# Sedimentation of a Colloidal Monolayer Down an Inclined Plane

B. Sprinkle, S. Wilken, S. Karapetyan, M. Tanaka, Z. Chen, J. R. Cruise, B.
Delmotte, M. M. Driscoll, P. Chaikin, and A. Donev

###### Abstract

We study the driven collective dynamics of a colloidal monolayer sedimentating
down an inclined plane. The action of the gravity force parallel to the bottom
wall creates a flow around each colloid, and the hydrodynamic interactions
among the colloids accelerate the sedimentation as the local density
increases. This leads to the creation of a universal “triangular”
inhomogeneous density profile, with a traveling density shock at the leading
front moving in the downhill direction. Unlike density shocks in a colloidal
monolayer driven by applied torques rather than forces [Phys. Rev. Fluids,
2(9):092301, 2017], the density front during sedimentation remains stable over
long periods of time even though it develops a roughness on the order of tens
of particle diameters. Through experimental measurements and particle-based
computer simulations, we find that the Burgers equation can model the density
profile along the sedimentation direction as a function of time remarkably
well, with a modest improvement if the nonlinear conservation law accounts for
the sub-linear dependence of the collective sedimentation velocity on density.

##  I Introduction

The dynamics of active and driven colloidal suspensions is interesting not
only because of its inherent out-of-equilibrium nature, but also because it is
often dominated by collective effects leading to the formation of large-scale
structures and flows. In the Stokes (overdamped) limit relevant to colloids,
the hydrodynamic interactions between the particles are long-ranged and
strongly depend on the presence of nearby boundaries such as confining walls.
While self-propelled colloids (microswimmers) are of great interest,
externally-driven colloids present a simpler system to analyze and study both
analytically and via computer simulations. In particular the only many-body
and long-ranged interactions in driven suspensions are hydrodynamic
interactions created by the generated solvent flow. While confining walls
generally screen hydrodynamic interactions to be less long-ranged than in bulk
suspensions, the nature of the hydrodynamic flows generated by the activity or
external driving mechanism crucially affects the resulting collective
behavior.

In prior work Rollers_NaturePhys ; MagneticRollers ; TwoLines_Rollers ;
NonlocalShocks_Rollers ; RollersLubrication , some of us studied the
collective behavior of microrollers: magnetic colloids sedimented above a
bottom floor (wall) in an external magnetic field rotating around an axis
parallel to the wall. Each spinning particle propels itself parallel to the
wall, but the collective motion in a non-dilute suspension is much faster than
that of an isolated colloid. For microrollers, the driving mechanism is an
applied torque, and the flow field created by a single particle corresponds to
a rotlet above a no-slip wall blake1971note ; OseenBlake_FMM . This flow
advects other particles both in the vertical direction (away or toward the
wall), as well as in the transverse directions parallel to the wall. The
resulting collective dynamics is surprisingly rich even at moderate densities,
for which in the absence of the external drive the colloids would form a
single monolayer with in-plane packing fractions $\phi\apprle 0.5$. Uniform
microroller suspensions develop a two-layer structure with a slow bottom layer
and a fast top layer RollersLubrication , and non-uniform suspensions develop
traveling-wave density shocks NonlocalShocks_Rollers  that are unstable to
transverse perturbations TwoLines_Rollers , leading to a fingering instability
that can create stable motile clusters of colloids (critters) held together
entirely by hydrodynamic interactions Rollers_NaturePhys .

For the case of a non-uniform suspension of microrollers, the formation and
dynamics of a density front can be described by a _non-local_ conservation
law, and the front has a finite width that is proportional to the typical
height of the particles above the wall NonlocalShocks_Rollers . Here we study
a similar system of colloids sedimented above a bottom wall but now apply a
force, rather than a torque, to drive collective dynamics. This can easily be
accomplished in the lab simply by tilting the bottom wall at an angle $\theta$
and letting the colloids sediment down the inclined plane. The flow field
created by a single particle corresponds to a Stokeslet above a no-slip wall
blake1971note ; OseenBlake_FMM , and advects other particles primarily in the
direction of the motion. As we demonstrate, the resulting collective density
dynamics can be modeled rather accurately by a _local_ conservation law that
can be approximated by a Burgers equation. This leads to sharp density fronts
in the form of propagating shock solutions of the inviscid Burgers equation.
Similar Burgers-like shocks have been observed for driven and active
suspensions confined in a narrow slit channel (top and bottom walls)
BurgersDroplets_Bartolo ; Beatus2009 ; Tsang2016 ; Lefauve2014 , but a crucial
difference is that the local flow field around a particle in these cases is
quasi-two-dimensional and corresponds to the flow created by a potential
dipole. While colloidal diffusion in a flat monolayer
DiffusionColloidalMonolayer  and sedimentation in a vertical channel
ColloidalRT_Gompper  have been studied both using simulations and experiments,
to our knowledge the sedimentation of colloids down an inclined plane has not
been studied before. Carpen and Brady studied theoretically the sedimentation
of a colloidal suspension in a thicker slit channel and predicted a transverse
instability created by unstable stratification due to shear-induced particle
migration Carpen2002 . Here we study a monolayer sedimenting above a single
wall and find different dynamics that we study by a combination of
experiments, computer simulations, and theory.

We begin by discussing the problem theoretically at a mean-field continuum
level in Section II, and then present results from experiments and particle-
based simulations and compare them to the predictions of the theory in Section
III.

##  II Burgers Model

We consider a monolayer of spherical colloids of radius $a$ sedimented above a
bottom wall tilted at angle $\theta$, as illustrated in Fig. 1. We take the
$x$ axis to be in the direction of the gravitational acceleration
$g\sin\theta$, and the $z$ axis to be in the direction perpendicular to the
wall and pointing away from the gravitational pull $\sim g\cos\theta$. Here we
consider the quasi-one-dimensional problem where initially the colloids are
uniformly distributed in the unbounded (in the theory, bounded at millimeter
scales in the experiments) or periodic (in simulations) $y$ direction, and in
the $x$ direction the colloids are initially contained in the _finite_
interval $[x_{b}(t=0),\;x_{f}(t=0)].$ We wish to quantify the collective
dynamics as the colloids sediment downhill as time $t\geq 0$ elapses.
Specifically, we will average along the $z$ direction and consider the coarse-
grained _number_ density of colloids $\rho(x,y,t)$ in the $xy$ plane (parallel
to the bottom wall). Although estimates of the Péclet number
$\text{Pe}=aV_{\mathrm{avg}}\left(k_{B}T/\left(6\pi\eta
a\right)\right)^{-1}\sim 10$ (where $V_{avg}\in[0.1,0.3]$ is estimated based
on Fig. 3) are not high, we will neglect in-plane diffusion in our continuum
models. Also, we will for now assume there is no transverse instability and
thus the density remains quasi-one-dimensional, $\rho(x,y,t)\approx\rho(x,t)$,
even though the left panel in Fig. 1 shows that this is not exactly true at
later times. We discuss the validity of this assumption in more detail in
Section III.4.1, and conclude that the roughness of the front remains small
compared to the extent of the density profile in the $x$ direction for all
times.

Figure 1: The left panel shows a frontal view of two snapshots from a typical
simulation of a particle suspension sedimenting down an inclined plane. We
show the particles at two separate times: the first (top) at a time
$t=10.3$min shortly after the particles have begun to sediment down the plane,
and the second at $t=171$min when the triangular density profile is well
formed (see text). The front of the suspension is highlighted by magenta
particles, visually emphasizing the coarsening of the density front in time
(see Section III.4.1). The right panel shows a side view of the suspension at
$t=10.3$min along with an inset zoom showing several particles near the front
at their typical Brownian height $h_{g}$. An animated version of the left
panel is available in the Supplementary Information.

Let us assume that an unbounded uniform suspension with
$\rho(x,t)\approx\rho_{0}$ sediments down the plane (in the positive $x$
direction) with collective velocity $v(\phi_{0})$, where $\phi=\rho\pi a^{2}$
is the in-plane packing fraction and $a$ is the radius of the colloids. We
will use $\phi(x,t)$ instead of $\rho(x,t)$ as a more physically-intuitive
variable. The collective sedimentation velocity can be estimated as a function
of packing fraction experimentally or via computer simulations, as we discuss
in Section III.3. Because particles interact hydrodynamically and advect other
particles via the flows they create, the function $v(\phi)$ is quite generally
monotonically increasing. For small $\phi\ll 1$ we expect the linear
approximation

$v\left(\phi\right)\approx v_{0}+\frac{S}{2}\phi,$ (1)

to hold, where $v_{0}$ is the sedimentation velocity of an isolated particle,
and $S/2$ is a constant that measures the strength of the hydrodynamic
interactions.

It is natural to expect that the density dynamics follows the _local_
conservation law

$\frac{\partial\phi}{\partial t}+\frac{\partial}{\partial
x}\left(v\left(\phi\right)\phi\right)=0,$ (2)

which at low densities is expected to be well-approximated by the Burgers
equation

$\frac{\partial\phi}{\partial t}+v_{0}\frac{\partial\phi}{\partial
x}+S\phi\frac{\partial\phi}{\partial x}=0.$ (3)

It is important to note that for colloidal microrollers, the local mean-field
approximation (2) is not appropriate, and one must take into account the
nonlocal nature of hydrodynamic interactions NonlocalShocks_Rollers . However,
for sedimentation, the hydrodynamic interactions are more local and we expect
that the local approximation (2) is suitable; we come back to this question in
Section IV.

