# The Type Ibn Supernova 2019kbj - Indications for Diversity in Type Ibn
Supernova Progenitors

Tom Ben-Ami Cavendish Laboratory, University of Cambridge, J. J. Thomson
Avenue, Cambridge, CB3 0HE, UK  The School of Physics and Astronomy, Tel Aviv
University, Tel Aviv 69978, Israel  Iair Arcavi The School of Physics and
Astronomy, Tel Aviv University, Tel Aviv 69978, Israel  CIFAR Azrieli Global
Scholars Program, CIFAR, Toronto, Canada  Megan Newsome  Department of
Physics, University of California, Santa Barbara, Santa Barbara, CA
93106-9530, USA  Las Cumbres Observatory, 6740 Cortona Dr Ste 102, Goleta, CA
93117-5575, USA  Joseph Farah  Department of Physics, University of
California, Santa Barbara, CA 93106-9530, USA  Las Cumbres Observatory, 6740
Cortona Dr Ste 102, Goleta, CA 93117-5575, USA  Craig Pellegrino Department of
Physics, University of California, Santa Barbara, CA 93106-9530, USA  Las
Cumbres Observatory, 6740 Cortona Dr Ste 102, Goleta, CA 93117-5575, USA
Giacomo Terreran  Department of Physics, University of California, Santa
Barbara, CA 93106-9530, USA  Las Cumbres Observatory, 6740 Cortona Dr Ste 102,
Goleta, CA 93117-5575, USA  Jamison Burke  Department of Physics, University
of California, Santa Barbara, CA 93106-9530, USA  Las Cumbres Observatory,
6740 Cortona Dr Ste 102, Goleta, CA 93117-5575, USA  Griffin Hosseinzadeh
Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson,
AZ 85721-0065, USA  Curtis McCully  Las Cumbres Observatory, 6740 Cortona Dr
Ste 102, Goleta, CA 93117-5575, USA  Daichi Hiramatsu Center for Astrophysics,
Harvard & Smithsonian, 60 Garden Street, Cambridge, Ma 02138, USA  The NSF AI
Institute for Artificial Intelligence and Fundamental Interactions, USA
Estefania Padilla Gonzalez Department of Physics, University of California,
Santa Barbara, CA 93106-9530, USA  Las Cumbres Observatory, 6740 Cortona Dr
Ste 102, Goleta, CA 93117-5575, USA  D. Andrew Howell  Department of Physics,
University of California, Santa Barbara, CA 93106-9530, USA  Las Cumbres
Observatory, 6740 Cortona Dr Ste 102, Goleta, CA 93117-5575, USA Iair Arcavi
<EMAIL_ADDRESS>
###### Abstract

Type Ibn supernovae (SNe) are a rare class of stellar explosions whose
progenitor systems are not yet well determined. We present and analyze
observations of the Type Ibn SN 2019kbj, and model its light curve in order to
constrain its progenitor and explosion parameters. SN 2019kbj shows roughly
constant temperature during the first month after peak, indicating a power
source (likely interaction with circumstellar material) that keeps the
continuum emission hot at $\sim 15,000$ K. Indeed, we find that the
radioactive decay of 56Ni is disfavored as the sole power source of the
bolometric light curve. A radioactive decay + circumstellar-material (CSM)
interaction model, on the other hand, does reproduce the bolometric emission
well. The fits prefer a uniform-density CSM shell rather than CSM due to a
steady mass-loss wind, similar to what is seen in other Type Ibn SNe. The
uniform-density CSM shell model requires $\sim 0.1M_{\odot}$ of 56Ni and $\sim
1M_{\odot}$ total ejecta mass to reproduce the light curve. SN 2019kbj differs
in this manner from another Type Ibn SN with derived physical parameters, SN
2019uo, for which an order of magnitude lower 56Ni mass and larger ejecta mass
were derived. This points toward a possible diversity in SN Ibn progenitor
systems and explosions.

Supernovae (1668), Core-collapse supernovae (304), Massive Stars (732)

[en-GB]ord=raise

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##  1 Introduction

Type Ibn supernovae (SNe) are a rare class of stellar explosions characterized
by a lack of hydrogen lines and the presence of narrow He I emission lines in
their spectra (Pastorello et al., 2007). These events are thought to be SNe
strongly interacting with H-poor, helium-rich circumstellar material (CSM;
e.g. Smith, 2016, and references therein). Only a few dozen of such events are
known (see Pastorello et al., 2016; Hosseinzadeh et al., 2017, for recent
compilations), and their progenitor systems remain a mystery.

The H-rich analogs of Type Ibn events, (i.e. explosions interacting with a
H-rich CSM), known as Type IIn SNe, show slowly evolving and diverse light
curves (e.g. Kiewe et al., 2012). These traits are explained by the fact that
CSM interaction injects extra luminosity through shocks, producing the
observed prolonged emission, while diverse CSM density distributions produce
the observed diversity in light-curve shapes. However, Hosseinzadeh et al.
(2017) showed that many type Ibn SN light curves are strikingly similar and
rapidly evolving, in contrast to the expectations from CSM-interaction-powered
emission (but see also outliers to this uniformity discussed in Pastorello et
al. 2016).

Even more puzzling is the discovery of a Type Ibn SN in a brightest cluster
galaxy (Sanders et al., 2013), specifically in an environment with extremely
low star formation, leading Hosseinzadeh et al. (2019) to conclude that some
(if not all) Type Ibn SNe might not even be explosions of massive stars, as
typically assumed.

Possible clues as to the progenitors of Type Ibn SNe can come from modeling
their bolometric light curves. Gangopadhyay et al. (2020) fit the bolometric
light curve of the Type Ibn SN 2019uo with the Chatzopoulos et al. (2012)
model that includes luminosity from both 56Ni decay and CSM interaction (after
disfavoring 56Ni decay as the sole power source). Their best fits require
$\sim 16M_{\odot}$ of ejecta and just $0.01M_{\odot}$ of 56Ni, with most of
the luminosity at peak coming from interaction of the ejecta with a few tenths
of a solar mass of CSM. They favor a uniform-density shell, rather than a
steady wind, for the distribution of the CSM. Pellegrino et al. (2022), on the
other hand, find a much smaller ejecta mass ($\sim 1M_{\odot}$) for the same
event, while finding a similar 56Ni mass, using the same models.

Here we present observations of SN 2019kbj, a well-observed member of the Type
Ibn class, with multiband photometry and multiepoch spectroscopy. We analyze
its light curve and spectra and model its bolometric light curve in a similar
way to that of Gangopadhyay et al. 2020 for SN 2019uo to deduce its physical
parameters. With this analysis we aim to increase the sample of Type Ibn
events with deduced physical parameters. We assume the Planck18 (Planck
Collaboration et al., 2020) cosmology throughout.

Table 1: Photometry of SN 2019kbj.

MJD | Filter | Magnitude | Error | Source
---|---|---|---|---
58663.49 | $c$ |  $<$19.89 |  | ATLAS
58665.49 | $o$ | 18.38 | 0.080 | ATLAS
58665.50 | $o$ | 18.17 | 0.078 | ATLAS
58665.50 | $o$ | 18.27 | 0.067 | ATLAS
58665.51 | $o$ | 18.14 | 0.059 | ATLAS
58667.46 | $c$ | 17.60 | 0.033 | ATLAS
58667.48 | $c$ | 17.64 | 0.034 | ATLAS
58667.50 | $c$ | 17.61 | 0.033 | ATLAS
58667.50 | $c$ | 17.55 | 0.028 | ATLAS
58668.39 | $B$ | 17.44 | 0.018 | Las Cumbres
58668.39 | $B$ | 17.36 | 0.009 | Las Cumbres
58668.40 | $V$ | 17.55 | 0.013 | Las Cumbres
58668.40 | $V$ | 17.55 | 0.013 | Las Cumbres
58668.40 | $g$ | 17.30 | 0.006 | Las Cumbres
58668.40 | $g$ | 17.30 | 0.006 | Las Cumbres

Note. — This table is published in its entirety in machine-readable format. A
portion is shown here for guidance regarding its form and content.

##  2 Discovery and Classification

SN 2019kbj was discovered on 2019 July 1 (UT used throughout) by the Asteroid
Terrestrial-impact Last Alert System (ATLAS; Tonry et al., 2018) transient
survey (Smith et al., 2020) as ATLAS19ohl (Tonry et al., 2019), at R.A.
01:00:39.619 and decl. +19:37:03.5 (J2000)111The event was independently
discovered on 2019 July 27 by the Panoramic Survey Telescope And Rapid
Response System (Pan-STARRS; Chambers et al., 2016) as PS19dzw.. A faint
(absolute magnitude $\sim-17$) and blue host galaxy is seen in archival PS1
images (Flewelling et al., 2020) at this position.

The event was initially classified on 2019 July 3 by Hiramatsu et al. (2019)
as a possible young Type II SN at a redshift of $z=0.048$, based on the strong
blue continuum, narrow H emission, and possible early flash-spectroscopy
features (short-lived high-ionization emission lines indicative of a confined
CSM; e.g. Khazov et al., 2016). However, it was later reclassified by Arcavi
et al. (2022) as a Type Ibn SN based on narrow He I emission lines (and a lack
of broad H features) seen in a spectrum taken one week later (the narrow H
emission being attributed to the host galaxy rather than the SN). The redshift
remained unrevised.

Table 2: Log of spectroscopic observations. Date | MJD | Phase | Telescope
---|---|---|---
|  | ($days$) |
2019-07-02 | 58666.68 | $-2.42$ | FTS 2m
2019-07-03 | 58667.49 | $-1.61$ | FTN 2m
2019-07-04 | 58668.43 | $-0.68$ | FTN 2m
2019-07-10 | 58674.43 | $5.32$ | FTN 2m
2019-07-13 | 58677.57 | $8.47$ | FTN 2m
2019-07-15 | 58679.52 | $10.42$ | FTN 2m
2019-07-18 | 58682.48 | $13.38$ | FTN 2m
2019-07-24 | 58688.56 | $19.45$ | FTN 2m
2019-07-28 | 58692.47 | $23.36$ | FTN 2m
2019-08-05 | 58700.52 | $31.41$ | FTN 2m
2019-08-09 | 58704.53 | $35.43$ | FTN 2m
2022-05-23 | 59722.52 | Host | FTN 2m
Figure 1: Extinction-corrected multiband light curve of SN 2019kbj. Vertical
red lines at the top indicate days when spectra were obtained. The arrow
indicates the last nondetection $5\sigma$ limit.

