect to
the content and the style by considering two problem characteristics during
training. One characteristic is that the target sentence shares the same
content with the source sentence, and the second characteristic is that the
target sentence shares the same style with the exemplar. These two contrastive
losses are incorporated into the general encoder-decoder paradigm. Experiments
on two datasets, namely QQP-Pos and ParaNMT, demonstrate the effectiveness of
our proposed constrastive losses. The code is available at
https://github.com/LHRYANG/CRL_EGPG.

##  1 Introduction

Paraphrase generation (Gupta et al., 2017; Li et al., 2019), aiming to
generate a sentence with the same semantic meaning of the source sentence, has
achieved a great success in recent years. To obtain a paraphrase sentence with
a particular style, Exemplar-Guided Paraphrase Generation (EGPG) (Chen et al.,
2019) has attracted considerable attention. Different from other controllable
text generation tasks whose constraints are taken from a finite set, e.g.,
binary sentiment or political slant (Yang et al., 2018; Prabhumoye et al.,
2018), multiple personas (Kang et al., 2019), over which a classifier can be
trained to guide the disentanglement process, the constraints of EGPG are
exemplar sentences that can be arbitrarily provided, making it more
challenging to learn a good representation for the style and the content. For
example, as shown in Table 1, when using the content embedding of $X$ to
retrieve a sentence with the most similar content in the target sentences
list, we observe that the ordinary model, which is described in Section 4.5,
can often match the sentence $Y^{\prime}$ whose content differs from $X$
instead of the correct target sentence $Y$. This reveals that the content
encoder cannot encode the content information of a sentence appropriately
which can result in inconsistent content of the generated sentence. The same
problem also exists in the style encoder.

source ($X$) | what is the easiest way to get followers on quora ?
---|---
exemplar ($Z$) | how do i avoid plagiarism in my article ?
target ($Y$) | how do i get more followers for my quora ?
retrieved ($Y^{\prime}$) | what are the better ways to ask questions on quora ?

Table 1: An example of EGPG

To learn a better content and style representations, we explore the
incorporation of contrastive learning in EGPG to design an end-to-end encoder-
decoder paradigm with multiple losses. Contrastive learning originates from
computer vision area (Chen et al., 2020a; Khosla et al., 2020) and now, it
also shows its powerfulness in natural language processing area. For instance,
Iter et al. (2020) employ contrastive learning to improve the quality of
discourse-level sentence representations. In our proposed model, besides the
basic encoder-decoder generation task, a content contrastive loss is designed
to force the content encoder to distinguish features of the same content from
features of different content. Similarly, a style contrastive loss is also
employed to obtain a similar distinguishing effect for the style features.
Experimental results on two benchmark datasets, namely QQP-Pos and ParaNMT,
show that superior performance can be achieved with the help of the
contrastive losses.

##  2 Related Work

Paraphrase Generation Researches on paraphrase generation has been for a long
time. Traditional methods solve this problem mainly through statistical
machine translation (Quirk et al., 2004) or rule-based word substitution
(Wubben et al., 2010). In the era of deep learning, approaches based on the
encoder-decoder framework have emerged in large numbers (Prakash et al., 2016;
Chen et al., 2020b). In addition to basic seq2seq model, Li et al. (2018) add
a pair-wise discriminator to judge whether the input sentence and generated
sentence are paraphrases of each other, with the help of reinforcement
learning. To generate diverse paraphrases, i.e., one to many mapping, Gupta et
al. (2017) combine the power of RNN-based sequence-to-sequence model and the
variational autoencoder. At decoding time, a noise sampled from the Gaussian
distribution are appended to input to generate a diverse output. Qian et al.
(2019) propose a approach which use multiple generators to generate diverse
paraphrases without sacrificing quality.

Exemplar-Guided Paraphrase Generation Making the generated paraphrases satisfy
the style of an exemplar sentence is recently a hot research topic. EGPH is
similar to other controlled text generation tasks whose constraints are
sentiment (Yang et al., 2018; Xu et al., 2021), gender (Prabhumoye et al.,
2018), topics (Wang et al., 2021). These tasks are highy related to
Disentangled Representation Learning (DRL) which maps different aspects of the
input data to independent low-dimensional spaces (Cheng et al., 2020). Iyyer
et al. (2018) and Kumar et al. (2020) directly utilise the parse tree
information of the exemplar as the style information without separating style
from sentences. Chen et al. (2019) propose a model which can directly extract
style features from a modified target sentence. Goyal and Durrett (2020)
provide a way to generate paraphrase which is a component rearrangement of the
original input through manipulating the parse tree.

