# Unscrambling the lensed galaxies in JWST images behind SMACS0723

Massimo Pascale Department of Astronomy, University of California, 501
Campbell Hall #3411, Berkeley, CA 94720, USA  Brenda L. Frye Department of
Astronomy/Steward Observatory, University of Arizona, 933 N. Cherry Avenue,
Tucson, AZ 85721, USA  Jose Diego FCA, Instituto de Fisica de Cantabria (UC-
CSIC), Av. de Los Castros s/n, E-39005 Santander, Spain  Lukas J. Furtak
Physics Department, Ben-Gurion University of the Negev, P. O. Box 653, Be’er-
Sheva, 8410501, Israel  Adi Zitrin Physics Department, Ben-Gurion University
of the Negev, P. O. Box 653, Be’er-Sheva, 8410501, Israel  Tom Broadhurst
Department of Physics, University of the Basque Country UPV/EHU, E-48080
Bilbao, Spain  DIPC, Basque Country UPV/EHU, E-48080 San Sebastian, Spain
Ikerbasque, Basque Foundation for Science, E-48011 Bilbao, Spain  Christopher
J. Conselice Jodrell Bank Centre for Astrophysics, University of Manchester,
Oxford Road, Manchester, M13 9PL, U.K.  Liang Dai Department of Physics,
University of California, 366 Physics North MC 7300, Berkeley, CA. 94720, USA
Leonardo Ferreira Centre for Astronomy and Particle Physics, University of
Nottingham, Nottingham, UK  Nathan J. Adams Jodrell Bank Centre for
Astrophysics, University of Manchester, Oxford Road, Manchester, M13 9PL, U.K.
Patrick Kamieneski Department of Astronomy, University of Massachusetts,
Amherst, MA 01003, USA  Nicholas Foo Department of Astronomy/Steward
Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721,
USA  Patrick Kelly School of Physics and Astronomy, University of Minnesota,
116 Church Street SE, Minneapolis, MN 55455, USA  Wenlei Chen School of
Physics and Astronomy, University of Minnesota, 116 Church Street SE,
Minneapolis, MN 55455, USA  Jeremy Lim Department of Physics, The University
of Hong Kong, Pokfulam Road, Hong Kong  Ashish K. Meena Physics Department,
Ben-Gurion University of the Negev, P. O. Box 653, Be’er-Sheva, 8410501,
Israel  Stephen M. Wilkins Astronomy Centre, University of Sussex, Falmer,
Brighton BN1 9QH, UK  Institute of Space Sciences and Astronomy, University of
Malta, Msida MSD 2080, Malta  Rachana Bhatawdekar European Space Agency,
ESA/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, NL Massimo Pascale
<EMAIL_ADDRESS>Rogier A. Windhorst School of Earth & Space
Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Department
of Physics, Arizona State University, Tempe, AZ 85287-1504, USA

###### Abstract

The first deep field images from the James Webb Space Telescope (JWST) of the
galaxy cluster SMACS J0723.3-7327 reveal a wealth of new lensed images at
uncharted infrared wavelengths, with unprecedented depth and resolution. Here
we securely identify 14 new sets of multiply imaged galaxies totalling 42
images, adding to the five sets of bright and multiply-imaged galaxies already
known from Hubble Space Telescope data. We find examples of arcs crossing
critical curves, allowing detailed community follow-up, such as JWST
spectroscopy for precise redshift determinations, and measurements of the
chemical abundances and of the detailed internal gas dynamics of very distant,
young galaxies. One such arc contains compact knots of magnification
$\mu\sim$750, and features a microlensed transient. We also detect an Einstein
cross candidate only visible thanks to JWST’s superb resolution. Our
_parametric_ lens model is available through the following
link111https://www.dropbox.com/sh/gwup2lvks0jsqe5/AAC2RRSKce0aX-
lIFCc9vhBXa?dl=0, and will be regularly updated using additional spectroscopic
redshifts. The model reproduces the multiple images to better than an rms of
$0.5^{\prime\prime}$, and allows for accurate magnification estimates of high-
redshift galaxies. The intracluster light extends beyond the cluster members,
exhibiting large-scale features that suggest a significant past dynamical
disturbance. This work represents a first taste of the enhanced power JWST
will have for lensing-related science.

dark matter – galaxies: clusters: general – galaxies: clusters: individual:
SMACS0723 – gravitational lensing: strong – galaxies: high redshift

##  1 Introduction

At long last, the first deep images from the James Webb Space Telescope (JWST)
were delivered on July 11, 2022. The target is the central region of SMACS
J0723.3-732 (SMACS0723 hereafter; $z_{d}$ = 0.39), which is part of the
southern extension of the MACS sample (Ebeling et al., 2010; Repp & Ebeling,
2018). SMACS0723 is a massive strong-lensing (SL) galaxy cluster which is rich
in galaxy images distorted by the gravitational lensing effect, as was seen in
recent _Hubble Space Telescope_ (HST) imaging taken as part of the
Reionization Lensing Cluster Survey (RELICS; Coe et al., 2019). The
$Planck$-derived mass is high 8.39 $\times$ 1014 M⊙, and there were nine
galaxies at $z>5.5$ and two candidates at $z=7$ based on their photometric
redshift estimation (Salmon et al., 2020; Strait et al., 2021). Three far-
infrared sources have also been detected in the field using the Herschel Space
Observatory (Sun et al., 2022).

A lens model for this cluster based on these previous HST images was published
recently (Golubchik et al., 2022). This model uses the Light-Traces-Mass (LTM)
method, which assumes that the galaxy light traces the underlying stellar and
dark matter (DM) but does not assume a parametrized mass function for the DM
(Broadhurst et al., 2005; Zitrin et al., 2009, 2015). In Golubchik et al.
(2022), the authors identify five strongly lensed galaxies and derive the
spectroscopic redshifts for three of those systems using publicly-available
ESO Very Large Telescope (VLT) Multi Unit Spectroscopic Explorer (MUSE; Bacon
et al., 2010) data. An alternative (still unpublished) lens model based on
Lenstool (Jullo et al., 2007, and references therein), and that also includes
the MUSE spectroscopic redshift constraints, will soon be available (or a
newer version thereof, see Mahler et al. (2022); J. Richard, private
communication). Lenstool is a parametric method which assumes both the cluster
galaxies and DM follow known analytical or fully-parametrized mass
distributions. Two additional models can be found in the RELICS
website222https://archive.stsci.edu/prepds/relics/, one also based on Lenstool
and the other on the Glafic (Oguri et al., 2012) modeling method. These
however – to the best of our knowledge – do not use the spectroscopic
information from MUSE.

Figure 1: Image stamps depicting the 19 image multiplicities in the SMACS0723
field, as labeled. The publicly-available color image of SMACS0723 is
depicted, which is valuable for the identification of image family members by
their similar colors and morphological components. We also require that the
model be able to reproduce the positions of the members of each image family.
A 5′′ bar is shown for reference.

This first set of images of SMACS0723 from JWST represents a milestone for not
only astronomy, but science in general. As with its predecessor, HST, this
first image from JWST reveals the distant universe with incredible detail.
Some of the most prominent arcs detected with the HST RELICS program now show
multiple unresolved substructures in JWST previously unseen (see for instance
system 4 in Figure 1). These substructures that can now be resolved by JWST
facilitate the identification of families of strongly lensed images (a family
consists of all the counter-images from the same background galaxy). The
greater sensitivity of JWST to small flux fluctuations and improved spatial
resolution will also allow us to search for fainter caustic or micro-caustic
crossing events of stars at $z<2$ such as Icarus (Kelly et al., 2018), or
Warhol (Chen et al., 2019; Kaurov et al., 2019), stars between $2<z<5$ such as
Godzilla (Diego et al., 2022), stars at $z\approx 6$ such as Earendel (Welch
et al., 2022) or even further up to the first stars as proposed in Windhorst
et al. (2018).