##  3 Observations and Data Reduction

We obtained $BVgri$-band imaging of SN 2019kbj with the Las Cumbres
Observatory (Brown et al., 2013) Sinistro cameras mounted on the network of
1-meter telescopes at the Cerro Tololo Inter-American Observatory (Chile), the
South African Astronomical Observatory (South Africa), the Siding Spring
Observatory (Australia), and the McDonald Observatory (United States), through
the Global Supernova Project, from 2019 July 4 to 2019 September 20. Reference
images were obtained on 2021 December 31, long after the SN faded. Standard
image-reduction procedures were applied by the Las Cumbres Beautiful
Algorithms to Normalize Zillions of Astronomical Images (BANZAI)
pipeline222https://github.com/LCOGT/banzai (McCully et al., 2018). We then
performed image subtraction and point-spread function (PSF) fitting using the
PyRAF-based lcogtsnpipe333https://github.com/LCOGT/lcogtsnpipe pipeline
(Valenti et al., 2016), which uses the High Order Transform of PSF ANd
Template Subtraction (HOTPANTS; Becker, 2015) implementation of the Alard &
Lupton (1998) algorithm. $BV$-band magnitudes are calibrated to the Vega
system, and $gri$-band magnitudes to the AB system. We also obtained $c$\- and
$o$-band host-subtracted photometry of SN 2019kbj from the ATLAS Forced
Photometry Server444https://fallingstar-data.com/forcedphot/ (Tonry et al.,
2018; Smith et al., 2020). We find the last pre-explosion ATLAS 5$\sigma$
nondetection limit to be on 2019 June 29 at a magnitude of $19.89$ in the $c$
band, constraining the explosion time to a window of only $2$ days between
2019 June 29 and 2019 July 1.

We downloaded images of SN 2019kbj taken by the Ultraviolet Optical Telescope
(UVOT; Roming et al. 2005) on board the Neil Gehrels Swift Observatory
(Gehrels et al., 2004), obtained under a Target of Opportunity request (PI:
Hiramatsu), from the High Energy Astrophysics Science Archive Research Center
(HEASARC)555https://heasarc.gsfc.nasa.gov/. We performed aperture photometry
with a 5$\arcsec$-radius circular region using the uvotsource package in
HEAsoft v6.18, with version 20200925 of the calibration database (CALDB),
following the standard guidelines from Brown et al. (2009). Host flux
subtraction was performed using images taken on 2022 April 12 (PI: Grupe),
long after the SN faded, following the prescriptions of Brown et al. (2014).

Table 3: Post-peak luminosity decline rates of SN 2019kbj in magnitudes per day. These values are typical for Type Ibn SNe. | $B$ | $g$ | $V$ | $o$ | $r$ | $i$
---|---|---|---|---|---|---
Decline rate | 0.099 | 0.078 | 0.092 | 0.083 | 0.12 | 0.091
Error | 0.003 | 0.031 | 0.003 | 0.006 | 0.004 | 0.005
Figure 2: Absolute magnitude $r$-band light curve of SN 2019kbj (black
circles) compared to $r$ and $R$-band light curves of other Type Ibn SNe and
the Type Ibn SN $r$-band template (shaded region) from Hosseinzadeh et al.
(2017). SN 2019kbj fits well within the population of Ibn SNe. The data for
ASASSN-14ms are taken from Wang et al. (2021), PTF11rfh, iPTF15ul, iPTF15akq,
iPTF14aki and SN 2015U from Hosseinzadeh et al. (2017), OGLE12-006 from
Pastorello et al. (2015b), PS1-12sk from Sanders et al. (2013), SN 2000er and
SN 2002ao from Pastorello et al. (2008a), SN 2005la from Pastorello et al.
(2008b), SN 2006jc from Pastorello et al. (2007, 2008a), SN 2010al and SN
2011hw from Pastorello et al. (2015a), SN2014av and SN 2014bk from Pastorello
et al. (2016), SN 2015G from Foley et al. (2015) and SN 2019uo from
Gangopadhyay et al. (2020).

We correct all photometry for Milky Way extinction using the Schlafly &
Finkbeiner (2011) calibrations of the Schlegel et al. (1998) maps, retrieved
via the NASA/IPAC Extragalactic Database
(NED)666https://ned.ipac.caltech.edu/. For the ATLAS $c$ and $o$ bands we use
extinction data for the $g$ and $r$ bands, respectively. We neglect extinction
in the SN host galaxy, as we find no evidence for strong Na I D absorption in
a spectrum taken of the host (see below). Our photometry is presented in Table
1 and in Figures 1–3.

We obtained 12 spectroscopic observations with the Las Cumbres Observatory
Floyds spectrographs mounted on the 2-meter Faulkes Telescope North (FTN) and
South (FTS) at Haleakala (United States) and Siding Spring (Australia)
observatories, respectively, through the Global Supernova Project. Spectra
were obtained through a 2″ slit placed on the SN along the parallactic angle
(Filippenko, 1982). One-dimensional spectra were extracted, and flux and
wavelength calibrated using the
floyds_pipeline777https://github.com/LCOGT/floyds_pipeline (Valenti et al.,
2013). One of the spectra is of the host galaxy, obtained long after the SN
faded. A log of the spectroscopic measurements is given in Table 2. All SN
spectra are presented in Figure 4. The host spectrum is presented in Figure 6.

##  4 Photometric Analysis

The multiband light curve of SN 2019kbj is shown in Figure 1. Using a
parabolic fit to the $r$-band data around peak (from MJD 58668.4 to 58677.1),
we determine the peak date to be MJD $58670.1\pm 0.26$, with an apparent peak
magnitude of $17.67\pm 0.24$, corresponding to an absolute peak magnitude of
$-18.99\mathbf{\pm 0.24}$ (errors are from the parabolic fit).

We calculate the post-peak decline rate using a linear fit to the magnitudes
between MJD $58670$ and $58700$ for each band (except the $c$ band for which
there are not enough epochs). Our results are presented in Table 3. We find a
decline rate in all bands similar to the typical $r$-band 0.1 mag day-1
measured for Type Ibn SNe by Hosseinzadeh et al. (2017).

Comparing the $r$-band light curve of SN 2019kbj to those of other Type Ibn
SNe (Fig. 2), we find that it is rather typical and fits well within the
template of Hosseinzadeh et al. (2017) around peak. SN 2019kbj shows excess
emission compared to the template starting at around 20 days after peak,
perhaps due to a larger amount of 56Ni compared to other events (see below).

The color evolution of SN 2019kbj is shown in Figure 3. Both its $B-r$ and
$B-V$ colors are roughly constant, as seen also in other Type Ibn SNe. SN
2019kbj is one of the bluest Ibn’s in the sample.

Figure 3: The color evolution of SN 2019kbj (black circles) compared to other
Type Ibn SNe. SN 2019kbj shows constant colors, as do some other Type Ibn SNe.
Colors, symbols and data sources are as in Figure 2.

##  5 Spectroscopic Analysis

Figure 4: Left: The spectral evolution of SN 2019kbj. Prominent spectral lines
and days relative to peak luminosity are noted. Right: The spectrum of SN
2019kbj 5.3 days after peak compared to other Type Ibn SNe at similar phases
(noted in days relative to peak).
---
Figure 5: The He I $5015\text{\AA}$ and $5047\text{\AA}$ blend (dashed black
lines) in SN 2019kbj, compared to other Type Ibn SNe, at various epochs. The
top axis denotes the velocity relative to $5015\text{\AA}$. All spectra are
continuum subtracted. For each epoch, only spectra taken ±5 days compared to
the phase of the spectra of SN 2019kbj are compared. The light blue dashed
line denotes the O III 5007Å line (which we attribute to the host galaxy).

The spectroscopic evolution of SN 2019kbj is shown in the left panel of Figure
4. A blue continuum is seen in the early spectra, with no prominent flash-
spectroscopy features. However, our earliest spectrum was obtained 2.41 days
before peak, which is later than when flash features were observed in other
Type Ibn events. In SN 2019uo (Gangopadhyay et al., 2020) prominent flash
features were seen only up to 3.7 days before peak, while in SN 2010al
(Pastorello et al., 2015a) flash features were seen 8 days before peak and
disappeared four days later. Since our earliest spectrum is later than these
times, we cannot rule out the existence of flash features for SN 2019kbj.

Prominent narrow He I emission lines can be seen throughout the evolution,
together with Si II, Mg I and Ca II lines, which are seen in other Type Ibn
SNe as well (right panel of Figure 4). A very prominent He I blend at $5015$
and $5047\text{\AA}$ develops shortly after peak. This blend is also seen in
some other Type Ibn SNe (Fig. 5). It appears after peak, and at later times
the $5047\text{\AA}$ component disappears. The $5015\text{\AA}$ component is
further blended with O III $5007\text{\AA}$ which we attribute to the
underlying host galaxy (Fig. 6).

Figure 6: A spectrum of the SN host galaxy taken after the SN faded. Narrow
H$\alpha$ and O III, seen in also in the spectra taken while the SN was
active, are present here and thus attributed to the host galaxy. No strong Na
I D absorption is detected, indicating little or no host-galaxy extinction.

Narrow H$\alpha$ emission is also seen in all epochs. This feature may be from
the host galaxy or from H in the CSM surrounding the SN progenitor. Here, we
attribute the narrow H$\alpha$ emission to the host galaxy for a few reasons.
First, it becomes stronger relative to other features as the SN fades.
Additionally, it is seen in our host-galaxy spectrum (Fig. 6) and as an
extended feature in the two-dimensional spectra of our SNe (an example two-
dimensional spectrum is shown in Figure 7). Since the host and SN spectra were
each taken under different seeing conditions and with different slit
orientations, it is not possible to accurately isolate the amount of H$\alpha$
or O III emission contributed by the host galaxy to each SN spectrum.
Therefore, we can neither robustly associate nor rule out an association of a
small amount of H$\alpha$ or O III with the SN.

Figure 7: The H$\alpha$ region of the two-dimensional calibrated spectrum of
SN 2019kbj taken on 2019 August 09, with the wavelength axis along the
horizontal direction and the spatial axis along the vertical direction. The
H$\alpha$ line, marked with yellow arrows, is adjacent to a sky line but can
be clearly seen as an extended emission feature. We thus attribute it to the
host galaxy.

We measure expansion velocites from the He I $5876$, $6678$, and
$7065\textrm{\AA}$ lines as was done for SN 2019uo by Gangopadhyay et al.
(2020). We first normalize the spectra with a parabolic fit to the continuum
and then model each He P Cygni absorption line with a Gaussian. The offset
between the best-fit Gaussian center and the line rest-frame wavelength is
then translated to an expansion velocity. Our results are shown in Figure 8.
All lines show expansion velocities of a few $10^{3}$ km s-1 which increase
with time during the first $\sim$30 days after peak. This is the same behavior
seen in the sample of Ibn SNe analyzed by Gangopadhyay et al. (2020) and
references therein.

Figure 8: He I expansion velocities measured from the P-cygni minima of each
line. These velocities and their time evolution are similar to those seen in
other Type Ibn SNe (Gangopadhyay et al., 2020, and references therein).

##  6 Light-curve Modeling

###  6.1 Blackbody Fits and Bolometric Light Curve

We fit the spectral energy distribution of each epoch to a blackbody using a
Markov Chain Monte Carlo (MCMC) routine implemented via the
lightcurve_fitting888https://github.com/griffin-h/lightcurve_fitting Python
library (Hosseinzadeh & Gomez, 2020). We include only epochs with at least
three distinct bands observed within one day and bin data taken within less
than one day of each other. The best-fit blackbody temperature and radius for
each epoch, together with the resulting bolometric luminosity, are presented
in Figure 9 and Table 4. As expected from the roughly constant colors, the
temperature is seen to be roughly constant at $\sim$15,000 K out to about a
month after peak luminosity. These temperatures are low enough that we do not
have to limit ourselves to epochs with ultraviolet coverage to ensure we are
correctly sampling the blackbody spectrum (Arcavi, 2022).

