# Half-integer conductance plateau at the $\nu=2/3$ fractional quantum Hall
state in a quantum point contact

J. Nakamura<EMAIL_ADDRESS>Department of Physics and Astronomy, Purdue
University  Birck Nanotechnology Center, Purdue University  S. Liang
Department of Physics and Astronomy, Purdue University  Birck Nanotechnology
Center, Purdue University  G. C. Gardner  Birck Nanotechnology Center, Purdue
University  Microsoft Quantum Lab West Lafayette  M. J. Manfra
<EMAIL_ADDRESS>Department of Physics and Astronomy, Purdue University
Birck Nanotechnology Center, Purdue University  Microsoft Quantum Lab West
Lafayette  Elmore Family School of Electrical and Computer Engineering, Purdue
University  School of Materials Engineering, Purdue University

###### Abstract

The $\nu=2/3$ fractional quantum Hall state is the hole-conjugate state to the
primary Laughlin $\nu=1/3$ state. We investigate transmission of edge states
through quantum point contacts fabricated on a GaAs/AlGaAs heterostructure
designed to have a sharp confining potential. When a small but finite bias is
applied, we observe an intermediate conductance plateau with
$G=0.5\frac{e^{2}}{h}$. This plateau is observed in multiple QPCs, and
persists over a significant range of magnetic field, gate voltage, and source-
drain bias, making it a robust feature. Using a simple model which considers
scattering and equilibration between counterflowing charged edge modes, we
find this half-integer quantized plateau to be consistent with full reflection
of an inner counterpropagating -1/3 edge mode while the outer integer mode is
fully transmitted. In a QPC fabricated on a different heterostructure which
has a softer confining potential, we instead observe an intermediate
conductance plateau at $G=\frac{1}{3}\frac{e^{2}}{h}$. These results provide
support for a model at $\nu=2/3$ in which the edge transitions from a
structure having an inner upstream -1/3 charge mode and outer downstream
integer mode to a structure with two downstream 1/3 charge modes when the
confining potential is tuned from sharp to soft and disorder prevails.

##  I Introduction

The quantum Hall effect occurs when a two-dimensional electron gas (2DEG) is
cooled to low temperature and placed in a strong magnetic field. Fractional
quantum Hall states [1, 2] exhibit fractionally quantized Hall conductance,
and have excitations that behave as fractionally charged quasiparticles which
obey anyonic braiding statistics [3, 4, 5, 6, 7, 8].

The concept of particle-hole symmetry plays a central role in the hierarchical
construction of daughter states from the $\nu=1/m$ Laughlin series [9, 10, 5].
If Landau-level mixing is neglected, particle-hole symmetry is expected for
each Landau level [10]; a similar approximate particle-hole symmetry exists
for composite fermions [11]. The $\nu=2/3$ fractional quantum Hall state can
be considered to be the hole-conjugate state to the $\nu=1/3$ state [10, 11].
In this picture, the fully filled $\nu=1$ state is considered to be the
vacuum, and holes form a $\nu=1/3$ state on top of this vacuum, leading to an
overall 2/3 filling factor. The 2/3 state has been investigated in numerous
theoretical works [12, 13, 14].

The edge mode structure in hierarchical states may possess several branches
[12, 15]. Moreover, multiple edge structures have been proposed for the 2/3
state. The edge structure which most straightforwardly follows from the hole-
conjugate nature of the state was proposed by MacDonald [12, 16]. In this
picture, the edge consists of an outer downstream integer edge mode (from the
underlying $\nu=1$ state) and an inner, counterpropogating -1/3 edge mode. In
this context, counterpropagating (or upstream) edge modes travel in the
direction opposite to the conventional quantum Hall chiral edge current (edge
modes following the conventional direction may be referred to as downstream).
Equilibration between the two edge modes leads to a total conductance of
$\frac{2}{3}\frac{e^{2}}{h}$. A different edge structure was proposed by Kane
and collaborators [17] in which disorder dominates and drives an edge phase
transition to a single downstream charge mode with conductance
$\frac{2}{3}\frac{e^{2}}{h}$ and a counterpropagating neutral mode. A model
developed by Meir and coworkers considered the impact of soft confining
potential in addition to disorder and predicted a reconstructed edge involving
the formation of a strip with filling factor $\nu=1/3$ at the edge leading to
two downstream charge modes with conductance $\frac{1}{3}\frac{e^{2}}{h}$
along with counterpropagating neutral modes [18, 19]; other theoretical works
have also examined the possibility of incompressible strips with fractional
fillings when the confining potential is soft [20, 21, 22]. Experimental
studies of the $\nu=2/3$ state in quantum point contacts have usually shown an
intermediate conductance plateau with $G=\frac{1}{3}\frac{e^{2}}{h}$ when the
QPC gates are negatively biased to bring the edges close together, which
supports the existence of the Meir edge structure in those experiments [23,
24, 25]. Experiments in which this $G=\frac{1}{3}\frac{e^{2}}{h}$ intermediate
plateau was observed also detected upstream noise attributed to
counterpropagating neutral modes [26, 25]. These neutral modes are likely to
be detrimental to interference experiments because their entanglement with the
charge modes leads to dephasing [27, 28].

The device investigated in our experiments consists of two quantum point
contacts (QPCs) separated by a pair of side gates, and utilizes a GaAs/AlGaAs
heterostructure with auxiliary screening wells above and below the main
quantum well (shown in Supp. Fig. 1 and described in Supp. Section 1). This
geometry can be used to define a Fabry-Perot interferometer [29, 30, 31, 32,
33, 8, 34], but in this work we probe the QPCs independently without inducing
interference. A false color SEM image is shown in Fig. 1a. The QPCs have a
separation of 300 nm, and the dimensions of the interferometer are 800 nm
$\times$ 800 nm. We probe the QPCs individually, measuring the conductance of
one QPC while tuning the gate voltage on the other to full transmission (in
this mode of operation no interference occurs since backscattering only occurs
in the QPC being probed). We apply a voltage on the source contact $V_{SD}$
which is a combination of an AC voltage and a DC voltage (the application of
DC bias is described where relevant). The AC bias typically used is $10$
$\mu$V. Using another pair of contacts, the voltage drop across the device is
measured, as illustrated in Fig. 1a, which makes it possible to calculate the
conductance as $G=\frac{I}{V}$. We stress that the semiconductor
heterostructure employed here has been designed to produce sharp confining
potentials consistent with our recent interferometry experiments [33, 8, 34].
Details of the interferometric measurements at $\nu=2/3$ will be detailed in a
future publication.

##  II Integer Regime

Figure 1: a) False-color SEM image of device with two QPCs. b) QPC sweeps at
$B$ = 0. The curve for QPC 2 is shifted by 0.5 V for clarity. c) QPC Sweeps at
$\nu=1$. Measurements are performed at $T=$ 10 mK. Figure 2: a) Bulk transport
$R_{xy}$ and $R_{D}$ measured across the device. For the $R_{D}$ measurement,
both QPCs and the side gates are set to -0.3 V so that the 2DEG under the
gates is depleted and current flows through the device, but minimal
backscattering occurs in the QPCs. b) QPC sweeps at $\nu=2/3$ with DC source-
drain bias of 0 V (dashed lines) and 50 $\mu$V (solid lines). With 50 $\mu$V
bias, an intermediate plateau at 0.5 $e^{2}/h$ appears in both QPCs. QPC 2 is
shifted by 0.5 V for clarity. c) Differential conductance for QPC 1 as a
function of QPC gate voltage and source-drain bias $V_{SD}$. The emergence of
the 0.5 $e^{2}/h$ plateau as $V_{SD}$ is increased can be seen; beyond
$V_{SD}\approx 25\mu$V the plateau does not change significantly and
conductance depends weakly on $V_{SD}$. White dashed lines indicate the
regions where $G\approx 0.5\frac{e^{2}}{h}$. d) Differential conductance for
QPC 1 versus magnetic field and QPC voltage with $V_{SD}=50$ $\mu$V. e) Line
cuts of conductance versus QPC voltage at different magnetic field.

In Fig. 1b we show the conductance of the individual QPCs, QPC 1 and QPC 2,
versus gate voltage at zero magnetic field. The QPCs exhibit quantized
conductance plateaus corresponding to fully transmitted conductance modes. In
Fig. 1c we show conductance versus gate voltage at the $\nu=1$ integer quantum
Hall state. Unlike at zero field, where the conductance gradually decreased in
steps as the applied gate voltage reduces the effective width of the QPC, at
$\nu=1$ the QPCs exhibit a single wide plateau (corresponding to full
transmission of the $\nu=1$ edge state) and a very abrupt drop in conductance
when the edge state is pinched off in the QPC. This abrupt pinchoff suggests
that the confining potential is sharp, as expected for devices utilizing the
screening well structure [35], since minimal backscattering occurs until the
edges are brought very close together. This behavior contrasts with the
behavior generally observed in QPCs on standard GaAs heterostructures without
screening wells at $\nu=1$, which often show gradual decreases in conductance,
resonances, and sometimes intermediate fractionally quantized plateaus due to
edge reconstruction [28, 24].