JWST is already providing breakthrough results in the study of the most
distant galaxies. Pointing JWST towards gravitational lenses results in a more
powerful combined telescope with an effective diameter a factor $\sqrt{|\mu|}$
times larger, where $|\mu|$ is the absolute magnification of the lensed
background object. For galaxies, typical magnifications can reach factors of a
few tens, making the combination JWST+SL cluster similar to a space telescope
analogue to JWST but with with 20-30 m diameter. For much smaller background
objects like magnified stars near caustics or in general for sub-pc structures
near caustics, the underlying magnification factor can be of order $\sim
1000$. This translates into effective apertures for JWST of $\approx 200$
meters! Even without the ultra-high magnification boosts near the critical
lines, SL has allowed us to probe several magnitudes deeper than blank fields,
i. e., down to rest-frame UV luminosities $M_{\mathrm{UV}}\lesssim-13$
magnitudes (Bouwens et al., 2017, 2022a, 2022b; Livermore et al., 2017; Atek
et al., 2018; Ishigaki et al., 2018) and stellar masses $M_{\star}\gtrsim
10^{6}\,\mathrm{M}_{\odot}$ (Bhatawdekar et al., 2019; Kikuchihara et al.,
2020; Furtak et al., 2021; Strait et al., 2021). With the redder wavelength
range, greater sensitivity, and resolving power of the JWST, we can expect
many more galaxies at even higher redshifts to be detected in the coming
months. In order to fully characterize them and study their physics, we will
need accurate SL magnification models.

In this paper we identify 14 new image families using the JWST data and
present a new _parametric_ SL model. The paper is organized as follows: In §2
we detail previous observations of the cluster which are relevant to
constructing the lens model, which is described in §3. In §4 we present and
discuss the results. The conclusion appears in §5. Throughout this work we use
a $\Lambda$CDM cosmology with $\Omega_{M}=0.3$, $\Omega_{\Lambda}=0.7$, and
$H_{0}=70$ km s-1 Mpc-1. Unless otherwise stated, we use AB magnitudes (Oke &
Gunn, 1983), and errors correspond to $1\sigma$.

##  2 Observations and Data

Observations with the Near Infrared Camera (NIRCam; e. g., Rieke et al., 2005)
aboard the JWST were executed as part of the Director’s Discretionary Time on
2022 June 06 (PI: Pontoppidan; Program ID 2736). Exposures were taken in
F090W, F150W, and F200W in the short-wavelength (SW), and F356W, F277W, and
F444W in the long-wavelength (LW) channels, totalling 12.5 h of integration
time. Near Infrared Spectrograph (NIRSpec; Jakobsen et al., 2022) observations
were made in the same field as a part of the same program. Two exposures were
taken in each of the F170LP and F290LP filters, totalling 11787 sec of
integration time in each filter. SMACS0723 was also observed using the Mid
Infrared Instrument (MIRI; Bouchet et al., 2015; Rieke et al., 2015) and the
Near Infrared Imager and Slitless Spectrograph (NIRISS; Doyon et al., 2012).
The raw data from all four instruments were processed using the JWST science
calibration pipeline, which performed the background subtraction, flat-
fielding, correction for cosmic ray hits, correction for image distortions,
repixelization by the drizzle approach onto a common astrometric reference
frame, co-addition to make the mosaic, and combination into a color image.

Using the NIRCam data, we extract photometry for our targets of interest using
forced photometry of small, 0.5 arcsecond diameter circular apertures centered
on the peak flux of the target in each band. The photometry is aperture
corrected for a point spread function using the simulated point spread
functions (PSFs) from WebbPSF (Perrin et al., 2014). This information is then
fed into the photometric redshift code LePhare (Arnouts et al., 1999; Ilbert
et al., 2006). LePhare operates by fitting a large grid of galaxy spectral
energy distributions to the photometry provided. We run LePhare with a suite
of galaxy templates from (Bruzual & Charlot, 2003), allowing for E(B-V) values
between 0 and 1.5 (Calzetti et al., 2000), redshifts between 0 and 12 and
applying the (Madau, 1995) treatment for absorption from the IGM. The
redshifts provided in Table 1 are the redshift of peak probability and errors
generated from a $\chi^{2}$ grid produced by LePhare based on the templates,
redshifts and dust attenuation combinations available. Several entries are
missing values as a result of various sources of contamination or by a lack of
detection. We refer to the Appendix for more details. We note that these
NIRCam data in the SMACS0723 field can be compared with bluer data using HST
taken as a part of the RELICS program (PI: D. Coe), and the _Spitzer Space
Telescope_ (PI: M. Bradac).

We also made use of the available NIRSpec data set. In particular, we analyzed
those spectra which were acquired at the positions of our image systems to
confirm our image system designations. We refer to §3.1 for more details. We
also consulted the MIRI images to test for achromaticity within each of our
image systems, for those systems that were detected.

Figure 2: Close-up view of system 5 with the $z=1.43$ critical curve marked in
the dashed line on a F090W+F150W+F200W composite color image. Two compact
sources in the inset, knots A and B, have a separation of $\sim
0.16^{\prime\prime}$, and have sizes that are consistent with the width of the
PSF. The knots bracket the critical curve that must pass in between them at an
angular separation of $\sim 0.08^{\prime\prime}$. We estimate high
magnification factors as a result of this close proximity to the critical
curve of $|\mu|\sim$750 for each source. A red knot is also detected at a
position slightly offset from knot A, Tr, which may be a microlensed
transient.

Overall, the arcs in this field make up a rich tapestry of distorted images
typical of lensed sources and at a level of detail that has never been seen
before. The increased spatial resolution reveals lensing constraints even down
to the small substructures within the arcs, since many of these small scale
sources are equally multiply-imaged, such as the double arc in system 5 (Figs.
1 and 2). Another surprise is that thanks to the remarkably dark infrared sky
background of JWST images, we can get a high signal-to-noise view of the
intra-cluster light (ICL). This cluster has an ICL that is elongated and
nonuniform. We refer to §4 for a discussion of how the ICL’s relatively unique
features suggest that this cluster is not dynamically-relaxed.

##  3 SL modeling of SMACS0723

We generate a new SL model exploiting the JWST data in which we identify the
new sets of multiple images, as is described in §3.1. Cluster member galaxies
used in the modeling are described briefly in §3.2. The modeling method is
described in §3.3.

Figure 3: Critical curve at $z=1.45$ from the SMACS 0723 lens model is
overlaid as a color composite image generated from the six existing JWST
NIRCam filters depicting the central 1.5 by 1 arcminutes of the cluster. The
model incorporates strong-lensing constraints from the 19 image families
identified in total; 14 of them are discovered by this work using the JWST
data). The two “+” symbols mark the positions of the two dark matter halos
used in this model. Shown in the inset is Image 2.2, which is rare for
containing $\geq 10$ bright knots located at large projected galactocentric
radii.

