# Effects of nucleation at a first-order transition between two
superconducting phases: Application to CeRh2As2

András L. Szabó  Institute for Theoretical Physics, ETH Zurich, 8093 Zurich,
Switzerland  Mark H. Fischer  Department of Physics, University of Zurich,
8057 Zurich, Switzerland  Manfred Sigrist  Institute for Theoretical Physics,
ETH Zurich, 8093 Zurich, Switzerland

###### Abstract

Recent experiments observed a phase transition within the superconducting
regime of the heavy-fermion system CeRh2As2 when subjected to a $c$-axis
magnetic field. This phase transition has been interpreted as a parity
switching from even to odd parity as the field is increased, and is believed
to be of first order. If correct, this scenario provides a unique opportunity
to study the phenomenon of local nucleation around inhomogeneities in a
superconducting context. Here, we study such nucleation in the form of sharp
domain walls emerging on a background of spatially varying material properties
and hence, critical magnetic field. To this end, we construct a spatially
inhomogeneous Ginzburg-Landau functional and apply numerical minimization to
demonstrate the existence of localized domain wall solutions and study their
physical properties. Furthermore, we propose ultrasound attenuation as an
experimental bulk probe of domain wall physics in the system. In particular,
we predict the appearance of an absorption peak due to domain wall percolation
upon tuning the magnetic field across the first-order transition line. We
argue that the temperature dependence of this peak could help identify the
nature of the phase transition.

_Introduction._ First-order phase transitions are ubiquitous in nature, with
the most palpable everyday example being that of the liquid-gas transition of
water. Increasing the vapor pressure in an air-water vapor mixture eventually
triggers condensation of liquid water, seeded at inhomogeneities, such as
dirt, in the medium. Such local nucleation leads to the spatial coexistence of
different phases and constitutes one of the hallmarks of first-order phase
transitions.

In spite of the vast tableau of unconventional superconductors, to this day
only a few compounds are known to feature multiple superconducting phases at
ambient pressure. For instance, UPt3 exhibits three distinct pairing phases
and an associated tetra-critical point in its magnetic field-temperature
($H$-$T$) phase diagram, albeit separated by second-order phase transition
lines [1]. In contrast, the recently discovered CeRh2As2 is believed to
undergo a first-order phase transition between two distinct superconducting
phases upon increasing a $c$-axis magnetic field at sufficiently low
temperature [2, 3]. This feature provides an intriguing opportunity to study
the effects of coexistence of the two phases for slightly inhomogeneous
samples.

The heavy-fermion superconductor CeRh2As2 has been subject to intense
experimental [4, 5, 6, 7, 8, 9, 10, 11, 12, 3] and theoretical [13, 14, 15,
16, 17, 18, 19, 20, 21] investigation in recent years. The most striking
features of the $H$-$T$ phase diagram have been attributed to the staggered
non-centrosymmetricity of this compound, where two inequivalent Ce sites
(constituting a sublattice degree of freedom) experience different crystal
fields from the surrounding Rh and As cages, giving rise to antisymmetric
Rashba spin-orbit coupling (ASOC) [22, 21]. While inversion symmetry is
locally broken at each Ce atom, the point group of the material is $D_{4h}$,
with an inversion center sitting between Ce sites. ASOC induced by local non-
centrosymmetricity and the resulting local parity mixing are believed to lend
this system a surprising robustness against $c$-axis magnetic fields, with an
extrapolated upper critical field of 14 T despite the low onset temperature of
$T_{\rm c}\approx 0.26$ K to superconductivity [23, 24]. The upper critical
magnetic field in this case rises in two stages when the temperature is
lowered with a kink feature at $T\approx 0.6T_{\rm c}$ and $H\approx 4$ T, see
Fig. 1(a). This anomaly is associated with the first-order phase boundary
line, which separates a low- and a high-field phase and is nearly temperature
independent [2].

Figure 1: (a) Schematic phase diagram showing the even-parity low-field A
(gray) and odd-parity high-field B (red) superconducting phases separated by a
first-order internal phase transition (dashed blue) line at $H=H_{t}$. The
inset shows the configuration of the order parameters $\eta_{\mu}^{j}$ in
layer $j$ with $\mu=0,(1)$ for even (odd) parity. Here, $u_{A}>v_{A}>0$ and
$v_{B}>u_{B}>0$. (b) Schematic depiction of nucleation. Deep in the A or B
phase the system is devoid of domain walls. At $H\lesssim H_{t}$ ($H\gtrsim
H_{t}$) the landscape is dominated by the A (B) phase, with bubbles of B (A).
Maximum domain wall proliferation is expected at $H\approx H_{t}$.