##  III QPC conductance at $\nu=2/3$

Next we operate the device at bulk filling factor $\nu=2/3$. Fig. 2a shows the
bulk Hall resistance $R_{xy}$ and the diagonal resistance $R_{D}$ measured
across the device with the 2DEG under the gates depleted, but with small
enough voltages on the gates that minimal backscattering occurs in the QPCs,
$V_{QPC1}=V_{QPC2}=-0.3$ V. A wide plateau is visible in $R_{xy}$ with
resistance $\frac{3}{2}\frac{h}{e^{2}}\approx 38.7$ k$\Omega$, corresponding
to the $\nu=2/3$ state, and $R_{D}$ exhibits a nearly quantized plateau over a
somewhat narrower region. Fig. 2b shows conductance versus gate voltage for
both QPCs at $B$ = 5.9 T, near the center of the plateau. When there is zero
applied DC bias (dashed lines), the QPCs exhibit exhibit a somewhat less sharp
pinchoff than at $\nu=1$. Between 0 and -2 V both QPCs show conductance close
to $\frac{2}{3}\frac{e^{2}}{h}$, indicating close to full transmission of all
edge states (note that the curve for QPC 2 is shifted by 0.5 V to the right
for clarity). Past the point where conductance starts to drop more rapidly,
both QPCs exhibit a nearly flat region before pinchoff. Unlike the experiments
in Ref. [23, 25], there is no intermediate quantized conductance plateau at
$G=\frac{1}{3}\frac{e^{2}}{h}$. The behavior changes when a finite source-
drain bias of 50 $\mu$V is applied, shown in the solid lines; in this
situation the applied source-drain bias is a combination of a 10 $\mu$V AC
bias which is used to probe the differential conductance and the 50 $\mu$V DC
bias. With the finite bias both QPCs exhibit an intermediate conductance
plateau; however, the value of the intermediate conductance plateaus is
0.5$\frac{e^{2}}{h}$ rather than the $\frac{1}{3}\frac{e^{2}}{h}$ seen in
previous experiments [23, 25] (the quantization is not exact, but the
conductance is within 2% of 0.5 $\frac{e^{2}}{h}$ for both QPCs). This
observation suggests that a different edge structure may be present in our
system, although it is not obvious why the intermediate plateau only occurs
when finite bias is applied. Intermediate conductance plateaus are generally
interpreted as occurring when one or more inner edge states are fully
reflected while the outer edge states are fully transmitted, leading to some
range of gate voltage before the next outer edge state starts to be
backscattered when there is an incompressible region in the middle of the QPC
and the conductance is constant.

In Fig. 2c we plot the differential conductance for QPC 1 as a function of
source-drain bias and QPC voltage; dashed lines indicate regions where
$G\approx 0.5\frac{e^{2}}{h}$. It appears that the nearly-flat region in
conductance observed at zero applied bias develops into the 0.5
$\frac{e^{2}}{h}$ plateau as finite bias is applied, and the effect is
symmetric around zero bias (there is a small offset of a few $\mu$V due to an
offset in the amplifier). The value of the intermediate plateau does not
change significantly when $V_{SD}$ is increased past $\approx 25$ $\mu$V. In
Fig. 2d we plot conductance of QPC 1 as a function of magnetic field $B$ and
QPC voltage $V_{QPC1}$ at $V_{SD}$ = 50 $\mu$V. Both the primary plateau at
$G=\frac{2}{3}\frac{e^{2}}{h}$ and the intermediate $G=0.5\frac{e^{2}}{h}$
plateau persist over a significant range of magnetic field from approximately
5.77 T to 6.05 T. Outside of this range the conductance drops and the plateaus
are no longer quantized, as expected from inspection of Fig. 2a. Line cuts at
several values of magnetic field are shown in Fig. 2e. Despite the requirement
of a small finite bias, the $G=0.5\frac{e^{2}}{h}$ plateau appears to be a
robust feature, since it appears in both QPCs, spans a significant range of
magnetic field, and does not have significant $V_{SD}$ dependence past $25$
$\mu$V. We have observed this $G=0.5\frac{e^{2}}{h}$ conductance plateau in
another set of QPCs on a different chip fabricated on the same wafer (Supp.
Fig. 2).

##  IV Edge model at $\nu=2/3$

Figure 3:

a) Filling factor profile in the MacDonald edge structure versus position on
each edge of the Hall bar. b) Schematic of edge states in a Hall bar in the
Macdonald picture, with a counterpropogating inner -1/3 edge state (red
arrows) and outer integer edge state (black arrows). Dashed white lines
indicate equilibration, which is expected to occur near the Ohmic contacts. c)
Qualitative plot of the chemical potential for the inner mode (red) and outer
mode (blue) on the bottom edge of the Hall bar. d) Schematic of the situation
of a QPC which fully transmits the outer edge state and fully reflects the
inner one. There will be additional equilibration in the vicinity of the QPC.
e) Plot of the chemical potential versus position for the Hall bar with QPC
and full reflection of the inner mode.

The 0.5 $\frac{e^{2}}{h}$ conductance plateau is not straightforward to
interpret, since no proposed edge structure contains an outer edge state with
$\Delta\nu=0.5$ which would carry 0.5 $\frac{e^{2}}{h}$ on its own (unlike the
$\nu=5/2$ fractional state, $\nu=1/2$ is expected to be a compressible sea of
composite fermions that does not form a quantum Hall state [36]). However, a
possible explanation for the 0.5 $\frac{e^{2}}{h}$ plateau could come from the
counterpropagating charge mode as proposed in the Macdonald edge structure
[12, 16]. Following the model of the $\nu=2/3$ state as a 1/3 state of holes
on top of a vacuum of a fully filled $\nu=1$ state, the filling factor must
increase from $\nu=2/3$ in the bulk to $\nu=1$ at the edge before decreasing
to zero, shown schematically in Fig. 3a. The re-entrant density profile is
enabled by the combination of the confining potential with the electrostatic
interaction between electrons in the vacuum $\nu=1$ state and holes that form
the inner -1/3 state [12, 16, 18]. This results in an inner counterpropagating
edge state and outer downstream edge state. In this case, the inner upstream
edge state and outer downstream edge state on one edge of a Hall bar can have
different chemical potentials because they are emitted from different Ohmic
contacts. The situation is shown schematically in Fig. 3b. Assuming the edge
modes have a small enough separation to allow charge transfer between them,
the counterflowing edge modes will equilibrate and reach the same chemical
potential. Based on the well-established experimental properties of quantum
Hall states in bulk samples, the equilibrium chemical potential of each edge
should be the potential of the contact from which the downstream, higher-
conductance edge state emanated from. This leads to a potential difference
$V_{Hall}=\frac{\mu_{S}-\mu_{D}}{e}$, and a two-terminal conductance
$G=\frac{2}{3}\frac{e^{2}}{h}$, consistent with the observed bulk conductance
properties of the 2/3 state. A quantum point contact which causes
backscattering will take the edge states out of equilibrium and reduce the
conductance of the device. Due to the somewhat more complicated nature of
equilibration between counterflowing edge states compared to coflowing ones,
this situation is less straightforward than the case of a QPC with all-
downstream edge states. We analyze the situation of a bulk Hall bar and of a
QPC when a counter-propagating edge mode is present.