Adopting the Burgers approximation (2) we can obtain several analytical
results. We will set $v_{0}=0$ for convenience since a nonzero self velocity
simply translates the solution to the right by $v_{0}t$. Let us first consider
an initial density profile that is a square wave, $\phi(x,t=0)=\phi_{0}$ for
$0\leq x\leq L$, and zero otherwise. The Burgers equation (3) can be solved
analytically, showing that at the front of the square wave there is a
propagating shock with position $x_{f}(t)$, with $x_{f}(0)=L$, and at the back
of the square wave, which stays fixed at $x_{b}(t)=0$, there is a rarefaction
wave. The rarefaction and shock waves meet at time

$t_{\text{triang}}=2\frac{L}{S\phi_{0}},\quad\text{when}\quad
x_{f}\left(t_{\text{triang}}\right)=2L.$ (4)

After this initial transient, there is a _triangular density profile_

$\phi\left(x,t\geq
t_{\text{triang}}\right)=\begin{cases}\frac{x}{x_{f}(t)}\sqrt{\frac{2M}{St}}=\frac{x}{St}&\text{if}\quad
0\leq x\leq x_{f}(t)\\\ 0&\text{otherwise}\end{cases},$ (5)

where the total conserved “mass” is

$M=\int\phi(x,t)dx=L\phi_{0},$ (6)

and the shock wave at the front of the triangle is located at

$x_{f}(t)=\sqrt{2SMt}.$ (7)

This remarkably simple triangle-wave solution is, in fact, universal and
independent of the initial conditions. In particular, it was proven by Lax
that any compactly-supported initial condition will for long times
asymptotically approach the triangle wave solution (5) HyperbolicLaws_Lax . It
was further shown by Goodman that shock solutions of the Burgers equation in
two dimensions are stable against perturbations in the transverse (i.e., the
$y$) direction Burgers2D_ShockStability . The reader should note that while
the equations of Stokes flow are time-reversible, once shocks form the Burgers
equation is no longer time reversible111For example, many initial conditions
can reach the same triangle solution (5) after some finite time
HyperbolicLaws_Lax . because of the implicit dissipation at the front caused
by the neglected diffusion.

##  III Results: Simulations and Experiments

We now compare results from experimental measurements and computer simulations
to the predictions of the Burgers model. We begin by describing briefly the
experimental setup and simulation methodology, and then present results for
the collective sedimentation velocity $v\left(\phi\right)$ for uniform
suspensions, before studying the formation and propagation of Burgers density
shocks. For the results presented here we incline the bottom floor at an angle
$\theta=45^{\circ}$, though we studied other angles as well and found that the
Péclet number controls the layering of the suspension. For larger angles
($\theta\gtrsim 60^{\circ}$), at larger packing densities some of the
particles get lifted away from the floor and the colloids are not in a
monolayer, while for smaller angles the sedimentation velocity is low and
diffusion becomes important. For $\theta=45^{\circ}$ and the Péclet numbers
considered in this work we find that the suspension remains in a monolayer.

###  III.1 Experiments

We performed sedimentation experiments with colloidal monolayers sedimenting
down an inclined plane at angle $\theta=45^{\circ}\pm 3^{\circ}$ placed inside
of a custom-built tilting microscope that sets the angle. The colloids are
polystyrene spheres (Duke Scientific) of diameter $d=2a=\left(4.2\pm
0.1\right)\,\mu$m suspended in mixtures of water ($H_{2}O$) and heavy water
($D_{2}O$) to modify the gravitational height
$h_{g}=k_{B}T/\left(m_{e}g\right)$, where $g$ is the acceleration of gravity,
$m_{e}$ is the buoyant mass, and the temperature $T$ is $\left(22\pm
3\right){}^{\circ}$C. Note that the normal distance between the surface of the
particles and the bottom wall is $\sim k_{B}T/\left(m_{e}g\cos\theta\right)$.
We use three mixtures with different mass fraction of heavy water: 0% heavy
water ($h_{g}=0.250\mu m$), 12.5% heavy water ($h_{g}=0.336\mu m$), and 25%
heavy water ($h_{g}=0.500\mu m$). The solution also contains 50mM BIS-TRIS to
stabilize the particles.

The sample chamber is a rectangular borosilicate capillary tube with
dimensions $6\times 25\times 0.3$mm. The glass surface is coated with
polyelectrolyte multilayers, specifically, three layers each of PDADMAC(+) and
PSS(-) to prevent particle sticking to the glass surface. The colloidal
suspensions are loaded into capillaries at a three-dimensional volume fraction
$5.0\times 10^{-4}$ and the sample chamber is centrifuged first along the
$z$-axis to rapidly drive particles to the bottom surface, and then
centrifuged along the $x$-axis “uphill" to create a densely-packed, partially
crystallized monolayer with area fraction of $0.7\pm 0.1$, extending over a
distance of approximately 100 particle diameters at the bottom of the
capillary. This is the initial condition of all sedimentation instability
experiments. Experiments to measure sedimentation velocity as a function of
density for uniform suspensions are prepared the same way without the $x$-axis
centrifugation.

Sedimentation density profiles are imaged with a custom built tilting
microscope. The camera, objective, sample, and back lighting (530nm LED) are
all mounted together and rotated about a single axis so that prepared
monolayers can be imaged while rotated from flat $\theta=0$ (relative to
gravity) to an incline at angle $\theta$, while the whole monolayer remains in
the focal plane. A photograph of the microscope can be found in the
Supplementary Information. Sample snapshots from the evolution of the
monolayer density observed in experiments are shown in Fig. 2. For experiments
with a uniform suspension we employ conventional particle tracking techniques
crocker1996methods  to count particles and obtain an accurate estimate of
$\phi$.

Large fields of view were needed to accurately measure the density evolution
over long periods of time, limiting the accuracy of particle tracking
techniques, especially at the highest packing fractions. We therefore we use
scattered intensity as a proxy for particle density in the $xy$ plane, see
Fig. 2. This is not sufficiently accurate to obtain precise measurements of
$\phi\left(x,y,t\right)$ since the intensity is not strictly linear in the
density, and also because of imaging artifacts; this is evidenced in the fact
that the total intensity is not conserved and fluctuates by $\sim 10-20$%
especially when the packing fraction is larger than $\phi\gtrsim 0.4$ (see top
of Fig. 8). Near the end of the experiments, when the density is lower,
$\phi\lesssim 0.2-0.3$, we are able to locate particles reliably, as confirmed
by the fact that the total number of particles is conserved to a few percent.
For such low densities we confirm that the scattered light intensity is a good
proxy for packing fraction. The total number of particles is approximately
conserved among all Burgers shock experiments since we start with the same
amount of stock colloidal solution in each capillary and then add water and
$D_{2}O$ to change $h_{g}$. The total number of particles
$N_{\text{\text{exp}}}\approx 78500$ in the viewing area was estimated using
particle tracking at later times, with the length of the frame being
$L_{y}=3344\mu$m, giving the total (conserved) “mass” (6) to be
$M_{\text{\text{exp}}}=N_{\text{\text{exp}}}\pi a^{2}/L_{y}\approx 325\
\mu\text{m}$. Knowing the total number of particles (total mass) allows us to
rescale the scattered intensity to a packing density, which can then be
compared to theoretical and computational predictions.

Figure 2: Microscope images of the density profile for experiment $\\#2$ at
$h_{g}=0.336\ \mu\text{m}$ at several times. The scattered light intensity is
roughly proportional to the density. As time progresses an inhomogeneous
(triangular) density profile develops (higher density on the right, the
direction of motion of the front). See Fig. 8 for averages along the $y$ axis,
and the middle panel in Fig. 4 for images of the front extracted from this
data. An animated version of this figure is available in the Supplementary
Information.

###  III.2 Simulations

The numerical methods used in our simulations are described in detail in
recent work by some of us RollersLubrication  on the collective dynamics in
uniform suspensions of microrollers. Briefly, our lubrication-corrected
Brownian Dynamics method simulates the translational and rotational dynamics
of all particles in the suspension in three dimensions. The method is based on
the method of Stokesian Dynamics and includes both far-field hydrodynamics (at
the Rotne-Prager level StokesianDynamics_Wall  without stresslets) as well as
semi-analytical lubrication corrections due to particles coming close to other
particles or the bottom wall. We consistently and efficiently account for
Brownian motion, which is essential in the particle simulations in order to
set the gravitational height of the particles.

In the simulations we take the radius of the particles $a=2.1\mu$m and the
density of the particles is set to $\rho_{p}=1041\text{kg/m}^{3}$, and we fix
the temperature at $22^{\circ}$C. We compute the density of the solvent
$\rho_{f}$ from the concentration of $D_{2}O$ from standard tables
swift1939densities ; the values are indicated in Table 1. Adding $D_{2}O$ to
water also changes the viscosity of the solution $\eta$ jones1936viscosity ,
as indicated in Table 1. The steric repulsion potential between the particles
and between the particles and the wall is approximated by RollersLubrication

$\Phi(r)=\Phi_{0}\begin{cases}1+\frac{d-r}{2a\delta_{\text{cut}}/\ln(10)}&r<d\\\
\text{exp}\left(\frac{d-r}{2a\delta_{\text{cut}}/\ln(10)}\right)&r\geq
d\end{cases},$ (8)

where $r$ is the distance from a particle to another particle or to the wall,
$d=a(1-\delta_{\text{cut}})$ for particle-wall repulsion and
$d=2a(1-\delta_{\text{cut}})$ for particle-particle repulsion 222Note that
while the case $r<d$ should not happen for hard particles, slight overlaps do
occur in numerical simulations.. We set the strength of the repulsion to
$\Phi_{0}=4k_{B}T$ and take $\delta_{\text{cut}}=10^{-2}$ to mimic
approximately hard sphere interactions through a “firm potential” (see section
3c of RollersLubrication ). To accurately resolve the suspension dynamics we
set the time step size to $\Delta t=4.88\times 10^{-3}(6\pi\eta
a^{3})/\left(k_{B}T\right)=0.2$s. Given this comparatively small $\Delta t$,
on the order of hundreds of thousands of time steps are needed to simulate the
long timescales observed in our sedimentation experiments, which limits the
number of particles we can include in our simulations relative to the
experiments.

