# Effects of electron drift on the collisionless damping of kinetic Alfvén
waves in the solar wind

Yuguang Tong11affiliation: Space Sciences Laboratory, University of
California, Berkeley, CA 94720, USA<EMAIL_ADDRESS>2 2affiliationmark:
, Stuart D. Bale11affiliation: Space Sciences Laboratory, University of
California, Berkeley, CA 94720, USA<EMAIL_ADDRESS>2 2affiliationmark:
, Christopher H. K. Chen33affiliation: Department of Physics, Imperial College
London, London SW7 2AZ, UK 1 1affiliationmark:  , Chadi S. Salem11affiliation:
Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
<EMAIL_ADDRESS>and Daniel Verscharen44affiliation: Space Science
Center, University of New Hampshire, Durham, NH 03824, USA

###### Abstract

The collisionless dissipation of anisotropic Alfvénic turbulence is a
promising candidate to solve the solar wind heating problem. Extensive studies
examined the kinetic properties of Alfvén waves in simple Maxwellian or bi-
Maxwellian plasmas. However, the observed electron velocity distribution
functions in the solar wind are more complex. In this study, we analyze the
properties of kinetic Alfvén waves in a plasma with two drifting electron
populations. We numerically solve the linearized Maxwell-Vlasov equations and
find that the damping rate and the proton-electron energy partition for
kinetic Alfvén waves are significantly modified in such plasmas, compared to
plasmas without electron drifts. We suggest that electron drift is an
important factor to take into account when considering the dissipation of
Alfvénic turbulence in the solar wind or other $\beta\sim 1$ astrophysical
plasmas.

22affiliationtext: Department of Physics, University of California, Berkeley,
CA 94720, USA<EMAIL_ADDRESS>
##  1 Introduction

One major question in space physics is how collisionless plasmas in the
extended corona and in the solar wind are heated. Observations in the solar
wind reveal that the fluctuations of the electric and magnetic fields show a
turbulent spectrum similar to the power-law spectrum of fluid turbulence as
described by Kolmogorov (Tu & Marsch, 1995; Bale et al., 2005; Bruno &
Carbone, 2013; Alexandrova et al., 2013). The turbulence in the solar wind
shows mainly Alfvénic polarization (Belcher & Davis, 1971) and becomes more
anisotropic during the cascade to higher wavenumbers $k$ (Goldreich & Sridhar,
1995; Horbury et al., 2008; Chen et al., 2010), resulting in $k_{\perp}\gg
k_{\parallel}$ at short wavelengths. At the proton scale, the turbulence is
thought to transition into a kinetic Alfvén wave (KAW) cascade (Schekochihin
et al., 2009; Sahraoui et al., 2010; Howes et al., 2011; Salem et al., 2012;
Boldyrev & Perez, 2012; Chen et al., 2013), which gradually dissipates energy
to the particles (Leamon et al., 1999; Howes et al., 2011).

Despite the nonlinear nature of turbulence, linear theory has been used in
studies of solar wind turbulence (see, for instance, Howes et al. (2014) for
review). These studies analyze turbulent fluctuations by means of the linear
propagation and damping characteristics of KAWs to help to understand the
dissipation of the turbulence and the heating of the solar wind. The vast
majority of these studies rely on representing the velocity distribution
functions (VDFs) by an isotropic or bi-Maxwellian background (e.g., Quataert
(1998); Leamon et al. (1999); Cranmer & van Ballegooijen (2003)). In this
work, we investigate how more realistic VDFs modify the damping of KAWs. In
the solar wind, both ions and electrons can be modeled by several populations
drifting with respect to each other. Recent studies show that the differential
flow between ions affects ion heating by both ion-cyclotron waves (Kasper et
al., 2013) and low-frequency KAWs (Chandran et al., 2013).

The solar-wind electron VDF can be modeled as a superposition of three
electron populations: a cool and dense “core”, a hot and less dense “halo”
(Feldman et al., 1975) and a beam-like one-sided “strahl” (Maksimovic et al.,
2005). In the proton frame, core (halo and strahl) electrons drift sunward
(anti-sunward) along the background magnetic field. Empirically, the solar
wind fulfills quasi-neutrality and the zero-current condition (Feldman et al.,
1975; Pulupa et al., 2014). The uncertainty in the fitting parameters for
electron core properties is smaller than the uncertainty in the fitting
parameters for halo and strahl properties. A drifting bi-Maxwellian population
models core electrons very well. In particular, the core electron bulk drift
speed is usually comparable to or larger than the Alfvén speed and shows a
clear statistical dependence on collisional age (Pulupa et al., 2014). In the
extrapolated asymptotic limit of no collisions, the core drift is as large as
three to four times the Alfvén speed.

In this letter, we examine how the drift between electron core and halo
affects the linear damping of KAWs. We model the solar wind electrons by a
superposition of a Maxwellian core and a Maxwellian halo drifting against each
other in the proton frame. Choosing a set of parameters typical for the solar
wind, we solve the full hot-plasma dispersion relation of KAWs in the
framework of Vlasov-Maxwell theory and identify the contribution to wave
damping from each plasma component. We show that, in the linear approximation,
electron drifts can lead to significant variations in both the KAW damping
rates and the relative energy transfer from the waves to protons and
electrons, the latter of which is another important unsolved problem in
turbulent plasma heating.

##  2 Theory and method

Motivated by observed solar wind electron VDFs, we consider a collisionless,
homogeneous, and warm proton-electron plasma in a constant uniform background
magnetic field. The proton temperature and density are denoted as $T_{p}$ and
$n_{p}$; the electron distribution consists of two shifted Maxwellian
populations, a cool ($T_{c}$) “core” and a hot ($T_{h}$) “halo.” As an initial
step to study the effects of core electron drifts on resonant damping, we use
isotropic temperatures for all plasma components. Both electron populations
drift along the background magnetic field
$\mathbf{B}_{0}=B_{0}\hat{\mathbf{z}}$ with
$\mathbf{v}_{c}=v_{c}\hat{\mathbf{z}}$ and
$\mathbf{v}_{h}=v_{h}\hat{\mathbf{z}}$ in the proton frame. The halo electron
drift adjusts to the core electron drift to guarantee the absence of net
currents in the plasma: $v_{h}=-v_{c}n_{c}/n_{h}$, where $n_{c}$ and $n_{h}$
denote core and halo electron densities. Figure 1 shows the plasma described
above schematically.

Figure 1: Schematic diagram for the plasma considered in this letter. We
annotate the parallel wave phase speed
$v_{\mathrm{res}}=\omega_{r}/k_{\parallel}$ for our resonance analysis in
Section 3.