We add a bolometric epoch prior to peak where we only have the single $o$-band
discovery detection, assuming the measured constant temperature can be
extrapolated backward to that epoch. We assume a temperature of $14,984\pm
650$ K (the average temperature and its standard deviation from all subsequent
epochs) to calculate a bolometric correction for the $o$-band data point using
the synphot999https://github.com/spacetelescope/synphot_refactor.git package
(STScI Development Team, 2018). This epoch is presented with an empty symbol
in Figures 9–11.

Table 4: Results of blackbody fits to the photometry of SN 2019kbj.

| Phase | Temperature | Radius | Luminosity
---|---|---|---|---
| ($days$) | ($K$) | ($10^{14}cm$) | ($10^{43}erg\,s^{-1}$)
| -3.61 | $14984_{-650}^{+650}$ | $5.98_{-0.24}^{+0.26}$ | $1.285_{-0.245}^{+0.250}$
| -0.7 | $13824_{-80}^{+89}$ | $11.89_{-0.09}^{+0.09}$ | $3.681_{-0.103}^{+0.110}$
| 0.26 | $12626_{-355}^{+411}$ | $13.04_{-0.98}^{+0.93}$ | $3.080_{-0.579}^{+0.594}$
| 1.26 | $16047_{-274}^{+282}$ | $9.76_{-0.19}^{+0.19}$ | $4.499_{-0.353}^{+0.361}$
| 2.0 | $13630_{-178}^{+179}$ | $10.89_{-0.26}^{+0.25}$ | $2.915_{-0.205}^{+0.205}$
| 3.21 | $13248_{-135}^{+138}$ | $11.43_{-0.17}^{+0.18}$ | $2.867_{-0.145}^{+0.148}$
| 4.98 | $15823_{-384}^{+369}$ | $8.91_{-0.22}^{+0.25}$ | $3.542_{-0.386}^{+0.385}$
| 6.68 | $14771_{-353}^{+408}$ | $9.11_{-0.29}^{+0.28}$ | $2.813_{-0.322}^{+0.354}$
| 8.0 | $13478_{-271}^{+310}$ | $9.01_{-0.26}^{+0.24}$ | $1.907_{-0.188}^{+0.203}$
| 9.13 | $17336_{-737}^{+803}$ | $6.35_{-0.30}^{+0.31}$ | $2.591_{-0.505}^{+0.542}$
| 10.21 | $17143_{-634}^{+689}$ | $6.13_{-0.25}^{+0.26}$ | $2.313_{-0.391}^{+0.420}$
| 13.22 | $18728_{-1388}^{+1828}$ | $4.85_{-0.42}^{+0.40}$ | $2.063_{-0.710}^{+0.875}$
| 17.6 | $19587_{-1451}^{+2083}$ | $3.85_{-0.36}^{+0.32}$ | $1.557_{-0.544}^{+0.710}$
| 19.26 | $18411_{-1496}^{+1876}$ | $3.46_{-0.32}^{+0.33}$ | $0.983_{-0.367}^{+0.441}$
| 20.32 | $19027_{-1822}^{+2119}$ | $3.52_{-0.35}^{+0.39}$ | $1.154_{-0.499}^{+0.574}$
| 24.11 | $9946_{-304}^{+287}$ | $6.92_{-0.37}^{+0.38}$ | $0.334_{-0.054}^{+0.053}$
| 28.31 | $11602_{-996}^{+1330}$ | $4.67_{-0.68}^{+0.70}$ | $0.282_{-0.127}^{+0.154}$
| 32.33 | $10719_{-1083}^{+1517}$ | $4.49_{-0.79}^{+0.82}$ | $0.189_{-0.102}^{+0.128}$
| 36.28 | $13775_{-3247}^{+5326}$ | $2.88_{-1.00}^{+1.32}$ | $0.213_{-0.250}^{+0.383}$
|  |  |  |

Note. — For the first epoch, where only one band is available, we assume the
temperature to be equal to the average temperature during the rest of the
evolution, and use our single-band data at that epoch to constrain the radius
and hence bolometric luminosity there.

Figure 9: The blackbody temperature, radius, and inferred bolometric
luminosity of SN 2019kbj. For the first epoch (empty symbol), where only one
band is available, we assume the temperature to be equal to the average
temperature during the rest of the evolution, and use our single-band data at
that epoch to constrain the radius and hence bolometric luminosity there. The
unbinned data are shown in black semitransparent points.

###  6.2 Modeling the Bolometric Light Curve

We fit the bolometric light curve of SN 2019kbj to two models: the radioactive
decay model from Arnett (1982), Valenti et al. (2007), and Chatzopoulos et al.
(2012), and the radioactive decay model with additional CSM-interaction power
from Chevalier (1982) and Chatzopoulos et al. (2012). Each model is fit to the
data using the
Bolometric_Modelling101010https://github.com/Tomariebenami/Bolometric_Modelling
module (Ben-Ami, 2022).

####  6.2.1 Radioactive Decay Model

The radioactive decay model assumes that the bolometric luminosity is powered
solely by the radioactive decay of 56Ni to 56Co to 56Fe with $\gamma$-ray
leakage taken into consideration (Valenti et al., 2007; Chatzopoulos et al.,
2012). The luminosity is given by

$\displaystyle L(t)$ $\displaystyle=$
$\displaystyle\frac{M_{Ni}}{t_{m}}e^{\frac{t}{t_{m}}}$ (1)
$\displaystyle\times$
$\displaystyle\left[\left(\epsilon_{Co}-\epsilon_{Ni}\right)\int_{0}^{x}B(z)\,dz+\epsilon_{Co}\int_{0}^{x}C(z)\,dz\right]$
$\displaystyle\times$ $\displaystyle\left(1-e^{At^{-2}}\right)$

where the free parameters are the ejecta mass $M_{ej}$, the 56Ni mass
$M_{Ni}$, the characteristic ejecta velocity $v_{ej}$, and the optical opacity
$\kappa_{opt}$ (we also fit for the explosion time relative to the peak,
$t_{0}$). $\epsilon_{Ni}=3.90\times 10^{9}$ erg s-1 g-1 and
$\epsilon_{Co}=6.78\times 10^{9}$ erg s-1 g-1 are the energy-generation rates
of the decays of 56Ni and 56Co respectively (Sutherland & Wheeler, 1984;
Cappellaro et al., 1997). The integrands $B(z)=2ze^{-2zy+z^{2}}$ and
$C(z)=2ze^{-2zy+2zs+z^{2}}$ are the luminosity outputs of the decays of 56Ni
and 56Co, with $y=t_{m}/2\tau_{Ni}$ and
$s=t_{m}(\tau_{Co}-\tau_{Ni})/(2\tau_{Co}\tau_{Ni})$. Both integrals are
evaluated up to $x=t/t_{m}$ with

$t_{m}=\left(\frac{\kappa_{opt}}{\beta
c}\right)^{1/2}\left(\frac{20M_{ej}^{2}}{3v_{ej}^{2}}\right)^{1/4}$ (2)

defined as the light curve timescale, and $\tau_{Ni}=8.8$ days and
$\tau_{Co}=111.3$ days the respective decay lifetimes (e.g. Nadyozhin, 1994).
Finally,

$A=\frac{3\kappa_{\gamma}M_{ej}}{4\pi v_{ej}^{2}}$ (3)

is the $\gamma$-ray leakage factor. We set the $\gamma$-ray opacity,
$\kappa_{\gamma}$, to $0.027$ cm2g-1 following Swartz et al. (1995) and
Cappellaro et al. (1997).

We use the MCMC fitting method, implemented through the emcee package
(Foreman-Mackey et al., 2013), with 500 burn-in steps, followed by 8,000
fitting steps with 150 walkers. We limit the 56Ni mass to be less than the
total ejecta mass and use a very broad ejecta velocity ($v_{ej}$) prior, since
otherwise the fit prefers an unphysical solution with more 56Ni than total
ejecta mass (see Table 9 in Appendix B.1; a similar result was obtained for
the extremely luminous Ibn SN ASASSN-14ms by Vallely et al. 2018 and Wang et
al. 2021).

Our fit is shown in Figure 10 and the best-fit parameters are given in Table
5. The corner plot of the fit is shown in Figure 13 in Appendix B. Although we
find a reasonable fit to the data, it requires a very high ejecta velocity (of
order 60,000 km s-1), which is not typically seen in any type of SN. In
addition, it requires a large 56Ni mass of $\sim$0.8 $M_{\odot}$, which is
also not typical of core-collapse SNe. The ejecta mass remains unconstrained
within the prior bounds. We conclude that radioactive decay is disfavored as
the sole power source of the light curve of SN 2019kbj.

Given the long-lived blue continuum and narrow He lines in Type Ibn SNe, CSM
interaction is a most likely additional source of power.

Figure 10: Radioactive decay model (100 lines, chosen at random from the MCMC walker distribution) compared to the bolometric light curve of SN 2019kbj (binned data in opaque points, unbinned data in semitransparent points). Table 5: Best-fit parameters for the radioactive decay model. $M_{Ni}$ | $M_{ej}$ | $v_{ej}$ | $\kappa_{opt}$ | $t_{0}$
---|---|---|---|---
($M_{\odot}$) | ($M_{\odot}$) | ($10^{3}km\,s^{-1}$) | ($cm^{2}g^{-1}$) | ($days$)
$0.776_{-0.015}^{0.016}$ | $10.08_{-6.60}^{6.75}$ | $59.05_{-24.34}^{17.20}$ | $0.0040_{-0.0010}^{0.0028}$ | $-5.32_{-0.17}^{0.16}$

####  6.2.2 Radioactive Decay + Circumstellar Material Interaction Model

We next fit a radioactive decay model with additional CSM-interaction power as
formulated by Chevalier (1982) and Chatzopoulos et al. (2012). In this model
the CSM density, $\rho_{csm}$, is described by a power law,
$\rho_{csm}=qr^{-s}$. The ejecta distribution is described by two power laws,
$\rho_{ej}\propto r^{-\delta}$ for $r$ smaller than a critical normalized
radius $x_{0}$, and $\rho_{ej}\propto r^{-n}$ for $r$ larger than $x_{0}$. The
total SN luminosity in this model is given by (Chatzopoulos et al., 2012)

$\begin{split}L(t)&=\frac{1}{t_{0}}e^{-\frac{t}{t_{0}}}\int_{0}^{t}e^{\frac{t^{\prime}}{t_{0}}}[\frac{2\pi}{(n-s)^{3})}g^{n\frac{5-s}{n-s}}q^{\frac{n-5}{n-s}}(n-3)^{2}(n-5)\\\
&\times\beta_{F}^{(5-s)}A^{\frac{5-s}{n-s}}(t^{\prime}-t_{i})^{\frac{2n+6s-ns-15}{n-s}}\theta(t_{FS,BO}-t^{\prime})\\\
&+2\pi\left(\frac{Ag^{n}}{q}\right)^{\frac{5-n}{n-s}}\beta_{R}^{5-n}g^{n}\left(\frac{3-s}{n-s}\right)\\\
&\times(t^{\prime}+t_{i})^{\frac{2n+6s-ns-15}{n-s}}\theta(t_{RS,*}-t^{\prime})]\\\
&+\frac{1}{t^{\prime}_{0}}e^{-\frac{t}{t^{\prime}_{0}}}\\\
&\times\int_{0}^{t}e^{\frac{t^{\prime}}{t^{\prime}_{0}}}M_{Ni}\left[(\epsilon_{Ni}-\epsilon_{Co})e^{-\frac{t^{\prime}}{t_{Ni}}}+\epsilon_{Co}e^{-\frac{t^{\prime}}{t_{Co}}}\right]dt^{\prime}\end{split}$
(4)

The model has 10 free parameters (in addition to the density power-law indices
$s$, $\delta$ and $n$, which we fix): the ejecta mass $M_{ej}$, the 56Ni mass
$M_{Ni}$, the CSM mass $M_{CSM}$, the characteristic ejecta velocity $v_{ej}$,
the density of the CSM shell, $\rho_{CSM,in}$, at its innermost radius
$r_{in}$ ($q=\rho_{CSM,in}r_{in}^{s}$), the efficiency of converting shock
energy to luminosity $\epsilon$, the normalized radius at which the ejecta
power law switches indices $x_{0}$, the optical opacity $\kappa_{opt}$, and
the explosion time $t_{0}$, relative to peak time.