###  3.1 New multiple images in SMACS0723

We identify new lensing constraints taking advantage of the superior quality
of the JWST images. We start by adopting the first five multiple image systems
published in Golubchik et al. (2022), following their numbering scheme. These
systems serve also as a model-independent guide to search for new systems
since nearby new systems can be easily found by association with already known
systems. For example, groups of galaxies at similar redshifts typically
maintain similar spatial distributions when distorted by a gravitational lens.
Moreover, amongst the galaxy images, counter images with negative and positive
parities are in general symmetric to one another with respect to the critical
curve. After visual inspection of the new JWST/NIRCam image, and corroboration
by available photometric and/or spectroscopy redshift constraints and model-
predicted locations, we identify 14 new sets of multiply lensed galaxies which
are reported in Table 1.

Fortunately, there are spectroscopic redshifts available for some of the image
systems. The redshifts of image systems 1, 2, and 5 are $z=1.450\pm 0.001$,
$z=1.378\pm 0.001$ and $z=1.425\pm 0.001$, respectively and were measured with
MUSE (Golubchik et al., 2022). Note that while JWST/NIRSpec spectroscopic
redshifts of 35 galaxies have been reported in this field with redshifts as
high as 8.3 as reported by the JWST press release. An investigation of the
NIRSpec spectroscopy uncovered spectra for only one of our 42 images from our
19 image families: image 4.1. However, an inspection of the spectrum in each
of the spectral band-passes did not produce any significant features that were
present in multiple visits and therefore did not yield a redshift. While
valuable, further spectroscopic redshifts are however not crucially necessary
for securing our image system identifications which relies on a large set of
image multiplicities vetted in several ways. We note that NIRISS spectroscopy
of SMACS0723 is also available but not used in this study. Its redshift
constraints will inform future lens models.

###  3.2 Cluster member galaxies

For our model we use the same the cluster member galaxy selection as in
Golubchik et al. (2022), which was based on the red sequence shown therein
(their Fig. 4). In addition, we add here 3-4 galaxies not used in the initial
model by Golubchik et al. (2022) which lie near the bright star 20′′ north of
the BCG (which hindered somewhat their previous detection), and are included
as they may affect the reproduction of nearby counter images. A revision of
this selection using spectroscopic data (such as e.g., the NIRISS data), is
deferred to future work.

###  3.3 SL modeling method

The LTM model presented in Golubchik et al. (2022) required a very strong
external shear, indicating that the cluster’s central mass distribution is
highly elongated. Since the LTM approach is limited in the intrinsic matter
ellipticity it can accommodate, and for comparison, we make use here of a new,
fast parametric method that we recently constructed (A. Zitrin; in
preparation; the method can also be referred to as analytic, i. e., it is not
limited to a grid’s resolution). The method is similar in nature to other
parametric lens modeling techniques such as Lenstool (Jullo et al., 2007),
Glafic (Oguri et al., 2010) or GLEE (Halkola et al., 2006; Grillo et al.,
2015). In such parametric methods, dark matter halos can be elliptical which
more easily accounts for the required elongation (which is also evident from
the distribution of arcs).

The models in our new parametric method have two main components. First, the
cluster members galaxies are modeled with double pseudo elliptical mass
distributions (dPIE; Elíasdóttir et al. 2007) while adopting the scaling
relations for the galaxy’s velocity dispersion ($\sigma$), core radius
$r_{c}$, and cut-off radius $r_{t}$, from Jullo et al. (2007). The second
modeling component is the set of cluster DM halos. These can in principle be
modeled either as elliptical Navarro-Frenk-White (NFW) profiles (Navarro et
al., 1996), or as pseudo elliptical mass distributions (PIEMD; e. g., Monna et
al. 2015); or dPIEs. The third and last component which can be added if
necessary is a two-component external shear.

The method is similar to our previous parametric implementation outlined in
Zitrin et al. (2015) which has been well vetted, but is not limited to the
assigned grid resolution. The new improved version used here has been already
applied to various clusters and has also been tested on simulated clusters,
accommodating both image- and source-plane minimization. The minimization of
the model is done via a Monte-Carlo Markov Chain (MCMC) with a Metropolis-
Hastings algorithm (e. g., Hastings, 1970). We include annealing in this
procedure, and the chain typically runs for several dozen thousand steps after
the burn-in stage. Errors are calculated from the same MCMC chain.

###  3.4 SMACS0723 SL model

For modeling SMACS0723 with our new method, we represent cluster members as
dPIE profiles, as explained above, and the cluster DM halos as PIEMDs (i. e.,
the main parameters for each halo aside from the ellipticity and its position,
are a core radius and a velocity dispersion). We use two DM halos, centered on
the two central galaxies respectively (marked by “+” symbols in Fig. 3). We do
not incorporate an external shear. Since galaxies can deviate from the assumed
scaling relations, we leave the four brightest galaxies to be freely weighted.
The BCG’s ellipticity parameters are also left free to be optimized by the
model. For the lensed sources, each multiply-imaged system should converge to
a single position in the source plane. To enforce this constraint, we minimize
the differences between the image positions in the source plane following the
prescription of Keeton (2010), which usually converges to a solution
relatively quickly and without loss of quality, as shown by Keeton (2010) in
their successful Hubble Frontier Fields (HFF; Lotz et al., 2017) lens models.

##  4 Results and Discussion

The best-fit SL model, which is the one for which $\chi^{2}$ is minimized, is
presented in Fig. 3. Critical lines are overlaid for $z_{s}$ = 1.45 (i. e.,
the redshift of image system 1). The figure illustrates the elongated
configuration of SMACS0723. The model was minimized using a positional
uncertainty of $\sigma_{pos}=0.5^{\prime\prime}$, resulting in a $\chi^{2}$ of
159.4 in the image plane, and an _rms_ of 0.48″ in reproducing the positions
of the multiple images.

Figure 4: The intracluster light for SMACS 0723. The pronounced ICL extends
along the long-axis of the cluster. Typically a smoothly-varying feature, in
SMACS0723 the ICL has significant structures, including a large “loop” feature
in the northwest component, and a large lobe-like feature in the southeast
component.

The effective Einstein radius at a given redshift is computed as $\theta_{E}$
= $\sqrt{A/\pi}$, with A being the area enclosed within the critical curves.
At $z$ = 2, $\theta_{E}$ = 18.4′′ $\pm$ 1.8′′, and the mass contained inside
the critical curve is (5.91 $\pm$ 0.83) $\times$1013 M⊙, which is overall
consistent with the values of $\theta_{E}$ = 16.9′′ $\pm$ 2′′, and $M$ =
$(4.15$ $\pm$ 0.58)$\times$ 1013 M⊙ obtained in the HST LTM model (Golubchik
et al., 2022). The uncertainties on the Einstein radius and mass are similar
for each of the models and are limited by the systematics.

The JWST/NIRCam images uncover fine details of the faint substructures within
the arcs. In particular, two compact sources in system 5, knots A and B, are
spatially-resolved on opposite sides of the critical curve (Fig. 2). The image
pair has a close angular separation to the critical curve of 0.08′′, implying
extremely high magnifications for each image and making it an ideal system in
the search for caustic crossing events. Our parametric model implies a
magnification of $\mu\approx 750$ for each image, whose critical curve for
this redshift passes between the two images, as expected. Magnification near
the critical curve is highly sensitive to systematics, and may vary
significantly between modeling approaches (Meneghetti et al., 2017).
Additionally, Meneghetti et al. (2017) demonstrated that the uncertainty in
magnification can reach greater than 30% at $\mu>10$ across all modeling
approaches. We compare our parametric approach with the free-form modeling
approach WSLAP+ which similarly finds very high magnification for these
images, agreeing to within 30%. Assuming these images are unresolved, this
could imply parsec or even subparsec sizes for this object. Given the arc’s
close proximity to the cluster center, however, microlensing from intracluster
stars could work to smooth out the critical curve, placing an upper limit on
the persistent magnification possible (Venumadhav et al., 2017; Dai, 2021).