Under the assumption of strong anisotropy in kinetic scale fluctuations in the
solar wind, we consider KAWs with wavevectors at a large angle with respect to
the magnetic field. We use constant values for the angle between $\mathbf{k}$
(wavenumber vector) and $\mathbf{B}_{0}$ ($89^{\circ}$ or $91^{\circ}$),
plasma beta, the electron-core-to-proton temperature ratio and the core-to-
halo density ratio, so that the only free parameters are $\mathbf{k}$,
$\mathbf{v}_{c}$ and $\mathrm{sign}(\mathbf{k}\cdot\mathbf{B}_{0})$. In
particular, we allow $\mathbf{B}_{0}$ to be either parallel or anti-parallel
to $\mathbf{v}_{c}$, and $\mathbf{k}$ has a finite component along
$\mathbf{B}_{0}$. In principle, each configuration
$(\mathbf{v}_{c},\mathbf{k},\mathbf{B}_{0})$ requires a separate treatment;
however, changing the direction of $\mathbf{B}_{0}$ only inverts the direction
of propagation and does not produce a new dispersion relation. Therefore, we
introduce the dimensionless core electron drift $\delta
v_{c}\equiv|v_{c}/v_{A}|\mathrm{sign}(\mathbf{k}\cdot\mathbf{v}_{c})$, where
$v_{A}\equiv\sqrt{B_{0}^{2}/4\pi n_{p}m_{p}}$ is the proton Alfvén speed. The
values of the remaining parameters are given in Table 1.

Quantity | Value
---|---
Proton plasma beta $\beta_{p}$ | $0.4$
Temperature ratio $T_{c}/T_{p}$ | $2$
$T_{h}/T_{p}$ | $10$
Density ratio $n_{c}/n_{h}$ | $9$
Proton bulk drift $v_{p}/v_{A}$ | $0$
Angle between $\mathbf{k}$, $\mathbf{B}_{0}$ |  $89^{\circ}$ or $91^{\circ}$
Table 1: Values of fixed plasma parameters in our study.

We study the dispersion relations of KAWs by numerically solving the full set
of the linear Maxwell-Vlasov equations. Linear Maxwell-Vlasov theory has been
described in detail in the literature (see, for instance, Swanson (1989) and
Stix (1992)). We summarize the relevant results here. Linear plasma waves are
eigenmodes of the wave equation:

$\mathbf{k}\times\left(\mathbf{k}\times\mathbf{E}\right)+\frac{\omega^{2}}{c^{2}}\boldsymbol{\epsilon}\cdot\mathbf{E}=0,$
(1)

where $\mathbf{E}$ is the fluctuating electric field in Fourier space. The
dielectric tensor $\boldsymbol{\epsilon}$ incorporates contributions from each
plasma component:
$\boldsymbol{\epsilon}=\boldsymbol{1}+\Sigma_{s}\boldsymbol{\chi}_{s}$, where
$\boldsymbol{\chi_{s}}$ is the susceptibility tensor for species $s$. We
obtain $\boldsymbol{\chi_{s}}$ from the linearized and Fourier-transformed
Vlasov equation and Maxwell’s equations.

To study the contribution to wave damping (growth) from each component, we
calculate the relative particle heating rates as (Stix, 1992)

$P_{s}\equiv\mathbf{E}^{\ast}\cdot\boldsymbol{\chi}^{a}_{s}\arrowvert_{\omega=\omega_{r}}\cdot\mathbf{E}/4W.$
(2)

where
$\boldsymbol{\chi}^{a}_{s}\equiv\left(\boldsymbol{\chi_{s}}-\boldsymbol{\chi}_{s}^{\dagger}\right)/2i$
is the anti-Hermitian part of $\boldsymbol{\chi_{s}}$,
$\omega_{r}\equiv\Re\left(\omega\right)$ and $W$ is the wave energy.

In the weak damping limit, $P_{s}$ gives the fraction of wave energy damped by
plasma component $s$ during one wave period. The total heating rate
$P_{total}\equiv\sum_{s}P_{s}$ corresponds to the wave energy dissipation rate
directly calculated from the damping rate, i.e., $1-e^{2\omega_{i}T}$, where
$\omega_{i}\equiv\Im\left(\omega\right)$ and $T\equiv 2\pi/\omega_{r}$ is the
wave period, as long as $\omega_{i}$ is small compared to $\omega_{r}$. In
this letter, we focus on the linear damping of KAWs. Electron drifts may,
however, alter wave–particle interactions to such a degree that the
corresponding waves become unstable, which we note for the sake of
completeness. Notice that $P_{s}$ may become negative, corresponding to
cooling of species $s$.

##  3 Results

Figures 2(a)-(b) show dispersion relations of KAWs in plasmas with $\delta
v_{c}\in[-4,4]$. Panel (a) demonstrates that electron drifts have little
effect on the real part of the KAW frequencies, consistent with Gary et al.
(1975). Indeed, the protons rather than the electrons mainly determine the
dynamics of low-frequency KAWs. Panel (b) compares damping rates of KAWs in
plasmas with different electron drifts. Negative (positive) $\delta v_{c}$
lead to an enhancement (reduction) of the KAW damping at all wavenumbers.
Panel (b) shows that $\delta v_{c}\sim-4$ leads to an increase in the damping
rate by $\sim 50\%$ compared to the case without electron drifts. For
sufficiently large positive $\delta v_{c}$, KAWs become unstable in certain
wavenumber ranges. This instability is an example of a “heat flux instability”
(Gary et al., 1975). The two-population electrons in our model introduce an
electron heat flux (third moment of the electron VDF), which may provide
energy to drive certain wave modes (e.g., whistler, Alfvén, and magnetosonic)
unstable (Gary et al., 1975, 1998a, 1999). These heat flux instabilities, in
return, regulate the electron heat flux and hence the electron drifts. We note
that there is no conflict between the damping and growth of KAWs and other
wave modes. For instance, parallel whistler waves, whose instability threshold
is much lower than that of the Alfvénic instability, are unstable even if
$\delta v_{c}>-4$. Therefore, the Alfvénic instability cannot regulate the
electron heat flux in the solar wind and is more of academic interest under
typical solar-wind conditions since the instability with the lowest threshold
constrains the electron heat flux once triggered. Figure 2(c) compares the
total particle heating rate (solid) with the wave energy dissipation rate
(dotted). When $1-e^{2\omega_{i}T}\lesssim 0.5$, i.e., the wave retains more
than half of its energy after a wave period, $P_{total}\approx
1-e^{2\omega_{i}T}$. Hence we show that $P_{s}$ is a good measure of energy
flow as long as damping is weak.

Figure 2: (a)-(b): Dispersion relation of KAWs in plasmas for different
$\delta v_{c}$. $\omega_{r}$ and $\omega_{i}$ are the real and imaginary parts
of the wave frequency. $\rho_{p}\equiv v_{Tp}/\Omega_{p}$ is the proton gyro-
radius, $v_{Tp}\equiv\sqrt{2k_{B}T_{p}/m_{p}}$ is the proton thermal speed,
and $\Omega_{p}\equiv eB_{0}/m_{p}c$ is the proton gyro-frequency. (c): Total
particle heating rates ($P_{total}$, solid lines) and wave energy dissipation
rates ($1-e^{2\omega_{i}T}$, dots) as functions of wavenumber.

Figures 3 (a)-(d) present heating rates for protons, all electrons (core +
halo), as well as separately for core electrons and halo electrons. Recall
that positive $P_{s}$ indicates heating for species $s$, and that negative
$P_{s}$ indicates cooling. Panel (a) shows that protons are always heated,
although electron drifts can slightly modify the values of the proton heating
rate. On the other hand, panels (b)-(d) show that an electron population can
experience both cooling and heating depending on $\delta v_{c}$. While both
core and halo are heated in the absence of bulk drifts, sufficiently large
positive $\delta v_{c}$ lead to core cooling and at the same time
significantly enhance halo heating. Negative $\delta v_{c}$ have the opposite
effect on electron heating. In general, electron drifts have a larger effect
on electron heating than on proton heating. Electron drifts modify the damping
rates of KAWs by changing the efficiency of wave–particle interactions for the
different electron populations.