$D2O$% | 0 | 12.5 | 25
---|---|---|---
$h_{g}=$ | $0.25\mu\text{m}$ | $0.336\mu\text{m}$ | $0.5\mu\text{m}$
$\rho_{f}=$ | $998\text{kg/m}^{3}$ | $1009\text{kg/m}^{3}$ | $1020\text{kg/m}^{3}$
$\eta=$ |  $0.95$mPas |  $0.98$mPas |  $1.01$mPas
$L_{y}=$ | $116\mu\text{m}$ | $106\mu\text{m}$ | $77\mu\text{m}$
$N=$ | $2759$ | $2592$ | $1811$
$T_{s}=$ |  $5.3$min. |  $10.2$min. |  $38$min.
Table 1: Parameters (rows) used in the simulations for different gravitational
heights (columns) $h_{g}=k_{B}T/m_{e}g$ of the colloidal monolayer.

Our simulations are unbounded in the positive $z$ direction, which is a good
approximation to the experiments where $L_{z}/a\approx 150\gg 1$. For uniform
suspensions, we use a domain that is periodic with period $L_{xy}$ in both the
$x$ and $y$ directions; we controlled the packing fraction by varying $L_{xy}$
while keeping the number of particles fixed. For Burgers shocks the simulation
domain is infinite in the $x$ direction (the direction of motion) and periodic
in the $y$ (the spanwise) direction with period $L_{y}$ indicated in Table 1;
the smallest $L_{y}/a\sim 37$, which we have confirmed is sufficiently large
to make periodic artifacts in the hydrodynamics negligible.

To generate an initial configuration of particles at time $t_{0}$ confined to
a region of the $xy$ plane of area $L_{x}\times L_{y}$, we perform Markov
Chain Monte Carlo equilibrium runs at a constant in-plane packing fraction
$\phi_{0}$ with $N_{0}$ particles. For uniform suspensions, $\phi_{0}=\phi$
and we keep all $N=N_{0}=1024$ particles. For Burgers shock simulations, we
need to generate an inhomogeneous density profile. Therefore, we first
generate a uniform one at the maximum density and then randomly remove
particles to reduce the density where needed. Specifically, we take the
initial density profile extracted from experiments
$\phi_{\text{exp}}\left(x,t_{0}\right),$ set 333The factor of $1.1$ gives us a
small buffer above the maximum.
$\phi_{0}=1.1\max\phi_{\text{exp}}\left(x,t_{0}\right)$ and $N_{0}=4000$, and
independently and uniformly randomly remove each particle with probability
$\left(1-\phi_{\text{exp}}(x,t_{0})/\phi_{0}\right)$. The final number of
particles $N$ after this rejection step is indicated in Table 1.

###  III.3 Uniform suspensions

Our computational and experimental results for the collective sedimentation
velocity $v\left(\phi\right)$ at the three different gravitational heights are
shown in Fig. 3. The apparent $x$ velocity of the particles is computed over
intervals of $1s$ (but the results are not sensitive to this choice), using
particle tracking in the experiments, and the average velocity is computed for
each packing fraction. We see a good agreement between the measured and
predicted collective velocities, to within experimental uncertainty. The
relationship is roughly linear as in (1). To obtain a more accurate functional
form of $v\left(\phi\right)$ to use in (2), we fit the simulation data with a
rational function (typically with degrees 3/2 but no larger than 5/2, not
shown). Since the simulation results for $v(\phi)$ shown in Fig. 3 are sub-
linear over the range of densities of interest ($\phi<0.6$), we refer to (2)
as the sub-Burgers equation.

Figure 3: Collective sedimentation velocity as a function of in-plane packing
fraction for each of the three gravitational heights, for both simulations and
experiments. Experimental measurements of $v(\phi)$ are shown as markers with
error bars of one standard deviation. The solid curve shows data from
simulations at $\theta=45^{\circ}$; the boundaries of the shaded region around
the simulation data are from simulations with $\theta=42^{\circ}$ (smaller
velocity) and $\theta=48^{\circ}$ (larger velocity), in order to account for
the experimental uncertainty in the sedimentation angle $\theta=45^{\circ}\pm
3^{\circ}$. In the simulations the colloids remained in a monolayer only for
$\phi\lessapprox 0.6.$

###  III.4 Burgers shock waves

In the remainder of this section we focus our attention to comparing our
experimental and simulation results to the prediction of the mean-field sub-
Burgers model (2) and its Burgers approximation (3).

####  III.4.1 Transverse (in)stability

Before we discuss results for the one-dimensional density profiles $\phi(x,t)$
modeled by Eqs. (2) and (3), we must understand whether the two-dimensional
density profiles $\phi(x,y,t)$ are actually effectively one-dimensional, that
is, whether the density front remains stable to transverse perturbations.

To do this, from the experimental images and binned simulation densities, we
extract the position of the density front $x_{f}\left(y;t\right)$ such that
the density is essentially zero for $x>x_{f}(y)$; see the left panel of Fig. 1
for an illustration of the particles determined to be at the density front at
two different times. The extracted fronts $x_{f}\left(y;t\right)$ are shown in
Fig. 4. For a rough comparison, we also perform a simulation at
$h_{g}=0.336\mu\text{m}$ with $N=8000$ particles and a wider domain with
periodic length $L_{y}=1260\mu$m, and a uniform initial packing density of
$\phi(0\leq x\leq L_{x},y,t)=0.6$ where $L_{x}=L_{y}/8.6$. We show the
simulated density front profiles overlayed on top of the experimental ones in
the middle panel of Fig. 4, but it should be noted that a direct comparison is
not possible because at present we cannot simulate a system of the same
dimensions as the experiments due to the very large number of particles in the
experiments. Due to the unmatched conditions between the simulation and
experiment, the shift in the mean position of the front in the simulations has
been scaled by an empirical factor of $2.6$ to align the fronts with the
experiments for easier visual comparison. This factor is consistent with a
rough estimate based on the Burgers time scale (4) assuming the initial
condition in experiments is a square wave,
$t_{\text{triang}}^{\text{(exp)}}/t_{\text{triang}}^{\text{(sim)}}=\left(L^{\text{(exp)}}\phi_{0}^{\text{(sim)}}\right)/\left(L^{\text{(sim)}}\phi_{0}^{\text{(exp)}}\right)\approx\left(500\mu\text{m}\cdot
0.6\right)/\left(147\mu\text{m}\cdot 0.65\right)\approx 3.1$.

Figure 4: Position of the density front $x_{f}\left(y;t\right)$ in one of the
experiments at each gravitational height. In the top panels, we overlay
snapshots of the density front in time increments of 1000s, where the opacity
of the curves increases with time. The middle panel also shows the results of
a particle simulation we ran for $h_{g}=0.336$ using $N=8000$ particles with
initial density $\phi_{0}=0.6$, where the time is scaled by a factor of $2.6$
to account for the different total number of particles and domain geometry.
The bottom panel overlays the shifted fronts $\Delta
x(y;t)=x_{f}\left(y;t\right)-\left\langle x_{f}\left(y;t\right)\right\rangle$
at the final time for each gravitational height, as well as the simulation
results for $h_{g}=0.336$. We see that the scale of the roughness and
characteristic “wavelength” of the front are roughly independent of $h_{g}$
and are comparable in experiments and simulations.

The results in Fig. 4 show that the density front becomes rough over time,
however, they do not show the formation of a transverse instability at a
precise wavelength, as is the case for microrollers MagneticRollers ;
TwoLines_Rollers . Instead, the roughness has a broad range of characteristic
length scales (as determined from the correlation function of
$x_{f}\left(y;t\right)$, not shown) and pin-pointing a precise “wavelength” of
the roughness is not possible due to the large statistical uncertainty.

Importantly, the relative roughness of the density shock appears to reach an
approximately constant magnitude, with the front position fluctuating over a
range of about $100\mu$m at the final time. To verify this, in Fig. 5 we show
the width of the rough profile $\sigma_{f}(t)$, as measured from the standard
deviation of $x_{f}\left(y;t\right)$. We normalize the roughness by the length
of the density profile $x_{f}(t)-x_{b}(t)$ (predicted to grow like $\sqrt{t}$
by the Burgers model (7)), where henceforth we denote the mean position of the
density front with $x_{f}\left(t\right)=\left\langle
x_{f}\left(y;t\right)\right\rangle$. To estimate the position of the back of
the front $x_{b}(t)$, we fit a line to the section of the density profile
corresponding to the first fifth of it’s extent in the $x$ direction, and
calculate $x_{b}$ as the intercept of this line. This is reasonably robust
except in the initial stages of the experiment when the density profile is far
from linear.

Figure 5:  The scale of the roughness of the density front
$\sigma_{f}(t)=\text{std}\left(x_{f}\left(y;t\right)\right)$, normalized by
the length of the density profile $x_{f}(t)-x_{b}(t)$, for two experiments at
each of the three gravitational heights. Time is scaled by a rough estimate of
the time it takes for the density profile to become (approximately)
triangular, $t_{\text{triang}}=20$min (see also (4)).

We see in Fig. 4 that in all experiments the roughness of the front remains
quite small ($\sim 1$%) compared to the length of the density profile, at all
times after an initial transient (predicted to be $t_{\mathrm{triang}}$ by the
Burgers model, see (4)) during which the triangular density profile predicted
by (5) is reached. Therefore, even though the front roughness is large
compared to the particle size (as much as $50a$), it is still reasonable to
approximate the density profiles as effectively one-dimensional,
$\phi(x,y,t)\approx\phi(x,t)$. Thus, unless otherwise stated, we focus on
analyzing the density $\phi(x,t)$ computed by averaging $\phi(x,y,t)$ along
the $y$ direction.

####  III.4.2 Sub-Burgers model

In this section, we compare the predictions of the sub-Burgers model (2),
using the estimated collective sedimentation velocity $v(\phi)$ shown in Fig.
3, to the Burgers approximation (3). Because particle tracking over the length
and time scales of interest was not possible in the experimental studies of
sedimenting Burgers fronts, we cannot do this comparison for the experiments
since we cannot accurately measure $\phi(x,t)$ in the experiments over the
whole range of time. Instead, we use computer simulations to evaluate the
accuracy of the models (2) and (3).