Contrastive Learning In the past few years, many unsupervised feature
extraction algorithms have emerged, for instance, variational autoencoder
(Kingma and Welling, 2014; Xu et al., 2020; Gao et al., 2019b, a), generalised
language models (Brown et al., 2020; Devlin et al., 2019). All the above
methods obtain the feature of input by reconstructing the original input or
predicting masked words and so on which do not take the relationships between
the inputs into consideration. Therefore, contrastive learning, whose loss is
designed to narrow down the distance between features of similar inputs and to
enlarge the distance of dissimilar inputs, has been proposed and achieved a
great success in both unsupervised (Chen et al., 2020a) and supervised (Khosla
et al., 2020) image feature extraction. There are also some works trying to
apply contrastive learning into natural language processing domain. For
instance, Iter et al. (2020) propose a pretraining method for sentence
representation which employs contrastive learning to improve the quality of
discourse-level representations. Giorgi et al. (2020) utilise it to pretrain
the transformer and btains state-of-the-art results on SentEval (Conneau and
Kiela, 2018). All of the above successes spur us to test whether contrastive
learning is helpful on EGPG.

##  3 Proposed Model

Given a source sentence $X_{i}$ and an exemplar sentence $Z_{i}$, our goal is
to generate a sentence $Y_{i}$ that has the same style (syntax) with $Z_{i}$
and retains the content (semantics) of $X_{i}$. As shown in Figure 1, we
design the encoders $E_{s}$ and $E_{c}$ for style and content respectively.
The decoder $D$ generates the output. Our model is trained by optimizing three
losses simultaneously: (1) generation loss; (2) content contrastive loss; (3)
style contrastive loss.

Generation Task For $X_{i}$ and $Z_{i}$, we firstly obtain their corresponding
content features $c_{X_{i}}$ and style features $s_{Z_{i}}$:

$\displaystyle c_{X_{i}}=E_{c}(X_{i})$ (1) $\displaystyle
s_{Z_{i}}=E_{s}(Z_{i})$ (2)

Then $c_{X_{i}}$ and $s_{Z_{i}}$ are concatenated and inputted into the
decoder as the initial hidden state to generate a sequence of probabilities
over vocabulary. At the step $t$, the predicted probability $p_{t}$ of the
$t$-th target word is obtained as follows

$\displaystyle p_{t}=softmax(Wh_{t})$ (3) $\displaystyle
h_{t}=GRU(h_{t-1},e(y_{t-1}))$ (4)

where $h_{0}$ is initialized as $\left[c_{X_{i}},s_{Z_{i}}\right]$ and $W$ is
a parameter matrix. $y_{t-1}$ is the word in the previous step $t-1$ and
$y_{0}$ is the special symbol [SOS] which represents the start of the
sentence. $e(y_{t-1})$ is the embedding of the word $y_{t-1}$.

Negative log-likelihood loss (NLL) is employed as the basic optimization
objective

$\mathcal{L}_{i}^{nll}=-\frac{1}{|Y_{i}|}\sum\limits_{t=1}^{|Y_{i}|}I(y_{t})^{T}\log{p_{t}}$
(5)

where $I(y_{t})$ represents the one-hot encoding of the word $y_{t}$ in the
vocabulary.

Content Contrastive Learning (CCL) Considering that $X_{i}$ and $Y_{i}$ share
the same content, their content features should be close with each other in
the content feature space. Contrastive Learning which is designed to minimize
the distance between positive pairs and maximize the distance between negative
pairs can help model this relationship. Formally, during training, given a
batch $\left\\{(X_{i},Y_{i},Z_{i})\right\\}_{i=1}^{n}$ where $n$ is the batch
size, we firstly obtain the corresponding content features of $X_{i}$ and
$Y_{i}$, denoted by $\left\\{(c_{X_{i}},c_{Y_{i}})\right\\}_{i=1}^{n}$. For
$c_{X_{i}}$, the positive pair is $(c_{X_{i}},c_{Y_{i}})$ and $c_{X_{i}}$ with
the other remaining features in this batch form $2n-2$ negative pairs. For
$c_{Y_{i}}$, the definition of positive/negative pairs is the same as
$c_{X_{i}}$. Then the contrastive loss is employed, giving