Figure 3: Dependence of $P_{proton}$ (a), $P_{electron}$ (b), $P_{core}$(c)
and $P_{halo}$ (d) on $k_{\perp}\rho_{p}$ in plasmas with varying $\delta
v_{c}$.

Figure 4 shows how the energy partition depends on electron drifts at
$k_{\perp}\rho_{p}=1$. $P_{c}/P_{p}$ and $P_{h}/P_{p}$ vary wildly with
$\delta v_{c}$. However, since electron drifts affect core heating and halo
heating in opposite ways, the total electron heating and consequently the
electron-proton energy partition reveal a more moderate dependence on electron
drifts. Nevertheless, a core drift of $\delta v_{c}\sim-4$ increases
$P_{e}/P_{p}$ by $\sim 25\%$. Without electron drifts, electron heating
dominates over proton heating in hydrogen plasmas at $k_{\perp}\rho_{p}\sim 1$
for $\beta\sim 1$ (Quataert, 1998). We see in Figure 4 that positive $\delta
v_{c}$ significantly reduces electron-to-proton heating ratio. At $\delta
v_{c}\sim 3$, electron heating becomes negligible compared to proton heating.
We note at this point that the dependence of energy partition on electron
drifts is qualitatively the same at other wavenumbers, which can be inferred
from Figure 3.

Figure 4: Ratio of energy partition between electrons and protons as a
function of electron drift.

We interpret the dependence of wave damping and particle heating on electron
drifts in terms of a simplified resonance analysis. Since $\omega_{r}$ is
almost independent of electron drifts, the proton heating rate shows only a
small variation. However, core and halo electron bulk drifts significantly
change the value and the gradient of the eVDF at the resonance speed,

$v_{\mathrm{res}}\equiv\frac{\omega_{r}-n\Omega_{e}}{k_{\parallel}},$ (3)

where $\Omega_{e}$ is the electron gyro-frequency and $n$ is an integer
depending on the polarization properties of the wave mode (Marsch, 2006).

In our case, the most relevant resonance for wave–particle interactions with
KAWs is the Landau resonance with $n=0$. Electrons with the (field-parallel)
speed $v_{\mathrm{res}}$ interact resonantly with the corresponding wave mode.
We illustrate the case for negative $\delta v_{c}$ schematically in Figure 1.

The gradient of the distribution functions at the resonance speed determines
if the particle species gains or loses energy, i.e., the signs of $P_{p}$,
$P_{c}$, and $P_{h}$. In the example shown in Figure 1, the resonance occurs
where the halo VDF has a positive gradient, and hence the KAW removes energy
from the halo electrons, leading to a negative value for $P_{h}$. In contrast,
core electrons and protons have resonances where the gradients of their VDFs
are negative, leading to positive values for $P_{c}$ and $P_{p}$. Similarly,
the dependence of $P_{s}$ on $\delta v_{c}$ can also be inferred from the
positions of the resonance points with respect to the VDFs. However, a
qualitative resonance analysis cannot provide a thorough comparison across the
plasma components. We find that $P_{s}$, defined in Eq. (2), gives a better
understanding of the energy transfer between waves and different plasma
components.

It is worth noting that electron drifts seem to provide a collisionless energy
coupling between core and halo electrons (see the case with $\delta v_{c}=-2$
for instance). Figure 2(c) shows that $1-e^{2\omega_{i}T}\approx
P_{c}+P_{h}+P_{p}$. With $P_{c},P_{p}>0$ and $P_{h}<0$ (from Figure 3),
$\left(1-e^{2\omega_{i}T}\right)+(-P_{h})\approx P_{c}+P_{p}$ , meaning that
energy flows from damped waves and halo electrons into core electrons and
protons. A similar energy transport among electron components was suggested by
Gary et al. (1998b). According to this study, the Alfvénic heat-flux
instability transfers energy from the drifting halo into the electron core
through the Landau-resonant absorption of the waves, leading to a lower limit
for $\beta_{c}$.

##  4 Discussion and conclusion

For the sake of clarity, we present results for a single propagation angle in
this letter. A careful analysis shows that other oblique angles do not lead to
any qualitative differences. Given a fixed KAW power spectrum, we anticipate
that the presence of electron drifts changes the wave-energy dissipation rate,
particle heating rates, and the proton-electron energy partition ratio
significantly.

In the context of the solar wind, since core electrons are nearly always
observed to drift sunward in the proton frame, positive (negative) $\delta
v_{c}$ correspond to KAWs propagating sunward (anti-sunward). Therefore, anti-
sunward KAWs experience stronger damping in the presence of electron drifts
and lead to a stronger core heating, halo electron cooling, and a stronger
total electron heating. Since the total energy flux typically points anti-
sunward in the solar wind, we suggest that electron drifts lead to stronger
electron heating than expected from previous calculations (Quataert, 1998;
Leamon et al., 1999). An interesting corollary of this work is that, since the
core electron drift speed depends on the collisionality of the solar wind
(Pulupa et al., 2014), the heating rate as calculated here may therfore also
indirectly depend on solar wind Couloumb collisions.

Our model includes relative drifts in the electron VDF, while it ignores
several additional features of solar wind electrons, namely the presence of
superthermal electrons, one-sided beams (strahl) and temperature anisotropies.
By using a Maxwellian halo, we ignore high energy tails in the electron VDF.
However, this assumption does not significantly affect the gradients of the
electron distribution function at $v_{\mathrm{res}}\sim v_{A}$ which mainly
determine the damping. We can apply a similar argument to strahl electrons,
which also occupy a different region in the velocity space. Regarding
temperature anisotropies, Gary et al. (1975) studied the dependence of the
core drift threshold for the Alfvénic instability on electron temperature
anisotropy and found that the dependence is weak in plasmas with
$\beta_{p}<0.25$. We expect a similar weak relation in our case, since Landau-
resonant instabilities show such a weak dependence in general (Verscharen &
Chandran, 2013), since the strength of this type of resonant interaction is
determined by the parallel gradients of the electron distribution function. If
the parallel temperature is kept constant, the introduction of temperature
anisotropy only changes the perpendicular gradients of the VDF and therefore
does not significantly alter the wave–particle interaction.

In this letter, we choose a fiducial set of representative solar wind plasma
parameters to demonstrate the effects of electron drifts on the damping of
KAWs. In order to fully account for all of the relevant effects in the solar
wind, it is important to conduct a full scan of the corresponding parameter
space. This endeavor is beyond the scope of this work and will be presented in
a future paper.

Our work shows that, despite our limiting assumption of a superposition of
Maxwellians to represent the electron distribution function, its fine-
structure has a strong influence on the propagation and damping properties of
KAWs. Therefore, our work is of relevance in the broader context of all
collisionless astrophysical plasmas in which non-Maxwellian electron
distributions can develop and persist. Considering that most astrophysical
plasmas are in a turbulent state and that KAW-turbulence is believed to be the
dominant type of plasma turbulence on small scales, our work suggests that the
effects of non-Maxwellian electron distributions be carefully accounted for in
studies of collisionless astrophysical plasmas in general.