Consider again the image pair consisting of knots A and B in Fig. 2. There is
a red knot offset from knot A that is detected only in some of the NIRCam
bands, called Tr. We present the argument that Tr is neither knot A nor knot
B. Assuming knots A and B are counter images, the pair will always be detected
together in any given band. Since the separation of these mirrored knots is
about 0.16′′, which is larger than the FWHM of any JWST filter in this dataset
(F444W, FWHM = 0.145′′, is the largest), JWST should be able to spatially
resolve this pair. We detect knots A and B in all the SW filters, but detect
only a single peak in each of the LW filters near to the position of knot A
(see appendix, section B). Since the image pair is not detected together
through the LW filters, this single peak must refer to Tr. Hence, Tr is
distinct from knots A and B. The lack of a counterimage, and its placement in
close proximity to the critical curve, suggest Tr is a microlensing event.
However we cannot rule out that it is a red foreground galaxy. Given the very
red colors and small angular sizes involved, confirmation of Tr as a transient
would require JWST follow-up observations. We note that there are no other
similar dual-color detections in any other objects in system 5 that would
suggest an image misalignment.

Figure 5: Projected mass density of SMACS0723. We show $\kappa$, the surface
mass density distribution in units of the critical density for strong lensing,
for the source redshift of system 1, at $z=1.45$.

The giant arcs also present some rather unusual features, such as system 2
with a spectroscopic redshift of $z$ = 1.38 first measured by Golubchik et al.
(2022). Image 2.2 has $>$10 prominent clumps all of a similar red color and
extending to high galactocentric radii (see Fig. 3, inset). While significant
sub-kpc structure of star formation regions is not unusual for star-forming
galaxies at $z=1-3$ (or even sub-100pc, e. g., Johnson et al. 2017), the very
large separations cast some doubt that the extended knots are identical in
nature to those in what might be the plane of a galactic disk. These clumps
also appear to be different (redder) than those typically detected in clumpy
galaxies (e. g., Shibuya et al., 2016). The physical characteristics are more
consistent with numerical predictions for globular clusters. For example,
Sameie et al. (2022) found in hydrodynamic simulations that the longest lived
globular clusters likely formed at high redshifts beyond the half-light radius
(up to hundreds of parsecs away from their host galaxy). Pozzetti et al.
(2019) go on to predict the color evolution for high redshift globular
clusters, but also point out that NIRCam colors are most likely insensitive to
the formation redshift. Vanzella et al. (2017) have reported detections of
candidate young ($<$10 Myr) globular clusters which are blue and at high
redshifts of $z$ = 3–6. Based on this information, it is tempting to speculate
that the clumps seen in system 2 may be redder and older ($\sim$Gyr)
counterparts of those young candidate globular clusters detected at the much
higher redshifts. Another possible explanation, red clumps fitting the
description of those seen in system 2 may arise as a result of ram pressure
stripping of dwarf galaxies in the dense environments near in projection to
its disk (e. g., Mayer et al., 2006; Boselli et al., 2022). Further follow-up,
such as detailed source plane reconstruction and photometric SED modeling, is
needed to uncover the nature of these sources.

A striking feature of this new JWST/NIRCam image is the morphology of the
baryonic component responsible for the intracluster light (ICL), which
exhibits a loop-like feature in the northwest component and a large lobe in
the southeast component, although some background noise can also be seen in
each of the four corners of the image due to unoptimized sky subtraction in
JWST reduction pipeline (Fig. 4). The ICL is due to stars stripped away from
their galaxies but still gravitationally bound to the cluster. Earlier work
has suggested that the ICL is a good tracer of the DM distribution (or vice-
versa) since both stars in the ICL and DM are expected to behave as
collisionless particles and thus respond only to gravity (Montes & Trujillo,
2018). The ICL in SMACS0723 extends beyond the current set of lensing
constraints but in combination with weak lensing derived from the JWST images
it should be possible to produce a lens model that covers the entire range of
the ICL in a way that gives insights as to the intriguing apparent correlation
between the ICL and the DM distribution. In particular, the presence of these
large-scale features in the ICL may motivate detailed simulations to examine
the merging scenarios that constrain the time since the major merger and
estimate the relative velocities involved.

We note that after this paper was submitted to the archive, and prior to
submission to ApJ, we have become aware of two other papers on SL modeling in
this field (Mahler et al., 2022; Caminha et al., 2022). There are some
differences in the results presented in these other papers, but we have
checked and found that including their results into our lens model does not
alter the results of this study.

##  5 Summary

We presented a new JWST parametric model for the massive cluster SMACS0723,
incorporating new multiple image family constraints identified in the JWST
press-release color image and in the NIRCam data set. Our model builds upon
the existing lens models (Golubchik et al., 2022) by increasing the SL
constraints with 14 newly identified image families, which represents a factor
of three improvement over the HST model. This parametric model has a large
impact because it provides a starting point for modeling SL clusters in the
era of JWST. The mass map reveals a somewhat complex and extended mass profile
and, in the detection of the image pair knots A and B opposite the critical
curve in system 5, also opens a route to the study of caustic transients in
the discovery of an apparent microlensed transient adjacent to knot A. The ICL
has a shape that is broadly-similar to that of the galaxies and the model, but
with rare larger-scale features that appear to retain the memory of its
dynamical history, a question which can be investigated further with numerical
simulations. In the future, spectroscopic and photometric redshifts will
bolster the reliability of our lens model, allowing also a more precise
placement of the critical curve needed to engage in caustic transient studies.

## acknowledgements

We wish to thank the RELICS and PEARLS collaborations for data products or
discussions that have stimulated this work, and of course the people behind
the JWST, its instruments and public release of this incredibly beautiful
first data set.

MP was funded through the NSF Graduate Research Fellowship grant No. DGE
1752814, and acknowledges the support of System76 for providing computer
equipment. BLF thanks Ori Ganor and the Berkeley Center for Theoretical
Physics for their hospitality during the writing of this paper. The BGU group
acknowledges support by Grant No. 2020750 from the United States-Israel
Binational Science Foundation (BSF) and Grant No. 2109066 from the United
States National Science Foundation (NSF), and by the Ministry of Science &
Technology, Israel. CC and NA acknowledge support from the European Research
Council (ERC) Advanced Investigator Grant EPOCHS (788113). J.M.D. acknowledges
the support of project PGC2018-101814-B-100 (MCIU/AEI/MINECO/FEDER, UE)
Ministerio de Ciencia, Investigación y Universidades and support by the
Agencia Estatal de Investigación, Unidad de Excelencia María de Maeztu, ref.
MDM-2017-0765.