In addition to the free parameters, $\theta(t_{FS}-t)$ and $\theta(t_{RS}-t)$
are Heaviside step functions corresponding to the termination of the forward
and reverse shock waves at times $t_{FS}$ and $t_{RS}$, respectively, which
are dictated by the free parameters (see Chatzopoulos et al. 2012 and
Chevalier 1982 for the full details), $g(n,\delta,M_{ej},v_{ej})$ is a scaling
parameter for the ejecta density, and $\beta_{R}$, $\beta_{F}$ and $A$ are all
constants found in Chevalier (1982). All parameters related to the radioactive
decay component (the second integral in Equation 4) are identical to those of
the radioactive decay model described in Section 6.2.1.

Here, we study two cases: $s=0$ (a uniform-density CSM shell) and $s=2$ (CSM
due to a steady mass-loss wind). For each case, we test both $\delta=0$ and
$\delta=2$, which are values typically assumed for the inner density profile
in SNe (Chatzopoulos et al., 2012). As for the outer density profile, $n$,
previous works used $n=10$ and $n=12$ (Gangopadhyay et al., 2020; Pellegrino
et al., 2022). However, Chatzopoulos et al. (2012) mention that $n=11.7$
corresponds to red supergiant progenitors (Matzner & McKee, 1999), while more
compact stars (such as the stripped-envelope progenitors expected for Type Ibn
SNe) are characterized by lower values of $n$. Therefore, $n=12$ is probably
not appropriate for Type Ibn SN progenitors, and even $n=10$ might be too
high. Chevalier (1981, 1982) find that $n=7$ is able to reproduce light curves
of Type Ia supernovae from white dwarf progenitors. Therefore the true value
of $n$ for Type Ibn progenitors is possibly somewhere between 7 and 10. Here
we test both edge values. In summary we test all combinations of $n=7,10$,
$s=0,2$, and $\delta=0,2$.

Given the large number of parameters, we fit each case using the dynamic
nested sampling method as implemented by the DYNESTY Python package (Speagle,
2020). We use uniform and log-uniform priors, as detailed in Appendix A. We
require the 56Ni mass to be less than the total ejecta mass in all fits.

Our fits are shown in Figure 11, best-fit parameters given in Table 6, and
corner plots are shown in Figures 14–21 in Appendix B.

Table 6: Best-fit parameters for the radioactive decay + CSM interaction model. $n$ | $s$ | $\delta$ | $M_{ej}$ | $M_{Ni}$ | $M_{csm}$ | $v_{ej}$ | $\rho_{csm,in}$ | $r_{in}$ | $\epsilon$ | $x_{0}$ | $\kappa_{opt}$ | $t_{0}$
---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  | ($M_{\odot}$) | ($M_{\odot}$) | ($M_{\odot}$) | ($10^{3}km\,s^{-1}$) | ($10^{-12}g\,cm^{-3}$) | ($10^{14}\,cm$) |  |  | ($cm^{2}g^{-1}$) | ($days$)
7 | 0 | 0 | $0.76_{-0.38}^{+0.42}$ | $0.08_{-0.03}^{+0.03}$ | $0.13_{-0.06}^{+0.07}$ | $9.34_{-2.22}^{+5.33}$ | $0.93_{-0.65}^{+1.99}$ | $9.20_{-5.23}^{+8.99}$ | $0.56_{-0.24}^{+0.23}$ | $0.60_{-0.17}^{+0.27}$ | $0.79_{-0.23}^{+0.15}$ | $-4.62_{-0.17}^{+0.19}$
|  | 2 | $0.78_{-0.28}^{+0.39}$ | $0.08_{-0.03}^{+0.02}$ | $0.13_{-0.04}^{+0.06}$ | $14.58_{-4.33}^{+3.01}$ | $0.73_{-0.55}^{+1.81}$ | $10.59_{-6.10}^{+5.91}$ | $0.46_{-0.28}^{+0.36}$ | $0.57_{-0.17}^{+0.24}$ | $0.78_{-0.26}^{+0.15}$ | $-4.63_{-0.16}^{+0.15}$
| 2 | 0 | $0.42_{-0.10}^{+0.09}$ | $0.23_{-0.03}^{+0.03}$ | $0.29_{-0.13}^{+0.12}$ | $14.02_{-2.15}^{+1.80}$ | $0.11_{-0.08}^{+0.10}$ | $5.17_{-1.41}^{+3.62}$ | $0.19_{-0.06}^{+0.10}$ | $0.22_{-0.05}^{+0.06}$ | $0.21_{-0.07}^{+0.15}$ | $-3.97_{-0.07}^{+0.12}$
|  | 2 | $0.28_{-0.05}^{+0.11}$ | $0.22_{-0.04}^{+0.04}$ | $0.12_{-0.02}^{+0.05}$ | $13.00_{-4.08}^{+4.95}$ | $0.13_{-0.11}^{+0.19}$ | $3.17_{-1.35}^{+5.21}$ | $0.41_{-0.14}^{+0.16}$ | $0.25_{-0.07}^{+0.19}$ | $0.66_{-0.29}^{+0.21}$ | $-3.97_{-0.10}^{+0.14}$
10 | 0 | 0 | $1.19_{-0.31}^{+0.57}$ | $0.10_{-0.04}^{+0.05}$ | $0.06_{-0.02}^{+0.03}$ | $11.25_{-3.18}^{+4.32}$ | $0.76_{-0.49}^{+1.45}$ | $3.92_{-2.53}^{+3.20}$ | $0.61_{-0.25}^{+0.26}$ | $0.54_{-0.22}^{+0.21}$ | $0.76_{-0.19}^{+0.17}$ | $-4.95_{-0.35}^{+0.22}$
|  | 2 | $1.42_{-0.52}^{+0.94}$ | $0.10_{-0.03}^{+0.04}$ | $0.07_{-0.02}^{+0.04}$ | $11.87_{-3.84}^{+4.18}$ | $0.65_{-0.39}^{+1.75}$ | $4.52_{-2.60}^{+4.56}$ | $0.46_{-0.22}^{+0.30}$ | $0.61_{-0.20}^{+0.21}$ | $0.78_{-0.23}^{+0.15}$ | $-4.95_{-0.27}^{+0.22}$
| 2 | 0 | $0.26_{-0.02}^{+0.03}$ | $0.23_{-0.02}^{+0.01}$ | $0.21_{-0.03}^{+0.03}$ | $13.53_{-0.94}^{+2.80}$ | $1.20_{-0.98}^{+0.53}$ | $1.72_{-0.21}^{+1.27}$ | $0.61_{-0.15}^{+0.08}$ | $0.45_{-0.04}^{+0.12}$ | $0.14_{-0.03}^{+0.13}$ | $-3.95_{-0.05}^{+0.05}$
|  | 2 | $0.23_{-0.02}^{+0.04}$ | $0.21_{-0.02}^{+0.02}$ | $0.08_{-0.01}^{+0.02}$ | $16.05_{-3.32}^{+0.95}$ | $0.60_{-0.36}^{+0.29}$ | $1.32_{-0.15}^{+0.65}$ | $0.96_{-0.08}^{+0.03}$ | $0.48_{-0.04}^{+0.19}$ | $0.54_{-0.13}^{+0.13}$ | $-3.92_{-0.06}^{+0.06}$
Figure 11: Radioactive-decay + CSM interaction model (50 lines, chosen at
random from the sampler’s distribution) compared to the bolometric light curve
of SN 2019kbj (binned data in opaque points, un-binned data in semi-
transparent points) for different values of the fixed parameters. For the
$n=7,\,s=2$ cases, the reverse shock contribution is $\lesssim
10^{40}erg/\,s^{-1}$, and is not shown. Small bumps seen in some models at
$\sim$30 days are numerical artifacts from the integration.

##  7 Discussion

SN 2019kbj is photometrically and spectroscopically similar to other Type Ibn
SNe, with a post-peak luminosity decline rate that is similar to that of the
average Type Ibn light curve (Fig. 2).

The blackbody temperature of SN 2019kbj is relatively constant around $15,000$
K, in contrast to the cooling seen in H-rich Type II SNe, for example (e.g.
Valenti et al., 2014). This indicates that an ongoing power source, likely CSM
interaction, continues to heat the ejecta as it expands. A constant color,
indicative of constant temperature, is seen also in other Type Ibn’s (but not
all; Fig. 3). The constant color and temperature might be an indication of a
common CSM-interaction power source for this class of events. Determining why
some events do not show constant color requires additional modeling of those
data, which we leave to future work.

The bolometric light curve of SN 2019kbj yields extreme parameter values when
fit by radioactive decay alone, but can be fit with much more reasonable
values with the addition of CSM-interaction luminosity.

The steady-wind CSM ($s=2$) models require higher Ni masses and lower ejecta
masses compared to a uniform-density CSM shell ($s=0$; Table 6). In fact, the
steady-wind CSM models require most ($\sim$50–90%) of the ejecta to be Ni,
while in the uniform-density CSM model less than 10% of the ejecta mass is Ni,
as seen in most core-collapse SNe. This is the case regardless of the value of
$n$ chosen. Therefore, we conclude that our models show a slight preference
for a uniform-density CSM shell over a steady-wind CSM. This is consistent
with the results of Karamehmetoglu et al. (2017) and Gangopadhyay et al.
(2020) who also prefer a uniform-density CSM shell over a steady-wind CSM to
explain the light curves of the Type Ibn SNe OGLE-2014-SN-131 and 2019uo.

In the uniform-density CSM case, the bolometric light curve of SN 2019kbj
requires a 56Ni mass of $0.08$–$0.1M_{\odot}$, which is an order of magnitude
higher than the $0.01\,M_{\odot}$ derived by Gangopadhyay et al. (2020) and
Pellegrino et al. (2022) for SN 2019uo (for both CSM cases). In the steady-
wind CSM case, we derive an even higher value of $0.22\,M_{\odot}$ for the
56Ni mass. The ejecta masses of $\sim 0.2$–$1.4\,M_{\odot}$ that we find are
substantially lower than the $\sim 16\,M_{\odot}$ derived for SN 2019uo by
Gangopadhyay et al. (2020), but overlap with the $\sim 1\,M_{\odot}$ found by
Pellegrino et al. (2022) for that event.

The ejecta masses deduced are not highly sensitive to the value of $n$, and
change only within a factor of two for $n=7$ vs. $n=10$. The 56Ni and CSM
masses are even less sensitive to $n$, and are in fact consistent within the
errors for the different $n$ values tested.