$\mathcal{L}_{X_{i}}^{ccl}=-log\frac{exp(c_{X_{i}}\cdot
c_{Y_{i}}/\tau)}{exp(\frac{c_{X_{i}}\cdot c_{Y_{i}}}{\tau})+\sum\limits_{j\neq
i\atop T\in\left\\{X,Y\right\\}}exp(\frac{c_{X_{i}}\cdot c_{T_{j}}}{\tau})}$
(6) $\mathcal{L}_{Y_{i}}^{ccl}=-log\frac{exp(c_{Y_{i}}\cdot
c_{X_{i}}/\tau)}{exp(\frac{c_{Y_{i}}\cdot c_{X_{i}}}{\tau})+\sum\limits_{j\neq
i\atop T\in\left\\{X,Y\right\\}}exp(\frac{c_{Y_{i}}\cdot c_{T_{j}}}{\tau})}$
(7)
$\mathcal{L}^{ccl}=\sum_{i=1}^{n}(\mathcal{L}_{X_{i}}^{ccl}+\mathcal{L}_{Y_{i}}^{ccl})$
(8)

where · represents the dot product between two vectors and $\tau$ denotes a
temperature parameter.

Style Contrastive Learning (SCL) aims to help $E_{s}$ learn a better style
representation by considering that $Z_{i}$ and $Y_{i}$ share the same style.
Similar to CCL, we firstly obtain the style features
$\left\\{(s_{Z_{i}},s_{Y_{i}})\right\\}_{i=1}^{n}$ and then apply the
contrastive loss to these features

$\displaystyle\mathcal{L}_{Y_{i}}^{scl}=-log\frac{exp(s_{Y_{i}}\cdot
s_{Z_{i}}/\tau)}{exp(\frac{s_{Y_{i}}\cdot s_{Z_{i}}}{\tau})+\sum\limits_{j\neq
i\atop T\in\left\\{Z,Y\right\\}}exp(\frac{s_{Y_{i}}\cdot s_{T_{j}}}{\tau})}$
(9) $\displaystyle\mathcal{L}_{Z_{i}}^{scl}=-log\frac{exp(s_{Z_{i}}\cdot
s_{Y_{i}}/\tau)}{exp(\frac{s_{Z_{i}}\cdot s_{Y_{i}}}{\tau})+\sum\limits_{j\neq
i\atop T\in\left\\{Z,Y\right\\}}exp(\frac{s_{Z_{i}}\cdot s_{T_{j}}}{\tau})}$
(10)
$\mathcal{L}^{scl}=\sum_{i=1}^{n}(\mathcal{L}_{Y_{i}}^{scl}+\mathcal{L}_{Z_{i}}^{scl})$
(11)

As a result, the total loss for a batch is as follows

$\mathcal{L}=\sum_{i=1}^{n}\mathcal{L}_{i}^{nll}+\lambda_{1}\mathcal{L}^{ccl}+\lambda_{2}\mathcal{L}^{scl}$
(12)

Figure 1: An Overview of Our Model

##  4 Experiments

###  4.1 Datasets

We conduct experiments on two benchmark datasets, namely ParaNMT (Chen et al.,
2019) and QQP-Pos (Kumar et al., 2020). ParaNMT consists of about 500k
training, 800 testing and 500 validation sentence pairs which are
automatically generated through backtranslation of the original English
sentences. QQP-Pos consists of 130k training, 3k testing and 3k validation
quora question pairs which are more formal than ParaNMT. The split size is the
same as previous works to have a fair comparison. Since the exemplar sentences
are not provided in both datasets, we adopt a method similar with Kumar et al.
(2020) to search an exemplar $Z_{i}$ for each source-target pair
$(X_{i},Y_{i})$ based on the POS tag sequence 222We use NLTK for POS tagging.
similarity (refer to Appendix A).

###  4.2 Baselines & Metrics

We compare our model with (1) SCPN Iyyer et al. (2018) which employs a parse
generator to output the full linearized parse tree as the style by inputting a
parse template; (2) SGCP (Kumar et al., 2020) which extracts the style
information directly from the parse tree of the exemplar sentence; (3) CGEN
(Chen et al., 2019), an approach based on variational inference (Kingma and
Welling, 2014).

The evaluation metrics are BLEU (Papineni et al., 2002), METEOR (Lavie and
Agarwal, 2007) and ROUGE (R) (Lin, 2004). We also conduct human evaluation to
investigate the quality of the generated sentences. Moreover, we propose
Content Matching Accuracy (CMA) to gauge the quality of the generated
embeddings for the content. CMA will be introduced in Section 4.5.