In this work, we investigate consequences of material inhomogeneity on the
properties of superconductivity in the vicinity of the first-order phase
boundary in CeRh2As2. Inhomogeneities give rise to nucleation when the phase
boundary is approached upon tuning the magnetic field, with parts of the
sample in the low- and others in the high-field phase, A and B, respectively,
see Fig. 1(b). In the following, we use the phenomenological Ginzburg-Landau
(GL) framework introduced earlier [15] to study the formation and
phenomenology of domain walls (DW). As the balance of coexisting regions of A
and B can be affected by pressure or strain, we study ultrasound coupling to
the DWs, which are shaken and thus provide non-resonant attenuation upon their
proliferation in the vicinity of the phase transition.

_Model._ The unit cell of CeRh2As2 is spanned by two inequivalent layers (or
sublattices) stacked in the crystallographic $c$ direction 111We use in the
following a coordinate system with $x$ and $y$ the in-plane coordinates with
alternating Rashba-like ASOC. A minimal GL model that reproduces the
experimentally observed phase diagram is based on local parity-mixed
$(s+p)$-wave pairing and associates the first-order phase boundary with a
global parity-switching transition [26, 15]. We introduce two layer-dependent
order parameter (OP) components with layer index $j$, namely $\eta^{j}_{0}$,
an $A_{1g}$ spin-singlet $s$-wave OP, and
$\bm{d}^{j}_{1}=\eta^{j}_{1}[k_{y},-k_{x},0]$, the $d$-vector of the odd-
parity component, transforming under the $A_{2u}$ representation of the point
group $D_{4h}$. The pertinent GL free energy density as an expansion in
$\eta^{j}_{0}$ and $\eta^{j}_{1}$ is written as

$\displaystyle f$
$\displaystyle=\sum_{j}\sum_{\mu=0,1}f_{\mu}^{j}+f_{\epsilon}+f_{J}+f_{H},\text{
with}$ $\displaystyle f_{\mu}^{j}$
$\displaystyle=a_{\mu}|\eta_{\mu}^{j}|^{2}+b_{\mu}|\eta_{\mu}^{j}|^{4}+K_{\mu}|\bm{D}_{\parallel}\eta_{\mu}^{j}|^{2},$
$\displaystyle f_{\epsilon}$
$\displaystyle=\sum_{j}(-1)^{j}\epsilon(\eta_{0}^{j\ast}\eta_{1}^{j}+\eta_{0}^{j}\eta_{1}^{j\ast}),$
$\displaystyle f_{J}$
$\displaystyle=J\sum_{j}\sum_{\mu}|\eta_{\mu}^{j+1}-\eta_{\mu}^{j}|^{2},$
$\displaystyle f_{H}$ $\displaystyle=\sum_{j}\chi H^{2}|\eta_{0}^{j}|^{2},$
(1)

where $a_{\mu}=a^{0}_{\mu}(T-T_{{\rm c},\mu})$, with $a^{0}_{\mu}$, $b_{\mu}$
and $K_{\mu}$ positive, real phenomenological constants, and $\epsilon$
quantifies the effect of ASOC leading to the coupling between the even- and
odd-parity OP and transforms under the $A_{2u}$ representation. Moreover,
$\bm{D}_{\parallel}=[-i\bm{\nabla}+2e\bm{A}]_{\parallel}$ is the in-plane
covariant derivative. Despite considering the situation in a magnetic field,
we do not include the property of the mixed phase and, therefore, omit the
vector potential $\bm{A}$ when discussing the phase diagram. The effect of the
magnetic field then enters only through the Zeeman coupling to the electron
spin, which involves paramagnetic limiting for the even-parity OP with
$\sum_{j}\chi|\eta_{0}^{j}|^{2}$ yielding a reduction of the Pauli spin
susceptibility. While we introduced the bare critical temperatures for both OP
components, their ASOC-induced coupling yields a higher effective onset of
superconductivity, $T_{\rm c}>T_{{\rm c},\mu}$.

Figure 2:  Effective magnetic field profiles (top row) and the resulting OP
configurations (bottom row) computed via numerical minimization. (a) features
hyperbolic tangent inhomogeneity with width $4\xi_{0}$, whereas (b) shows a
double DW configuration. All $\tilde{H}(x)$ profiles are symmetric with
respect to $\tilde{H}_{t}$ with a maximum deviation of $5\%$. For the
numerical calculations, we fix temperature to $T/T_{c,0}=0.5$ and use the
parametrization: $b_{\mu}=b$, $K_{\mu}=K$, $-a_{0}/b=K/|a_{0}|=1$,
$a_{1}/a_{0}=0.105$, $J/|a_{0}|=1$, and $\epsilon/|a_{0}|=2$. Lengths are
expressed in units of $\xi_{0}=\sqrt{K/|a_{0}|}$ and the OP as
$\Psi_{\mu}^{j}=\sqrt{-b/a_{0}}\eta_{\mu}^{j}$.