The conductance of a pair of counterflowing edge modes can be treated in a
simple model where the current carried by each is equal to the mode’s
conductance $G_{i}$ times its local chemical potential $\mu_{i}(x)$ at its
position along the edge (similar models were discussed in Refs. [37, 38]),
$I_{1}(x)=\mu_{1}(x)G_{1}$ and $I_{2}(x)=\mu_{2}(x)G_{2}$. Equilibration
(which has been studied theoretically [37, 39, 40]) is taken into account by
allowing charge to be exchanged between the two modes and assuming a tunneling
current per unit length between mode 1 and mode 2 $dI_{12}/dx$ proportional to
the chemical potential difference:

$dI_{12}=\frac{e^{2}}{h}\frac{\mu_{2}-\mu_{1}}{l_{0}}dx$ (1)

Here $l_{0}$ is the characteristic equilibration length between the two edge
modes. Conservation of current requires $I=\mu_{1}(x)G_{1}-\mu_{2}(x)G_{2}=$
constant. Eqn. 1 can be used to obtain differential equations for $\mu_{1}$
and $\mu_{2}$:

$\frac{d\mu_{1}}{dx}=\frac{(\mu_{2}-\mu_{1})G_{0}}{G_{1}l_{0}}$ (2)

$\frac{d\mu_{2}}{dx}=\frac{(\mu_{1}-\mu_{2})G_{0}}{G_{2}l_{0}}$ (3)

$G_{0}\equiv\frac{e^{2}}{h}$ is the conductance quantum. Considering the
bottom edge of the Hall bar in Fig. 3b where the inner edge emanates from the
source contact, $\mu_{1}(0)=\mu_{S}$, and the outer edge from the drain
contact, $\mu_{2}(L)=\mu_{D}$, the differential equations are straightforward
to solve. They yield:

$\mu_{1}(x)=\frac{I}{G_{1}-G_{2}}+\left(\mu_{S}-\frac{I}{G_{1}-G_{2}}\right)e^{-\alpha
x}$ (4)

$\mu_{2}(x)=\frac{I}{G_{1}-G_{2}}+\frac{G_{1}}{G_{2}}\left(\mu_{S}-\frac{I}{G_{1}-G_{2}}\right)e^{-\alpha
x}$ (5)

$I=\frac{(\mu_{D}-\mu_{S}\frac{G_{1}}{G_{2}}e^{-\alpha
L})(G_{1}-G_{2})}{1-\frac{G_{1}}{G_{2}}e^{-\alpha L}}$ (6)

Here $\alpha\equiv\frac{G_{0}(G_{2}-G_{1})}{l_{0}G_{1}G_{2}}$, and $L$ is the
length of the edge of the Hall bar. For large $L$ (much larger than the
characteristic equilibration length $l_{0}$) $I\approx\mu_{D}(G_{1}-G_{2})$,
reflecting the fact that the edge states equilibrate at the chemical potential
of the contact that the higher conductance outer edge state emanates from. The
chemical potentials of the inner and outer edge states, $\mu_{1}$ and
$\mu_{2}$, are qualitatively sketched as a function of length along the Hall
bar in Fig. 3c. An equivalent relationship will hold on the top edge of the
Hall bar so that the total current
$I_{total}=(\mu_{S}-\mu_{D})(G_{2}-G_{1})=\frac{2}{3}\frac{e^{2}}{h}(\mu_{S}-\mu_{D})$,
thus recovering the two-terminal conductance $\frac{2}{3}\frac{e^{2}}{h}$
observed in macroscopic quantum Hall samples at $\nu=2/3$. Furthermore, in
this limit $\mu_{2}(0)=\mu_{D}+\frac{G_{1}}{G_{2}}(\mu_{S}-\mu_{D})$ and
$\mu_{1}(L)=\mu_{D}$.

This solution can be applied to the case of a QPC that fully transmits the
outer mode and fully reflects the inner mode, as illustrated in Fig. 3d. The
solutions to the differential equations can be applied to each quadrant of the
Hall bar, allowing the chemical potential $\mu_{QPC}^{BL}$ on the bottom left
edge of the QPC and $\mu_{QPC}^{UR}$ at the upper right edge of the QPC to be
solved (note that on the top left and bottom right edges the inner and outer
modes will not be at equilibrium due to the backscattering of the QPC, so
there will be additional equilibration at those positions, as indicated by the
white dashed lines). Applying the solutions to the differential equations in
the limit $L>>l_{0}$ gives the equations:

$\mu_{QPC}^{BL}=\mu_{QPC}^{UR}\frac{G_{1}}{G_{2}}+\mu_{D}\left(1-\frac{G_{1}}{G_{2}}\right)$
(7)

$\mu_{QPC}^{UR}=\mu_{QPC}^{BL}\frac{G_{1}}{G_{2}}+\mu_{S}\left(1-\frac{G_{1}}{G_{2}}\right)$
(8)

Solving yields $\mu_{QPC}^{BL}=\frac{\mu_{D}G_{2}+\mu_{S}G_{1}}{G_{2}+G_{1}}$
and $\mu_{QPC}^{UR}=\frac{\mu_{S}G_{2}+\mu_{D}G_{1}}{G_{2}+G_{1}}$. This
results in a total current:

$I_{QPC}=(\mu_{S}-\mu_{D})\frac{G_{2}-G_{1}}{1+\frac{G_{1}}{G_{2}}}$ (9)

For the case of $G_{1}=\frac{1}{3}\frac{e^{2}}{h}$ and $G_{2}=\frac{e^{2}}{h}$
(as expected for the MacDonald edge structure), the result is
$G_{QPC}=\frac{1}{2}\frac{e^{2}}{h}$, matching the value of the intermediate
plateaus observed in Fig. 2b for $V_{SD}$ = 50 $\mu$V. The chemical potential
on the bottom edge in this situation is sketched in Fig. 3e. An abrupt
discontinuity occurs for $\mu_{1}$ in the middle of the Hallbar at the
position of the QPC since at that point the inner mode is fully reflected.

Although inner edge modes are usually assumed to be reflected before outer
ones as more negative gate voltages are applied, at $\nu=2/3$ achieving full
reflection of the inner edge state while maintaining full transmission of the
outer one would seem to require an unusual situation where the filling factor
in the middle of the QPC is $\nu=1$, higher than the bulk density of
$\nu=2/3$. The Macdonald model arrives at a re-entrant density profile in
which the density at the edge increases from the bulk filling factor value of
2/3 to $\nu=1$ due to the combined electrostatic potential of the vacuum state
of the fully-filled N = 0 Landau level and the external confining potential
[12, 16] as shown in Fig. 3a. Full reflection of the inner mode would be
achieved by moving the edges together via more negative gate voltage until the
outer strips of $\nu=1$ fluid merge in the middle of the QPC so that the
interface between $\nu=1$ and $\nu=2/3$ is absent inside the QPC; thus the
inner mode cannot propagate through. This would be a somewhat unusual
situation since QPCs are usually considered to be regions of lower density
than the bulk. The lack of a fully quantized plateau at zero bias might
indicate that the electrostatics in the QPC do not enable a region reaching
full $\nu=1$ filling inside the QPC region once the inner mode is fully
reflected, but rather the filling is somewhat lower, resulting in a small
amount of simultaneous backscattering of the outer mode and
$G<0.5\frac{e^{2}}{h}$ as observed in Fig. 2b after the initial sharp drop in
conductance. Disorder-mediated tunneling may also be a contributing factor
[24]. Finite bias tends to reduce backscattering in Luttinger liquids [29], so
the emergence of the quantized intermediate plateau at $V_{SD}=50$ $\mu$V
could be due to the suppression of backscattering for the outer mode in this
regime. A specific prediction of Luttinger liquid theory is that when $V_{SD}$
is increased, transmission of the edge state through a barrier will increase
until it reaches full transmission, which agrees well with our observation
that after a small $V_{SD}$ is applied the conductance increases to the half-
integer quantized value indicating full transmission of the outer edge state,
and then remains nearly constant [41]. Although integer quantum Hall edge
states are generally expected to exhibit Fermi liquid rather than Luttinger
liquid behavior based on theory [41], when an integer edge state lies parallel
to a co-propagating or counter-propagating edge state this may induce
Luttinger liquid behavior [42, 43]. Additionally, non-linear conductance
suggestive of Luttinger liquid behavior has been observed for the $\nu=1$
integer quantum Hall state in QPCs [44], suggesting that in real systems even
isolated integer edge states may have an interaction parameter that is not
exactly 1 and may thus diverge from ideal Fermi liquid behavior.

An assumption for applying this model to our device is that the equilibration
length $l_{0}$ is much smaller than the length from the QPC to the source and
drain Ohmic contacts. In our devices, this length is $\approx 500$ $\mu$m.
Measurements in which both QPCs are tuned to backscatter the inner edge
indicate that the edges partially, but not fully, equilibrate on the 800 nm
length separating the two QPCs (see Supp. Section 3 and Supp. Fig 3), which
makes it very likely that on the much longer length scale from the QPC to the
Ohmic contacts, the edges will indeed fully equilibrate. Equilibration at
$\nu=2/3$ has been investigated in Hall bar geometries in GaAs. Lin et al.
found an equilibration length of $\approx 8$ $\mu$m [38] at $B=6.5$ T. Maiti
et al. found an equilibration length which depended sharply on magnetic field,
varying from $\approx 50$ $\mu$m at $B=8.8$ T to $\approx 800$ $\mu$m at
$B=10.8$ T [45]; since our magnetic field of 5.9 T is much smaller, it is
reasonable that the equilibration length should be smaller. Notably, however,
is not clear what the edge structure was in these previous experiments given
that they used different types of GaAs/AlGaAs heterostructures than the one
used in our experiment, so the equlibration length scales may not be directly
comparable. Measurements of the $\nu=2/3$ state in graphene have shown
evidence for upstream transport, but charge equilibration appears to occur on
short length scales [46].