###  4.3 Implementation Details

Each sentence is trimmed with a maximum length 15. The word embedding is
initialized with 300-$d$ pretrained GloVe (Pennington et al., 2014). We use a
BERT-based (Devlin et al., 2019) architecture for the style encoder $E_{s}$
and the dimension of style features is 768. For content encoder $E_{c}$, we
use GRU (Chung et al., 2014) with hidden state size 512. During training, the
teacher forcing technique is applied with the rate 1.0. The balancing
parameters $\lambda_{1}$ and $\lambda_{2}$ are both set to 0.1. The
temperature parameter $\tau$ is set to 0.5. We train our model using Adam
optimizer with the learning rate 1e-4 and the training epochs are set to 30
and 45 for ParaNMT and QQP-Pos respectively.

###  4.4 Results

As summarized in Table 2, our model outperforms SCPN, SGCP and CGEN by a large
margin on automatic evaluation metrics. We also conduct human evaluation to
investigate the holistic quality of the generated sentences. For each dataset,
we firstly choose two source sentences and then randomly select 25 exemplars
for each source sentence to generate a total of 50 sentences. Table 5 shows
the results of human assessment. It can be seen that our model obtains a
higher score than SGCP and CGEN, which is consistent with the automatic
evaluation results. These results are expected because SCPN and SGCP use a
parse tree as the style which is lack of the lexical information and very
unstable. Moreover, CEGN is VAE-based which is intrinsically harder to train
(Bowman et al., 2016).

###  4.5 Ablation Study

We conduct ablation study with three variants, namely ours without SCL
(Ours-w/o-SCL), ours without CCL (Ours-w/o-CCL), ours without both SCL and CCL
(Ours-w/o-both). We show that our model is better than the three variants to
demonstrate the effectiveness of the contrastive losses.

QQP-Pos
---
Model | BLEU | R-1 | R-2 | R-L | METEOR
SCPN | 15.6 | 40.6 | 20.5 | 44.6 | 19.6
SGCP | 36.7 | 66.9 | 45.0 | 69.6 | 39.8
CGEN | 34.9 | 62.6 | 42.7 | 65.4 | 37.4
Ours | 45.8 | 71.0 | 52.8 | 73.3 | 45.8
Ours-w/o-CCL | 43.1 | 70.0 | 50.6 | 72.3 | 43.5
Ours-w/o-SCL | 42.7 | 69.7 | 49.9 | 71.8 | 43.6
Ours-w/o-both | 40.8 | 68.4 | 48.4 | 70.8 | 41.6
ParaNMT
SCPN | 6.4 | 30.3 | 11.2 | 34.6 | 14.6
SGCP | 15.3 | 46.6 | 21.8 | 49.7 | 25.9
CGEN | 13.6 | 44.8 | 21.0 | 48.3 | 24.8
Ours | 16.2 | 50.6 | 25.3 | 52.1 | 28.4
Ours-w/o-CCL | 15.3 | 50.8 | 25.2 | 52.4 | 28.0
Ours-w/o-SCL | 15.2 | 50.2 | 24.4 | 51.5 | 28.0
Ours-w/o-both | 15.3 | 50.2 | 24.9 | 51.6 | 27.7

Table 2: Automatic Evaluation Results.

Model | Ours | Ours-w/o-CCL | Ours-w/o-SCL | Ours-w/o-both
---|---|---|---|---
QQP-Pos
ED-E | 2.49 | 2.42 | 2.56 | 2.57
ED-R | 2.64 | 2.65 | 2.78 | 2.82
ParaNMT
ED-E | 4.36 | 4.47 | 4.49 | 4.49
ED-R | 4.22 | 4.24 | 4.28 | 4.25

Table 3: Style Evaluation

SOURCE: how do i develop good project management skills ?
---
EXEMPLAR | GENERATION
which is the best laptop model to buy within 30k ? | which is the best way to develop project management skills ?
how many cups of coffee should i consume in a day ? | from what skills can i start in a project management ?
which subjects are important to become a chartered accountant ? | what skills are necessary to develop a project management ?

Table 4: An Example Generated by Our Model Model | Ours | SGCP | CGEN | Ours-w/o-CCL | Ours-w/o-SCL | Ours-w/o-both
---|---|---|---|---|---|---
QQP-Pos | 3.71 | 3.12 | 2.97 | 3.59 | 3.45 | 3.33
ParaNMT | 2.53 | 1.9 | 2.05 | 2.51 | 2.53 | 2.38
Table 5: Human evaluation results. Each sentence is given a score ranging from
one to five to assess the holistic quality. We report the average value of two
annotators. Higher score is better. The Spearman’s correlation coefficients of
these two annotators are 0.707 for QQP-Pos and 0.37 for ParaNMT.