In the limit of vanishing interlayer coupling incorporated by the Josephson-
like $J$-term, the staggered system consists of independent noncentrosymmetric
layers, naturally hosting mixed-parity pairing states. Due to the alternating
sign of the $\epsilon$-term, the relative sign between the two OP components
alternates as well, being “$+$” for even $j$ and “$-$” for odd $j$ in our
setup. A finite $J$ explicitly restores inversion symmetry, enabling us to
label the solutions as even and odd under inversion operation, which exchanges
the two layers. Assuming that at zero magnetic field the even-parity OP is
dominant ($T_{{\rm c},0}>T_{{\rm c},1}$), the interlayer coupling stabilizes a
configuration, where $\eta_{0}^{j}$ has the same phase in all layers while
$\eta_{1}^{j}$ alternates its sign. This corresponds to the low-field A phase:
$\eta_{0}^{j}=\eta_{0}^{j^{\prime}}=u_{A}$,
$-\eta_{1}^{j}=\eta_{1}^{j^{\prime}}=v_{A}$ with $u_{A}>v_{A}>0$ and $j=2n$
(even) and $j^{\prime}=2n+1$ (odd). In contrast, in the high-field B phase,
$\eta_{0}^{j}$ is suppressed through the paramagnetic limiting effect such
that the now dominant $\eta_{1}^{j}$ has the same phase for all layers with an
alternating sign for $\eta_{0}^{j}$:
$-\eta_{0}^{j}=\eta_{0}^{j^{\prime}}=u_{B}$,
$\eta_{1}^{j}=\eta_{1}^{j^{\prime}}=v_{B}$ with $v_{B}>u_{B}>0$, as described,
for instance, in Ref. [15]. It is straightforward to show that the transition
occurs at a magnetic field given by $H_{t}=\sqrt{(a_{1}-a_{0})/\chi}$. The
model outlined in Eq. (1) is geared towards capturing the internal phase
transition and does not account for e.g. orbital depairing that ultimately
destroys the B phase at high fields. Nevertheless, the above formula for
$H_{t}$ provides a good approximation even in the presence of the vortex
lattice [15]. Because the inversion operation exchanges even and odd layers,
we may characterize A as even\- and B as odd-parity phase.

At sufficiently low temperature, both phases correspond to separate minima of
the GL free energy, where at $H=H_{t}$ they exchange their role as the global
minimum and give rise to a first-order transition, as can be shown also based
on general thermodynamic arguments [27, 28]. Importantly, in a spatially
inhomogeneous material, we expect the transition to not happen everywhere at
the same field $H_{t}$, but to show regions of one phase embedded within the
other, whereby the OPs rearrange between even and odd configurations on a
length scale of order coherence length $\xi_{0}=\sqrt{K/|a_{0}|}$,
constituting sharp DWs.

_Domain walls._ Inhomogeneities in the sample lead to spatially varying
parameters and thus, critical field. We incorporate such inhomogeneities in
our GL model through a position-dependent parameter $\chi(\bm{r})$ assuming a
relatively slow variation in space, which only enters the Zeeman term $f_{H}$
in the free energy. In order to investigate the structure of a DW, we restrict
ourselves to a one-dimensional spatial dependence, $\chi(x)$, use the
parametrization $\sqrt{\chi(x)}H\equiv\tilde{H}(x)$, and, for a model
calculation, consider a step-like dependence,
$\tilde{H}(x)=H_{0}+H_{1}\tanh(x/\delta)$ with
$H_{0}-H_{1}<\tilde{H}_{t}<H_{0}+H_{1}$ and $\tilde{H}_{t}=\sqrt{a_{1}-a_{0}}$
corresponding to the transition point. In this way, the A (B) phase is favored
for $x<0$ ($x>0$). We minimize the free energy numerically using the one-step
relaxed Newton-Jacobi method [29] and obtain a smooth, narrow DW between the
two phases, as displayed in Fig. 2 (a). Using a profile for $\tilde{H}(x)$
with two opposite steps shows an “island” of B phase inside the A phase [Fig.
2 (b)], as it may occur at the verge of the bulk phase transition. The
position of the DW is pinned by the specific $x$ dependence of $\tilde{H}(x)$,
roughly at the position $\tilde{H}(x_{0})=\tilde{H}_{t}$, say $x_{0}=0$ in
Fig. 2 (a). In what follows, we consider a harmonic pinning potential for the
DW position.