This work is based on observations made with the NASA/ESA Hubble Space
Telescope (HST) and NASA/ESA/CSA James Webb Space Telescope (JWST) obtained
from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope
Science Institute (STScI), which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127
for JWST, and NAS 5–26555 for HST. These observations are associated with
program 14096 for HST, and 2736 for JWST. This work is also based on
observations made with ESO Telescopes at the La Silla Paranal Observatory
obtained from the ESO Science Archive Facility. The authors thank the Centre
for Astronomy and Particle Theory (CAPT) of University of Nottingham for
providing all computational infrastructure to run the JWST Reduction pipeline,
and Philip Parry for technical support. LF acknowledges financial support from
CAPES - Brazil. We also thank Anthony Holloway and Sotirios Sanidas at JBCA
for critical help with computer infrastructure that made this work possible.

This research made use of Astropy,333http://www.astropy.org a community-
developed core Python package for Astronomy (Astropy Collaboration et al.,
2013; Price-Whelan et al., 2018) as well as the packages NumPy (van der Walt
et al., 2011), SciPy (Virtanen et al., 2020), matplotlib (Hunter, 2007), and
some of the astronomy MATLAB packages (Ofek, 2014).

##  Appendix A Arc systems in SMACS0723

We present the list of all multiply-imaged systems below. The image families
are vetted in multiple ways: by their similar morphological components,
similar colors, similar redshifts (photometric and/or spectroscopic), and/or
consistency with the lens model. The IDs are given in the first column, where
the “?” indicates an image member candidate, by which we mean that it fails
one or more of the above criteria, or there is more than one candidate that
fits these criteria. The photometric redshift estimates, $z_{NIRCam}$, are
computed off of the six bands of NIRCam imaging using the SED fitting code
LePhare, as discussed in the main text. An entry has no $z_{NIRCam}$ value if
the lensed source was significantly contaminated by a stellar diffraction
spike, a bright cluster member galaxy or other projection effects, or if it
was too faint to be detected in two or more of the NIRCam bands. The model-
predicted redshifts, $z_{model}$ and $z_{NIRCam}$ agreed to within 1$\sigma$
in all but three cases. System 12 is an exception, for which
$z_{NIRCam}-z_{model}>5\sigma$, a difference that is noteworthy given that the
lensed image is relatively isolated, although faint and failing to be detected
in more than four bands. System 15 is another exception, for which
$z_{NIRCam}-z_{model}>3\sigma$. The system’s only image with a photometric
redshift, 15.2, is both relatively faint and located near the central BCG,
thereby contaminating the fainter background galaxy light. System 8 is the
last exception, for which $z_{model}\gg z_{NIRCam}$. Here image 8.1 fails to
meet the minimum filter bandpass requirement, image 8.2 has $z_{NIRCam}$
$\approx$ $0.73^{+0.18}_{-0.10}$ as well as a secondary peak at $z$ $\approx$
7, and image 8.3 has $z_{NIRCam}$ = 0.76${}^{+3.67}_{-0.06}$ and a secondary
peak at $z$ $\approx$ 4.5. These values are different from the lens-predicted
redshift of $z_{model}>4.67$. The difference may arise because this elongated
arc image has two peaks of different colors that are not well represented by
the 0.5” circular aperture imposed on these data. We also note that that the
lens models are limited by the arc systematics. Lens predictions may change as
image system constraints become improve, for example by the measurement of new
spectroscopic redshifts.

##  Appendix B Image Pair in System 5

Knots A and B of system 5 are counterimages which are situated opposite the
critical curve and thus likely highly magnified. As shown in Fig. 6, the image
pair appears in each of the SW filters and is spatially resolved, with an
angular separation of $\sim 0.16^{\prime\prime}$. In SW filter F200W, the
microlensed transient, Tr, is detected as well; it is bright and offset from
the position of knot A, resulting in the red knot seen in Fig. 2. In the LW
filters, the knots A and B drop out, leaving only the redder Tr visible as a
single peak.

Table 1: List of arc systems IDa | R.A | Decl. | $z_{NIRCam}^{b}$ | $z_{\mathrm{model}}$
---|---|---|---|---
| J2000.0 | J2000.0 |  |
1.1 | 07:23:21.8012 | -73:27:03.467 | 1.45c |
1.2 | 07:23:22.3430 | -73:27:17.077 | 1.45c |
1.3 | 07:23:21.4174 | -73:27:31.329 | 1.45c |
2.1 | 07:23:21.3288 | -73:27:03.369 | 1.38c |
2.2 | 07:23:21.8238 | -73:27:18.337 | 1.38c |
2.3 | 07:23:20.8184 | -73:27:31.378 | 1.38c |
3.1 | 07:23:19.3406 | -73:26:54.554 | – | 1.81 [1.65 – 1.91]
3.2 | 07:23:19.6709 | -73:27:18.562 | $1.09^{+0.04}_{-0.06}$ | ”
3.3 | 07:23:18.0861 | -73:27:34.507 | $1.50^{+0.02}_{-0.12}$ | ”
3.4 | 07:23:17.6180 | -73:27:17.238 | – | ”
4.1 | 07:23:13.3027 | -73:27:16.373 | $2.05^{+0.51}_{-0.95}$ | 2.02 [1.94 – 2.48]
4.2 | 07:23:13.7402 | -73:27:30.116 | $2.14^{+0.44}_{-0.88}$ | ”
4.3 | 07:23:15.2214 | -73:26:55.308 | $2.16^{+0.38}_{-0.93}$ | ”
5.1 | 07:23:17.7775 | -73:27:06.454 | 1.43c |
5.2 | 07:23:17.4012 | -73:27:09.692 | 1.43c |
5.3 | 07:23:17.0777 | -73:27:36.422 | 1.43c |
6.1 | 07:23:20.6382 | -73:27:06.170 | $0.47^{+0.38}_{-0.06}$ | 1.44 [1.27 – 2.02]
6.2 | 07:23:20.8642 | -73:27:10.805 | – | ”
6.3 | 07:23:20.2857 | -73:27:39.168 | $6.86^{+0.06}_{-0.04}$ | ”
7.1 | 07:23:10.9765 | -73:26:54.832 | – | 6.27 [2.95 – 8.38]
7.2 | 07:23:10.7520 | -73:26:56.676 | $4.78^{+0.10}_{-0.40}$ | ”
7.3 | 07:23:11.9016 | -73:26:49.389 | $4.79^{+0.11}_{-0.14}$ | ”
8.1 | 07:23:12.6279 | -73:27:36.552 | – | 5.93 ($>$ 4.67)
8.2 | 07:23:11.9399 | -73:27:19.101 | – |
8.3 | 07:23:15.1738 | -73:26:48.223 | – |
9.1 | 07:23:12.7404 | -73:27:17.641 | – | 2.90 [2.57 – 3.14]
9.2 | 07:23:13.2719 | -73:27:32.036 | $4.63^{+0.36}_{-0.42}$ | ”
9.3 | 07:23:15.0263 | -73:26:53.194 | $3.78^{+0.18}_{-0.68}$ | ”
10.1d | 07:23:17.6727 | -73:27:06.073 | $1.28^{+1.53}_{-0.32}$ |
10.2d | 07:23:17.2165 | -73:27:09.979 | – |
10.3d | 07:23:16.9616 | -73:27:36.214 | $2.69^{+0.13}_{-1.69}$ |
11.1 | 07:23:14.4676 | -73:27:21.001 | – | 1.66 [1.22 –1.98]
11.2 | 07:23:14.6783 | -73:27:25.882 | – | ”
12.1 | 07:23:17.3278 | -73:26:56.724 | – | 1.56 [1.52 – 1.71]
12.2 | 07:23:15.5468 | -73:27:15.540 | – | ”
12.3 | 07:23:16.2054 | -73:27:33.241 | $6.83^{+0.06}_{-0.11}$ | ”
13.1 | 07:23:19.1576 | -73:26:56.027 | – | 2.34 [2.29 – 2.77]
13.2 | 07:23:17.3314 | -73:27:14.825 | – | ”
13.3 | 07:23:17.6167 | -73:27:41.842 | $2.73^{+0.06}_{-1.60}$ | ”
13.4 | 07:23:19.8353 | -73:27:15.697 | – | ”
14.1d | 07:23:12.4242 | -73:27:29.857 | – | 1.83 [1.68 – 2.03]
14.2d | 07:23:12.4965 | -73:27:31.974 | – | ”
14.3d | 07:23:12.5821 | -73:27:32.465 | – | ”
15.1? | 07:23:16.7116 | -73:26:55.135 | – | 2.21 [1.67 –2.29]
15.2 | 07:23:14.7745 | -73:27:16.356 | $0.52^{+0.18}_{-0.07}$ | ”
15.3 | 07:23:15.4182 | -73:27:32.298 | – | ”
Table 1: Cont.