The mass-loss rate, $\dot{M}$, that produced the CSM can be obtained from the
continuity equation:

$\begin{split}\dot{M}\left(r\right)&=4{\pi}r^{2}\rho_{CSM}\left(r\right)v_{w}\left(r\right)\\\
&=4{\pi}r^{2}qr^{-s}v_{w}\left(r\right)\\\ \end{split}$ (5)

where $v_{w}$ is the CSM wind velocity, and we recall that
$q=\rho_{CSM,in}r_{in}^{s}$. If we assume a constant wind velocity, then the
mass-loss rate is

$\dot{M}\left(r\right)=4{\pi}r^{2-s}\rho_{CSM,in}r_{in}^{s}v_{w}$ (6)

For the $s=2$ case, this results in a constant $\dot{M}$. Typical Wolf-Rayet
wind velocities are of order 1000 km s-1 (Crowther, 2007), which is consistent
with the order of magnitude of the earliest He velocity we measure in Section
5 (before the CSM might have accelerated significantly due to impact from the
SN ejecta). With our $s=2$ best-fit parameters we thus find a mass-loss rate
on the order of
$\sim$0.5$\left(\frac{v_{w}}{1000\,\textrm{km\,s}^{-1}}\right)$ $M_{\odot}$
yr-1 (for both $n=7$ and $n=10$). At this mass-loss rate, to reach the total
CSM mass from each fit, the mass-loss episode that shaped the light curve of
SN 2019kbj would have lasted only $\sim$0.2–1.1 years.

The mass-loss rate found here is similar to the mass-loss rate derived for the
Type IIn SN iPTF13z (0.1–2 ${M}_{\odot}$ yr-1; Nyholm et al. 2017).
Gangopadhyay et al. (2020) found a much higher value for SN 2019uo
($\sim$200$\left(\frac{v_{w}}{1000\,\textrm{km\,s}^{-1}}\right)$ $M_{\odot}$
yr-1) which motivated them to rule out the $s=2$ model for that event.

For $s=0$, the mass loss rate is not constant for a constant $v_{w}$. Using
the best fit parameters for this case, the mass loss rate at the inner CSM
radius, $\dot{M}\left(r_{in}\right)$, is
$\sim$16$\left(\frac{v_{w}}{1000\,\textrm{km\,s}^{-1}}\right)$ $M_{\odot}$
yr-1 for $n=7$ and
$\sim$2.5$\left(\frac{v_{w}}{1000\,\textrm{km\,s}^{-1}}\right)$ $M_{\odot}$
yr-1 for $n=10$. We can not derive a timescale for the ejection of this shell,
without knowing the difference between $r_{in}$ and the progenitor radius
(which we can not constrain here). In addition to these uncertainties, $v_{w}$
might also not be constant in this type of CSM.

Although the light curve of SN 2019kbj is $\sim$1–2 magnitudes brighter than
that of SN 2019uo, both are within the observed spread of Type Ibn SN
luminosities (Fig. 2). Therefore, our results indicate a possible diversity in
Type Ibn SN progenitor systems and explosions. However, this apparent
diversity may be due, at least in part, to the different model implementation
and fitting methods used for each event. As noted previously, Pellegrino et
al. (2022) also fit a Ni decay + uniform-density CSM model to SN 2019uo, but
find a very different ejecta mass than that found by Gangopadhyay et al.
(2020), $\sim 1M_{\odot}$ vs. $\sim 16M_{\odot}$, using the same data.
Comparing physical parameters between events requires fitting their light
curves with the same models and methods. We plan to perform such systematic
comparisons in future work (T. Ben-Ami et al. 2023, in preparation).

##  8 Summary and Conclusions

SN 2019kbj is similar both photometrically and spectroscopically to other Type
Ibn SNe.

We show that the radioactive decay of 56Ni is likely not enough to explain the
light curve, but that an additional power source is needed. This is also
evidenced by the roughly constant blackbody temperature of SN 2019kbj.

We fit the bolometric light curve of SN 2019kbj with a radioactive decay + CSM
interaction model, and find that a uniform-density CSM shell produces more
reasonable fits compared to a steady-wind CSM.

Other Type Ibn SNe show lower 56Ni masses and higher ejecta masses compared to
SN 2019kbj. This diversity might be intrinsic to Type Ibn SN progenitor
systems and explosions, but it might also arise from differences in the way
physical parameters have been inferred for different events. A systematic
study of Type Ibn light curves could elucidate this issue and provide
additional clues as to the puzzling nature of these events.

We thank the anonymous referee for useful comments that helped make the
results of this paper more robust and insightful. T.B.-A acknowledges support
from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation program (grant No. 852097). IA is a CIFAR Azrieli
Global Scholar in the Gravity and the Extreme Universe program and
acknowledges support from that program, from the ERC under the European
Union’s Horizon 2020 research and innovation program (grant No. 852097), from
the Israel Science Foundation (grant No. 2752/19), from the United States -
Israel Binational Science Foundation (BSF), and from the Israeli Council for
Higher Education Alon Fellowship. The Las Cumbres group is supported by
AST-1911151, AST-1911225, and NASA Swift grant No. 80NSSC19K1639. This work
made use of data from the Las Cumbres Observatory global network of robotic
telescopes, and of data from the Asteroid Terrestrial-impact Last Alert System
(ATLAS) project. ATLAS is primarily funded to search for near earth asteroids
through NASA grant Nos. NN12AR55G, 80NSSC18K0284, and 80NSSC18K1575; by-
products of the NEO search include images and catalogs from the survey area.
This work was partially funded by Kepler/K2 grant No. J1944/80NSSC19K0112 and
HST GO-15889, and STFC grant Nos. ST/T000198/1 and ST/S006109/1. The ATLAS
science products have been made possible through the contributions of the
University of Hawaii Institute for Astronomy, the Queen’s University Belfast,
the Space Telescope Science Institute, the South African Astronomical
Observatory, and The Millennium Institute of Astrophysics (MAS), Chile. This
work also made use of the NASA/IPAC Extragalactic Database (NED), which is
funded by the National Aeronautics and Space Administration and operated by
the California Institute of Technology, and of data, software, and web tools
obtained from the High Energy Astrophysics Science Archive Research Center
(HEASARC), a service of the Astrophysics Science Division at NASA/GSFC and of
the Smithsonian Astrophysical Observatory’s High Energy Astrophysics Division.

##  Appendix A Model Priors

The priors chosen for the radioactive decay model are shown in Table 7 and
those for the radioactive decay + CSM interaction model in Table 8. In
addition, a limit on $M_{Ni}$ was given such that samples with $M_{Ni}>M_{ej}$
were rejected by the algorithm. The prior on the explosion time $t_{0}$ is
based on the explosion window discussed in Section 3.

Table 7: Bounds for the priors used when fitting the radioactive decay model. | $M_{ej}$ | $M_{Ni}$ | $v_{ej}$ | $\kappa_{opt}$ | $t_{0}$
---|---|---|---|---|---
| $(M_{\odot})$ | $(M_{\odot})$ | $(10^{3}km\,s^{-1})$ | $(cm^{2}g^{-1})$ | ($days$)
Lower bound | $10^{-3}$ | $10^{-4}$ | 1.0 | $10^{-3}$ | -5.5
Upper bound | 20.0 | 10.0 | 100.0 | 1.0 | -4.1
Type | Log-uniform | Log-uniform | Uniform | Uniform | Uniform
Table 8: Bounds for the priors used when fitting the radioactive decay + CSM interaction model. | $M_{ej}$ | $M_{Ni}$ | $M_{csm}$ | $v_{ej}$ | $\rho_{csm,in}$ | $r_{in}$ | $\epsilon$ | $x_{0}$ | $\kappa_{opt}$ | $t_{0}$
---|---|---|---|---|---|---|---|---|---|---
| $(M_{\odot})$ | $(M_{\odot})$ | $(M_{\odot})$ | $(10^{3}km\,s^{-1})$ | $(10^{-12}g\,cm^{-3})$ | $(10^{14}\,cm)$ |  |  | $(cm^{2}g^{-1})$ | ($days$)
Lower bound | $10^{-3}$ | $10^{-4}$ | $10^{-4}$ | 1.0 | 0.01 | 0.01 | 0.1 | 0.1 | $10^{-3}$ | -5.5
Upper bound | 20.0 | 10.0 | 12.0 | 20.0 | 1.0 | 20.0 | 1.0 | 1.0 | 1.0 | -4.1
Type | Log-uniform | Log-uniform | Log-uniform | Uniform | Uniform | Uniform | Uniform | Uniform | Uniform | Uniform

##  Appendix B Model Convergence

For the radioactive decay + CSM interaction model fits, we use the original
stopping function offered by Dynesty, which is robust for most applications
(Speagle, 2020). The algorithm performs a “baseline” run, which is stopped
when 99% of the evidence has been explored, followed by a stopping function
for the additional batch runs, based on whether the posterior has been
estimated well enough (see Speagle 2020 for more details).

Taking the $s=0$, $\delta=0$ case (Fig. 14) as an example, we can see two
types of posterior distributions. Some (e.g. those for $M_{Ni}$ and $t_{0}$)
are Gaussian-like, while others (e.g. for $x_{0}$) have broader, more
complicated distributions. While this might be interpreted as not ‘converged’
in an MCMC fit, the entire relevant phase space of the priors has been
explored (Fig. 12). This is the case for all model variations fit here.
Therefore we conclude that the fits are converged but that there exist
inherently complex degeneracies between some of the parameters.

Figure 12: Corner plot of the samples constructed for the radioactive decay +
CSM model with $s=0$ and $\delta=0$. Colors represent each sampling’s weight
in calculating the posterior. The relevant parameter space was covered well by
the sampling, leading us to conclude that the fits are converged. The same is
true for all other radioactive decay + CSM models fit here.

###  B.1 Corner Plots and Fit Parameters

Figure 13 shows the corner plot for the radioactive decay only fit, and Table
9 lists the best-fit parameters from the unconstrained model. Corner plots for
the radioactive decay + CSM fits are shown in Figures 14–21.