We are grateful to Christopher C. Chaston, Marc P. Pulupa, Eliot Quataert and
Kristopher G. Klein for helpful discussions. Y. Tong is supported by NASA
grant APL-975268 and Charles K. Kao Scholarship. S. D. Bale is supported by
NASA grant APL-975268. C. H. K. Chen is supported by an Imperial College
Junior Research Fellowship. C. Salem is supported by NASA grant NNX14AC07G. D.
Verscharen is supported by NASA grant NNX12AB27G.

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# Extract, Integrate, Compete:
Towards Verification Style Reading Comprehension

Chen Zhang, Yuxuan Lai, Yansong Feng , Dongyan Zhao
Wangxuan Institute of Computer Technology, Peking University, China
The MOE Key Laboratory of Computational Linguistics, Peking University, China
{zhangch, erutan, fengyansong, zhaody} @pku.edu.cn
Corresponding author.

###### Abstract

In this paper, we present a new verification style reading comprehension
dataset named VGaokao from Chinese Language tests of Gaokao. Different from
existing efforts, the new dataset is originally designed for native speakers’
evaluation, thus requiring more advanced language understanding skills. To
address the challenges in VGaokao, we propose a novel Extract-Integrate-
Compete approach, which iteratively selects complementary evidence with a
novel query updating mechanism and adaptively distills supportive evidence,
followed by a pairwise competition to push models to learn the subtle
difference among similar text pieces. Experiments show that our methods
outperform various baselines on VGaokao with retrieved complementary evidence,
while having the merits of efficiency and explainability. Our dataset and code
are released for further research111https://github.com/luciusssss/VGaokao.

##  1 Introduction

Reading comprehension has been frequently used in various standardized
examinations to evaluate one’s language understanding skills, where test-
takers are expected to read a long article, answer a series of questions, or
verify a given statement according to the passage. For example, in the Chinese
Language tests of Gaokao (also known as China National College Entrance
Examination), approximately half of the reading comprehension questions are in
a verification style. As shown in Table 1 (bottom), students are expected to
read a passage, and then select from four choices (A~D) the best statement
that is the most consistent with the passage, or sometimes, contracts the most
to the passage.

While the question answering styled tasks have been intensively studied in the
NLP community Rajpurkar et al. (2016); Lai et al. (2017); Yang et al. (2018);
Sun et al. (2020), the verification styled MRC task actually receives much
less attention. Here, as indicated in the Gaokao
Instructions222http://gaokao.neea.edu.cn/, the abilities of gathering multiple
evidence pieces from long articles, distilling supportive evidence, and making
decisions accordingly by capturing the subtle difference among similar text
pieces (i.e., choices), are necessary skills for Chinese Language learning.
This type of questions actually provides an ideal test-bed for natural
language understanding research.

Figure 1: An example of iterative evidence extraction. The darker tokens in
bold are more important for the updated query.

In this paper, we present a verification style reading comprehension dataset
named VGaokao to highlight the language understanding challenges mentioned
above. VGaokao is constructed from the Chinese Language tests of Gaokao.
Figure 1 shows an example in VGaokao, where a statement (one of the 4 choices)
should be verified according to the given passage. To do so, we need to
extract two evidence sentences from the passage, combine them together to
examine how well the statement is supported by the evidence, and finally
compare with other choices to arrive at the answer.

As constructed from standardized language test for native speakers, VGaokao
involves more language understanding challenges than the datasets constructed
from tests for second language learners such as C3 Sun et al. (2020) and RACE
Lai et al. (2017). For example, VGaokao involves more diverse vocabulary and
more complex sentence structures. Besides, nearly half of the statements in
VGaokao require multiple evidence to verify. Compared with the fact checking
tasks such as FEVER Thorne et al. (2018), where each claim is tagged with a
definite label individually, most statements in VGaokao are not absolutely
correct nor absolutely incorrect, which requires models to carefully compare
one statement with another to choose the most suitable answer according to the
given passage.

To address the above challenges in VGaokao, we propose a novel Extract-
Integrate-Compete framework, where two query updating strategies, hard masking
and soft masking, are designed to iteratively extract multiple complementary
evidence for a given statement. Figure 1 shows an example of using soft
masking to highlight the tokens whose corresponding evidence has not been
found up to current iteration. After evidence extraction, we adaptively filter
irrelevant evidence sentences and dynamically determine the number of evidence
pieces to be integrated. Options in each question are then verified against
retrieved evidence and are compared in a pairwise style to select the most
plausible answer.

We empirically investigate the performance of our Extract-Integrate-Compete
approach on VGaokao. Experiments shows that our method outperforms end-to-end
methods with passage chunking and various evidence selection methods in
evidence retrieval F1. Performance gains in evidence selection can further
propagate to the final question answering performance.

Our contributions can be summarized as: 1) We propose a novel verification
style reading comprehension dataset, VGaokao, which embeds more advanced
language understanding skills. 2) We propose a new Extract-Integrate-Compete
approach to iteratively select complementary evidence from long articles
through a novel query updating mechanism. Our hinge loss based competition
component can push the model to capture fine-grained differences among
different choices. 3) Experiments show that our approach outperforms a variety
of baselines in both evidence retrieval F1 and QA accuracy on VGaokao while
showing the merits of efficiency and explainability.

##  2 VGaokao: Verification Style Reading Comprehension Dataset

Standardized language tests have been considered as a test-bed to harvest
machine reading comprehension datasets. While most existing efforts focus on
SQuAD-like QA datasets Yang et al. (2018); Kwiatkowski et al. (2019), or cloze
style questions Zhang et al. (2018); Zheng et al. (2019), few efforts are made
to verification style questions.

In the Chinese Language test of Gaokao, approximately half of the reading
comprehension questions instruct students to select a statement (i.e., an
option from four choices) that is the most consistent or contradicting with
the given passage. These questions are designed to evaluate students’ ability
in extracting and integrating information from long passages, and analyzing
certain linguistic phenomena or semantic relations among several similar
sentences333According to the Syllabus of Chinese Language in China by the
Ministry of Education.. According to the target language skills, we call these
questions verification style questions and convert them into the task of
verifying given statements against the articles. Our task is similar in spirit
to the fact checking task, FEVER Thorne et al. (2018). But, unlike the claims
tagged with a definite label in FEVER (Supported, Refuted or Not-Enough-Info),
the statements in Gaokao questions are designed to be not absolutely correct
nor absolutely incorrect. In other words, the options of a question in VGaokao
differ in how much they are supported by the passage, which is difficult to be
quantified with a value between 0 and 1. The design of relative correctness is
in the purpose of evaluating test-takers’ ability to disambiguate very similar
options through considering the subtle difference among them.

In this work, we construct a verification style reading comprehension dataset
named VGaokao from the Chinese Language test of Gaokao to assess a model’s
skills of extracting evidence from articles and verifying statements against
the retrieved evidence pieces and other options.