To our knowledge half integer quantized conductance in a QPC at $\nu=2/3$ has
not previously been reported; instead, an intermediate plateau at
$G=\frac{1}{3}\frac{e^{2}}{h}$ is usually observed [23, 25, 24]. This may
reflect the fact that modulation doped GaAs/AlGaAs heterostructures used for
quantum Hall experiments usually have shallow confining potentials due to the
large setback of the doping layers from the quantum well and large distance of
the surface gates from the quantum well (typically on the order of 100 nm).
Such shallow confining potentials may be likely to place devices in the regime
described by Meir in which there are two downstream edge modes with
conductance $\frac{1}{3}\frac{e^{2}}{h}$. On the other hand, in a few
experiments a conductance plateau with $G=1.5\frac{e^{2}}{h}$ has been
observed in QPCs at $\nu=5/3$ [47, 48, 49], which is the equivalent of the
$\nu=2/3$ state with opposite spin. It is noteworthy that these experiments
used techniques likely to increase the density of the 2DEG in the QPC. In Ref.
[47] and Ref. [49], doping well heterostructures were used, and gate biases
were applied at an elevated temperature of 4 K and 6 K, allowing electrons in
the X-band of the AlAs layers next to the doping wells to equilibrate with the
2DEG and partially screen the gate voltage [50]. The $G=1.5\frac{e^{2}}{h}$
plateau was then observed when the gate voltage was increased above the
annealed-in value. This unusual decrease in conductance from
$\frac{5}{3}\frac{e^{2}}{h}$ to $\frac{3}{2}\frac{e^{2}}{h}$ suggests that the
half-integer plateau occurred when the density in the center of the QPC was
increased above the bulk density due to increasing of the gate voltage after
annealing. In Ref. [48], an additional gate in the middle of the device had a
positive bias applied, which would be expected to yield higher electron
density in the middle of the QPC. A possible explanation for the
$G=\frac{3}{2}\frac{e^{2}}{h}$ plateau is that the techniques of Refs. [47,
48, 49] forced the density in the center of the QPC to be higher than the bulk
by their external gate voltages, thus yielding $\nu=2$ in the QPC, which with
full equilibration of the additional edge modes in the QPC results in
quantized conductance $G=\frac{3}{2}\frac{e^{2}}{h}$. Similar to the QPC gate
voltage dependence in Ref. [49], Ref. [48] shows a non-monotonic dependence on
the center gate voltage, supporting the possibility that the 2DEG density in
the middle of the QPC is being forced above the bulk value by the external
gate potential. A notable difference in our experiment compared to these
previous works is that in our device, the conductance increases nearly
monotonically with gate voltage, with the primary
$G=\frac{2}{3}\frac{e^{2}}{h}$ plateau occurring at higher gate voltage
compared the $G=0.5\frac{e^{2}}{h}$ plateau, suggesting that the lower-
conductance intermediate plateau does not occur because the externally applied
gate voltages have forced the density in the QPC to be higher, but because the
intrinsic interactions of the electrons favor the formation of a $\nu=1$ strip
and re-entrant density profile at the edge.

Similar to the previous experiments [47, 48, 49], we also observe an
intermediate plateau at $G=1.5\frac{e^{2}}{h}$ at $\nu=5/3$ in both QPCs
(Supp. Fig. 4a and Supp. Section 4), which suggests that an edge structure
occurs at $\nu=5/3$ similar to the one at $\nu=2/3$ in our device. On the
other hand, at the particle-like fractional quantum Hall states $\nu=4/3$ and
$\nu=2/5$, we do not observe anomalous intermediate plateaus that would imply
a re-entrant density profile, which is consistent with the expectation that
the $\nu=1$ strip and re-entrant density profile occur only for hole-like
fractional quantum Hall states. This further distinguishes our work from Ref.
[49], in which anomalous plateaus were observed even for particle-like states
such as $\nu=4/3$.

It is also noteworthy that evidence for counter-propagating charge transport
at short distances has been observed at $\nu=2/3$, but only in the spin-
unpolarized state [51]. Due to the fact that our 2DEG has relatively high
density and uses a wide, symmetric quantum well, the 2/3 state is very likely
polarized in our system [52, 53]. Notably, numerical studies in the composite
fermion picture predict counterpropagating modes for both the spin polarized
and unpolarized $\nu=2/3$ states [13]. The interplay of spin polarization and
confining potential at $\nu=2/3$ requires more investigation.

##  V Comparison to a QPC on a non-screening well structure

Figure 4:  a) Layer stack of the non-screening well heterostructure grown by
MBE. b) Gate sweep at $\nu=1$ for the non-SW QPC. A quasi-plateau at
$G=\frac{1}{3}\frac{e^{2}}{h}$ is visible. c) Gate sweep at $\nu=2/3$ for the
non-SW QPC. A clear intermediate plateau at $G=\frac{1}{3}\frac{e^{2}}{h}$ is
visible.

In order to confirm that the use of the screening well heterostructure enables
the observation of the $G=\frac{1}{2}\frac{e^{2}}{h}$ plateau, we have also
measured a QPC fabricated on a standard non-screening well heterostructure.
The standard heterostructure uses a single GaAs/AlGaAs interface rather than a
quantum well to confine the 2DEG. Fig. 4a shows the standard structure. Fig.
4b shows conductance versus gate voltage at $\nu=1$ (note that the range of
gate voltage is smaller because the gate potential is not screened by the
screening layers). In contrast to the wide plateau and very sharp pinchoff in
the screening well QPCs, this standard structure QPC shows a narrow primary
plateau with $G=\frac{e^{2}}{h}$ and a much more gradual decrease in
conductance. At $\nu=1$ there also appears to be an intermediate quasi-plateau
at $G\approx\frac{1}{3}\frac{e^{2}}{h}$, consistent with the phenomenon of
edge reconstruction reported in [28]. Fig. 4c shows conductance versus gate
voltage at $\nu=2/3$, where a clear intermediate plateau at
$G=\frac{1}{3}\frac{e^{2}}{h}$ is present, consistent with previous results
using non-screening well heterostructures [25, 28]. These results support the
theoretical picture that a soft confining potential (as usually realized in
standard GaAs/AlGaAs heterostructures not utilizing screening layers) results
in a reconstructed edge at $\nu=2/3$ with an outer strip of filling
$\nu=\frac{1}{3}$ and two downstream $\frac{1}{3}\frac{e^{2}}{h}$ charge
modes, as described by the Meir edge structure [18, 19]. The absence of this
$G=\frac{1}{3}\frac{e^{2}}{h}$ plateau in the QPCs with sharp confinement
indicates that the outer $\nu=\frac{1}{3}$ strip does not form, and thus a
different edge structure is present. This demonstrates the profound effect
that confining potential can have on edge structure in the quantum Hall
regime.

##  VI Conclusions

We have measured conductance across QPCs at the $\nu=2/3$ fractional quantum
Hall state. When a small finite source-drain bias is applied, both QPCs
fabricated on the screening well heterostructure exhibit an intermediate
conductance plateau with $G\approx 0.5\frac{e^{2}}{h}$; this plateau is robust
over a moderate range of magnetic field, gate voltage, and source drain bias.
A simple model taking into account equilibration between counterflowing edge
modes suggests that this plateau may be explained in terms of the Macdonald
edge structure as being due to full transmission of the outer downstream
integer edge mode and full reflection of the inner fractional edge mode.
Measurements of a QPC fabricated on a standard, non-screening well
heterostructure reveal instead an intermediate conductance plateau with
$G=\frac{1}{3}\frac{e^{2}}{h}$, which suggests that in this type of structure
there is an outer strip with filling factor $\nu=1/3$ when the bulk is at
filling factor $\nu=2/3$, as occurs in the Meir edge structure. This suggests
that, as predicted by theory, a transition from the Macdonald edge structure
to a reconstructed edge given by the Meir edge structure occurs when the
confining potential changes from sharp to soft.

Our experiments clearly show the importance of confining potential on edge
structure in the quantum Hall regime. The lack of edge reconstruction may
explain why it has been possible to observe Aharonov-Bohm interference
interference at quantum Hall states such as $\nu=1$ and $\nu=1/3$ in devices
using the screening well heterostructure [33, 8, 34], but not in devices using
standard non-SW heterostructures [28, 54].