We do our best to make the initial conditions in the simulations mimic the
experiments by using the experimental scattered light intensity, scaled using
the total number of particles estimated by particle tracking, as a proxy for
$\phi(x,t)$. Since this is a particularly bad approximation at the very high
packing densities in the initial configuration in the experiments, we skip an
amount of time $T_{s}$ in the beginning of each experiment so that the maximum
packing density falls to around $0.4$; the times $T_{s}$ are indicated in
Table 1. For the particle-based simulations, we generate initial conditions
from the experimentally measured $\phi(x,T_{s})$. For comparison, we also
numerically solve the sub-Burgers equation (2) using a high-resolution Godunov
method444We thank Wenjun Zhao for implementing this method in one dimension
and improving the handling of limiting. SemiLagrangianAdvection_2D  starting
with $\phi(x,T_{s})$ as the initial condition.

Figure 6: Evolution of the density profile $\phi(x,t)$ for each gravitational
height (Top: $h_{g}=0.25\mu$m, Middle: $h_{g}=0.33\mu$m, Bottom:
$h_{g}=0.5\mu$m). The filled density profile shows the initial condition used
in each case, taken from our experimental data after an initial relaxation
period (indicated in the figure). Each panel shows the evolution of the
density profile in a single particle simulation (solid lines, results are
reproducible in statistically independent simulations), the sub-Burgers model
(2) (dashed lines), and the Burgers approximation (3) (dotted lines).
Evolution of the density profiles in each case is shown using decreasing
transparency with increasing time (indicated in the figure). An animated
version of this figure is available in the Supplementary Information.

The results of our computations are summarized in Fig. 6. We see that the
initial condition quickly evolves into an approximately triangular density
profile, after which the sub-Burgers model (2) and the Burgers approximation
(3) (see Section III.4.3) both agree quite well with the results from the
particle simulations. At early times, when the density profile is not yet
triangular, the sub-Burgers equation shows reasonable agreement with the
particle simulations, but the Burgers approximation does not, as expected.
This is particularly evident in the bottom panel of the figure for
$h_{g}=0.5\mu$m; similar behavior is seen at earlier times (not shown) for the
other values of $h_{g}$

We compare the predictions from our simulations to the experimental
measurements in Fig. 7. While we cannot measure the density profile accurately
in the first part of the experiments due to the inability to track particles,
$x_{f}(t)$ can be determined accurately from the experimental images at all
times. In Fig. 7 we compare predictions for the mean front position $x_{f}(t)$
between the experiments, particle simulations, the sub-Burgers model (2), and
the Burgers approximation (3). The sub-Burgers model is once again seen to
agree with the particle simulations rather well over the whole time interval,
for all gravitational heights. At the same time, we observe a moderate ($\sim
10-15$%) difference between the particle simulations and experiments for the
smallest gravitational height $h_{g}=0.25\mu$m, with the agreement becoming
much better for the largest $h_{g}=0.5\mu$m. The systematic difference
persists even if we start simulations from snapshots of the experiments at
later times, when the density is lower and the scattered intensity is a better
proxy for the true density. This suggests that there is a (yet unidentified)
discrepancy in either the particle interactions (e.g., electrostatics), or the
hydrodynamics, between the simulations and experiments 555It should also be
noted that a one-to-one comparison is difficult to make because the width
$L_{y}$ is much smaller in the simulations to reduce the overall number of
particles and thus control the computational effort (e.g., $L_{y}\sim 3.35$mm
is the width of the viewing frame in the experiments, while $L_{y}\sim
100\mu$m in the simulations).. At the largest $h_{g}$, the particles are
furthest from each other and the floor, and we expect the direct and
hydrodynamic interactions between particles to have less of an impact. We
further compare experiments and simulations quantitatively in Section III.4.3.

Figure 7: Mean position of the density front $x_{f}(t)$ for each of the three
gravitational heights (increasing from left to right). The experimental
results (experiment #2) are shown with symbols (circles), and the Burgers fit
to the experimental data (see Section III.4.3 for details) is shown with a
dotted line. We only show one of the experiments but the difference between
experiments is smaller than the symbol size. The results of particle
simulations are shown with a solid line along with corresponding shaded
regions bounded by the results obtained when the angle $\theta$ was changed by
$\pm 3$ degrees, which is roughly the experimental uncertainty in setting the
microscope orientation. The predictions of the sub-Burgers model (2) are shown
with a thick dashed line of the same color as the particle results, while the
Burgers approximation to the simulations (3) is shown with a thin dashed line
of a different color (see legend).

####  III.4.3 Burgers model

In order to compare our simulation results to the predictions of the Burgers
model (3), we fit the mean position of the front $x_{f}(t)$ and the back of
the front $x_{b}(t)$ to the theoretical prediction (7), accounting also for
the fact that $v(\phi=0)$ is nonzero,

$\displaystyle x_{b}(t)$ $\displaystyle=v_{0}t+x_{0}$ (9) $\displaystyle
x_{f}(t)-x_{b}(t)$ $\displaystyle=\sqrt{2SM\left(t-t_{0}\right)},$ (10)

where $v_{0}=v(\phi=0)$ is the numerically-estimated self velocity of an
isolated particle (see Table 2), $S=2\,dv\left(\phi=0\right)/d\phi$ is
estimated from the slope of the rational fit to the simulation data shown in
Fig. 3 (see Table 2), and the total mass $M=N\,\pi a^{2}/L_{y}$. To account
for the fact that the initial condition is not a square wave, we obtain the
time shift $t_{0}$ and the position shift $x_{0}$ from
$x_{f}\left(t_{f}\right)$ and $x_{b}\left(t_{f}\right)$ at the final time
$t_{f}$. We remind the reader that the Burgers equation predicts that any
compactly supported initial condition will asymptotically approach a triangle
wave (5) with a time and space shift that depends on the initial conditions.

Table 2: Fitted or computed values of the parameters $S$ and $v_{0}$ in units of $\mu\text{m}/s$ in the Burger’s model (3). For the particle simulations, the values are computed from the simulation data shown in Fig. 3 (see text). For two independent experiments, the value of $S$ is obtained from the experimental data shown in Fig. 7 over the time period where $\phi(x,t)<0.4$ (see text). We also show estimates of $v_{0}$ obtained by fitting the experimental $x_{b}(t)$ to (9). $h_{g}$ ($\mu$m) | $0.25$ | $0.336$ | $0.5$
---|---|---|---
Particle Sim. |  $S=1.33$, $v_{0}=0.144$ |  $S=1.11$, $v_{0}=0.108$ |  $S=0.85$, $v_{0}=0.07$
Exp. #1 |  $S=1.61$, $v_{0}=0.154$ |  $S=1.24$, $v_{0}=0.12$ |  $S=0.732$, $v_{0}=0.0723$
Exp. #2 |  $S=1.67$, $v_{0}=0.167$ |  $S=1.29$, $v_{0}=0.112$ |  $S=0.766$, $v_{0}=0.0653$

In Table 2 we compare the parameter $S$ and the self velocity $v_{0}$ in the
Burger’s model (3) between experiments and simulations. In the experiments, we
can unambiguously and accurately track the mean front position $x_{f}(t)$ over
all times, while the estimates for the end of the profile $x_{b}(t)$ are less
reliable and more noisy, especially at early times. Nevertheless, we estimate
$v_{0}$ by fitting the experimental $x_{b}(t)$ to (9). The results, shown in
Table 2, demonstrate that $v_{0}$ is quite consistent between experiments and
simulations. To obtain $S,$ $t_{0},$ and $x_{0}$, we match the experimental
data to Eqs. (9,10) at later times, when the triangular density profile is
well formed, by restricting the analysis to the time interval $t_{i}<t<t_{f}$
after the maximum of the estimated density is sufficiently low for the Burgers
approximation to be apply, $\max\phi(x,t_{i})<0.4$. We first determine $x_{0}$
from $x_{b}\left(t_{f}\right)$, since the scattered intensity is the best
proxy for the density at the final time, using the self velocity $v_{0}$
estimated from simulations (see Table 2) in order to avoid using the less
reliable $x_{b}\left(t_{i}\right)$. Then, we compute $S$ and $t_{0}$ from
$x_{f}\left(t_{i}\right)$ and $x_{f}\left(t_{f}\right)$. The resulting Burgers
prediction (10) with the estimated parameters is shown in Fig. 7, and is in
excellent agreement with the experimental data over nearly the whole time
interval. The experimental estimates of the parameter $S$ in Table 2 show the
same qualitative trends with gravitational height, but an imperfect
quantitative agreement, between simulations and experiments, as already seen
in Fig. 7.

Figure 8: The top panel shows the total mass of the density profile
$M={\displaystyle\int\phi(x,t)dx}$ for experiment $\\#2$ at $h_{g}=0.336$, as
measured by scattered intensity re-scaled to be in units of particle density
based on the estimated total number of particles $N_{\text{exp}}$. The mass
remains constant to within 5% after about $t_{i}=70.8$min, so we compare the
experiment data to the Burgers model for $t>t_{i}$. The bottom panel compares
snapshots in time of the Burgers model (5) along with the experimental
measurements of the density profile. The curves have been colored to increase
in opacity as time increases, and the times of each snapshot are indicated by
vertical bars in the top panel using a corresponding transparency. The
experimental measurements of the density profile have been averaged along the
$y$ direction either without (labeled “unaligned”) or with alignment (labeled
“aligned”) of the front $x_{f}\left(y;t\right)$ (see text). An animated
version of this figure is available in the Supplementary Information.