C3 |
---|---
…他呆呆地站在那里，面色尴尬至极，双手拧来拧去无处可放。上课前他自以为成竹在胸，所以就没带教案和教材。整整10分钟，教室里鸦雀无声，所有的学生都好奇地等着这位新来的老师开口…(共498字) Q: 沈从文没拿教材，是因为他觉得（ ） A. 讲课内容不多 B. 自己准备得很充分 $\surd$ C. 这样可以减轻压力 D. 教材会限制自己的发挥 |  …He stood there motionlessly, extremely embarrassed. He wrung his hands without knowing where to put them. Before class, he believed that he had had a ready plan to handle different situation so he did not bring his teaching plan and textbook. For up to 10 minutes, the classroom was in perfect silence. All the students were curiously waiting for the new teacher to open his mouth… (498 Chinese characters in total) Q: Congwen Shen did not bring the textbook because he felt that ( ) A. there were not many teaching contents. B. he was well prepared. $\surd$ C. he could relieve his mental pressure in this way. D. the textbook was likely to restrict his ability to give a lecture.
VGaokao |
…如果孕妇怀孕期间睾丸素水平较高，生下的孩子就更容易成为左撇子，也更容易在日后得心脏疾病或孤僻症。这也许可以解释为什么世界上左撇子只占总人口的10％。同样，雌性激素水平较高的孕妇，所生的女孩食指通常短于无名指，而日后患乳腺癌的可能性也较高。… (共1126字) Q: 下列说法符合原文意思的一项是（ ） A. 在400万年进化史中，人类的手逐渐演变成使人具有高度智慧的重要器官和大自然所能创造出的最完美的工具。 B.通常，左撇子的无名指之所以比食指长，是因为孕妇怀孕期间的睾丸素水平较高。$\surd$ C.大脑控制手的活动的区域的运动中枢与语言中枢之间存在着密切的神经联系，使得手势成为人类沿袭至今的唯一的肢体语言。 D. 大脑控制手的活动区域，面积达大脑皮层1/4。因此大脑皮层特别强烈的兴奋会使一个简单的手动作顺利实现。 |  …If pregnant women have higher testosterone levels during pregnancy, their children are more likely to be left-handed and more likely to develop heart disease or autism in the future. This may explain why left-handers only account for 10% of the total population in the world. Similarly, pregnant women with higher levels of estrogen usually give birth to girls whose index finger is shorter than the ring finger, and they are more likely to develop breast cancer in the future… (1126 Chinese characters in total) Q: Which statement is most consistent with the passage? ( ) A. In 4-million-year evolutionary history, human hands have gradually evolved into an essential organ enabling human to have high-degree intelligence and the most perfect naturally created tool. B. In general, the fact that the left-handed ring finger is longer than the index finger is because of the higher testosterone levels during pregnancy.$\surd$ C. There is a close neural connection between the motor center and the language center in the area where the brain controls the activity of the hands, making gestures the only body language that has been inherited by humans. D. The brain controls the active area of hands, which reaches 1/4 of the cerebral cortex. Thus, particularly intense excitement in cerebral cortex makes a simple hand movement smoothly realized.
Table 1: Example articles and questions from C3 (Sun et al., 2020, top) and from VGaokao (bottom). | Passage | Question | Option
---|---|---|---
Average Length (Char.) | 1,159 | 18 | 47
Max Length (Char.) | 2,568 | 60 | 147
Vocabulary Size | 96,806 | 1,245 | 34,789
Total Vocabulary Size | 87,945
Table 2: Statistics of the VGaokao dataset.

###  2.1 Dataset Construction

We construct VGaokao from the Chinese Language examinations in Gaokao and the
official mock tests provided by each province. The test questions are designed
by the Ministry of Education of China and the examination centers of each
province, which are available to the public. We first collect the original set
of test article-question pairs and discard the articles and questions that are
not of verification style444We filter out fictions, proses, and poems from the
collection, which focus on evaluating students’ ability of aesthetic
appreciation. We also discard the questions asking for word meaning
explanation or summarizing a certain topic. . The remaining articles cover a
wide range of topics, including analyzing issues or arguments, introducing
recent discoveries in science or engineering, and discussing popular social
topics. The remaining questions ask the test-takers to select a statement that
is the most consistent with the article or contracts the most with the
article, which we can convert into the form of statement verification.

In total, we collect 2,786 passages and 3,512 questions. Each question is
paired with 4 options. We randomly sample 80% of the questions for training
and the rest of the questions are used for test.

To quantitatively evaluate the model performance in evidence selection, we
randomly sample 25 questions (100 options) from the test set of VGaokao and
manually annotate their evidence sentences from the article. On average, there
are 1.6 evidence sentences for each option, and the distance between evidence
varies from 1 to 9 sentences. This indicates that one has to collect 6.4
evidence on average from the whole passage to answer one question with four
options, which makes VGaokao a dataset requiring the ability of gathering and
processing multiple evidence.

###  2.2 Dataset Analysis

The basic statistics of VGaokao is shown in Table 2, illustrating challenges
from the following aspects.

#### Advanced Language Comprehension

Constructed from standardized language tests designed for native speakers,
VGaokao requires models to understand more complex passages, compared to other
datasets from examinations for second language learners such as C3 Sun et al.
(2020). The main differences can be summarized in three folds. Firstly, in
VGaokao, the vocabulary size is 1.6 times larger than that of C3, which brings
more diverse words. Secondly, at the sentence level, the average sentence
length of VGaokao is 1.6 times longer than that of C3, and the average
dependency tree depth of VGaokao is 1.2 times larger than that of C3. Longer
sentences and more complicated syntactic structures usually exhibit rich
linguistic phenomena, thus requiring models to learn more sophisticated
language understanding skills. Lastly, the passages in VGaokao, which contain
1,159 Chinese characters on average, are approximately 3 times longer than
that of RACE Lai et al. (2017) and 10 times longer than that of C3 Sun et al.
(2020). The length of most passages even exceeds the maximum input length of
general pre-trained language models such as BERTDevlin et al. (2019). To
exploit the long passages, models may need to take discourse structures into
consideration so as to better integrate multiple evidence sentences.

As shown in the sample articles and questions from VGaokao and C3 in Table 1,
the example article from VGaokao involves domain-specific terminologies such
as testosterone and estrogen. The sentences in the VGaokao example are longer
and involves more complicated sentence structures such as compound sentences.
Besides, the options in VGaokao seem to be more confusing: Option C and D both
discuss the subtle relationship between the brains and hands, which requires
one to carefully discriminate between them based on the passage, while in the
C3 example, only Option B is explicitly mentioned in the passage. These
comparisons indicate that VGaokao can be used to evaluate the language
comprehension ability at a higher level compared to previous works.

#### Requirement of Multiple Evidence

Longer passages usually require skills of gathering multiple disjoint evidence
pieces to verify and compare the candidate statements. As a pilot study, we
randomly sample 100 options and manually annotate their golden evidence
sentences from their corresponding passages. We find that 47% of the sampled
options require more than one evidence sentences. Furthermore, there are
usually certain discourse relationship among multiple evidence pieces required
by one statement, such as causality, comparison, or expansion. In the VGaokao
example of Table 1, to support Option B, we need to extract the first and the
third sentences in the sample text as evidence and recognize the causal
relationship between them. This observation indicates that more sophisticated
skills such as discourse analysis may be helpful for exploiting the evidence
pieces.

Figure 2: An illustration of our proposed Extract-Integrate-Compete approach.

##  3 Our Extract-Integrate-Compete Approach

We propose a novel Extract-Integrate-Compete approach to address the
challenges in VGaokao. As illustrated in Figure 2, our approach includes three
stages, iterative evidence extraction, adaptive evidence integration and
pairwise option competition.