IDa | R.A | DEC. | $z$ | $z_{\mathrm{model}}$
---|---|---|---|---
| J2000.0 | J2000.0 |  |
16.1 | 07:23:16.9967 | -73:27:09.328 | – | 1.07 [0.82 –1.04]
16.2 | 07:23:16.9296 | -73:27:10.256 | – | ”
17.1d | 07:23:21.8176 | -73:27:41.814 | – | 1.31 [1.15 – 1.58]
17.2d | 07:23:22.4453 | -73:27:40.964 | $1.49^{+0.88}_{-0.13}$ | ”
17.3?d | 07:23:22.4781 | -73:27:41.727 | $1.49^{+0.88}_{-0.13}$ | ”
18.1 | 07:23:17.5975 | -73:27:20.571 | – | 1.72 [1.68 – 1.92]
18.2 | 07:23:17.7931 | -73:27:26.849 | – | ”
18.3 | 07:23:19.1779 | -73:26:50.524 | – | ”
19.1 | 07:23:17.2313 | -73:27:02.060 | – | 1.33 [1.24 – 1.37]
19.2 | 07:23:16.0440 | -73:27:13.482 | – |
19.3 | 07:23:16.3551 | -73:27:32.183 | – |
Einstein cross | 07:23:02.7975 | -73:27:08.814 |  |

aafootnotetext: The first five image systems are drawn from Golubchik et al.
(2022).

bbfootnotetext: These are the photometric redshift estimates using the six
bands of NIRCam imaging.

ccfootnotetext: These redshifts are spectroscopic values from Golubchik et al.
(2022).

ddfootnotetext: These systems were not used to constrain the parametric SL
model, but were confirmed in the WSLAP+ model.

Note. — _Column 1:_ ID; _Columns 2 & 3:_ Right Ascension and Declination;
_Column 4:_ Redshift. For systems 1, 2 and 5 we quote the spectroscopic
redshift from MUSE (Golubchik et al., 2022), and note that the NIRISS spectrum
for system 1 confirms the stated redshift. _Column 5:_ The redshift of the
system as predicted from the SL model. Candidate images whose identification
is not secure are marked with “?.” Note that these were therefore not used in
the minimization.

Figure 6: The image pair A and B of system 5 across all six available JWST
filters. In each filter we center on the positions of A and B with rings of
radius $0.16^{\prime\prime}$, which is roughly equal to their angular
separation. The F090W, F150W, F200W filters exhibit two separate knots
consistent with the marked positions of A and B. F200W, however, also shows
the bright source Tr that is slightly offset from the position of knot A. Only
a single peak is detected in each of the LW filters, which is also slightly
offset from the position of knot A. Since knot A and knot B are counterimages
of one another and must appear together, the Tr object seen in F200W and the
LW filters is instead understood to be a microlensing event.

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# Use of Transformer-Based Models for Word-Level Transliteration of the Book
of the Dean of Lismore

###### Abstract

The Book of the Dean of Lismore (BDL) is a 16th-century Scottish Gaelic
manuscript written in a non-standard orthography. In this work, we outline the
problem of transliterating the text of the BDL into a standardised
orthography, and perform exploratory experiments using Transformer-based
models for this task. In particular, we focus on the task of word-level
transliteration, and achieve a character-level BLEU score of 54.15 with our
best model, a BART architecture pre-trained on the text of Scottish Gaelic
Wikipedia and then fine-tuned on around 2,000 word-level parallel examples.
Our initial experiments give promising results, but we highlight the
shortcomings of our model, and discuss directions for future work.

Keywords: Low-Resource Neural Machine Translation, Transformer-Based Models,
Scottish Gaelic, Historical Manuscript

languageresourceLanguage Resources

Use of Transformer-Based Models for Word-Level Transliteration of the Book of
the Dean of Lismore

Edward Gow-Smith1, Mark McConville2, William Gillies3,
---
Jade Scott2, Roibeard Ó Maolalaigh2
1University of Sheffield, 2University of Glasgow, 3University of Edinburgh
<EMAIL_ADDRESS><EMAIL_ADDRESS>

Abstract content

## 1\. Introduction

As a material object, the Book of the Dean of Lismore (henceforth BDL) is a
manuscript consisting of 159 paper folios, thought to have been assembled
between 1512 and 1526 in eastern Perthshire, primarily by James MacGregor
(c.1480–1551), the vicar of Fortingall and titular Dean of St. Moluag’s
Cathedral on Lismore [Thomson (1993, 59–60]. It is believed to have been
acquired by James MacPherson, the Ossian ‘translator’, from a Portree
blacksmith around 1760, and was handed over to the Highland Society of
Scotland in 1803. It is now located in the National Library of Scotland
(Adv.MS.72.1.37).

As an information object, the BDL is primarily an eclectic collection of
traditional Gaelic poetry, including bardic, heroic and informal verse, by
diverse authors, both professional and amateur, Scottish and Irish. Perhaps
the most notable feature of the manuscript is that the Gaelic verse was not
written in the traditional, morphophonemic Gaelic system of orthography but
rather in a heterodox, semi-phonemic system based on the one used for writing
Scots at that time. Consider, for example, the following two versions of the
first line of p.128:

  * •

Ne wlli in teak mir a hest a zramm a der a weit trane

  * •

Ní bhfuil an t-éag mar a theist, a dhream adeir a bhith tréan

The first version is essentially the one that appears in BDL itself, and the
second is a reconstruction of how this would have been written in the
traditional Gaelic orthography of the time. Note the seventh word _hest_
:_theist_. The initial consonant in this word would have been pronounced as
the voiceless glottal fricative [h] and this is clearly reflected in the
Scots-based orthography. However, the reconstructed Gaelic _th_ includes a
representation of the underlying morphophoneme T which is associated with (at
least) two different phonemes – the fortis /t/ (written as _t_) and the lenis
/h/ (written as _th_). The vowel in the final word _trane_ :_tréan_ is another
example – the vowel here is the front mid [e:], represented in Scots
orthography using the discontinuous digraph _a_e_ and in Gaelic as the (non-
discontinuous) digraph _éa_.