Finally, in Fig. 8 we compare the Burgers prediction (5,7) for the density
profile to experimental data. For this comparison, we focus on experiment
$\\#2$ at $h_{g}=0.336$, for which the total scattered intensity (proportional
to the total mass $M$) was constant for $t_{f}\geq t>t_{i}=70.8$min to within
$5$%, suggesting that the scattered intensity was a good proxy for
$\phi(x,t>t_{i})$. The scattered intensity has a small (at most couple of
percent of max intensity) constant background intensity (varying slowly over
time) both in front of and behind the support of $\phi$. To compute the mass
of the density profiles we offset $\phi(x,t)$ to remove the estimated
background intensity, and match $M=M_{\text{exp}}$ at the final time $t_{f}$.
We estimate the position of the back $x_{b}\left(t_{f}\right)$ by first
estimating the position of the front $x_{f}\left(t_{f}\right)$ and then
finding the value of $x_{b}\left(t_{f}\right)$ that minimizes the $L_{2}$
error between $\phi(x,t_{f})$ and a triangle of area $M$ extending from
$x_{f}\left(t_{f}\right)$ to $x_{b}\left(t_{f}\right)$. Using the experimental
data for 666We note that the experimental $x_{b}(t>t_{i})$ was in excellent
agreement with the theoretical prediction (9) and the value of $v_{0}$
extracted from the simulations (see Table 2). $x_{b}\left(t_{f}\right)$,
$x_{f}\left(t_{f}\right),$ and $x_{f}\left(t_{i}\right)$ and Eqs. (9,10), we
estimate $t_{0}=6.8$min and $S=1.24$ (compare to data in Table 2). In Fig. 8
we compare the theoretical prediction for the triangular density profile (5)
with the extracted parameters to the experimental density profile $\phi(x,t)$
obtained by averaging the experimentally measured $\phi(x,y,t)$ along $y$, and
subtracting the offset due to the nonzero background intensity. We also
compute the average density along $y$ by first shifting the profile
$\phi\left(x,y,t\right)$ for each $y$ in the $x$ direction by
$x_{f}\left(y;t\right)-\left\langle x_{f}\left(y;t\right)\right\rangle$. By
construction, this shifting preserves the mean and therefore the aligned
density profile has the same mean front position $x_{f}(t)$. The alignment
does however allow us to examine the variation in density along the $x$
direction at scales comparable to the particle size, which is not possible
with the un-aligned profiles because of the smearing caused by the roughness
of the front.

We observe in Fig. 8 that both the aligned and un-aligned density profiles
exhibit the expected triangular shape, and are in reasonable agreement with
the Burgers prediction. The aligned data shows a sharp density front, but also
exhibits a small peak at the front. Numerical simulations suggest that right
at the front, the particles get lifted above the floor to heights larger than
$h_{g}$, and can therefore reach higher in-plane packing densities. The height
of the particles at the front depends on the balance between the self-induced
motion due to gravity (pulling them toward the wall) and the upward flow away
from the wall, induced by the force acting on the particles behind the front.
This effect is more pronounced for larger incline angles $\theta$, and for
sufficiently large $\theta$ we find that the particles do not remain in a
monolayer, especially near the density maximum at the front.

##  IV Conclusions

We examined the driven evolution of the planar density profile of a colloidal
monolayer sedimenting down an inclined plane, using experiments and
simulations. We found that, starting from an approximately constant density in
a stripe of finite width, the monolayer develops an inhomogeneous triangular
density profile with a shock front at the front edge. At the same time, the
front becomes rough, but the _relative_ roughness saturates to an
approximately constant amplitude and remains stable. We found that a simple
one-dimensional sub-Burgers equation predicts the shape of the density profile
well over all times, and a Burgers approximation is accurate at later times
when the density is sufficiently low. These simple models only require as
input the collective sedimentation velocity of a uniform suspension at a given
density, which can be obtained easily in either experiments or simulations.
The Burgers equation can be solved analytically and only requires a single
input, the slope of the collective velocity as a function of density. We found
a modest but systematic difference in the Burgers parameters estimated from
fitting experimental data and from simulations, perhaps attributable to
unaccounted interactions between the particles and the particles and the
floor.

There are many avenues for improving the simple Burgers model we focused on in
this work, to try to improve the match between theory, simulations, and
experiments. For example, since the roughness of the density front is large
compared to the particle size, a natural step would be to consider a two-
dimensional conservation law instead of a one-dimensional one. However, the
two-dimensional Burgers equation is stable to transverse perturbations
Burgers2D_ShockStability  and would not develop the roughness we observe.

For colloidal microrollers, the local mean-field approximation (2) is not
appropriate. Assuming the colloids lie approximately in a plane at height $h$
above the bottom floor, it was shown in NonlocalShocks_Rollers  that one
should instead use a _nonlocal_ conservation equation

$\displaystyle\frac{\partial\rho}{\partial t}$ $\displaystyle\approx$
$\displaystyle-\frac{\partial\left[\rho\left(K_{\text{roll}}^{(h)}*\rho\right)\right]}{\partial
x},$ (11)

where star denotes convolution with a translationally-invariant kernel

$K_{\text{roll}}^{(h)}(x)\sim hx^{2}/\left(x^{2}+4h^{2}\right)^{2}$

that describes the flow field created by a unit rotlet above a no-slip plane
blake1971note ; OseenBlake_FMM . The kernel $K_{\text{roll}}^{(h)}(x)$ is zero
at the origin, which shows that the collective motion arises due to _non-
local_ hydrodynamic interactions of particles at distances $O(h)$ rather than
neighboring particles. However, the Blake solution for a Stokeslet above a no-
slip plane blake1971note ; OseenBlake_FMM  can be used to show that the
corresponding kernel for sedimentation

$K_{\text{sed}}^{(h)}(x)\sim
4h^{2}\frac{3x^{2}+4h^{2}}{\left(x^{2}+4h^{2}\right)^{2}}+\ln\left(1+\frac{4h^{2}}{x^{2}}\right)$

is singular at and peaked around the origin, which suggests that collective
motion arises primarily due to _local_ hydrodynamic interactions among
neighboring particles. It is therefore reasonable to expect that the local
approximation (2) is reasonable for sedimentation 777In fact, our attempts to
solve the nonlocal equation (11) with the kernel $K_{\text{sed}}^{(h)}(x)$ (or
the corresponding two-dimensional generalization) numerically indicate that
the nonlocal equation develops singular solutions where all the particles
clump together at the shock front reaching unphysically high densities in
finite time. This unphysical behavior arises because steric repulsion is not
accounted for in the simple model (11); it is not straightforward to add
particle repulsion in continuum models..

Since we know that the hydrodynamic interactions driving the collective
dynamics are non-local and the front is rough, it is natural to consider (two-
dimensional) non-local conservation laws. However, we find that steric
repulsion has to be accounted for in such models because otherwise the density
develops unphysically-large peaks near the front. This is not straightforward
to do and would lead to nonlinear nonlocal conservation laws which could not
be solved numerically using standard methods (in fact, performing the particle
simulations is likely just as fast and simpler!), nor would they lead to the
physical insight that the simple Burgers model does. In the end, the success
of the Burgers equation in describing the collective density dynamics is
unexpected but in large part owed to its simplicity and to the universal
nature of Burgers shocks at long times HyperbolicLaws_Lax .

###### Acknowledgements.

We thank Wenjun Zhao for sharing with us her code for a high-resolution
advection solver in one dimension. We also thank Jonathan Goodman for helpful
discussions regarding the Burgers equation. This work was supported primarily
by the MRSEC Program under award DMR-1420073. Additional funding was provided
by the National Science Foundation under award number CBET-1706562. B.S. and
A.D. were supported by the National Science Foundation via the Research
Training Group in Modeling and Simulation under award RTG/DMS-1646339. B.S.
and A.D. also thank the NVIDIA Academic Partnership program for providing GPU
hardware for performing the simulations reported here. P. Chaikin was
partially supported by NASA under Grant Number NNX13AR67G.

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#  Tldr: Extreme Summarization of Scientific Documents

Isabel Cachola† Kyle Lo† Arman Cohan† Daniel S. Weld†‡
†Allen Institute for Artificial Intelligence
‡Paul G. Allen School of Computer Science & Engineering, University of
Washington
<EMAIL_ADDRESS>
###### Abstract

We introduce tldr generation for scientific papers, a new automatic
summarization task with high source compression, requiring expert background
knowledge and complex language understanding. To facilitate research on this
task, we introduce SciTldr, a dataset of 3.9K tldrs. Furthermore, we introduce
a novel annotation protocol for scalably curating additional gold summaries by
rewriting peer review comments. We use this protocol to augment our test set,
yielding multiple gold tldrs for evaluation, which is unlike most recent
summarization datasets that assume only one valid gold summary. We present a
training strategy for adapting pretrained language models that exploits
similarities between tldr generation and the related task of title generation,
which outperforms strong extractive and abstractive summarization
baselines.111https://github.com/allenai/scitldr

##  1 Introduction

We introduce the task of tldr generation of scientific papers.222tldr is an
acronym that stands for “too long; didn’t read,” which is often used in online
informal discussion (e.g., Twitter or Reddit) about scientific papers. For
visual clarity, we omit the semi-colon.

An alternative to abstracts, tldrs of scientific papers leave out nonessential
background or methodological details and capture the key important aspects of
the paper, such as its main contributions. This is similar to the tasks of
extreme summarization Narayan et al. (2018) and title generation Vasilyev et
al. (2019), which seek to produce single phrase or sentence summaries of news
articles.

Writing a tldr of a scientific paper requires expert background knowledge and
complex domain-specific language understanding to identify the salient aspects
of the paper, while maintaining faithfulness to the source and correctness of
the written summary. An example of a tldr is shown in Figure 1.

Figure 1:  A tldr is an extreme summary of a scientific paper. Above is an
example of a tldr and its corresponding paper. tldrs could involve
paraphrasing and abstraction from multiple sentences from the paper to convey
the main topic or contribution of a given paper in a concise way.

To support this proposed task, we introduce SciTldr, a dataset of 3,935 tldrs
in the scientific domain. SciTldr is built from a combination of tldrs written
by human experts and author-written tldrs of computer science papers from
OpenReview.333https://openreview.net/ Most summarization datasets provide a
single gold summary for a given document, despite early work in summarization
evaluation identifying variety in human-generated summaries Zechner (1996);
Harman and Over (2004). We consider this overly simplistic, especially for a
high-compression task like tldr generation. To address this limitation,
SciTldr includes multiple gold tldrs for each paper in the test set, where one
tldr is written by the author while the rest are human-written tldrs that are
obtained from peer review comments. In the latter type of tldrs, we employ a
novel approach in collecting the summaries where, instead of having human
annotators read a given paper, we ask them to read peer review comments about
a paper and rewrite them into a tldr. Peer reviews are written by domain
experts and they often include a few sentences summarizing the paper, which
facilitates our tldr data collection and ensures high quality.