Note that, unlike deep in the A or B phase, within the DW the OP does not
adhere to global parity classification. We also remark that the deformation of
OPs in the vicinity of the DW combined with the local non-centrosymmetricity
yields a non-vanishing spin current along the domain boundary [30, 31].
However, we do not dwell on this feature in the following, but rather consider
the effects of strain in the system.

_Ultrasound probe._ Recent experiments observed a significant effect of
hydrostatic pressure on the superconducting phase diagram of CeRh2As2. Most
glaringly, pressure decreases the overall $T_{\rm c}$ and affects the balance
between A and B phases [9]. Owing to its tetragonal symmetry, the phase
diagram of CeRh2As2 under hydrostatic pressure can also be appreciated
qualitatively by considering that strain along the $c$ axis changes the ratio
between the strength of parity mixing and interlayer coupling, namely
$\epsilon/J$. While this aspect may be more purposefully investigated by
uniaxial $c$-axis strain, here we propose a related experiment based on
ultrasound modes.

For this purpose, we first discuss the coupling of DWs to ultrasound. DWs
represent a boundary between two phases with vortex lattices of different flux
density and, thus, different mean magnetization [15]. Naturally, this induces
a supercurrent flowing within the layers along the domain boundary. The
temporal variation of strain through the ultrasound waves leads to a periodic
displacement of the DW and yields a dissipation via the motion of currents as
well as the vortices near the DW. Thus, we expect an extra contribution to
ultrasound absorption due to local nucleation in the vicinity of the first-
order phase boundary.

To formulate this concretely, we introduce an ultrasound mode as a
longitudinal plane wave of frequency $\omega$ propagating in the $z$ direction
(crystallographic $c$ axis), $\bm{u}(\bm{r},t)=\hat{z}u_{0}e^{ikz-i\omega t}$,
where $\bm{u}$ is the lattice displacement field and $k$ is the wave vector
along $z$, which depends on the properties of the medium. This mode transforms
under the trivial $A_{1g}$ representation and hence is not symmetry breaking.
Since the only relevant element in the strain tensor is
$\epsilon_{zz}=\partial_{z}u_{z}$, we focus in the discussion of the
deformation energy and strain-OP coupling on this component only. Then the
corresponding additional terms to the free energy include the elastic energy
$f_{\rm el}$ and the coupling term, $f_{\rm s\eta}$, yielding [32]

$\displaystyle f_{\rm el}$
$\displaystyle=\frac{c_{33}}{2}\epsilon_{zz}^{2}=\frac{c_{33}}{2}(\partial_{z}u_{z})^{2},$
$\displaystyle f_{\rm s\eta}$
$\displaystyle=\sum_{j}\Big{(}\gamma_{0}\epsilon_{zz}|\eta_{0}^{j}|^{2}+\gamma_{1}\epsilon_{zz}|\eta_{1}^{j}|^{2}\Big{)},$
(2)

with $c_{33}$ the elastic constant and $\gamma_{0,1}$ phenomenological
coupling constants. These terms would be sufficient to describe the
modification of the phase diagram under $c$-axis uniaxial strain. The DWs are
pinned by the spatial inhomogeneities of $\tilde{H}(\bm{r})$, which we model
by a harmonic potential around a given equilibrium position. Strain then
imposes a force to shift this position. With this in mind, we write the DW
potential term as

$\displaystyle f_{\rm DW}$
$\displaystyle=\frac{1}{2}c(\tilde{H})\bar{x}^{2}+\gamma\epsilon_{zz}\bar{x},$
(3)

where $\bar{x}$ is the position of the DW, which rests at $x=0$ in the absence
of strain. For simplicity, we assume a DW that is infinitely extended in $y$\-
and $z$-direction such that we can model our system in one spatial dimension,
$x$. The coefficient of the quadratic term $c(\tilde{H})$ depends on the
details of $\tilde{H}(x)$, and by linearizing we find to leading order that
$c(\tilde{H})\propto(\partial\tilde{H}(x)/\partial x)\rvert_{x=0}$ [31].
Intuitively, a steeper inhomogeneity profile yields a stiffer potential
restricting the DW motion. On the other hand, $\gamma$ is independent of
$\tilde{H}(x)$ and can be approximated through the different strain dependence
of energy densities in the A and B phases, $f_{A}$ and $f_{B}$ respectively,
such that [31]

$\displaystyle\gamma\propto\bigg{(}\frac{\partial
f_{A}}{\partial\epsilon_{zz}}-\frac{\partial
f_{B}}{\partial\epsilon_{zz}}\bigg{)}\bigg{\rvert}_{\epsilon_{zz}=0}.$ (4)

Note that the equilibrium position $\bar{x}=-\gamma\epsilon_{zz}/c(\tilde{H})$
still depends on the details of $\tilde{H}(x)$.