---
Figure 13: Corner plots of the radioactive decay fit to the bolometric light curve of SN 2019kbj. The units for the parameters are given in Table 5. Left: fit in which the 56Ni mass is constrained to be lower than the total ejecta mass and the velocity prior is extended up to $100\times 10^{3}$ km s-1. Right: fit in which the 56Ni mass is not constrained by the ejecta mass and the velocity priors are limited to $\leq 20\times 10^{3}$ km s-1. In this case the preferred 56Ni mass is larger than the total ejecta mass, making the solution unphysical. Table 9: Best-fit parameters for the unconstrained radioactive decay model. The larger Ni than total mass makes this model unphysical. $M_{Ni}$ | $M_{ej}$ | $v_{ej}$ | $\kappa_{opt}$ | $t_{0}$
---|---|---|---|---
($M_{\odot}$) | ($M_{\odot}$) | ($10^{3}km\,s^{-1}$) | ($cm^{2}g^{-1}$) | ($days$)
$0.787_{-0.017}^{+0.018}$ | $0.48_{-0.41}^{+0.44}$ | $13.02_{-7.79}^{+5.00}$ | $0.020_{-0.006}^{+0.029}$ | $-5.38_{-0.19}^{+0.18}$
Figure 14: Corner plot for the radioactive decay + CSM interaction fit to the
bolometric light curve of SN 2019kbj, with fixed parameters
$n=7,s=0,\delta=0$. The units for the parameters are given in Table 6. Figure
15: Corner plot for the radioactive decay + CSM interaction fit to the
bolometric light curve of SN 2019kbj, with fixed parameters
$n=7,s=0,\delta=2$. The units for the parameters are given in Table 6. Figure
16: Corner plot for the radioactive decay + CSM interaction fit to the
bolometric light curve of SN 2019kbj, with fixed parameters
$n=7,s=2,\delta=0$. The units for the parameters are given in Table 6. Figure
17: Corner plot for the radioactive decay + CSM interaction fit to the
bolometric light curve of SN 2019kbj, with fixed parameters
$n=7,s=2,\delta=2$. The units for the parameters are given in Table 6. Figure
18: Corner plot for the radioactive decay + CSM interaction fit to the
bolometric light curve of SN 2019kbj, with fixed parameters
$n=10,s=0,\delta=0$. The units for the parameters are given in Table 6. Figure
19: Corner plot for the radioactive decay + CSM interaction fit to the
bolometric light curve of SN 2019kbj, with fixed parameters
$n=10,s=0,\delta=2$. The units for the parameters are given in Table 6. Figure
20: Corner plot for the radioactive decay + CSM interaction fit to the
bolometric light curve of SN 2019kbj, with fixed parameters
$n=10,s=2,\delta=0$. The units for the parameters are given in Table 6. Figure
21: Corner plot for the radioactive decay + CSM interaction fit to the
bolometric light curve of SN 2019kbj, with fixed parameters
$n=10,s=2,\delta=2$. The units for the parameters are given in Table 6.

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# A Two-Stage Approach towards Generalization in Knowledge Base Question
Answering

Srinivas Ravishankar∗ June Thai+ Ibrahim Abdelaziz∗ Nandana Mihidukulasooriya∗
Tahira Naseem∗ Pavan Kapanipathi∗ Gaetano Rossiello∗ Achille Fokoue∗
∗IBM Research +UMass Amherst

###### Abstract

Most existing approaches for Knowledge Base Question Answering (KBQA) focus on
a specific underlying knowledge base either because of inherent assumptions in
the approach, or because evaluating it on a different knowledge base requires
non-trivial changes. However, many popular knowledge bases share similarities
in their underlying schemas that can be leveraged to facilitate generalization
across knowledge bases. To achieve this, we introduce a KBQA framework based
on a 2-stage architecture that explicitly separates semantic parsing from the
knowledge base interaction, facilitating transfer learning across datasets and
knowledge graphs. We show that pretraining on datasets with a different
underlying knowledge base can nevertheless provide significant performance
gains and reduce sample complexity. Our approach achieves comparable or state-
of-the-art performance for LC-QuAD (DBpedia), WebQSP (Freebase),
SimpleQuestions (Wikidata) and MetaQA (Wikimovies-KG).

##  1 Introduction

Knowledge Base Question Answering (KBQA) has gained significant popularity in
recent times due to its real-world applications, facilitating access to rich
Knowledge Graphs (KGs) without the need for technical query-syntax. Given a
natural language question, a KBQA system is required to find an answer based
on the facts available in the KG. For example, given the question “Who is the
director of the film Titanic", a KBQA system should retrieve the entity
corresponding to “James Cameron". This would be dbr:James_Cameron111dbr:
http://dbpedia.org/resource/ in DBpedia (Auer et al. 2007), wd:Q42574222wd:
http://www.wikidata.org/entity in Wikidata (Vrandečić and Krötzsch 2014), and
fb:m.03_gd333fb: http://rdf.freebase.com/ns/ in Freebase (Bollacker et al.
2008).

KBQA has been evaluated on multiple different KGs such as Freebase (Bollacker
et al. 2008), Wikidata (Vrandečić and Krötzsch 2014), DBpedia (Auer et al.
2007), and MetaQA (Zhang et al. 2018). Most existing heuristic-based KBQA
approaches such as NSQA (Kapanipathi et al. 2020), gAnswer (Zou et al. 2014),
and QAmp (Vakulenko et al. 2019) are typically tuned for a specific underlying
knowledge base making it non-trivial to generalize and adapt it to other
knowledge graphs. On the other hand, WDAqua (Diefenbach, Singh, and Maret
2017), a system with a focus on being generalizable, ignores question syntax,
thereby showing reduced performance on datasets with complex multi-hop
questions.

Recently, there has been a surge in end-to-end learning approaches that are
not tied to specific KGs or heuristics, and hence can generalize to multiple
KGs. GrailQA (Gu et al. 2021) in particular categorized different forms of
generalization, such as novel relation compositionality and zero-shot
generalization. They also demonstrated transfer across QA datasets, but within
the same KG. On the other hand, GraftNet (Sun et al. 2018) and EmbedKGQA
(Saxena, Tripathi, and Talukdar 2020) demonstrated their ability to generalize
over multiple KGs by demonstrating state-of-the-art performance on MetaQA
(Wikimovies) as well as WebQSP (Freebase). The two techniques, however, are
highly sensitive to the training data; failing to generalize in terms of
relation compositionality within a KG. EmbedKGQA and GraftNet show significant
drops (between 23-50%) in performance on relation compositions that are not
seen during training. Furthermore, it is unclear how these systems transfer
across KGs because of their tight-integration with KG-specific embeddings.

In this work, we present a novel generalizable KBQA approach STaG-QA (Semantic
parsing for Transfer and Generalization) that works seamlessly with multiple
KGs, and demonstrate transfer even across QA datasets with different
underlying KGs. Our approach attempts to separate aspects of KBQA systems that
are softly tied to the KG but generalizable, from the parts more strongly tied
to a specific KG. Concretely, our approach has two stages: 1) The first stage
is a generative model that predicts a query skeleton, which includes the query
pattern, the different sparql operators in it, as well as partial relations
based on label semantics that can be generic to most knowledge graphs. 2) The
second stage converts the output of the first stage to a final query that
includes entity and relations mapped to a specific KG to retrieve the final
answer.

Our contributions are as follows:

  * •

A simple Seq2Seq architecture for KBQA that separates aspects of the output
that are generalizable across KGs, from those that are strongly tied to a
specific KG.

  * •

To the best of our knowledge, our approach is the first to evaluate on and
achieve state-of-the-art or comparable performance on KBQA datasets
corresponding to four different knowledge graphs, i.e, LC-QuAD (DBpedia),
WebQSP (Freebase), SimpleQuestions (Wikidata) and MetaQA (Wikimovies).

  * •

Our extensive experimental results shows that the proposed architecture: (a)
facilitates transfer with significant performance gains in low-resource
setting; (b) generalizes significantly better (23-50%) to unseen relation
combinations in comparison to state-of-the-art approaches.

##  2 Proposed Architecture

The KBQA task involves finding an answer for a natural language question from
a given KG. Following the semantic parsing techniques for KBQA (Chen et al.
2021; Kapanipathi et al. 2020; Yih et al. 2015), we attempt to solve this task
by predicting the correct structured sparql query that can retrieve the
required answer(s) from the KG, i.e, by estimating a probability distribution
over possible sparql queries given the natural language question.

Figure 1: Two-stage system architecture that comprises of: (a) On the left:
Softly-tied semantic parse generation that takes an input question return a
KG-agnostic parse, and (b) On the right: Knowledge Graph Integration process
to eventually return the SPARQL query.

In this work, we aim to design a model architecture that generalises across
different KGs such as DBpedia, Wikidata, and Freebase. In order to achieve
this goal, we have a 2-stage approach as shown in Figure 1, where we separate
generic sparql query-sketch learning from KG-specific mapping of concepts.
Specifically, the following 2-stages are:

  * •

Softly-tied query sketch: This is the first stage of our approach where we
intend to learn aspects of the sparql query generation that are generic to any
knowledge graph. Specifically, we observe the following: (i) multi-hop
patterns are mostly generic to question answering over KGs. (ii) across many
KGs, analogous relations have semantic or lexical overlap. Therefore, we focus
on 2 sub-tasks in this stage, query skeleton generation and partial relation
linking. We call the output of this stage a softly-tied semantic parse,
because the exact output is partially dependent on the specific KG in use, but
our choice of representations and architecture ensures that transfer across
KGs is a natural consequence.

  * •

KG alignment: This is the next step where we introduce all vocabulary specific
to the knowledge graph in order to generate an executable sparql query. To do
so, we bind the softy-tied semantic parse strongly to the KG to find the
answer by (i) resolving the textual relations to KG relations, (ii)
introducing KG specific entities into the sparql skeleton, and (iii) rank the
obtained sparql queries based on its groundings in the KG.

KG | Query Graph Structure
---|---
DBpedia |

    ?var <director> <entity>
    ?var <language> ?ans

Wikimovies |

    ?var <directed by> <entity>
    ?var <In language> ?ans

Wikidata |

    ?var <director> <entity>
    ?var <original language
            of film> ?ans

Table 1: Query sketch for the question “The films directed by John Krasinski
are in which language?"

###  2.1 Softly-tied Query Sketch

As mentioned above, the goal is to create a representation and architecture
that can generalize easily not only across examples within a dataset, but also
across KGs. To accomplish this, we define 2 subtasks: (a) Skeleton Generation,
and (b) Partial relation linking.

Skeleton Generation: A sparql’s skeleton captures the operators needed to
answer the question; i.e. ask, select, count or filter, as well as the query
graph structure, with placeholder nodes for entities (e.g. :ent0), relations
(e.g. :prop0) and variables (e.g. ?var0). For many questions, the generated
sparql skeletons across different KGs are similar, if not identical. The
skeleton structures unique to a KG, e.g. reification (present in Wikidata but
not DBpedia), can be learnt when fine-tuning on a dataset with that underlying
KG. An example of a sparql skeleton for our running example in Figure 1 “The
films directed by John Krasinski are in which language?" is:

⬇

SELECT ?var0 WHERE {

?var1 :prop0 :ent0 .

?var1 :prop1 ?var0 .

}

As shown in Figure 1, the question is passed through a transformer-based
Seq2Seq model which is trained to produce the sparql skeleton corresponding to
the question text. The encoder of the Seq2Seq model is a bi-direction
transformer, while the decoder is auto-regressive with a causal self-attention
mask.

Given a question text, we tokenize it using BERT tokenizer and add special
[CLS] and [SEP] symbols in the beginning and the end of the question,
respectively. This tokenized input is passed through a transformer encoder,
producing encoder hidden states for each token at each layer. The encoder is
initialized with pretrained BERT model (Devlin et al. 2018), which helps
generalization with respect to different question syntax.

We then use a transformer decoder with cross attention mechanism. At each time
step $i$, the decoder considers the encoder states via cross-attention and
previous decoder states via self attention. It produces a distribution over
possible skeleton output tokens. The decoder output vocabulary $\mathcal{V}$
comprises of entity place holder tokens $\mathcal{V}_{e}$, relation place
holder tokens $\mathcal{V}_{r}$ and sparql operators $\mathcal{V}_{o}$; each
of these is a small closed set of tokens. The output of each decoding step is
a softmax over possible operators $s_{i}\in\mathcal{V}$. Unlike the encoder,
no pre-trained model is used for the decoder, and paramerters are initialized
randomly.