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##  VII Acknowledgements

This work is supported by the U.S. Department of Energy, Office of Science,
Office of Basic Energy Sciences, under award number DE-SC0020138.


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##  13\. Acknowledgments

The arithmetic Langlands program has been a bustling field of activity in the
past $30$ years with many deep results by a number of extraordinary
mathematicians. To be part of this field (mostly as an observer but
occasionally as a contributor) has been an amazing experience. I would like to
thank my collaborators all of whom have taught me so much, with special thanks
to Matthew Emerton and Toby Gee who have in addition been my close friends.
Thanks to Toby Gee and Ravi Ramakrishna for a number of useful suggestions and
corrections on the first version of this survey. Finally, special thanks to
those mathematicians who allowed me to share some of their personal
recollections in this paper, in particular Christophe Breuil, Ana Caraiani,
Pierre Colmez, Fred Diamond, Michael Harris, Mark Kisin, Peter Scholze,
Richard Taylor, and Andrew Wiles.


11institutetext: TIB Leibniz Information Centre for Science and Technology,
Hannover, Germany 22institutetext: Gottfried Wilhelm Leibniz Universität
Hannover, Germany 33institutetext: L3S Research Center, Leibniz University of
Hannover, Germany
33email<EMAIL_ADDRESS>
# Evaluating Prompt-based Question Answering
for Object Prediction in the
Open Research Knowledge Graph††thanks: Supported by TIB Leibniz Information
Centre for Science and Technology, the EU H2020 ERC project ScienceGraph (GA
ID: 819536) and the BMBF project SCINEXT (GA ID: 01lS22070).

Jennifer D’Souza 11 0000-0002-6616-9509 Moussab Hrou 22 Sören Auer 1133
0000-0002-0698-2864

###### Abstract

There have been many recent investigations into prompt-based training of
transformer language models for new text genres in low-resource settings. The
prompt-based training approach has been found to be effective in generalizing
pre-trained or fine-tuned models for transfer to resource-scarce settings.
This work, for the first time, reports results on adopting prompt-based
training of transformers for scholarly knowledge graph object prediction. The
work is unique in the following two main aspects. 1) It deviates from the
other works proposing entity and relation extraction pipelines for predicting
objects of a scholarly knowledge graph. 2) While other works have tested the
method on text genera relatively close to the general knowledge domain, we
test the method for a significantly different domain, i.e. scholarly
knowledge, in turn testing the linguistic, probabilistic, and factual
generalizability of these large-scale transformer models. We find that (i) per
expectations, transformer models when tested out-of-the-box underperform on a
new domain of data, (ii) prompt-based training of the models achieve
performance boosts of up to 40% in a relaxed evaluation setting, and (iii)
testing the models on a starkly different domain even with a clever training
objective in a low resource setting makes evident the domain knowledge capture
gap offering an empirically-verified incentive for investing more attention
and resources to the scholarly domain in the context of transformer models.

###### Keywords:

Question Answering Prompt-based Question Answering Natural Language Processing
Knowledge Graph Completion Open Research Knowledge Graph.

##  1 Introduction

A cloze test is a language assessment where certain words (cloze text) are
removed from language fragments and the participant must fill them in [19].
This type of test helps language learners demonstrate certain necessary skills
around language comprehension: syntax, contextual understanding, vocabulary,
and factual knowledge. This philosophy of language learning has been applied
to transformer language models such as BERT [7] and RoBERTa [10]. These models
are pre-trained on large-scale text corpora to predict missing words or the
next sentence, producing models with language comprehension abilities, around
syntax, contextual understanding, vocabulary, and factual knowledge, similar
to language learners.

The seminal work by Petroni et al. [13] opened the avenue for testing these
language models for their vasts store of linguistic and factual knowledge with
explicit relational cloze objectives for extracting new facts from the
language models for knowledge base (KB) population as a downstream task. KBs
are effective solutions for accessing gold-standard relational data such as
(Michael Jordan, born-in, x). The traditional method for populating such KBs
with additional facts would otherwise leverage complex NLP pipelines involving
entity extraction, co-reference resolution, entity linking, and relation
extraction components [18] that are known to be plagued by the error
propagation problem from earlier to later components in the pipeline. Instead,
the powerful transformer language models as rich stores of linguistic and
factual information having been pre-trained on billion-word corpus from
encyclopedic sources were probed for additional facts, showing to outperform
the traditional NLP pipeline method for generating relational knowledge to
populate KBs as a downstream task [13].

While the pre-training objective prepares task-agnostic language models from
large-scale corpora which were probed in the work by Petroni et al. [13],
these language models can be further fine-tuned as an additional step with
task-specific objectives which stimulates their task-specific suitability for
a downstream task. To probe the transformer language models for relational
facts as discussed in the earlier paragraph, the knowledge of the original
models was accessed by conditioning on their latent context representations.
On the other hand, to obtain a model specifically for the Question Answering
(QA) downstream task, as a concrete example and the focus of this work, better
versions of the models are obtained when the original models’ weights are used
to first initialize a task-agnostic model which is then further fine-tuned to
obtain a QA task-specific model given instances of the downstream task, e.g.
as defined in the Stanford Question Answering Dataset (SQuAD) [15, 14]. This
work focuses on fine-tuning language models for the QA task inspired after the
SQuAD dataset. The goal is to obtain a model that can extract answers from
context paragraphs based on questions, and to optimize for scholarly knowledge
rather than encyclopedic knowledge by tapping into the pre-trained model’s
cloze task ability and the SQuAD QA fine-tuned model’s structural
representation. The next two paragraphs introduce the why and how of our work.

Why focus on the scholarly domain? In the face of rapid publication rates at
an alarming rate of millions of articles per year [6], researchers are
immensely challenged in keeping up with the latest findings in scholarly
publications. To address this problem, the Open Research Knowledge Graph
(ORKG) [1], leveraging next-generation semantic scholarly knowledge publishing
tools [17], was created to make scholarly contributions more accessible and
machine-actionable, enabling smart information access methods via Comparisons,
Visualizations, and Benchmarks thereby alleviating the researchers’ knowledge
comprehension problem from months or days to a matter of minutes. This growing
KB of structured science-wide scholarly contributions is an unexplored
resource that could be used as a testbed for discovering new facts with the
help of powerful transformer language models. This could be realized in the
long-run as a potential NLP service that assists ORKG users in scholarly
knowledge curation and completion. Specifically, the service, directly
inspired by Petroni et al’s fact probing method [13], could be based on
optimal, fine-tuned versions of the language models to discover additional
objects for new incoming relations. Table 1 shows some example instances of
the proposed task. As evident from these examples, the task aims to extract
objects as answers from scientific paper abstracts given a relation/predicate
as a question. The task is modeled similarly to the SQuAD QA task, which
extracts facts from unstructured encyclopedic knowledge using a question and
answer format. We have chosen the SQuAD-based task formulation for three mains
reasons: 1) the SQuAD QA task formulation intuitively transfers to the
scholarly domain; 2) to exploit the vast collection of options to choose from
of state-of-the-art language models fine-tuned on the QA task; and 3) to test
whether these existing models’ encoded statistical regularities to extract
answers from a given encyclopedic knowledge context can transfer easily to the
scholarly domain. We present a detailed empirical investigation for the first
time of the linguistically-rich fine-tuned SQuAD QA models’ capacity to
transfer to a new domain, i.e. the scholarly domain, which has thus far
remained unexplored.

Table 1: Example instances depicting our Cloze-style adaptation of SQuAD
Question Answering task as an extractive objective from the context given a
question prompt. The “Context” column shows the relevant snippet from
scholarly paper abstract given as input to the system. The “Cloze task” column
shows the four question variants created by appending a “Wh” question word
given an input predicate as: no label, What, Which, and How questions. The
examples are selected to show the diversity in terms of the applicability of
the appended question “Wh” question word and in terms of the various expected
answer types as: a word, number, or a phrase. Text color-coded in blue show
the answer extraction object from the context; text color-coded in red show
the appended prompt elements including “Wh” question words and the “?” symbol.