In addition to the unique technical challenges, tldr generation has important
real-world applications. Researchers are commonly faced with large collections
of papers to process (e.g., a search result page or daily feed of new papers).
Given the increasing pace of publication Van Noorden (2014), the ability to
quickly discern a paper’s key points and decide whether it’s worth reading is
critical for keeping up with the literature. Automatically-generated tldrs
could be a time-saving alternative to skimming abstracts.

We further present a method for generating tldrs of scientific papers using
BART Lewis et al. (2019), a pretrained language model with strong performance
on summarization. Drawing upon connections between tldrs and a related task,
title generation, we propose a multitask learning strategy using a title
generation scaffold Swayamdipta et al. (2018); Cohan et al. (2019) for
improving tldr generation for finetuning pretrained language models. We show
that this method, while simple, is effective in extreme summarization for the
scientific domain. Our contributions are summarized below:

  1. 1.

We introduce the task of tldr generation, a new form of extreme summarization
in the scientific domain.

  2. 2.

We release SciTldr, a new dataset of 3,935 tldrs including author-written
summaries, and a test set that is additionally augmented with human-written
summaries derived from the reviewer comments.

  3. 3.

We propose a multitask learning strategy that exploits the related task of
title generation to improve tldr generation. We demonstrate its effectiveness
against strong baselines using pretrained language models.

##  2 Scientific paper tldrs

A scientific paper tldr is an extreme summary of a given scientific paper,
conveying its main message or key contributions in one or two sentences
(typically between 15 to 30 tokens in length). tldrs are significantly less
verbose than abstracts, allowing the reader to quickly understand what the
paper is about and decide whether they want to continue reading it. tldrs are
already being used on some scholarly platforms.
OpenReview444https://openreview.net/ is one such example where authors are
asked to submit tldrs of their papers that communicate the main content of the
paper to both reviewers and other interested scholars. tldrs of scientific
papers are also common on social media platforms, such as Twitter.

Category | Example phrase
---|---
| Domain, field or
---
area of study
| reinforcement learning,
---
dependency parsing
[0.4pt/2pt] Problem of interest |  | mode collapse, catastrophic
---
forgetting
[0.4pt/2pt] Mode of contribution |  | method, dataset, treebank,
---
theorem
[0.4pt/2pt]  | General description
---
of proposed method
| using graph convolution
---
operations with dynamically
computed graphs
[0.4pt/2pt]  | Main results or findings
---
| improved performance on
---
ImageNet
[0.4pt/2pt] Value of work |  | state-of-the-art, simple
---
but effective
Table 1: Example categories of information a tldr might contain Reviewer comment |  |  The authors proposed a new clustering algorithm named deep continuous clustering (DCC) that integrates autoencoder into continuous clustering. As a variant of continuous clustering (RCC), DCC formed a global continuous objective for joint nonlinear dimensionality reduction and clustering. The objective can be directly optimized using SGD like method. Extensive experiments on image and document datasets show the effectiveness of DCC. However, part of experiments are not comprehensive enough. The idea of integrating autoencoder with continuous clustering is novel, and the optimization part is quite different. The trick used in the paper (sampling edges but not samples) looks interesting and seems to be effective. In the following, there are some detailed comments: 1. The paper is well written and easy to follow, except the definition of Geman-McClure function is…
---
[0.4pt/2pt] Peer Review tldr |  |  Deep Continuous Clustering is a clustering method that integrates the autoencoder objective with the clustering objective then train using SGD.
---
[0.4pt/2pt] Author-tldr |  |  A clustering algorithm that performs joint nonlinear dimensionality reduction and clustering by optimizing a global continuous objective.
---
Table 2: Example of a reviewer’s comment rewritten as a tldr

Table 1 provides a (non-exhaustive, non-disjoint) categorization of content
that can appear in a tldr, illustrated with example phrases taken from our
dataset. We observe that there is often large variability in how tldrs are
written and any individual tldr may contain only a subset of these aspects due
to limited length. Further, what a paper’s tldr looks like or what information
it should include is subjective and follows (community-specific) commonsense
rather than a formally defined procedure.

For example, the tldr “A BERT model trained on scientific text” omits the
problem being solved and focuses on the method. But another tldr “A simple
approach for preventing mode collapse in conditional GANs” focuses on the
problem being solved but omits the method. An alternative tldr for the first
example could explain the term BERT at a cost of being more verbose (e.g. “A
Transformer-based bi-directional language model trained on scientific text”).
But in this example, since the majority of readers who work in the same domain
know about “BERT,” explaining it again in the tldr just adds more verbosity
without providing any new information about the paper. Since tldrs are
inherently ultra-short, they are not necessarily self-contained statements,
and understanding them requires some level of expertise within their
respective scientific domain. Therefore, when designing our dataset, we assume
readers have sufficient background knowledge to follow a general research
topic in a given domain. This eliminates the need to include explanations for
the common concepts or terms within a domain (e.g., “PennTreeBank,” “LSTM,”
“BERT”).

##  3 Dataset

We introduce SciTldr, a multi-target dataset of 3,935 tldrs of scientific
articles in the Computer Science domain. The dataset is specific to the AI
related papers that are hosted on OpenReview, a popular open publishing
platform. SciTldr includes a total of 3,229 papers each with at least one gold
tldr.

We use the OpenReview publishing platform as the basis of our data
collections. Most papers on this platform are accompanied by an author-
provided tldr, making it a convenient data source. We use the OpenReview API
555https://github.com/openreview/openreview-py to collect pairs of papers and
tldrs, and access PDFs of papers. We then use the pipeline from S2ORC Lo et
al. (2020) to convert PDFs to structured, machine-readable full text. We use
ScispaCy Neumann et al. (2019) sentence segmentation for the baselines that
require sentence boundaries.

Note that a small fraction of our dataset ($<5\%$) did not have an available
PDF file, so we could not parse their full body text. Although these papers
only have abstracts, we still include them in the dataset, since one can
generate a tldr from an abstract alone. We split the dataset randomly into
three sets of training, development, and test (with 60/20/20 ratios).

Figure 2: Annotation protocol for deriving tldrs from peer reviews harvested
from OpenReview.

###  3.1 Deriving tldrs from peer reviews

There is often variability in human written summaries, as discussed in §2.
Standard automated evaluation methods for summarization, such as the Rouge
framework, rely on comparing system generated summaries with gold human-
written summaries. Therefore, considering only one gold tldr for each paper as
a basis of evaluation, might result in inaccurate system quality assessment
because content that might appear in a tldr can have large variability (recall
Table 1).

To address this limitation, we additionally collect a second type of gold
summary for the papers in our test set. Compared with author written tldrs,
these tldrs are from the reader’s point of view. Having multiple targets
allows us to capture the natural variation inherent in summarization and
particularly in extreme summarization.

Writing tldrs of scientific papers requires domain expertise and is
challenging and expensive to crowdsource. To facilitate this and ensure a
high-quality dataset, instead of writing a tldr from the paper, we propose a
new approach of writing a tldr from peer reviews. This annotation approach
makes it easier for annotators with sufficient background knowledge to write
tldrs without having to read the entire paper. Peer reviews often include one
introductory paragraph with some sentences summarizing the key points in a
paper. We ask annotators to extract the summary of the paper from a paper’s
review and rewrite it into a tldr. Table 2 contains an example of a peer
review and its corresponding tldr next to the author-written tldr. In
addition, this approach provides a deeper level of abstraction, as the peer
reviews already include summary statements of the paper and are rewritten into
tldrs.

Dataset | # Docs |  | Doc
---
length
| Summ.
---
length
| Comp.
---
ratio
Target
XSUM (2018) | 226K | 431 | 23 | 18.7 | single
CNN (2015) | 93K | 760 | 46 | 16.1 | single
DailyMail (2015) | 220K | 653 | 55 | 11.9 | single
ArXiv (2018) | 215K | 4938 | 220 | 4.5 | single
[0.5pt/0.5pt] SciTldr |  |  |  |
$\mathrm{\mbox{{SciTldr}}_{Full}}$ | 3.2k | 5009 | 19 | 263.6 | multi
$\mathrm{\mbox{{SciTldr}}_{Abst}}$ | 3.2k | 159 | 19 | 8.3 | multi
$\mathrm{\mbox{{SciTldr}}_{AIC}}$ | 3.2k | 993 | 19 | 52.3 | multi

Table 3: Comparison of datasets. The lengths are in tokens. Target summary can
be single (only one gold summary per document) or multi (multiple gold
summaries for each document). Compression ratio shows the ratio of document
length to summary length. $\mathrm{\mbox{{SciTldr}}_{Full}}$ refers to SciTldr
with full-text while $\mathrm{\mbox{{SciTldr}}_{Abst}}$ only includes abstract
and $\mathrm{\mbox{{SciTldr}}_{AIC}}$ includes abstract, introduction and
conclusion sections.

For this task, we hire 12 annotators, at a rate of $20 USD per hour.666This is
in line with the median hourly wage in the Washington State at the time of
writing. The annotators have experience reading natural language processing
papers and we provide them with an hour of training to learn how to complete
the task. We then manually check the annotations for factual correctness and
revise or discard the lower quality tldrs accordingly. This process is
depicted in Figure 2. We obtain peer review comments from OpenReview, which
publishes reviews for certain conferences (e.g., ICLR). We then use these
comments as inputs for our human annotation process.

###  3.2 Dataset Analysis

Table 3.1 provides statistics of our SciTldr dataset compared with existing
summarization datasets. There are a few key differences to note. First,
SciTldr is a smaller dataset than existing datasets. Extreme summaries of
scientific papers are significantly more difficult and expensive to collect
because they require domain expertise to write and assess for quality. In
contrast, other datasets such as XSUM, were collected automatically from the
web.