Over the last 100 years, attempts have been made to transcribe some of the
poems in BDL (i.e. decode the handwriting) and then to transliterate these
into some version of traditional Gaelic orthography, e.g. [Quiggin (1937, Ross
(1939, Gillies (1977, Meek (1982]. However, until recently an internally
consistent transcription and transliteration of the full manuscript had not
been attempted. Since BDL is an indispensable part of the textual foundation
for the _Faclair na Gàidhlig_ project, which aims to create a comprehensive
dictionary of Scottish Gaelic on historical principles, this has now become a
priority. This paper reports on the first two phases of this work: (a) the
production of a consistent transcription of the full BDL; and (b) initial
experiments in constructing an automatic transliterator from the Scots-based
orthography into traditional Gaelic orthography using a small amount of
parallel training data.

## 2\. Data

The work on creating a consistent digital transcription of the whole of BDL
was undertaken by the third and fourth listed authors. The first phase of this
project involved digitally re-transcribing the manuscript transcription of BDL
produced by Rev. Walter McLeod in 1893, when the BDL folios were in better
physical condition than they are nowadays (NLS MS.72.3.12). Once this had been
completed, a second iteration involved comparing this digital transcription
with the handwriting in the BDL itself, in order to identify and correct any
apparent errors in McLeod’s manuscript. (We are grateful to NLS for providing
us with high-resolution digital images of both manuscripts.) In creating the
digital transcription, a standard set of Unicode character points was used to
encode non-ASCII glyphs in the BDL. In general, scribal contractions were not
expanded. Some light markup was included for scribal insertions and deletions,
and page and line numbers.

In order to provide some training data for our automatic transliterator, the
third listed author provided reconstructed ‘Dean’s Text’ transliterations for
twelve of the poems in the BDL. Due to the small amount of data available, we
decided to run experiments on word-level transliteration. Thus, the original
transcriptions and reconstructed transliterations were aligned, where
possible, at the word level. The majority of the data is word-to-word
transliterated, but there are some cases where one word in the BDL is
transliterated into multiple words in Scottish Gaelic, and vice versa, making
up 7.4% of the data. A discussion of the shortcomings of this approach is
given in Section 5.1. In total there were 1,962 examples, and 50 examples were
randomly selected to give eval and test sets.

## 3\. Experiments

We are interested in transliterating from the BDL to Scottish Gaelic
(henceforth referred to as bdl-gd) and vice versa (likewise referred to as gd-
bdl), although the first direction is of greater practical importance.
Character-level BLEU score [Papineni et al. (2002] is used as an evaluation
metric. We ran experiments on this task using Transformer-based models,
implemented in Fairseq [Ott et al. (2019]111We release our data and scripts
for running our experiments at
https://github.com/edwardgowsmith/transliteration-book-of-the-dean-of-
lismore.. For all experiments, tokenisation was performed at the character-
level. The maximum sequence length was set at 20, to cover all of the
available data whilst keeping computational requirements low. We also set the
batch size at 1 due to the limited size of the training data, and the known
problem of poor generalisation with large batch sizes [Keskar et al. (2016].
For all of our models, the best performing model (by epoch) on the eval set
was taken and evaluated on the test set. Full results are shown in Table 1,
and in the rest of this section we discuss the various models and approaches
used.

| bdl-gd | gd-bdl
---|---|---
Model | eval | test | eval | test
Transformer (tiny) | 35.32 | 41.16 | 30.17 | 46.26
BART (tiny) | 44.93 | 38.64 | 21.04 | 22.18
BART (base) | 58.68 | 53.32 | 36.17 | 30.15
BART (base) + p/t longer | 62.47 | 53.75 | 36.77 | 38.88
BART (base) + p/t longer + f/t longer | 59.46 | 52.09 | 36.94 | 34.68
BART (base) + p/t longer + homophones | 59.60 | 54.15 | 34.75 | 31.77
Table 1:  Character-level BLEU scores of the models on the eval and test
splits. Best results are shown in bold.

### 3.1. Parallel Data Only

Our first experiments were using just the available parallel data. We trained
a Transformer [Vaswani et al. (2017] architecture with 2 layers and 2
attention heads for the encoder and decoder, and an embed dimension of 64,
referred to as Transformer (tiny). We experimented with larger architectures,
but found they were unable to learn from the available data. Our model was
trained for 100,000 updates ($\sim$52 epochs), with a linear warm-up of the
learning rate for 4,000 updates to 5e-4, then a linear decay to zero. We used
the Adam optimizer [Kingma and Ba (2014] with $\epsilon=$1e-6,
$\beta=(0.9,0.98)$. On bdl-gd, this model achieved BLEU scores of 35.32 on the
eval set and 41.16 on the test set. On gd-bdl, this model achieved BLEU scores
of 30.17 on the eval set and 46.26 on the test set (Table 1).

### 3.2. Monolingual Pre-Training

The next approach was to utilise monolingual Scottish Gaelic data for the
task, so that the model would hopefully learn something of Scottish Gaelic
orthography. For this, we used the text of Scottish Gaelic
Wikipedia222https://gd.wikipedia.org/, split to the word level, giving
$\sim$600,000 words. We then pretrained BART [Lewis et al. (2019]
architectures with the denoising task on this data. We first implemented a
model with 2 layers, 2 attention heads, and embed dimension of 64 (referred to
as BART (tiny) in reference to the Transformer model). We trained this model
for 100,000 updates ($\sim$43 epochs). This model was then fine-tuned on the
parallel training data, with the same hyperparameters as for Transformer
(tiny). On bdl-gd, this model achieved BLEU score of 44.93 on the eval set,
performing better than Transformer (tiny), and 38.64 on the test set,
performing worse than Transformer (tiny). On gd-bdl, this model achieved BLEU
scores of 21.04 on the eval set and 22.18 on the test set (Table 1),
performing significantly worse than Transformer (tiny). It is expected that
pre-training on monolingual Scottish Gaelic data will not be of help in this
direction, but the significantly worse performance is surprising (see Section
4).

We next tried the default BART (base) architecture, consisting of 6 layers, 12
attention heads, and an embed dimension of 768. On bdl-gd, this model achieved
BLEU scores of 58.68 on the eval set and 53.32 on the test set, significantly
outperforming Transformer (tiny). On gd-bdl, this model achieved BLEU scores
of 36.17 on the eval set and 30.15 on the test set. We also ran the same model
with additional pretraining, up to 400,000 updates ($\sim$172 epochs), which
has been shown to be of benefit to other Transformer-based models [Liu et al.
(2019]. On bdl-gd, this model achieved BLEU scores of 62.47 on the eval set
and 53.75 on the test set, showing an increase in performance on both. On gd-
bdl, this model achieved BLEU scores of 36.77 on the eval set and 38.88 on the
test set, also showing an increase in performance on both (Table 1). We also
experimented with finetuning for longer (also 400,000 updates compared to
100,000), but this was found to lead to a general decrease in performance in
both directions, although it did improve the performance on the eval set for
gd-bdl (Table 1).