Context | Cloze task |  Answer
---|---|---
… In the following process oriented knowledge management as it was defined in the EU-project PROMOTE (IST-1999-11658) is presented and the KM-Service approach to realise process oriented … | Approach name? ___ |  PROMOTE
What approach name? ___
Which approach name? ___
How approach name? ___
… to investigate processes of community assembly contributing to biotic resistance to an introduced lineage of Phragmites australis, a model invasive species in North America. … | Continent? ___ |  North America
What continent? ___
Which continent? ___
How continent? ___
… Studies done during different months (January and late February-early March) of the northeast monsoon 2003 revealed a fivefold increase in the average euphotic zone integrated uptake … | Sampling year? ___ |  2003
What sampling year? ___
Which sampling year? ___
How sampling year? ___
Solid lipid nanoparticles (SLNs) are nanocarriers developed as substitute colloidal drug delivery systems parallel to liposomes, lipid emulsions, polymeric nanoparticles, and so forth. … | Type of nanocarrier? ___ |  Solid lipid nanoparticles
What type of nanocarrier? ___
Which type of nanocarrier? ___
How type of nanocarrier? ___

How to obtain an optimal model for a new domain? To pre-train or fine-tune a
language model for QA on a new domain, the traditional method is to use
expensive human-labeled data. Instead, inspired from prior work [5, 16, 25],
this study uses two strategies: 1) template-based unsupervised generation of
structured data similar to SQuAD QA data from the ORKG KB, and 2) structural
prompt-based learning over state-of-the-art SQuAD-specific fine-tuned
transformer models for the scholarly domain. How to obtain an optimal model on
a new domain? The similar structured QA data can serve as prompts to stimulate
the knowledge acquired in the fine-tuned language models to model knowledge
generalizations over the new domain based on the unified input schema in turn
resulting in an optimal trained model in a resource-scarce setting. The idea
is to apply a “Wh” question template on an ORKG structured contribution
predicate, and then generate a question based on that predicate whose answer
is the ORKG object that can be found as a contiguous span in the paper’s
abstract. Having created a question for all (context, answer) pairs, we then
reserve a portion of the data for prompt-based fine-tuning of variants of
state-of-the-art SQuAD transformer models on this data and evaluate on the
remaining held-out version of the synthetically generated ORKG QA data.

Summarily, our contributions are: 1) we introduce a template-based
unsupervised question generation framework for the scholarly domain, similar
in format to the SQuAD dataset; 2) we report, for the first time, a detailed
empirical analysis of the scholarly domain object prediction task using
prompt-based QA task and state-of-the-art transformer models as rich stores of
linguistic, probabilistic, and factual parameters, thereby testing the
transferability of these pre-trained models on a novel domain. Our dataset,
code, and models are publicly released.

##  2 Task Definition

The article introduces a new task of object extraction for RDF knowledge graph
statements, which is structurally formulated based on the SQuAD QA task
dataset [15, 14]. The task is an extractive task in a machine reading
comprehension setting, where the model is expected to extract the answer as a
contiguous span to a given question. Our task is: given an ORKG predicate
formulated as a question using an unsupervised template-based generation
prompting function $f_{prompt}(x)$, to extract the object answer from the
corresponding paper Abstract context. For unsupervised question generation as
$f_{prompt}(x)$, a static template pattern is defined. Inspired by the prior
seminal work on this theme [5], the $f_{prompt}(x)$ template is:
“Wh”+predicate+“?”, where “Wh” $\in$ {What, Which, How} as the most common
question types. Each “Wh” question results in a question-type-specific
homogeneous dataset where the same prompt template considering the specific
question-type word was applied to all predicates. Finally, a note on the
expected object answer granularity considered in this task: They include three
different granularities: tokens, span as a short multi-token phrase, and
sentences.

##  3 Prompt-ORKG: Our Scholarly Knowledge Question Answering Corpus

We aim to create a high-quality corpus of questions to prompt language models
to extract the correct answer from a context-question pair. For this, we adopt
the structural format of the SQuAD dataset to prompt already fine-tuned
language models and aim to stimulate the models in the most optimal setting to
demonstrate their transferability on a new domain.

Figure 1: A scholarly paper structured contribution view in the Open Research
Knowledge Graph with the backend graph structure overlay on the frontend
interface. The original paper can be accessed here
https://orkg.org/paper/R44743/

###  3.1 The Open Research Knowledge Graph as a Knowledge Base

The ORKG semantic scholarly publishing model represents scholarly
contributions in a structured and machine-actionable way. Scholarly
contributions refer to the specific content of a scholarly article that
highlights its central findings [4]. In general, a contribution describes the
research problem addressed and has salient properties that need to be modeled
with a generalization objective so that it can be compared with other articles
addressing the same research problem. [12]. E.g., the predicates basic
reproduction number, confidence interval (95%), location, and time period are
used to describe Covid-19 reproductive number estimates across various
epidemiology articles (https://www.orkg.org/orkg/comparison/R44930). Figure 1
illustrates a structured contribution discussed in this example on the ORKG
platform.

The ORKG semantic web publishing model uses a set of contribution triples to
describe a paper in a structured format using RDF subject-predicate-object
triples statement paradigm. Users can add new properties or attributes at any
time using the ORKG frontend interface. Reusing our earlier running example,
some of its triples would be: (Contribution, location, Wuhan City, China),
(Contribution, basic reproduction number, 4.38), (Contribution, Time period,
2020-01-10 - 2020-01-23).

In the context of the ORKG data explained, we follow a sequence of steps to
tailor the KB as scholarly knowledge object prediction formulated as
extractive QA structured per the SQuAD dataset. To satisfy this task
objective, with the help of the ORKG Rest API we queried only portions of the
graph to extract specifically all triples in the ORKG KB that hinged on the
Contribution node as the subject. Now our challenge is to obtain the (context,
question, answer) data instances. First, we address our creation of the
preliminary data for the question-and-answer units. As preliminary data, for
the question unit, the predicates in each triple were chosen as candidates,
and, for the answer unit, their corresponding object nodes were selected. Some
statistics of this initial raw dataset are depicted in the ‘Before’ column of
Table 2. Notably, in our data, the number of contributions is greater than the
number of papers since a paper can have more than one contribution. Also the
(predicate, object) pairs are relatively sparse spanning over 200 different
research fields in the ORKG research fields taxonomy.

Table 2: Our scholarly knowledge question answering for object prediction task dataset statistics on the raw data (‘Before’ column) and after data cleaning (‘After’ column). Statistic parameter | Before | After
---|---|---
number of unique papers | 9,379 | 2,710
number of unique contributions | 14,499 | 3,059
number of (predicate,object) pairs | 116,421 | 5,909
number of unique predicate labels | 3,436 | 853
number of unique object labels | 38,234 | 3,524
avg. number of tokens per predicate label | - | 2.01
avg. number of tokens per object label | - | 2.43
number of unique abstracts | - | 2649
avg. number of tokens per paper abstract | - | 196.97
number of abstracts with more than 510 tokens | - | 37
number of unique abstracts with more than 510 tokens | - | 14

###  3.2 Template-based Questions Generation

This section describes how the question unit is created of the needed
(context, question, answer) data instance. Based on the predicate, we generate
four variants of our dataset based on the $f_{prompt}$ function: 1) 3 variants
with the 3 most common “Wh” question words (i.e. What, Which, and How) which
are generated in an unsupervized manner following the $f_{prompt}$ template
“Wh+predicate+?,” and 2) 1 variant as a cloze-style question but instead of
using the [MASK] token, we use the “?” symbol following the template
“predicate+?.” While, our experimental settings are defined on these four
corpus variants based on the generated question unit, we additionally evaluate
a dataset called “unchanged.” In this dataset, the predicate is posed as a
question unit as it is with neither the “?” symbol or question words appended,
nor case changes. Thus we can contrast evaluation results with the “unchanged”
dataset to show the effectiveness of adopting the specially designed SQuAD-
format prompt-based QA setting.

###  3.3 Obtaining a SQuAD-format Corpus for the Scholarly Domain

Having addressed the question unit, this section explains how the SQuAD
(context, question, answer) structured corpus is generated by addressing the
remaining units starting with the context. Unlike the SQuAD dataset, in our
corpus, the context is posited as the paper Abstract. The ORKG abstracts
fetching script was used to query external metadata services such as Crossref
or SemanticScholar with the paper DOI or title (when DOI is absent) to create
an abstracts corpus to serve as the context unit. However, not all papers in
the ORKG get abstracts from these external services. Specifically, we were
able to obtain abstracts for 5,486 (58,5%) out of the 9,379 papers in the raw
data. This results in pruning all the rows in our triples dataset whose
abstracts could not be fetched.

Next, we focus on the answer unit i.e. from all object candidates selecting
those that are suitable for our extractive QA task. A precondition for
selecting suitable objects was to ensure that they can be found in the paper
Abstract. Thus, the 116,421 (predicate, object) pairs in the raw dataset were
reduced to 14,499 (predicate, object) pairs considering papers whose abstract
could be fetched and where the object label was found in the abstract. The
resulting data was then cleaned via a two-step methodology: 1) deduplication,
i.e. all rows with the same (predicate, object) and context were dropped; and
2) a heuristics-based method to clean the dataset of object labels that were
deemed as unsuitable extraction targets. These included whole numbers from 0
to 999, the hyphen symbol, alphabets, boolean values as T/F/yes/no, not
applicable string i.e. na, stop words such as all/and/or etc., and a
collection of non-informative phrases like “any track” or “method” etc.
Finally, our dataset comprised 5,909 (predicate, object) pairs coupled with a
context (see row 3 in Table 2) which we name the Prompt-ORKG corpus.