The next notable difference is the length of the documents and summaries.
Table 3.1 compares the average summary and document length of SciTldr with
other existing datasets. The compression ratio (ratio of document length to
tldrs) is significantly higher compared to existing datasets, making it a more
challenging summarization dataset. It is possible for models to only consider
some sections of the paper as input (e.g., abstract or abstract + introduction
+ conclusion). This reduces the total document length and makes the task more
manageable for models, at the cost of potentially missing some important
information from other sections of the paper. We therefore define
$\mathrm{\mbox{{SciTldr}}_{Abst}}$ as a variant of the dataset that only has
abstract as input while $\mathrm{\mbox{{SciTldr}}_{AIC}}$ has abstract,
introduction and conclusion sections, and in
$\mathrm{\mbox{{SciTldr}}_{Full}}$, the entire paper is considered as input.
Even when limiting the input to the abstract, introduction, and conclusion
sections, the compression ratio of SciTldr is still significantly higher than
other existing summarization datasets.

| 1-gram | 2-gram | 3-gram
---|---|---|---
XSUM | 35.76 | 83.45 | 95.50
CNN | 16.75 | 54.33 | 72.42
DailyMail | 17.03 | 53.78 | 72.14
Arxiv | 17.5 | 48.1 | 71.4
[0.5pt/0.5pt] SciTldr |  |
$\mathrm{\mbox{{SciTldr}}_{Full}}$ | 5.65 | 21.57 | 62.60
$\mathrm{\mbox{{SciTldr}}_{Abst}}$ | 25.99 | 65.75 | 79.62
$\mathrm{\mbox{{SciTldr}}_{AIC}}$ | 11.30 | 47.60 | 68.54

Table 4: Percentage of n-grams in summary that are not in source document. For
SciTldr we show analysis of different sections as the source document.

Another critical difference is that SciTldr is multi-target. SciTldr has no
fewer than two gold tldrs for each paper in the test set, one written by the
authors (Author-tldr) and the others manually written from peer review
comments (PR-tldr) as described in §3.1. The standard evaluation measure in
summarization is Rouge Lin (2004), which quantifies lexical overlaps between a
system generated and a gold summary as a score for evaluating quality. In
scientific tldrs, we observe high lexical variability in human-written
summaries for the same paper, while all these summaries are perfectly valid.

This is evidenced by the low Rouge overlap between Author-tldrs and PR-tldrs.
Comparing Author-tldrs and PR-tldrs achieves a Rouge-1 score of only 27.4.
Furthermore, PR-tldrs overlap less with the titles than Author-tldrs.
Comparing the tldrs to the paper titles, Author-tldrs receive a Rouge-1 of
34.1 while PR-tldrs only receive a Rouge-1 of 24.7. This stresses the
importance of the multi-target evaluation setting in extreme summarization, as
a single paper can have multiple, sufficiently different tldrs.

##  4 TldrGen

We propose TldrGen, a novel method for learning to generate tldrs. Our
approach addresses two main challenges: (1) the limited size of the training
data and (2) the need for domain knowledge in order to produce high quality
tldrs. To address these challenges, we propose utilizing titles of scientific
papers as additional generation targets. As titles often contain key
information about a paper, we hypothesize that training a model to generate
titles will allow it to learn how to locate salient information in the paper
that will be also useful for generating tldrs. In addition, all papers have a
title, and thus we have an abundant supply of paper-title pairs for training.
Following previous success utilizing control codes Keskar et al. (2019), we
append control codes specifying the style of the output to the source
documents and perform training in a multitask manner by shuffling paper-title
pairs with paper-tldr pairs.

We utilize an additional dataset of approximately 20K paper-title pairs from
arXiv in the computer science domain for the title generation task. 777This
includes all papers on arXiv with at least one of the following tags cs.CL,
cs.CV, cs.LG, cs.AI, cs.NE, and stat.ML _and_ have identified introduction and
conclusion sections in S2ORC Lo et al. (2020). S2ORC is a dataset that
provides structured full text for academic papers, including those in arXiv.
We then up-sample SciTldr to match the size of the title dataset. We shuffle
SciTldr and the arXiv data together, appending each source with control tags
$\langle|$TLDR$|\rangle$ and $\langle|$TITLE$|\rangle$, respectively. This
allows the parameters of the model to learn to generate tldrs and titles at
the same time, taking advantage of the close relationship between the two
tasks. To test if both the multitask setup and the control codes are important
to this setup, we also conduct the following experiments: (1) the same
multitask setup but without the control codes and (2) pretraining on title
generation before finetuning on SciTldr (§6).

##  5 Experiments

| $\mathrm{\mbox{{SciTldr}}_{Abst}}$ | $\mathrm{\mbox{{SciTldr}}_{AIC}}$
---|---|---
Method | Rouge-1 | Rouge-2 | Rouge-L | Rouge-1 | Rouge-2 | Rouge-L
Ext. Oracle | 47.7 | 24.7 | 38.5 | 52.4 | 29.0 | 42.9
PACSUM Zheng and Lapata (2019) | 22.5 | 7.5 | 17.4 | 23.0 | 7.4 | 17.8
BERTSUMEXT Liu and Lapata (2019) | 36.7 | 15.8 | 29.4 | 28.3 | 10.4 | 23.5
| BART
---
Lewis et al. (2019) 41.6 | 19.8 | 33.8 | 42.0 | 20.5 | 34.9
| BART.XSUM Lewis et al. (2019)
---
41.2 | 19.7 | 33.4 | 43.2 | 21.2 | 35.6
|  TldrGen (Ours)
---
42.6 | 21.0 |  34.8 | 43.4 | 21.0 | 35.6

Table 5: Main results of tldr generation comparing our method with extractive
and abstractive baselines. In $\mathrm{\mbox{{SciTldr}}_{Abst}}$ the input is
the abstract, while in $\mathrm{\mbox{{SciTldr}}_{AIC}}$ the input to the
models is abstract+introduction+conclusion sections. All baselines are
finetuned on SciTldr, except for PACSUM, our unsupervised baseline.

In this section we discuss our experimental setup, baselines that we use for
SciTldr, as well as implementation and training details.

###  5.1 Input space

Previous studies have found that the most salient information in a paper for
writing a summary is often found in the abstract, introduction, and conclusion
sections Sharma et al. (2019). In our analysis of SciTldr, we also found that
an oracle extractive model that uses the full-text of the paper only slightly
improves over a model that uses abstract, introduction, and conclusion
sections (see §6). This further suggests that most salient information
relevant to tldr generation exists in these sections. Therefore, we
hypothesize that a model should be able to learn to generate tldrs by relying
mainly on these sections. This simplifies our experimental setup both for our
approach and the baselines.888Most pretrained Transformer models have an input
length constraint and will not scale well for long documents.

The abstract, alone, is another reasonable input space. From a practical
application point of view, production level systems do not always have access
to the full-text of the paper. In these cases, having the ability to generate
a tldr solely from the abstract would be useful. Also, considering this
additional experimental setting allows us to compare quality of tldrs using
these two separate input spaces.

###  5.2 Baselines

We evaluate the task of tldr generation with both extractive and abstractive
state-of-the-art summarization baselines.

#### Extractive methods

We consider both unsupervised and supervised extractive methods. For our
unsupervised extractive baseline, we focus on the state-of-the-art
unsupervised summarization model, PACSUM Zheng and Lapata (2019). PACSUM is an
extension of TextRank Mihalcea and Tarau (2004), utilizing directed edges and
a pretrained BERT model as a sentence encoder. Additionally, we include a
state-of-the-art supervised extractive summarization baseline, BERTSumExt Liu
and Lapata (2019). This model uses BERT as a sentence encoder augmented with
inter-sentence Transformer layers to capture interactions between sentences.

| Rouge-1 | Rouge-2 | Rouge-L
---|---|---|---
$\mathrm{\mbox{{SciTldr}}_{Abst}}$ | 47.7 | 24.7 | 38.5
$\mathrm{\mbox{{SciTldr}}_{AIC}}$ | 52.4 | 29.0 | 42.9
$\mbox{{SciTldr}}_{FullText}$ | 54.5 | 30.6 | 45.0
Table 6: Sentence-level extractive oracle results

#### Abstractive methods

Since tldrs often include information that is spread across multiple
sentences, we hypothesize that abstractive summarization models would be
strong baselines for this task. We particularly focus on BART-large, a state-
of-the-art pretrained model with strong results in text generation and
summarization Lewis et al. (2019). Additionally, we utilize BART finetuned on
XSUM, hypothesizing that the task of extreme summarization on news articles
might transfer to scientific papers when further finetuning on SciTldr. For
brevity, we will refer to these models as BART and BART.XSUM, respectively. We
use the Fairseq Ott et al. (2019) implementation of the BART model.

###  5.3 Training and implementation details

All our experiments are done on Titan V or V100 GPUs. Below, we describe
training hyperparameters for the baselines, as well as our multitask
finetuning approach. Hyperparameters for the baselines and our method are
selected based on best performance on the validation set.

#### Baselines

BERTSumExt is trained with a batch size of 3000 sentences per batch and for
50000 total steps. We use a learning rate of 2e-3 and a dropout rate of 0.1.
For $\mathrm{\mbox{{SciTldr}}_{Abst}}$, the document is truncated at 512
tokens, and for $\mathrm{\mbox{{SciTldr}}_{AIC}}$, 1500 tokens. For the BART
finetuning experiments, we train all the models for 500 steps and 100 warmup
steps, for an approximate training time of 45 minutes. We use a learning rate
3e-5, an update frequency of 1, and a max tokens per batch of 1024.