###  3.1 Iterative Evidence Extraction

Generally, in evidence sentence extraction, models are to extract a subset of
evidence sentences $\left\\{s_{1},~{}s_{2},~{}\cdots,~{}s_{n}\right\\}$
according to query $q$. One can use an encoder (e.g., averaging over the
presentation of each word in the embedding space) to embed query $q$ and
evidence candidate $s_{i}$ into dense vectors $\bm{q}$ and $\bm{s_{i}}$, and
then use a similarity function $\rm{sim}(\cdot)$ (e.g., cosine similarity) to
obtain the relevance score $f$, i.e.,
$f(q,s_{i})={\rm{sim}}(\bm{q},\bm{s_{i}})$. This method treats each candidate
evidence independently, and produces a ranking list. However, when a query
requires multiple evidence sentences, independently selecting top $k$ ranked
sentences may ignore the complementary relationship between evidence
sentences, thus producing inferior results.

In this work, we propose an iterative way to collect multiple evidence for a
given query, where the query representation is updated with newly-retrieved
information at each extraction iteration. To emphasize the complementary
relation between the evidence sentences while avoiding too much overlap, we
propose to use masking strategy to reduce the relevance between queries and
their retrieved evidence pieces.

Specifically, we assume
$e^{t}=\\{c^{t}_{1},~{}c^{t}_{2},~{}$$\cdots,~{}c^{t}_{m}\\}$ is the evidence
sentence retrieved at the the $t$-th step, $c^{t}_{j}$ is the $j$-th token in
$e^{t}$. To search for complementary evidence pieces, we propose to reduce the
influence of some parts in $q$ that have been covered by the retrieved
evidence sentence $e_{t}$ so that the query representation $\bm{q_{t+1}}$ for
the next step will pay more attention to the parts whose corresponding
evidence has not been found.

We design two masking strategies for iterative evidence extraction, i.e., Hard
Masking and Soft Masking.

Hard Masking After the $t$-th iteration, we just discard the query tokens that
exactly appear in the extracted evidence $e^{t}$. Formally, in the query
representation $\bm{q_{t+1}}$ for $(t+1)$-th step, the weight $\beta^{t}_{i}$
of the $i$-th query token $q_{i}$ is:

$\beta^{t+1}_{i}=\frac{\alpha^{t+1}_{i}}{\sum_{k}\alpha^{t+1}_{k}}$ (1)

$\alpha^{t+1}_{i}=\left\\{\begin{array}[]{rr}0,&q_{i}\in{e^{t}}\\\
\alpha^{t}_{i},&q_{i}\notin{e^{t}}\end{array}\right.$ (2)

Afterwards, we compose the new query representation $\bm{q_{t+1}}$ for the
$(t+1)$ step by performing a weighted sum of the query token embeddings:

$\bm{q^{t+1}}=\sum_{i}\beta^{t+1}_{i}\bm{q_{i}}$ (3)

In this way, the new query representation is restricted to focus on the
unmatched tokens.

Soft Masking Instead of directly assigning zero weights in the hard masking
method, soft masking strategy reduces the weights of the already-addressed
tokens in the next-step representation. The weight of the $i$-th query token
$q_{i}$ is inversely correlated to its matching score to its most similar
token in the retrieved evidence set. In practice, we use the dot products of
token embeddings to measure the relevance between tokens. Then we calculate
the weight $\beta^{t+1}_{i}$ for the $i$-th query token at the $(t+1)$-th
retrieval step by adding a negative sign to its highest similarity score and
applying a softmax over all the query token weights:

$\beta^{t+1}_{i}=\frac{e^{\lambda\alpha^{t+1}_{i}}}{\sum_{k}e^{\lambda\alpha^{t+1}_{k}}}$
(4)
$\alpha^{t+1}_{i}=-\max{\left(\max_{j}(\bm{q_{i}}\cdot\bm{c^{t}_{j}}),-\alpha^{t}_{i}\right)}$
(5)

where $\lambda$ is used to adjust the extent to which we want to widen the
weight gap between the matched tokens and the unmatched tokens.

Afterwards, we can obtain the new query representation $\bm{q_{t+1}}$
similarly to Eq.3.

###  3.2 Adaptive Evidence Integration

In practice, different queries require various amount of evidence pieces.
Fixing the numbers of evidence sentences may introduce noise for queries
requiring fewer or more evidence sentences. To alleviate this problem, we
introduce an evidence integration module to adaptively determine how many
complementary evidence pieces are needed for each query.

Specifically, after $t$ steps of beam search, we obtain several evidence
chains consisting of $t$ different evidence sentences. In each chain, we
reorder and concatenate the evidence sentences according to their order in the
original passages, in the hope to maintain the potential discourse
relationship between evidence sentences. Then, we feed the integrated evidence
chains obtained from different numbers of retrieval steps into a reranker,
further comparing their semantic similarity to the query. The highest scored
evidence chain will be selected as the final evidence chain of the query. This
evidence integrator measures the candidate evidence chains as a whole and
adaptively filters irrelevant evidence pieces introduced in later iterations.

###  3.3 Pairwise Option Competition

As mentioned in Section 2, we need to carefully discriminate among several
options to arrive at the final answer. We thus introduce a pairwise option
competition component to the option selection step. We adopt a pre-trained
language model $g(\cdot)$ to calculate how the statement $d$ is supported by a
retrieved evidence set $c$. During training, for a question that requires
choosing the option that is most consistent with the passage, we have a
correct option $d^{+}$ and several incorrect options
$d^{-}_{1},d^{-}_{2},...,d^{-}_{k}$, paired with their retrieved evidence sets
$c^{+},c^{-}_{1},c^{-}_{2},...,c^{-}_{k}$. We calculate a hinge loss for the
pairwise option competition:

$\displaystyle L(d^{+},d^{-}_{1},d^{-}_{2},...,d^{-}_{k})=$ (6)
$\displaystyle\sum_{i=1}^{k}\max(0,-g(d^{+},c^{+})+g(d^{-}_{i},c^{-}_{i})+0.5)$

Similarly, for a question that requires choosing the most contradictive
option, we will have an incorrect option $d^{-}$ and several correct options
$d^{+}_{1},d^{+}_{2},...,d^{+}_{k}$, paired with their retrieved evidence
chains $c^{-},c^{+}_{1},c^{+}_{2},...,c^{+}_{k}$, the loss will be:

$\displaystyle L(d^{-},d^{+}_{1},d^{+}_{2},...,d^{+}_{k})=$ (7)
$\displaystyle\sum_{i=1}^{k}\max(0,-g(d^{+}_{i},c^{+}_{i})+g(d^{-},c^{-})+0.5)$

During inference, we select the option with the highest score as the answer
for a question requiring choosing the option that is the most consistent to
the passage. Similarly, we select the option with the lowest score for a
question asking for the option that contradicts most to the passage.

###  3.4 Implementation Details

For the iterative extractor, we use jieba555https://github.com/fxsjy/jieba to
perform Chinese word segmentation. We use pre-trained word vectors Qiu et al.
(2018) to perform unsupervised iterative extraction with our query updating
strategies. The $\lambda$ in Eq. 4 is set to 1. Since 83% of the options with
multiple evidence pieces require two evidence sentences, we set the maximum
number of iterations to 2. Considering that maintaining all evidence chains
during iterative extraction has exponential complexity to the steps, we use
beam search, where only top 2 evidence sentences remain in each step.