####  3.3.1 Object categorization

The final step to obtain a SQuAD-format corpus was to carry out a coarse-
grained categorization of the objects. The object types in our dataset while
inspired by the SQuAD 10 syntactic types [15] were finally chosen to reflect
the peculiarities of our data. They range between generic syntactic types
(e.g., noun, adjective, noun phrase, sentence) and domain-specific types
(e.g., research problem, url, count/measurement). Table 3 shows the types and
their coverage with a supporting example for clarity. The object typing was
carried out as described below.

  * •

research problem: any object label in a row with the predicate label “has
research problem.”

  * •

url: any object label that starts with “http.”

  * •

location: any object label with predicate label in [country, city, location,
continent, has location, study location, countries].

  * •

year/date: any whole number between 1000 and 2100.

  * •

number: any object label consisting of only digits after removing the minus
symbol (-), dot (.), and comma (,).

  * •

count/measurements: any object label that contains at least a number in
addition to another string(s). E.g., “5 meters.”

  * •

noun: spaCy was leveraged to determine the noun part-of-speech for a token.

  * •

adjective: spaCy classified adjective part-of-speech.

  * •

acronym: token with one upper case alphabet.

  * •

noun phrase: objects with between 2 and 5 tokens and the last token is a noun.

  * •

adjective phrase: objects with between 2 and 5 tokens and the last token is an
adjective.

  * •

sentence: any object with more than 4 tokens that does not fall under any
other category.

To ensure the objects were typed as only one category, the categorization
heuristics were precedence-ordered following the listing above. Thus an object
was typed per the earliest heuristic that applied to it. From Table 3, we can
see that with a 58.9% coverage, nouns or noun phrases were the most common.

Table 3: The heuristically assigned categories for the objects in Prompt-ORKG. | Object category | % Coverage | Example
---|---|---|---
1 | Noun | 29.85 | Transistors
2 | Noun phrase | 28.74 | data mining
3 | Acronym | 10.12 | HMM
4 | Research problem | 9.53 | Performance of thin-film transistors
5 | Adjective | 4.72 | high
6 | Location | 4.37 | Serbia
7 | Number | 3.93 | 4977
8 | Count/measurement | 3.47 | 2.45 GHz
9 | Sentence | 2.76 | raw data dumps and HDT files
10 | Year/date | 1.95 | 2011
11 | URL | 0.30 | https://github.com/giannisnik/mpad
12 | Adjective phrase | 0.27 | Unsupervised and Adaptive

##  4 Models

With the Prompt-ORKG dataset for the scholarly domain in place, we relegated
attention to selecting three optimal transformer model variants to test as
machine learners on our newly introduced, previously unexplored problem
setting. The machine learning test specifically sought out empirical evidence
for the transferability of the probabilistic parameters of the existing large-
scale transformer models. In this respect, we were interested in two main
strengths of the transformer models: to query over an open class of relations
[13] and the ability to train them on structurally similar data [5, 16]. Thus
selecting optimal SQuAD transformer model variants were a natural choice since
the structural patterns in the Prompt-ORKG dataset emulate SQuAD.

###  4.1 Three Optimal SQuAD Transformer Model Variants

The selected language model variants are based on BERT [3] which seminally
introduced the “masked language model” (MLM) cloze-based pre-training
objective based on a bidirectional self-attention architecture [21]. The
traditional setup includes two steps: pre-training on a large-scale corpus
with a cloze objective for language comprehension, and fine-tuning the
initialized pre-trained model parameters using labeled data from the SQuAD QA
downstream task.

BERT pretrained, SQuAD2.0 finetuned For the first language model, we sought
out the state-of-the-art BERT-based variant from HuggingFace. This model is
called deepset/bert-base-cased-squad2. It leverages the standard BERT-base
cased, initialized model parameters that were pre-trained on the BookCorpus
[26] plus English Wikipedia; these were then further fine-tuned using the
SQuAD2.0 corpus [14]. This model reports 74.67% F1-score on SQuAD2.0.

RoBERTa pretrained, SQuAD2.0 finetuned The second language model variant was
chosen based on RoBERTa [11]. RoBERTa transformer model pre-training improves
upon BERT in several aspects: (1) improved BERT design choices and training
strategies using longer training time, bigger batches, longer sequences,
dynamic masking patterns, and removing the next sentence prediction objective;
and (2) increased underlying training data size to include BookCorpus [26],
CommonCrawl News, OpenWebText from Reddit, and Stories [20]. The selected
HuggingFace model is called deepset/roberta-base-squad2. It was further fine-
tuned on SQuAD2.0, and reports 82.91% F1-score.

MiniLM pretraining distillation, SQuAD2.0 finetuned The third variant is
selected from the line of work that focused on compressing large pre-trained
models into small and fast pre-trained models while achieving competitive
performance with the specific objective of serving in practical applications.
From these models, generically referred to as distilled variants of the base
pre-trained models such as BERT, we select the outperforming MiniLM [22]
variant. The selected model after reviewing the HuggingFace collection is
called deepset/minilm-uncased-squad2 which was fine-tuned similar to the prior
two variants on SQuAD2.0. It achieves 79.49% F1-score.

Each of these respective models has been fine-tuned over massive amounts,
ranging on 100,000+ instances, of SQuAD QA data. Over these model variants,
this work investigates an additional step of prompt-based training that has
been shown to optimally stimulate a fine-tuned model’s probabilistic
parameters to generalize in a resource-scarce setting [9] that we defined as
the Prompt-ORKG corpus.

##  5 Results and Discussion

###  5.1 Experimental Setup

Dataset. Prompt-ORKG presents a few-shot learning scenario. On this corpus, we
need to obtain relevant training and evaluation dataset splits. The dataset
was split based on the predicate labels as follows. For predicate labels with
10 or more instances, 75% of the corresponding data instances are assigned to
the training data and the rest are reserved as the evaluation set. The
remaining data snapshot based on predicate labels with less than 10 instances
is simply relegated as the training set. Finally, for each of the four
templated dataset variants and the fifth “unchanged” variant discussed in
section 3, the training dataset consists of 4745 data points (82% of the
entire dataset) while the evaluation set consists of 1036 data points (18%).

Hyper-parameter tuning. All models are tuned for 4 epochs, learning rate $\in$
{0.0001, 0.00005}, train batch size = 8, eval batch size = 8, and weight decay
= 0.01. At the end of the training phase of each experiment, only the best
model is saved and used in the evaluation phase.

Metrics. Evaluations are considered in two main settings: 1. strict, i.e.
exact match; and 2. relaxed, i.e. containment match where the gold answer is
checked to be contained in the predicted answer. In both settings, the main
metric is F1 score and secondarily accuracy is also applied. Note that after
prediction, the answers undergo minimal post-processing to be suitable for
evaluation. This entailed trimming the trailing and leading white spaces,
converting all answers to lower case, and removing the following special
characters: ., comma, ;, :, -, ), (, _ and +, if they are at the end of the
answers.

###  5.2 Evaluations

In this section, we present the results and discuss observations from each of
our 30 total experiments considering 5 dataset variants, 3 optimal SQuAD QA
models, and 2 experimental settings i.e. vanilla and after prompt-based
learning. The core experimental results are depicted in Tables 4 and 5 in
terms of F1-scores, and parenthesized accuracies, in the exact-match vs.
relaxed settings, respectively. We discuss the experimental results with
respect to three main research questions.

RQ1: What is the impact of the Prompt-ORKG SQuAD-format structural QA task
formulation on the transferability of the large-scale SQuAD fine-tuned
language models? This question subsumes two sub-questions. RQ1.1: How do the
BERT model performances contrast when queried out-of-the-box, i.e. as vanilla
models, versus after being trained on our corpus variants? RQ1.2: Is it
effective to adopt the SQuAD-format structural representation to optimally
query the large-scale SQuAD fine-tuned language models? For RQ1.1, examining
both F1 scores and accuracies, in the exact match setting (Table 4), the
results from the trained models on our corpus variants are approximately 25%
(and 35%) higher, respectively, than when testing the untrained “vanilla”
models on data from a new domain. For RQ1.2, examining the *row avg* exact
match F1 scores in Table 4, we see the results from the SQuAD-format dataset
variants are 5% or 6% higher than the “unchanged” dataset. Note the SQuAD-
format dataset variants report results in the range 21% to 22% F1 scores,
while the “unchanged” dataset evaluations report only 16% F1 score. Thus we
can conclude that indeed the SQuAD-format task formulation as the four
variants in the Prompt-ORKG corpus is an effective strategy to optimally
stimulate the probabilistic parameters of the SQuAD fine-tuned language models
towards their transferability on a new domain, i.e. the scholarly domain.