Partial Relation Linking: For each relation placeholder in the sparql skeleton
(:prop0, :prop1, etc), we need to identify the appropriate relation that can
replace the placeholder to produce the correct semantic representation of the
query. We have noted previously that relations across KGs share lexical and
semantic similarities. For example, in Table 1 the three KGs (DBpedia,
Wikimovies, and Wikidata) represent the relationship “Directed by" with very
similar lexical terms “Director" and “Directed by". We can thus leverage large
pre-trained language models to allow generalization and transfer of such
relations across KGs. In each KG, we first map the relations to their
respective surface forms, using either label relations from the KG, or by
extracting some semantically meaningful surface form from the relation URI.
These are the “textualized relations" shown in Figure 1. Table 2 shows some
more examples of relation labels for 3 KGs. Note that this mapping can be
many-to-one. For example, both dbo:language and dbp:language map to the same
relation label “language".

KG | KG Relation | Derived Surface Form
---|---|---
DBpedia | dbo:language | language
dbp:language | language
dbp:languages | languages
Wikidata | P397 | official language
P364 | original language of film or TV show
FreeBase | people.ethnicity.languages_spoken | languages spoken
location.country.languages_spoken | languages spoken
Table 2: Examples of textualized relations for different KGs, obtained either
using the relation label from the KG (DBpedia, Wikidata) or by extracting a
part of the relation URI (Freebase)

Our goal is to identify which relation surface form best matches each relation
placeholder in the skeleton. We thus train the Seq2Seq decoder and relation
encoder to project into the same space. Concretely, the decoder hidden state
corresponding to each relation placeholder is optimised to be closest to the
encoded representation of the correct relation, using a cross-entropy loss.
For example, in Figure 1, the decoder state for :prop0 should have maximum
inner product with the encoded representation for the relation surface form
“Directed by", compared to the encoded representations of all other relations.
Our relation encoder is a transformer model whose parameters are initialized
with pretrained BERT model. Given that BERT-based representations of lexically
or semantically similar relations across KGs will be close, it is easy to see
why transfer across KG is possible. The final outcome of partial relation
linking is a ranked list of relation surface forms for each placeholder in the
skeleton.

The skeleton generation loss and partial relation linking loss are optimized
jointly. The sparql skeleton together with the partial relation linking
produces a ranked list of softly-tied query sketches. In the case of multiple
placeholders, the score of each pair of relation surface forms is the product
of their individual scores. Sometimes this phase produces multiple semantic
interpretations, either due to noisy surface forms (for instance, DBpedia KG
includes Wikipedia infobox keys “as is” when they can not be mapped to the
ontology relations) or due to the presence of semantically identical or
similar relations with distinct identifiers (eg. dbo:language and
dbp:language). For the example, “The films directed by John Krasinski are in
which language?", this stage will produce the following sketches:

⬇

P=0.87 SELECT ?var0 where {

?var1 director :ent0.

?var1 language ?var0.}

P=0.76 SELECT ?var0 where {

?var1 director :ent0.

?var1 languages ?var0.}

...

###  2.2 KG Interaction

In order to generate an executable sparql query, we need to introduce
vocabulary specific to the KG. The KG interaction stage performs this task.
Concretely, given a list of candidate query sketches, this stage performs the
following steps to produce the final question answer: 1) link the different
entities to their corresponding placeholders in the skeleton, 2) disambiguate
relations’ textual form and link it to the specific KG relations, and 3)
select the correct sparql based on the actual facts in the KG.

In our approach, we leverage a pre-trained off-the-shelf entity linker, BLINK
(Wu et al. 2020). BLINK provides tuples of (surface form, linked entity)
pairs. The entity placeholder resolution step aligns the entities with the
entity place holders in the query sketch. In the example above, :ent0 will be
linked to dbr:John_Krasinski in DBpedia, or wd:Q313039 in Wikidata. When
multiple entities are present in the question, the position of the
corresponding textual span defines the alignment to the entity placeholder
variable. During training, the first entity in the question corresponds to
:ent0, the second entity by :ent1, etc. This pattern is repeated by the system
when decoding during inference, making entity placeholder resolution trivial.

The next step is to disambiguate relations’ textual form and link them to the
specific KG relations. Recall from Table 2 that each surface form in a query
sketch can map to one or more KG relations. In our example using DBpedia as a
KG, the surface form “director" could map to both [dbo:director, dbp:director]
whereas “language" could map to both [dbo:language, dbp:language]. The
semantic parsing stage cannot hope to distinguish between these, and thus we
rely on the KG to determine the specific relation that should be chosen.
Concretely, we replace every relation surface form with each of the possible
KG relations it could map to. Thus, each softly-tied query sketch produces one
or more fully executable sparqls. For example, the 2 softly-tied sketches from
the previous stage in our example produce 4 possible sparqls, see Table 3. As
the final step, we execute the candidate sparql queries against the KB and
choose the highest-ranked sparql that produces an answer for select queries.
Since ask queries do not necessarily have to be valid in the KG, we only
consider the model score in such cases.

Rank | Predicted SPARQL Query
---|---
1 |

    SELECT ?var0 where {
      ?var1 dbo:director dbr:John_Krasinski.
      ?var1 dbo:language ?var0. }

1 |

    SELECT ?var0 where {
      ?var1 dbp:director dbr:John_Krasinski.
      ?var1 dbo:language ?var0. }

2 |

    SELECT ?var0 where {
      ?var1 dbo:director dbr:John_Krasinski.
      ?var1 dbp:languages ?var0. }

2 |

    SELECT ?var0 where {
      ?var1 dbp:director dbr:John_Krasinski.
      ?var1 dbp:languages ?var0. }

Table 3: Top predicted SPARQL queries for the question “The films directed by
John Krasinski are in which language?"

##  3 Experiments

In this section, we compare STaG-QA to other state-of-the-art approaches on
datasets from multiple KGs. We validate 2 claims: (1) STaG-QA achieves state-
of-the-art or comparable performance on a variety of datasets and KGs. (2)
STaG-QA generalizes across KBs and hence facilitating transfer. The results
show that pre-training our system achieves improvement in performance with
better gains in low-resource and unseen relation combination settings.

| KG | Train | Valid | Test
---|---|---|---|---
LC-QuAD 1.0 | DBpedia | 3,650 | 200 | 1,000
SimpleQuestion | Wikidata | 15,000 | 2,000 | 2,280
WQSP-FB | Freebase | 2898 | 200 | 1,596
MetaQA 1-hop | Wikimovies | 86,470 | 9,992 | 9,947
MetaQA 2-hop | Wikimovies | 118,980 | 14,872 | 14,872
MetaQA 3-hop | Wikimovies | 114,196 | 14,274 | 14,274
Table 4: Dataset Statistics

###  3.1 Datasets

To evaluate the generality of our approach, we used datasets across a wide
variety of KGs including Wikimovies-KG, Freebase (Bollacker et al. 2008),
DBpedia (Auer et al. 2007), and Wikidata (Vrandečić and Krötzsch 2014). In
particular, we used the following datasets (Table 4 shows detailed statistics
for each dataset): (a) MetaQA (Wikimovies-KG) (Zhang et al. 2018) is a large-
scale complex-query answering dataset on a KG with 135k triples, 43k entities,
and nine relations. It contains more than 400K questions for both single and
multi-hop reasoning. (b) WQSP-FB (Freebase) (Yih et al. 2016) provides a
subset of WebQuestions with semantic parses, with 4737 questions in total. (c)
LC-QuAD 1.0 (DBpedia) (Trivedi et al. 2017): A dataset with 5,000 questions
(4,000 train and 1,000 test) based on templates. It includes simple, multi-
hop, as well as aggregation-type questions. LC-QuAD 2.0 is another version of
LC-QuAD based on Wikidata. It has 30K question in total and also template-
based. Due to the larger underlying KB and the extensive pattern covered, we
used LC-QuAD 2.0 dataset for pretraining and showing our transfer results. (d)
SimpleQuestions-Wiki (Wikidata) (Diefenbach et al. 2017): a mapping of the
popular Freebase’s SimpleQuestions dataset to Wikidata KB with 21K answerable
questions.

###  3.2 Baselines

In this work, we evaluate against 8 different KBQA systems categorized into
unsupervised (Kapanipathi et al. 2020; Sakor et al. 2020; Vakulenko et al.
2019; Diefenbach, Singh, and Maret 2017) and supervised approaches (Sun et al.
2020; Maheshwari et al. 2019; Saxena, Tripathi, and Talukdar 2020; Sun,
Bedrax-Weiss, and Cohen 2019; Sun et al. 2018). 1) NSQA (Kapanipathi et al.
2020; Abdelaziz et al. 2021) is state-of-the-art system for KBQA on DBpedia
datasets. 2) QAMP (Vakulenko et al. 2019) is an unsupervised message passing
approach that provides competitive performance on LC-QuAD 1.0 dataset. (3)
WDAqua (Diefenbach, Singh, and Maret 2017) is another system that generalises
well across a variety of knowledge graphs. (4) Falcon 2.0 (Sakor et al. 2020)
is a heuristics-based approach for joint detection of entities and relations
in Wikidata. Since this approach does not predict the query structure, we
tested it on SimpleQuestions dataset only. (5) EmbedKGQA (Saxena, Tripathi,
and Talukdar 2020) is the state-of-the-art KBQA system on MetaQA and WebQSP
datasets, (6) PullNet (Sun, Bedrax-Weiss, and Cohen 2019) is recent approach
evaluated on MetaQA and WebQSP datasets, (7) GraftNet (Sun et al. 2018)
infuses both text and KG into a heterogeneous graph and uses GCN for question
answering, and (8) EmQL (Sun et al. 2020) is a query embedding approach that
was successfully integrated into a KBQA system and evaluated on WebQSP and
MetaQA datasets.

###  3.3 KBQA Evaluation

Table 5 shows our system results on all four datasets in comparison to
existing approaches. We show two versions of our system, one pre-trained with
LC-QuAD 2.0 datatset (Dubey et al. 2019) (STaG-QApre) and another trained from
scratch on the target dataset only (STaG-QA). As noted earlier, to the best of
our knowledge, we are the first to show generality across knowledge graphs by
evaluating on datasets from DBpedia, Wikidata, Freebase, and Wikimovies-KG.

Our approach achieves significantly better performance compared to Falcon 2.0
on SimpleQuestions-Wiki dataset with 24% better F1 score. While Falcon 2.0 is
not a KBQA system itself, it jointly predicts entities and relations given a
question. Since SimpleQuestions-Wiki requires only a single entity and a
single relation, we used Falcon 2.0 output to generate the corresponding
sparql query required for KBQA evaluation. On MetaQA dataset, our system as
well as the baselines achieve near perfect scores indicating the simplicity of
this dataset.