$X$ | can you view a private facebook profile?
---|---
$Z$ | how would you learn a new programming language?
$Y$ | how do you view a private facebook profile?
$Y^{\prime}$ | can you see who visited your instagram last?
Ours | how do you see a private facebook profile?
Ours-w/o-SCL | how can you view a private facebook profile?
Ours-w/o-both | how can you view a private instagram profile?

Table 6: A failed example without CCL

As presented in Table 2, we can see that Ours can achieve better results than
the three variants on all automatic metrics for QQP-Pos. Particularly, Ours,
Ours-w/o-CCL and Ours-w/o-SCL outperform Ours-w/o-both a lot, demonstrating
the usefulness of the contrastive losses. For ParaNMT, Ours obtains the
highest score on BLEU, ROUGE-2, MENTOR while it lags behind Ours-w/o-CCL on
ROUGE-1 and ROUGE-L. This phenomena may be caused by the poor quality of the
dataset. The human evaluation results are also listed in Table 5. Our model
can generally generate fluent sentences on QQP-Pos. But the overall quality of
sentences generated by all models on ParaNMT is unsatisfactory which shows
that a high-quality dataset is necessary for training a good model.

We also provide the style evaluation of ED-E (edit distance between the POS
tag sequence of the generated paraphrase and the exemplar) and ED-R (edit
distance between the POS tag sequence of the generated paraphrase and the
ground truth reference) in Table 3. We can see that models with style
contrastive losses have smaller edit distance.

To directly assess the quality of the generated embeddings for the content we
propose Content Matching Accuracy. To calculate CMA, firstly we input all the
source and target sentences into $E_{c}$ to get the content representations
$\textbf{A},\textbf{B}\in\textbf{R}^{m\times k}$, where $m$ is the size of the
test dataset and $k$ is the dimension of content feature vectors. Then, we
calculate the similarity matrix $\textbf{S}=\textbf{A}\textbf{B}^{T}$. In
ideal situation, each diagonal element $\textbf{S}_{[i,i]}$ should be the
largest value in row $i$ since the content embedding $\textbf{A}_{i}$ of the
$i_{th}$ source sentence should have the greatest similarity with the content
embedding $\textbf{B}_{i}$ of its corresponding target sentence. Therefore,
the content matching accuracy (CMA) is defined as:

$CMA=\frac{\sum_{i=1}^{m}\mathbbm{1}(argmax(\textbf{S}_{i})=i)}{m}$ (13)

where $\mathbbm{1}(s)$ equals 1 if $s$ is true, otherwise 0. The results are
illustrated in Figure 2. We notice that models with CCL can achieve higher
accuracy than Ours-w/o-both. It signifies that the content encoder $E_{c}$ is
improved with the help of CCL. We provide a failed example in Table 6.
$Y^{\prime}$ is the sentence retrieved given $X$ under the model
Ours-w/o-both. $Y$ is the target sentence and it is also the sentence
retrieved given $X$ under the model Ours or Ours-w/o-SCL. We can see that the
content generated by Ours-w/o-both is incorrect (changing facebook to
instagram) and instagram exists in $Y^{\prime}$. This illustrates that the
poor-quality content embedding of $X$ can cause the incorrect content of the
generated sentence. In general, matching accuray can also be calculated for
the style. However, the exemplar selection process has a high probability of
dropping the sentence with the most similar style of $Y$. Therefore, style
matching accuracy is not provided here. Instead, we list some retrieved
sentences based on the style embedding in Appendix B.

Figure 2: Content Matching Accuracy

###  4.6 Case Study

Some examples generated by our model are shown in Table 4. It can be observed
that our model can generally generate high-quality sentences which have
similar style with the exemplar and retain the semantic meaning of the source
sentence. Moreover, our model does not directly copy the style words from the
exemplar, but instead adopts the overall structure of the exemplar to generate
sentences, for example, the second one. More examples are provided in Appendix
C.

###  4.7 Explanations

We attempt to provide some possible explanations about why the model with
these two contrastive losses can achieve better performance. The first reason
is that adding additional losses on the output of encoders can alleviate
gradient vanishing which is a serious issue when training the encoder-decoder
model. The second reason is that the overfitting issue may be prevented, since
the contrastive losses restrict the free adjustment of parameters in the model
by forcing the encoder and decoder to focus on their own tasks, i.e., feature
extraction and sentence generation.