We use Sentence-BERT Reimers and Gurevych (2019, 2020) to measure the
relevance between the query and the evidence chains in the adaptive
integrator. For the pairwise option competition, we use Chinese RoBERTa-wwm-
ext-Large Cui et al. (2019) with Transformers toolkit Wolf et al. (2020). We
first fine-tune our model on OCNLI Hu et al. (2020), a Chinese natural
language inference dataset before fine-tuning on VGaokao, which has 8 epochs,
with maximum input length 256, batch size 64, and learning rate 2e-5.

##  4 Experiments

We conduct experiments on our proposed VGaokao dataset and compare our
Extract-Integrate-Compete approach with several baselines.

RoBERTa-Large-Chunk Liu et al. (2019) is an end-to-end method without explicit
evidence retrieval. This model splits the long passages into fix-length chunks
of 200 tokens. Candidate answers are obtained from each chunk using existing
MRC models, which are further aggregated over all chunks. We use the pre-
trained Chinese RoBERTa-wwm-ext-Large Cui et al. (2019).

BM25 Robertson and Zaragoza (2009) is a bag-of-words retrieval method, which
uses sparse features to retrieve evidence sentences. We use the version
implemented by Pyserini666https://github.com/castorini/pyserini.

Sent-BERT Reimers and Gurevych (2019) uses BERT to obtain contextualized dense
representations for the texts and retrieve evidence sentences via cosine
similarity.

BeamDR Xiong et al. (2021); Zhao et al. (2021) is an iterative evidence
selection technique with beam search and dense retrieval. It updates the query
by appending the newly-extracted evidence in each iteration.

The BM25, Sent-BERT, and BeamDR are evidence extraction methods, which are
combined with our proposed pair-wise option competition method to obtain the
final question-level results. For BM25 and Sent-BERT, which cannot address the
problem of multiple evidence, we report their experiment results with top 1 or
top 2 evidence sentences selected. To make fair comparison, we do not
intensively tune any models, including ours. Specifically, we first search
hyperparameters for the BM25 model, and apply the same hyperparameters to
other baselines and our method.

We use three metrics to evaluate evidence quality on the subset annotated with
golden evidence sentences: precision (P), recall (R), and F1 (F1). The
accuracy of predicted answers (Acc.) is used to evaluate the performance on
the question level.

| Evidence Metrics | QA Metrics
---|---|---
| P | R | F1 | Acc.
RoBERTa-L-Chunk | — | — | — | 41.9
BM25 Top 1 | 93.0 | 71.1 | 77.9 | 47.6
BM25 Top 2 | 64.5 | 87.7 | 71.6 | 48.4
Sent-BERT Top 1 | 87.0 | 67.3 | 73.4 | 48.4
Sent-BERT Top 2 | 55.5 | 79.1 | 62.8 | 48.9
BeamDR | 52.5 | 74.0 | 59.2 | 48.9
Hard Masking | 82.5 | 79.5 | 79.2 | 49.3
Soft Masking | 82.5 | 77.5 | 78.0 | 49.6
Table 3: Performance of baselines and our methods on VGaokao (%). RoBERTa-L-
Chunk is short for RoBERTa-Large-Chunk.

###  4.1 Main Results

As we can see in Table 3, our Extract-Integrate-Compete approach outperforms
the end-to-end baseline and other evidence retrieval methods in both evidence
quality and answer prediction accuracy. We analyze the results by comparing 1)
passage chunking and evidence selection, 2) one-off evidence selection and
iterative evidence selection, and 3) different query updating strategies.

#### Passage Chunking vs. Evidence Selection

RoBERTa-Large-Chunk simply chunks passages into pieces, which is a common
practice for end-to-end MRC models Devlin et al. (2019); Kwiatkowski et al.
(2019). It obtains a question-level accuracy of 41.9%, lagging behind the
methods with additional evidence extraction step by at least 5.7%. We think it
is because the evidence sentences of a statement may appear in different
chunks. Without evidence selection, models have to split the long article,
which results in incomplete evidence for training and harm the performance.
Even such simple methods as BM25 outperform the chunking method thanks to the
retrieved evidence that is more relevant to the statement. Moreover, by
introducing evidence selection, we can have a small-sized but focused
supportive candidates to be feed the MRC model, greatly reducing required
computational resources. These results illustrate the necessity of selecting
evidence pieces from the long articles before performing verification.

Statement: 互联网颠覆传统制造业的现象在发达国家已出现；国内互联网巨头主动涉足传统制造业，互联网去工业化初现端倪。 The phenomenon
of the Internet subverting traditional manufacturing has already appeared in
developed countries; domestic Internet giants have taken the initiative to set
foot in traditional manufacturing, and the de-industrialization of the
Internet has begun to take shape.
---
S-BERT Top 1 Evidence: ② Soft Masking Evidence: ①② Golden Evidence: ①②
①互联网的去工具化从百度、腾讯等互联网巨头纷纷主动涉足传统制造业已经初现端倪。 The de-instrumentation of the Internet
has begun to emerge from Internet giants such as Baidu and Tencent, which take
the initiative to set foot in traditional manufacturing.
②而互联网对传统制造业带来的颠覆在发达国家也已出现。 The disruption of the traditional manufacturing
industry brought by the Internet has also appeared in developed countries.
Statement: 美国某款新能源汽车生产者运用了物联网概念，取消了4S店的商业模式，自己销售产品并提供保养、维修等各项服务。 A new-energy
vehicle manufacturer in the United States used the concept of the Internet of
Things, abandoned the business model of the 4S shop, sold its own products and
provided various services such as maintenance and repair.
S-BERT Top 2 Evidence: ①② Soft Masking Evidence: ① Golden Evidence: ①
①美国的某款新能源汽车，由于运用了物联网概念，已经取消了传统的4S店商业模式，不仅销售不需要，甚至保养、维修也不再需要4S店。
A new energy vehicle in the United States, due to the use of the Internet of
Things concept, has abandoned the traditional 4S shop business model. Not only
does it not need to be sold, but even maintenance and repairs do not require
4S shops.
②在工业4.0阶段，互联网已经不再是传统意义上的信息网络，更是物质、能量和信息互相交融的物联网，传递的也不仅是传统意义上的信息，还可以包括物质和能量的信息。
In the 4.0 stage of industry, the Internet is no longer an information network
in the traditional sense. It is an Internet of Things that integrates
material, energy and information. It transmits not only information in the
traditional sense, but also information about matter and energy.
Statement: 佛教禅宗的坐忘、顿悟等与空灵美的琼澈晶莹境界看来相似，实则相反，因二者赖以存在的基础完全不同。 Buddhism Zen’s “sit
and forget” and “insight” are similar to crystal artistic realm of ethereal
beauty, but they are opposite, because the bases of their existence are
completely different.
BeamDR Evidence: ①② Soft Masking Evidence: ①③ Golden Evidence: ①③
①佛教禅宗的“坐忘”“顿悟"与空灵之美的那种琼澈晶莹的艺术境界，从表面上看，颇有些异曲同工之处。 On the surface, there are
some similarities between the “sit and forget” and “insight” of Zen Buddhism,
and the crystal clear artistic realm of ethereal beauty.
②空灵美不是老庄的“虚静”，佛教的“空忘”那样引人出世的“禅意”，而是一种实与虚、有限与无限的契合统一。 This kind of ethereal
beauty is not the “emptiness and quietness” of Taoism or the “emptiness and
forgetfulness” of Buddhism, but a combination of reality and emptiness, of
limitation and infinity.
③实际上，佛道两教是主观唯心主义的东西，空灵之美则恰恰相反，它根植于绚丽多彩的现实生活。 In fact, Buddhism and Taoism are
subjective idealism, while ethereal beauty is just the opposite and rooted in
colorful real life.
Table 4: Case study of the evidence retrieved by different methods. Golden
evidence and its corresponding part in the statement are marked with the same
color (red or blue).