####  TldrGen

Our implementation is based on the Fairseq framework Ott et al. (2019). On
$\mathrm{\mbox{{SciTldr}}_{Abst}}$, we train our TldrGen model for 11,000
total steps and on $\mathrm{\mbox{{SciTldr}}_{AIC}}$, we train for 45,000
total steps. For both, we used a learning rate 3e-5, a linear warmup and
linear decay learning rate scheduler with 20% warmup steps proportion.

| $\mathrm{\mbox{{SciTldr}}_{Abst}}$ | $\mathrm{\mbox{{SciTldr}}_{AIC}}$
---|---|---
Method | Rouge-1 | Rouge-2 | Rouge-L | Rouge-1 | Rouge-2 | Rouge-L
| BART.XSUM $\to$ SciTldr
---
41.2 | 19.7 | 33.4 | 43.2 | 21.2 | 35.6
1-7 $\to$ arXiv titles $\to$ SciTldr | 17.7 | 2.7 | 13.9 | 21.9 | 2.2 | 17.8
$\to$ arXiv titles + SciTldr (no codes) | 40.5 | 19.5 | 33.5 | 42.6 | 21.0 | 34.8
|  $\to$ Title + SciTldr (with codes)
---
42.6 | 21.0 |  34.8 | 43.4 | 21.0 | 35.6
Table 7: Alternative training configurations. Arrows “$\to$” indicate
finetuning. Plus signs “+” indicate multitask training with shuffled data. The
final model is TldrGen.

###  5.4 Evaluation

We use the current standard evaluation metric in summarization, the Rouge Lin
(2004) framework. Following recent work on summarization Narayan et al.
(2018); Lewis et al. (2019), we use Rouge-1, Rouge-2, and Rouge-L as our
automatic metrics. The main difference with existing datasets is that we use
multi-target summaries as references. That is, for each paper, we calculate
Rouge score of the system-generated tldr with respect to each of the gold
tldrs individually, and then take the maximum Rouge score over these gold
tldrs as the final Rouge score for that paper. An alternative approach to
aggregate scores would be to take the average. However, we argue that taking
the maximum, rather than average, over the targets for each prediction is
appropriate for the task of tldr generation. That is because, given the
variability in human written tldrs, a good tldr generation model should be
able to generate a tldr that is close to one of the human written tldrs, and
not necessarily close to all of them. For example, the gold tldrs shown in
Table 2 are lexically different while both are perfectly valid. Therefore, if
a system generates a tldr that is lexically very similar to one of the tldrs,
it should not be penalized for not being similar to the other gold tldr.

###  5.5 Oracle

We include a sentence-level extractive oracle as an upper-bound of Rouge
performance for the methods. This oracle captures the maximum extractive Rouge
score possible given a gold tldr. We select a single sentence in the document
with the highest Rouge-1 overlap for each gold tldr and output that as the
oracle tldr.999Including an abstractive oracle is not meaningful as an
abstractive oracle trivially always gets Rouge score of 1.0 by generating the
gold tldr. While it is possible for abstractive methods to outperform the
extractive oracle, we consider the extractive oracle as a reasonable
performance upper-bound for both the extractive and abstractive the methods.

##  6 Results

Table 5 shows the main results comparing all baselines with our proposed
method over the two input spaces, abstract
($\mathrm{\mbox{{SciTldr}}_{Abst}}$) and abstract+introduction+conclusion
($\mathrm{\mbox{{SciTldr}}_{AIC}}$).

Gold (Author) |  A comparison of five deep neural network architectures for detection of malicious domain names shows surprisingly little difference.
---|---
Gold (Peer Review) |  Authors propose using five deep architectures for the cybersecurity task of domain generation algorithm detection.
BART.XSUM $\rightarrow$$\mathrm{\mbox{{SciTldr}}_{Abst}}$ |  In this paper, we present an empirical comparison of the effectiveness of different deep learning architectures for the detection of Domain Name Corruption (DGA).
BART.XSUM $\rightarrow$$Inthispaper,wecomparetheperformanceoffivedifferentdeeplearningarchitecturesforcharacterbasedtextclassification$ |
$\mathrm{\textsc{TldrGen}_{Abst}}$ |  We compare various deep neural networks for character based text classification.
$\mathrm{\textsc{TldrGen}_{AIC}}$ |  We compare five different deep neural network architectures for character based text classification of domain names generated by malware.

Table 8: Example of generated and gold tldrs. Arrows “$\to$” indicate
finetuning.

#### Oracle

The oracle score gives an upper-bound on the performance on sentence-level
extraction. As shown in Table 6, by increasing the input space from
$\mathrm{\mbox{{SciTldr}}_{Abst}}$ to $\mathrm{\mbox{{SciTldr}}_{AIC}}$, the
oracle achieves, on average, approximately 5 points of Rouge-1 improvement,
indicating that the introduction and conclusion sections include additional
information helpful for generating tldrs. However, there is a smaller
performance boost when increasing the input space from
$\mathrm{\mbox{{SciTldr}}_{AIC}}$ to $\mbox{{SciTldr}}_{FullText}$. This
supports our hypothesis that the most salient information to a tldr is in the
abstract, introduction, and conclusion.

#### Baselines

As shown in Table 5, we observe that BART finetuned on SciTldr achieves a high
performance, even when finetuned on a small amount of data. Furthermore,
finetuning BART on XSUM appears to give performance boosts to
$\mathrm{\mbox{{SciTldr}}_{AIC}}$ but not $\mathrm{\mbox{{SciTldr}}_{Abst}}$.
We also observe that the extractive methods achieve Rouge scores closer to the
oracle on $\mathrm{\mbox{{SciTldr}}_{Abst}}$. Despite the high oracle score on
$\mathrm{\mbox{{SciTldr}}_{AIC}}$, the extractive methods generally do not
perform well. In the case of PACSUM, we find that PACSUM heavily prefers to
extract sentences from the abstract, even when provided with additional
context. Furthermore, we can see that BERTSUMEXT performs worse on
$\mathrm{\mbox{{SciTldr}}_{AIC}}$ than $\mathrm{\mbox{{SciTldr}}_{Abst}}$.
This is likely because there is not enough data for the model to properly
learn which sentences to extract.

####  TldrGen

Our TldrGen method (described in §4) outperforms all other baselines.
Specifically, we observe 1 to 1.4 points in Rouge improvement over the best
next baseline models. This indicates the value of the title generation task
and our proposed multitask framework in generating tldrs. Furthermore, to test
the utility of both the multitask setting and the control codes, we conduct
similar title-based experiments but (1) without the control codes and (2)
finetuning on titles rather than utilizing the multitask setting, before
further finetuning on SciTldr. As shown in Table 7, title only finetuning
performs poorly. We can also see that, while the multitask model without
control codes performs well, it does not outperform BART.XSUM finetuned on
SciTldr. This is likely because the model is unable to differentiate between
the two tasks without the control codes. Finally, TldrGen, multitask training
with control codes, outperforms all of our baselines and alternative
configurations of the title training. This serves as evidence that both the
multitask learning strategy and the use of control codes is important to the
performance of TldrGen.

Table 6 shows a randomly sampled example for which each BART model variant
generates a different prediction. We observe that most of the generated tldrs
are sensible with subtle differences which highlights the domain knowledge
required to analyze the tldrs. Looking at the difference between the
$\mathrm{\textsc{TldrGen}_{Abst}}$ and $\mathrm{\textsc{TldrGen}_{AIC}}$ we
observe that $\mathrm{\textsc{TldrGen}_{AIC}}$ includes more phrases that are
in the gold tldrs, a trend that is we also commonly see throughout the entire
dataset. This suggests that the $\mathrm{\textsc{TldrGen}_{AIC}}$ model with
access to abstract, introduction and conclusion sections is better able to
find salient information from various input locations compared with the
abstract-based $\mathrm{\textsc{TldrGen}_{Abst}}$.

##  7 Related work

#### Extreme summarization

This work builds on previous work in both scientific document summarization
and extreme summarization. All previous work in extreme summarization has been
in the news domain. To our knowledge, the only other existing dataset is XSUM,
introduced by Narayan et al. (2018). XSUM consists of news articles and single
sentence summaries. Our work introduces an extreme summarization dataset in
the scientific domain. Additionally, various pretraining methods of
transformer models have been found to be successful in extreme summarization
Zhang et al. (2019); Lewis et al. (2019); Liu and Lapata (2019); Bi et al.
(2020). While our multitask and domain transfer approaches are built upon BART
Lewis et al. (2019), a state-of-the-art generation model, our setup is general
and can be applied to any other pretrained models.

#### Scientific document summarization

In the scientific domain, previous work has focused on longer summaries.
Existing datasets include the arXiv dataset introduced by Cohan et al. (2018),
an abstract generation task, and SciSummNet, introduced by Yasunaga et al.
(2019), which includes human annotated reference summaries. Previous work has
also leveraged additional context to aid in summary generation, such as
citation context Qazvinian and Radev (2008); Cohan and Goharian (2017) or
recordings of conference talks Lev et al. (2019). Other work has also
attempted to generate citation contexts, given two papers Luu et al. (2020).
By introducing the task of tldr generation, our work bridges the gap in
existing summarization efforts in the scientific domain that mostly focus on
generating long summaries.

##  8 Conclusion

We propose the task of tldr generation in the scientific domain. We introduce
SciTldr, a new dataset of scientific tldrs including author-written summaries,
and a test set that is additionally augmented with summaries derived from
reviewer comments. We propose a multitask learning approach which improves
tldr generation using a title generation scaffold task when finetuning
pretrained language models, and show that our approach outperforms strong
baselines.

Although our results are promising, future work can leverage the full text of
the paper in the methodology, capturing more context of the paper.
Furthermore, we make multiple assumptions about the background knowledge of
the reader. A potential future direction is to work on explicitly modeling the
reader’s background knowledge, creating personalized tldrs. Additionally, our
annotation process of converting peer review comments to tldrs can be applied
to a number of sources that contain summaries of a paper. For example, future
work can leverage the wide use of scientific tldrs on social media, such as
Twitter and Reddit, to build a more informal version of the dataset. Finally,
our model is currently trained on English-language papers in the computer
science domain. Future work can expand to other languages and scientific
domains.

## References

  * Bi et al. (2020) Bin Bi, Chenliang Li, Chen Wu, Ming Yan, and Wei Wang. 2020.  Palm: Pre-training an autoencoding and autoregressive language model for context-conditioned generation.  _ArXiv_ , abs/2004.07159.
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