##  5 Conclusion

We introduce the content contrastive loss and the style contrastive loss into
EGPG to design a multi-losses scheme without requiring additional labeled
data. This scheme can obtain better results compared with the baseline and
ablative models, which demonstrates the effectiveness of contrastive learning
for learning better representations. Moreover, the proposed framework is
general and may benefit other similar NLP tasks.

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##  Appendix A Exemplar Searching Algorithm

Algorithm 1 Searching Exemplar Sentences

0: dataset $\mathbb{D}=(\mathbb{D}_{X},\mathbb{D}_{Y})$

1: for $Y$ in $\mathbb{D}_{Y}$ do

2: find the sentence set $\mathbb{C}_{1}\subseteq\mathbb{D}_{X}$ that each
$C\in\mathbb{C}_{1}$ satisfies $\left|len(C)-len(Y)\right|\leq 2$

3: find the sentence set $\mathbb{C}_{2}\subseteq\mathbb{C}_{1}$ that for each
$C\in\mathbb{C}_{2}$, the number of shared words between $C$ and $Y$, denoted
by $c$, satisfies $c+2\leq len(Y)$

4: find the exemplar $Z\in\mathbb{C}_{2}$ which has the smallest POS tag
sequence editdistance with $Y$

5: end for

The detailed steps for exemplar sentence searching are described in Algorithm
1. Step 2 is done to accelerate the searching procedure since sentences with
similar style tend to have similar token lengths. Step 3 guarantees that the
content information of $Y$ and the selected $Z$ does not overlap much.

##  Appendix B Style Embedding Quality

We list some sentences retrieved by ablative models given the style embedding
of a sentence $S$ in Table 7. For each model, we obtain the top-5 sentences
which are most similar to $S$. We can see that the sentences retrieved by Ours
and Ours-w/o-CCL are more similar to $S$ in style dimension than Ours-w/o-both
on the whole. For example, in the second case, the fifth sentence of
Ours-w/o-both lacks the adverbial modifier compared with $S_{2}$.

$S_{1}$ | what are newton ’s laws of motion?
---|---
Ours | what are the after effects of masturbation ?
what are the health benefits of coffee ?
what are the safety precautions on handling shotguns ?
what are some interesting facts about bengaluru ?
what are some unknown facts about football ?
Ours-w/o-CCL | what are the health benefits of coffee ?
what are the good things about pakistan ?
what are some interesting facts about bengaluru ?
what are some unknown facts about football ?
what are considered abiotic factors of grasslands ?
Ours-w/o-both | what were nelson mandela ’s greatest accomplishments ?
what are craig good ’s qualifications to talk about nutrition ?
what are reasons of china ’s success ?
what are president obama ’s greatest accomplishments and failures ?
what is newton ’s third low of motion with examples ?
$S_{2}$ | how do i impress a girl on chat ?
Ours | how do i become an engineer in robotics ?
how do i get a job in europe countries ?
how do i get the crown on musical ly ?
how do i make a website responsive without bootstrap ?
how do i find the best seo company in dellhi ncr ?
Ours-w/o-CCL | how do i become an engineer in robotics ?
how do i get a job in europe countries ?
how do i leave a girl without hurting her feelings ?
how do i get the crown on musical ly ?
how do i root a galaxy s550 at t ?
Ours-w/o-both | how do i become an engineer in robotics ?
how do i get a job in europe countries ?
how do i buy a suit online ?
how do i get the crown on musical ly ?
how can i help a friend get off drugs ?

Table 7: Sentences Retrieved by Style Embedding

##  Appendix C Multiple Paraphrase Sentences Generation

$X_{1}$ | which is the best anime to watch ?
---|---
$Z_{11}$ | can you jailbreak an ios 8 3 ?
$Y_{11}$ | can you recommend the best anime ?
$Z_{12}$ | which are the best mba colleges in gwalior ?
$Y_{12}$ | what are the best anime films of all time ?
$Z_{13}$ | how can i earn from online ?
$Y_{13}$ | what anime should i watch now ?
$X_{2}$ | what type of music do you listen ?
$Z_{21}$ | is equatorial guinea really rich ?
$Y_{21}$ | which music is really good ?
$Z_{22}$ | what tv series have you watched and why did you like them ? explain
$Y_{22}$ | what type of music do you like ? and how do you recommend ?
$Z_{23}$ | what is the best way to reduce weight ?
$Y_{23}$ | what is the best music to listen to ?

Table 8: Generate different sentences given different exemplars.