On LC-QuAD 1.0, our approach significantly outperforms existing DBpedia-based
approaches. When pretrained on LC-QuAD 2.0, the performance is 9% better F1
compared to NSQA; the state-of-the-art system on DBpedia. The large
improvement indicates that STaG-QA was able to generalize and learn similar
patterns between LC-QuAD 1.0 and LC-QuAD 2.0. As for WebQSP, both versions of
our approach are inferior compared to EmQL. However, it is also worth noting
that EMQL also leverages KBC embeddings, which is not currently utilized STaG-
QAȮverall, the results show that STaG-QA shows better or competitive
performance on 3 out of four datasets and when pretrained on another dataset,
the performance improves across all datasets. In the next section, we analyze
different datasets in terms of the degree of challenge they pose for KBQA
systems. We propose evaluation splits that will allow us to better
discriminate different systems in terms of their performance on these
datasets.

| SimpleQuestions-Wiki | LC-QuAD 1.0 | WebQSP | MetaQA
---|---|---|---|---
System | P | R | F1 | P | R | F1 | Hits@1 |  | Hits@1
---
1-Hop
| Hits@1
---
2-Hop
| Hits@1
---
3-Hop
WDAqua | - | - | - | 22.0 | 38.0 | 28.0 | - | - | - | -
QAMP | - | - | - | 25.0 | 50.0 | 33.0 | - | - | - | -
NSQA | - | - | - | 44.8 | 45.8 | 44.4 | - | - | - | -
Falcon 2.0 | 34 | 41.1 | 36.3 | - | - | - | - | - | - | -
GraftNet | - | - | - | - | - | - | 70.3 | 97.0 | 99.9 | 91.4
PullNet | - | - | - | - | - | - | 69.7 | 97.0 | 99.9 | 91.4
EmbedKGQA | - | - | - | - | - | - | 66.6 | 97.5 | 98.8 | 94.8
EMQL | - | - | - | - | - | - | 75.5 | - | 98.6 | 99.1
STaG-QA | 59.4 | 62.7 | 61.0 | 76.5 | 52.8 | 51.4 | 65.9 | 100.0 | 100.0 | 99.9
STaG-QApre | 60.2 | 63.2 | 61.7 | 74.5 | 54.8 | 53.6 | 68.5 | 100.0 | 100.0 | 100.0

Table 5: Performance against previous state-of-the-art approaches. Following
these techniques, we report precision, recall and F1 scores on SimpleQuestions
and LC-QuAD 1.0, and Hits@1 performance on WebQSP and MetaQA datasets. The
subscript ${pre}$ indicates the “pre-trained" version of our system using LC-
QuAD 2.0 dataset.

###  3.4 Effect of Pretraining

Figure 2: System performance on MetaQA 2-hop questions using different number
of training examples, with and without pretraining on LC-QuAD 2.0. Figure 3:
System performance on LC-QuAD 1.0 using different number of training examples,
with and without pretraining on LC-QuAD 2.0.

Our architecture is designed to allow transfer learning between entirely
different QA dataset/KG pairs. As it is harder to show improvements with pre-
training on larger datasets, we consider low-resource settings to demonstrate
the benefit of transfer, even across KGs. This is useful when there is
scarcity of training data for a new target KG. We investigate the benefit of
pretraining the semantic parsing stage using LC-QuaD 2.0 (Wikidata KG), before
training on the 2-hop dataset in MetaQA (MetaQA-KG) and the LC-QuAD 1.0
dataset (DBpedia). Figures 2 and 3 show the performance of STaG-QA on each
dataset with and without pre-training. We make note of the following
observations. First, without any fine-tuning on either datasets, the pre-
trained version STaG-QApre was able to achieve 18% Hits@1 on MetaQA and 8% F1
on LC-QuAD 1.0, indicating the model ability to do zero-shot transfer across
knowledge graphs. Second, the pre-trained version provides better performance
and is able to converge much faster. For example, in MetaQA (Figure 2), STaG-
QApre was able to reach almost 100% Hits@1 with 100 training examples only. To
reach the same 100% Hits@1, STaG-QA without pretraining required 1,000
examples, an order of magnitude more training data. The same behaviour can be
observed on LC-QuAD 1.0, where STaG-QApre is better than STaG-QA, but with
both versions continuing to improve as more training data becomes available.

###  3.5 Generalization to novel relation composition

Common KBs have a large number of relations. For example, DBpedia (v2016-10)
has around $\sim$60K relations, Wikidata (as of March 2020) has $\sim$8K
relations, whereas Freebase contains $\sim$25K relations. In multi-hop
queries, these relations can be arranged as paths (e.g., director
$\rightarrow$ language) where possible path combinations grow combinatorially.
With learning-based approaches, seeing all or most possible relation
combinations at training would indeed result in performance improvement at the
testing phase. However, this is impractical and hard to enforce in practical
scenarios with most KBs as it would require significantly large training data
to cover all combinations. Instead, an effective KBQA system should be able to
generalise to unseen relation paths. In this section, we first analyse
existing KBQA datasets to see to which extent this ability is being tested
currently. We then create a development set specifically for testing the
ability of KBQA systems to generalise to unseen multi-hop relation paths.

We show in Table 6 the number of test questions in LC-QuAD 1.0, MetaQA and
WebQSP datasets that contain relation combinations never seen at training. For
instance, MetaQA does not test for any unseen relation paths (0%) where WebQSP
contains only 2.06% of such questions. In contrast, in LC-QuAD 1.0 roughly
half of the test questions contain novel relation compositions.

Dataset | # of questions with unseen paths
---|---
LC-QuAD 1.0 | 490/1,000 (49 %)
WebQSP | 45/1,638 (2 %)
MetaQA 2-hop | 0/14,872 (0 %)
MetaQA 3-hop | 0/14,274 (0 %)
Table 6: Unseen path combinations of seen relations

#### MetaQA Unseen Challenge Set:

In order to further investigate how this issue affects current KBQA systems,
we created a subset from MetaQA, the largest dataset in Table 6 and yet having
no unseen relation combinations at testing. We modified the train and dev sets
of MetaQA as follows: From the 2-hop training set, we removed training
examples containing two randomly chosen relation paths (
actor_to_movie_to_director and director_to_movie_to_actor) and split the dev
set into two, one containing 13,510 questions with all seen relations path in
training and another containing 1,361 questions with all unseen relation
paths. It is important to note that for each of the unseen relation
combinations, the individual relations are present in the training set, i.e,
this experiment is designed to test compositionality rather than zero-shot
relation linking ability.

System | 2-Hop Seen | 2-hop Unseen
---|---|---
EmbedKGQA | 99.00 | 50.00
GraftNet-KB | 97.90 | 75.2
GraftNet-Text | 51.2 | 43.3
GraftNet-Both | 99.13 | 95.41
STaG-QA | 99.9 | 99.7
Table 7: MetaQA Unseen Challenge Set Setting

We then trained STaG-QA, EmbedKGQA and GraftNet on the new reduced training
set and tested the performance on our new development sets (seen and unseen).
Table 7 shows the results for each system on 2-hop questions on seen relation
paths vs unseen ones. The results clearly demonstrate that there is a
significant drop in performance in methods that rank directly across entities
in the KG to predict answers. This is most clearly observed in EmbedKGQA, as
well as GraftNet-KB, though the use of text (GraftNet-Text and GraftNet-Both)
does alleviate this issue. In contrast, our approach is able to maintain
exactly the same level of performance for novel relation compositions using KB
information alone.

##  4 Related Work

There have been a wide variety of Knowledge Base Question Answering (KBQA)
systems (Chen et al. 2020; Saxena, Tripathi, and Talukdar 2020; Maheshwari et
al. 2019; Zou et al. 2014; Diefenbach, Singh, and Maret 2017; Vakulenko et al.
2019; Kapanipathi et al. 2020), trained on datasets that are either question-
sparql pairs (strong supervision) or question-answer pairs (weak supervision).
More generally, the former can use any logical form that expresses the
question as an RDF-query, which is then run on the KG to retrieve the answer.
We describe some KBQA systems in this section.

As mentioned above, the first category of KBQA approaches focus on translating
the natural language questions into an intermediate logical form to retrieve
results from the knowledge base. Generating this kind of semantic parse of the
question has shown improved performance compared to weak-supervision based
approaches (Yih et al. 2016). Furthermore, the intermediate structured
representation of the question provides a level of interpretability and
explanation that is absent in systems that directly rank over entities in the
KG to produce answers. This category can further be classified into (a) rule-
based approaches such as gAnswer (Hu et al. 2017), NSQA (Kapanipathi et al.
2020), and (b) learning-based approaches such as MaSP (Shen et al. 2019) and
GrailQA (Gu et al. 2021).

The rule based approaches primarily depend on generic language based syntactic
(Zou et al. 2014) or semantic parses (Abdelaziz et al. 2021; Kapanipathi et
al. 2020) of the question and build rules on it to obtain a query graph that
represents the sparql query. NSQA, the state of the art approach for DBpedia
based datasets such as LC-QuAD-1.0 (Trivedi et al. 2017) and QALD-9 (Usbeck et
al. 2017), falls in this category. The system uses Abstract Meaning
Representation (AMR) parses of the question and a heuristic-based graph-driven
methodology to transform the AMR graph to a query graph that represents the
sparql query. Many of these systems have components or aspects that are
specific to the KG they evaluate on, and do not trivially generalize to other
KGs. In particular GAnswer, NSQA, and QAmp are specific to DBpedia and do not
evaluate their approaches on any other KGs.

On the other hand, MaSP is a multi-task end-to-end learning approach that
focuses of dialog-based KGQA setup. MaSP uses a predicate classifier which
makes transfer across KGs non-trivial. We adapt the architecture to make it
generalizable across KGs, by replacing the relation classifier with a BERT-
based ranker that leverages similarities in label semantics between KGs. A
prominent work, Krantikari (Maheshwari et al. 2019) is on regular KBQA and has
a ranking based approach that is heavily dependent on the knowledge graph. The
approach ranks all candidate graph patterns retrieved from the knowledge graph
based on the grounded entity. In multi-hop settings, as in MetaQA with 3-hop
questions, retrieving all possible candidates upto $n$-hops (for an arbitrary
choice of $n$) and then ranking across all of them is expensive. In contrast,
our work focuses on a generative approach to modeling query graph patterns.
GrailQA is an end-to-end learning approach that generates logical S-forms. It
characterizes a few forms of generalization such as compositionality and zero-
shot generalization. It also introduces a method that transfers across QA
datasets, but within the same KG. On the other hand, we demonstrate transfer
across KGs.

The final category of KBQA approaches are trained solely with question-answer
pairs ignoring the intermediate logical representation of the question.
EmbedKGQA (Saxena, Tripathi, and Talukdar 2020) and GraftNet are two such
approaches that directly ranks across entities in the knowledge base to
predict an answer, by leveraging either KG embeddings from Knowledge Base
Completion (KBC); or creating a unified graph from KB and text. However, these
approaches do not generalize well to novel relation compositions not seen
during training. Finally, it is unclear how to transfer KBC embedding-based
approaches such as EmbedKGQA across KGs since the learnt KG embeddings are
tightly coupled with the specific KG in question.

##  5 Conclusion

In this work, we show that a simple 2-stage architecture which explicitly
separates the KG-agnostic semantic parsing stage from the KG-specific
interaction can generalize across a range of datasets and KGs. We evaluated
our approach on four different KG/QA pairs, obtaining state-of-the-art
performance on MetaQA, LC-QuAD 1.0, and SimpleQuestions-Wiki; as well as
competitive performance on WebQSP. Furthermore, we successfully demonstrate
transfer learning across KGs by showing that pre-training the semantic parsing
stage on an existing KG/QA-dataset pair can help improve performance in low-
resource settings for a new target KG; as well as greatly reduce the number of
examples required to achieve state-of-the-art performance. Finally, we show
that some popular benchmark datasets do not evaluate generalization to unseen
combinations of seen relations (compositionality), an important requirement
for a question answering system.

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