Thus our findings cumulatively are as follows. Training the models on our
corpora produce more effective predictors compared to the vanilla models with
performances as low as 1% reflecting the domain gap of the language models
between the generic domain and the scholarly domain. To obtain optimal
versions of the SQuAD fine-tuned language models, formulating the task dataset
in SQuAD format is an effective strategy to obtain optimally trained models.

RQ2: Which dataset variant produced the most optimal models? Given that we
have 2 evaluation tables, the F1 scores in the exact match setting shown in
Table 4 were considered the reference evaluations on which to base
conclusions. Examining the *row avg* results in the Table, we observed that
the results from the which variant of the Prompt-ORKG corpus was statistically
insignificantly better than the what variant with 22.6% F1 score versus 22.2%
F1 score. This indicates directions for future work to examine the automated
generation of the questions by selecting and applying the most suitable
question type which or what for the predicates. Across all four tables,
examining the *column avg* results, the RoBERTa SQuAD model proved optimal for
transferability to a new domain.

Table 4: F1-score (and parenthesized Accuracy) results in the exact-match setting over the 4 dataset variants from the 3 models with cell values as “vanilla models”/“after prompt-based training.” Dataset variant |  bert-base-cased -squad2 |  roberta-base -squad2 |  minilm-uncased -squad2 | *row avg*
---|---|---|---|---
unchanged | 0.5/11.2 (1.0/29.4) | 2.5/22.7 (1.8/35.5) | 0.5/16.2 (0.4/35.5) | 1.2/16.7 (1.1/33.5)
none | 1.4/23.5 (1.4/31.7) | 4.0/23.0 (2.5/37.5) | 3.6/18.0 (3.5/35.4) | 1.8/21.5 (2.5/34.9)
what | 1.5/25.7 (1.0/33.8) | 5.1/21.2 (4.3/35.9) | 6.3/19.8 (5.1/36.1) | 4.3/22.2 (3.5/35.3)
how | 0.3/19.8 (0.5/34.0) | 3.0/20.9 (2.2/36.4) | 4.6/22.3 (4.0/33.8) | 2.6/21.0 (2.2/34.7)
which | 1.9/17.8 (1.6/33.5) | 5.5/24.0 (4.5/36.6) | 5.9/25.9 (5.5/36.8) | 4.4/22.6 (3.9/35.6)
*column avg* | 1.1/19.6 (1.1/32.5) | 4.0/22.4 (3.1/36.4) | 4.2/20.4 (3.7/35.5) | -
Table 5: F1-score (and parenthesized Accuracy) results in the relaxed setting over the 4 dataset variants from the 3 models with cell values as “vanilla models”/“after prompt-based training.” Dataset variant |  bert-base-cased -squad2 |  roberta-base -squad2 |  minilm-uncased -squad2 | *row avg*
---|---|---|---|---
unchanged | 6.7/17.1 (9.2/42.9) | 7.6/23.7 (5.7/49.7) | 18.6/22.9 (18.2/47.5) | 11.0/21.2 (11.0/46.7)
none | 6.2/31.7 (5.9/43.4) | 20.3/32.3 (14.8/50.6) | 21.3/26.1 (16.0/48.3) | 15.9/30.0 (12.2/47.4)
what | 7.3/34.6 (5.6/46.0) | 22.8/31.0 (17.0/49.5) | 24.4/26.2 (16.5/46.0) | 18.2/30.6 (13.0/47.2)
how | 6.8/27.6 (8.2/45.2) | 23.7/30.4 (16.5/51.2) | 22.7/28.5 (16.3/47.0) | 17.7/28.8 (13.7/47.8)
which | 8.3/24.0 (7.4/43.9) | 25.1/35.9 (18.2/48.6) | 23.0/36.4 (18.0/47.9) | 18.8/32.1 (14.5/46.8)
*column avg* | 7.1/27.0 (7.2/44.3) | 19.9/30.7 (14.4/49.9) | 22.0/28.0 (17.0/47.3) | -

RQ3: Which of the Prompt-ORKG corpus object types was easiest/challenging to
predict? Examining the results in Table 6, we see that the Location,
Adjective, Noun, Acronym, Research problem, and Year/date object types were
easiest to predict with accuracies above 40% with values 53.3%, 50%, 44.6%,
43.5%, 43.4%, and 42.9%, respectively. The Sentence type could not be
predicted at all by any of the models and thus presented the most challenging
type. This is somewhat an expected result since the fine-tuned language models
were trained only over object types of a few tokens thus base model parameters
were lacking to generalize over object types with many more tokens. The low
performance on the noun phrase object type can be similarly attributed. Table
7 offers some insights into the average number of tokens in our corpus versus
the average tokens from the model predictions obtained. Low performance on the
URL object type can be attributed to its under-representation in our corpus.

Table 6: Fine-grained accuracy results for the 12 object categories in the exact-match/relaxed settings for best model (RoBERTa) and dataset variant (which) combination. Object category |  % Coverage in the evaluation dataset | % Accuracy
---|---|---
Sentence | 3 | 0.0/3.3
Count/measurement | 3 | 7.1/14.3
Number | 0.5 | 20/40.0
Noun phrase | 30 | 25.8/37.4
URL | 0.25 | 33.3/33.3
Year/date | 1 | 42.9/57.1
Research problem | 14 | 43.4/53.8
Acronym | 9 | 43.5/59.8
Noun | 30 | 44.6/58.7
Adjective | 3 | 50/57.1
Location | 6 | 53.3/57.4
Table 7: Average number of tokens for gold answers and for the predicted answers from the vanilla/fine-tuned models on the most effective prompt-based dataset variant. Model |  Gold Avg. # tokens |  Predicted Avg. # tokens
---|---|---
bert-base-cased-squad2 | 2.4 | 4/7.3
roberta-base-squad2 | 2.4 | 9.3/5.5
minilm-uncased-squad2 | 2.4 | 17/5.7

###  5.3 Discussion

In this section, we dive deeper into the results from the relaxed match
settings, where the predictions were simply checked to contain the gold
answer, shown in Table 5 to offer insights into whether our formulated QA task
over the scholarly domain is promising for further explorations as future
work. From Table 5, we see that prompt-training the language models in a few
shot learning setting over data from the new scholarly domain still achieves
F1 scores close to or above 35% in the optimal settings and accuracies above
45% in most settings and 50% in some settings. Given this, we can conclude
that the language models show promise of transferring effectively to the new
scholarly domain provided the underlying task dataset formulation is suitably
made incorporating the original language models task dataset formulation. Thus
we elicit specific areas of further exploration from our present study as the
scope for future work as follows. 1) The creation of a heterogeneous corpus
with questions formulated based on the automated selection of suitable
question words depending on the predicate or the answer. 2) Testing a
different prompting method for the language models, i.e. the instructional
prompting method that proved very effective for the language models when
tested in various zero-shot learning scenarios [23]. Furthermore, with the
instructional prompt writing or task dataset formulation, the collection of
pre-trained language models to experiment with is even broader without being
restricted to the SQuAD fine-tuned models as in our present work. 3) This work
has released uniform conclusive experimental results for the following
experimental setup: commonsense pretraining domain + commonsense QA finetuning
domain from SQuAD + Prompt-ORKG scholarly finetuning domain. The hypothesis
then tested was these commonsense-trained-tuned models parameter
generalizability to the scholarly domain. We test this hypothesis because we
noted that the commonsense domain receives a lot of attention in the release
of annotated data for various machine learning tasks. On the other hand, the
scholarly domain–not so much. So we want to advocate for the use of these
commonsense models in the best transfer learning settings. Nevertheless, given
the availability of scholarly domain pretrained language models like SciBERT
[2] or BioBERT [8], their systematic investigations in future work is
recommended, where inspired from this work, the experimental setup would be:
scholarly pretraining domain + commonsense QA finetuning domain from SQuAD +
Prompt-ORKG scholarly finetuning domain.

##  6 Conclusions

The prompt-based learning paradigm [9, 24] is increasingly used in NLP for
fine-tuning BERT-based QA models on domains with less training data. In this
work, we demonstrated the applicability of SQuAD-based prompt format training
of BERT models on scholarly data for object prediction in the ORKG. Our
experiments showed promising results in terms of domain transferability of the
models with the right training strategy, however, the model performances
reflect a vast scope for further improvement.

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