#### One-off Selection vs. Iterative Selection

In Table 3, our methods, with either hard masking or soft masking, outperform
one-off evidence selection methods, BM25 and Sent-BERT settings, by 2~16% in
the evidence extraction F1.

Specifically, by selecting the top 1 evidence sentence, these methods ensure a
high precision but fail to provide sufficient evidence to the statements that
require more evidence sentences. For example, in the first case of Table 4,
the top 1 evidence sentence selected by S-BERT only covers the second half of
the statement while our method with soft masking strategy succeeds in
retrieving the complete evidence chain with iterative extraction.

On the other hand, by selecting top 2 evidence sentences, Sent-BERT and BM25
achieve a high recall but may introduce irrelevant evidence to the statements
requiring fewer evidence sentences. For the second case in Table 4, using the
top 2 evidence sentences will introduce a noisy sentence, while our method
correctly determines that the statement only needs one evidence sentence with
the adaptive evidence integrator.

Our evidence selection module achieves a balance between the precision and
recall of the retrieved evidence pieces, obtaining the highest F1 scores among
all methods. By iteratively extracting possible partial evidence, our methods
ensure a relatively high recall of over 80%; by adaptively integrating truly
complementary evidence pieces, our methods lead to a relatively high precision
of nearly 80%. Therefore, our methods with iterative extraction and adaptive
integration achieve the highest F1 scores among competitive counterparts.
Besides, the higher evidence performance also results in better QA
performance, with an improvement of more than 0.7%. This indicates that
carefully retrieved evidence produces more reliable evidence chains for the
verification module, improving the explainability of our methods.

#### Query Updating Strategy

Our query updating strategies, hard masking and soft masking, outperform
BeamDR by approximately 20% in evidence retrieval F1. After each iteration,
BeamDR appends the extracted evidence sentence to the query for following
iterations. This strategy may put more emphasis on the overlap between
retrieved evidence and queries, while the unmatched parts are likely to
receive less attention. This tendency prevents the model from gathering
complementary evidence sentences. By contrast, our query updating methods
highlight the tokens in the query whose corresponding evidence is still
missing, thus, being more likely to retrieve complementary evidence pieces.

For the third case of Table 4, the second evidence sentence returned by BeamDR
shares the same topic with the first one, but irrelevant to the given
statement. On the contrary, the second evidence sentence returned by our
method is a complementary one that supports the second half of the statement.
A possible reason is that our soft masking strategy can highlight the phrases
such as opposite, basis of existence that are absent in the first retrieved
evidence, pushing the retriever to collect complementary evidence.

Our two masking strategies, hard masking and soft masking, perform comparably
on both metrics. The hard masking is easy to implement and requires little
computation when updating queries; the soft masking can to some extent
maintain the information in the matched tokens, which may be useful in the
next step evidence retrieval. To summarize, our query updating strategies can
make the retrieval target of each iteration more focused and boost the
performance in both evidence extraction and the final answer selection.

###  4.2 Ablation Study

To reveal the effectiveness of each module in our approach, we conduct
experiments with three ablated settings with soft masking for the iterative
extractor. As we can see in Table 5, After we remove each of the three
modules, the performance drops substantially in evidence F1 and question-level
accuracy, demonstrating the effectiveness of each part in our approach.

Specifically, after removing the iterative extraction module, we can observe a
decrease of 6.3% in the evidence F1 and a decrease of 1.9% in the question-
level accuracy, because one-off evidence extraction fails to gather sufficient
complementary evidence pieces. Thus the option competition module is unlikely
to make a thoughtful decision based on an incomplete evidence chain.

When we remove the adaptive integration module, the evidence F1 drops by 15.1%
and the question-level test accuracy drops by 2.2%. This may result from
irrelevant evidence pieces introduced in the later iterations of evidence
extraction. The adaptive integration module can screen out this kind of noisy
information by evaluating the associativity between extracted evidence, i.e.,
the property that evidence pieces are logically connected to cover the
information in the query.

Without the pairwise option competition, the question-level accuracy decreases
by 0.9%. This indicates that pairwise option competition is superior to
independent treatment of each option, because pairwise competition can push
the model to capture the subtle difference between options.

Methods | Evi. F1 | Qu. Acc.
---|---|---
Soft Masking | 78.0 | 49.6
w/o Iterative Extraction | 71.7 ( -6.3) | 47.7 (-1.9)
w/o Adaptive Integration | 62.9 (-15.1) | 47.4 (-2.2)
w/o Pairwise Competition | — | 48.7 (-0.9)
Table 5: Ablation study of our soft masking method on VGaokao.

##  5 Related Works

Several previous datasets are constructed from different subjects of Gaokao,
including Geography Huang et al. (2019), English Lai et al. (2017); Sun et al.
(2019), and History Guo et al. (2017). Different from these efforts, we focus
on Chinese subject to introduce native-speaker level reading comprehension
challenges.

Evidence extraction based methods have been studied in MRC Talmor and Berant
(2018); Perez et al. (2020) and fact verification Thorne et al. (2018). In
this work, we introduce evidence extraction to our method for solving the long
article challenge in VGaokao.

Iterative evidence extraction can be seen as a sort of question decomposition
method, a technique widely used in QA tasks with complex questions Talmor and
Berant (2018); Perez et al. (2020). However, in VGaokao, the queries may
interweave by implicit semantic relationship, so that models could not
explicitly separate the queries into independent sub-queries. We thus adopt an
iteative extractor with an adaptive integrator to decompose queries in an
implicit way.

Another stream of works adopt an iterative framework by updating the queries.
Qi et al. (2019) iteratively generate new queries by selecting a span from the
question and retrieved evidence while Xu et al. (2019); Xiong et al. (2021);
Zhao et al. (2021) directly append retrieved evidence to the query. Compared
with these works, we introduce two novel query updating techniques, hard
masking and soft masking, together with an evidence integration module to
avoid too much overlap between evidence and to dynamically determine the
number of required evidence sentences.

##  6 Conclusion

In this paper, we present a novel verification style reading comprehension
dataset named VGaokao from the Chinese Language tests of Gaokao for Chinese
native speakers, which embed multiple advanced language understanding skills.
To address the challenges in VGaokao, we propose a new Extract-Integrate-
Compare approach for complementary evidence retrieval/integration and option
discrimination. Experiments show that our approach outperforms several strong
baselines, with additional merits of efficiency and explainability. We believe
VGaokao is a challenging test-bed for natural language understanding in
Chinese and encourage further research in verification style reading
comprehensionn.

## Acknowledgements

We thank the anonymous reviewers for the helpful comments and suggestions.
This work is supported by Hi-Tech R&D Program of China (No.2018YFB1005100).

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