### 3.3. Data Augmentation

Next, approaches were taken at augmenting the available training data, a
common approach in low-resource neural machine translation [Haddow et al.
(2021]. Since we are interested in word-level transliteration, and thus a word
may be transliterated into a homophone of the provided example with a
different spelling (specifically, a heterograph), we took an approach to
augment the training data with homophones. We used IPA information for
Scottish Gaelic provided by English Wiktionary333https://en.wiktionary.org/ \-
the data was parsed in order to find homophones for words it the training
data. Unfortunately, IPA information was only available for a small number of
items, which increased the training data from 1,862 to 1,938 examples (an
increase of $\sim$4%). With the addition of this augmented training data, the
BLEU score of BART (base) on the eval set decreased (from 62.47 to 59.60), but
the BLEU score on the test set increased (from 53.75 to 54.15), which makes
sense as the introduction of heterographs should allow the model to generalise
better (although we note that the increase in performance is small).
Interestingly, this model performs significantly worse in the reverse
direction, with BLEU scores of 34.75 and 31.77 on the eval and test sets,
respectively (discussed in Section 4). It should be noted that this approach
assumes that heterographs in modern Scottish Gaelic were also heterographs at
the time of the BDL, which should be a valid assumption. An alternative
approach to augmenting the data would be to use a rule-based approach, which
we leave to future work.

## 4\. Discussion

In this section we discuss our results. From Table 1 we can see that, in
general, the performance on gd-bdl is significantly worse than that on bdl-gd.
This is to be expected, since the models have access to a large amount of
monolingual Scottish Gaelic (gd) data, but BDL (bdl) is effectively an unseen
language, which previous work has shown results in poor performance (see e.g.
?)). What is perhaps unexpected, however, is that our best-performing model on
bdl-gd, BART (base) + p/t longer + homophones, performs significantly worse
than the best in the opposite direction (31.77 compared to 46.26 on the test
set). In fact, our best-performing model on gd-bdl, Transformer (tiny), does
not use any monolingual Scottish Gaelic data. It seems likely that our models
are overfitting on the train and eval sets, as a result of their small sizes.
Attempts to avoid this could be made, including using multi-fold cross-
validation. Additionally, it is hoped that we will have access to more
parallel data in the future which will alleviate this problem, as well as the
variance of performance across the eval and test splits.

### 4.1. Error Analysis

In this section, we perform an error analysis by taking our best-performing
model and investigating which examples in the test set this model performed
worse on (by character-level BLEU score). These are shown in Table 2. We note
that these examples are relatively long; for shorter examples, our model
generally performs better, which is typically expected but likely exaggerated
in this case due to the increasing ambiguity of a word in the BDL as length
increases. We note that our model struggles with spaces: no space is added
when transliterating “eflay”, and a space is erroneously added when
transliterating “waiwill” (although the space is correctly removed when
transliterating “dwgis i”). Since examples containing spaces on either the
source or target side only make up a small amount of the parallel data, and
the pretraining data contains no spaces, this is an expected area of
difficulty, which we discuss further in Section 5.2. We also note that, out of
the seven examples here, our model appears to output only three true Scottish
Gaelic words (“mha fháil” meaning “if found”, “chuaiseach” meaning “cavities”,
and “mhíos” meaning “month”). This is not necessarily a problem, since we want
our model to be able to output unseen words, for example old-fashioned
spellings and proper nouns. However, contextual information may help to
determine the validity of a given transliteration, though the limited data
available may prove to limit the efficacy of such an approach. Interestingly,
the model transliterates “di” as the “[UNK]” token, which is problematic.

### 4.2. Learning of Scottish Gaelic Spelling Rules

We note that all of the outputs from our best model are _plausible_ words, in
that they obey the spelling rules of Scottish Gaelic. This is not the case for
the Transformer (tiny) model trained only on the parallel data — as an example
“dwgis” is transliterated by this model into “duigas”, which is not an
acceptable Scottish Gaelic word, since a medial consonant must be surrounded
by vowels of the same type [Gillies (2009]. This suggests that the training on
monolingual data has allowed our model to learn the rules of Scottish Gaelic
spelling, which has in turn improved performance on the transliteration task.

Input | Output | Reference
---|---|---
eflay | e’léamh | a’ phláigh
dwgis i | duise | dtugas-sa
chotlytsyt | chuaiseach | chodlas-sa
wawaill | mha fháil | bhfaghbha’il
deinar̄ | díonar | d’éinfhear
feanē | fén | phéin
zonicht | dhuanancht | dhona
di | [UNK] | do
gawe | gáimh | gabh
weißt | mhíos | bhíos
Table 2:  The ten examples that our best performing model performed worse on
for the test split (from bdl-gd).

## 5\. Future Directions

Our preliminary experiments have shown promise in the task of transliterating
the BDL, however there are many areas for improvement that we hope to address
in future work.

### 5.1. Whole Sequence Transliteration

Since our work here is on word-level transliteration, it is unclear how this
will extend to longer sequences, especially in the case of many-to-one
transliteration. We take an example of transliterating a whole sequence with
our model, shown in Table 3.

Input |  A wēnit za dwgis i grawġ
---|---
Output | a bhean dhá duis a’ grádh
Reference | A bhean dhá dtugas-sa grádh
Table 3:  Transliterating a whole sequence with our model.

In order to transliterate this whole sequence, we split it on whitespace and
then pass each word individually to the model. Since, in this case, “dwgis i”
is transliterated into a single word, our model cannot capture this (although
note that this model fails to correctly transliterate these two words anyway
(see Table 2)). An alternative approach to transliterating multi-word
sequences may therefore be needed. Currently, due to our models being set at a
max sequence length of 20, longer sequences cannot be directly given to the
model.

### 5.2. Handling of Spaces

A related problem is the tendency of the models to struggle with handling
spaces, both in the case of one-to-many and many-to-one transliteration. In
order to help with this problem, it is likely we will need to include examples
containing spaces during pre-training, or perform oversampling on the
available training data to balance the number of examples with spaces and
those without.

### 5.3. Data for Pre-Training

As stated in Section 3.2, we used data from Scottish Gaelic Wikipedia for
pretraining, which is written in standardised modern Scottish Gaelic. For the
purposes of our task, we are interested in generating transliterations which
are faithful to the pronunciation at the time of the BDL. Hence, other data
sources may provide more relevance for pre-training, such as Corpas na
Gàidhlig444https://dasg.ac.uk/corpus which contains transcribed texts dating
back to the 17th century, and this is a direction of future work.

## 6\. Related Work

There is no previous work, to the best of our knowledge, that uses
Transformer-based models for tasks involving Scottish Gaelic. However, such
approaches have been applied to other languages in the Celtic family:
multilingual BERT [Devlin et al. (2019] contains Irish, Welsh and Breton in
its training data, and there is a monolingual BERT for Irish [Barry et al.
(2021] which was shown to outperform multilingual BERT on a dependency parsing
test. There have been previous approaches at applying Transformer-based models
to the task of word-level transliteration. ?) applied the vanilla Transformer
to the NEWS 2015 shared task [Zhang et al. (2015], outperforming previous
models. ?) also applied various sizes of Transformer architectures to the task
of transliterating Hindi and Punjabi to English.

## 7\. Conclusion

In this paper we discuss approaches to training Transformer-based models on
the task of transliterating the Book of the Dean of Lismore (BDL) from its
idiosyncratic orthography into a standardised Scottish Gaelic orthography. In
particular, we outline our preliminary experiments training these models for
word-level transliteration using both parallel word-level transliteration data
for finetuning and monolingual Scottish Gaelic data for pretraining. Our best
performing model was able to achieve a character-level BLEU score of 54.15 on
the test set, showing significant promise, although there are many directions
for improvement and future work, including extending this work to sequence-
level (multi-word) transliteration.

## 8\. Acknowledgements

This work was supported by _Faclair na Gàidhlig_ and the Centre for Doctoral
Training in Speech and Language Technologies (SLT) and their Applications
funded by UK Research and Innovation [grant number EP/S023062/1].

## 9\. Bibliographical References

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