We model non-resonant absorption by the overdamped oscillation of the DW
position and write the equation of motion for $\bar{x}$ as well as the
displacement field $u_{z}$ as

$\displaystyle\eta\partial_{t}\bar{x}=-\frac{\partial f_{\rm
tot}}{\partial\bar{x}},\hskip
11.38092pt\rho\partial_{t}^{2}u_{z}(\bm{r},t)=\sum_{i}\partial_{i}\frac{\partial
f_{\rm tot}}{\partial[\partial_{i}u_{z}(\bm{r},t)]}.$ (5)

Here $f_{\rm tot}=f+f_{\rm el}+f_{\rm s\eta}+f_{\rm DW}$, $\eta$ is a
phenomenological viscosity constant, resulting from the dissipation due to the
motion of the DW, and $\rho$ is a mass density. For an external drive of
frequency $\omega$, the resulting wave vector reads

$\displaystyle
k=\frac{\sqrt{\rho}\omega}{\sqrt{c_{33}-\frac{\gamma^{2}}{i\omega\eta+c}}}.$
(6)

This finally yields the ultrasound absorption coefficient [31]

$\displaystyle\alpha$ $\displaystyle=-{\rm Im}\
k=\frac{\gamma^{2}}{2c_{33}c_{s}\eta}\frac{\omega^{2}}{\omega^{2}+\omega_{0}^{2}},$
(7)

where $c_{s}=\sqrt{c_{33}/\rho}$ denotes the sound velocity and
$\omega_{0}=c/\eta$ is a characteristic frequency of the DW. The coefficient
$\alpha$ is a measure for the absorption per unit area of the DW. The total
absorption is proportional to the spatial average of $\alpha$, as well as the
DW density in the system for a given external magnetic field. Below we
elaborate on the evolution of the latter as one tunes the magnetic field
across $H_{t}$. As pointed out earlier, larger value of $c$ (steeper
inhomogeneity profile) describes stronger pinning, which in turn results in
less movement of the DW and therefore less absorption, which is reflected in
Eq. (7). Hence, $c$ is in general position dependent. The origin of the
viscosity parameter $\eta$ is analogous to that of vortex motion in the mixed
phase of a superconductor, but depends on the microscopic details of the DW.

Our simple model accounts for the contribution to ultrasound absorption per
unit area of a DW. As such, the total ultrasound absorption depends on the DW
density upon driving the external magnetic field through the phase boundary at
$H_{t}$. As the magnetic field approaches $H_{t}$ from below, islands of the
high-field phase B appear due to inhomogeneities within the A phase, as
schematically shown in Fig. 1(b). In our one-dimensional model, such a B-phase
bubble is depicted in Fig. 2(b). Upon increasing the field, the islands
bounded by a DW proliferate and eventually DWs percolate through the sample. A
further rise of the magnetic field leads to the shrinkage of A domains in a
landscape dominated by the B phase [see Fig. 1(b)]. Naturally, the largest
contribution to sound absorption is expected when the DWs percolate and their
density is largest, such that the absorption shows a peak as a function of the
external field.

Finally, let us make some practical remarks on the experimental signatures
that would help identify the absorption mechnanism in a material like
CeRh2As2. To date, the first-order nature of the internal phase transition has
not been unambiguously established. Since a possible second-order phase
transition could also yield an absorption peak upon tuning across the
transition line (analogous to critical opalescence), the observation of an
absorption peak alone may not be conclusive. However, if temperature is
lowered when the system is on the verge of a second-order phase transition,
the critical region narrows down with the accompanying absorption peak
becoming sharper. On the other hand, the superconducting coherence length,
given in our model by $\xi_{0}=\sqrt{K/|a_{0}|}$, decreases with decreasing
temperature, whereby the OPs can realize a DW on a smaller length scale, thus
in a wider magnetic field range. For this reason, a first-order phase
transition with accompanying local nucleation tends to broaden the absorption
peak as function of field when the temperature is lowered, as the opposite
phase can nucleate more easily on smaller inhomogeneities. The evolution of an
absorption peak as a function of temperature may therefore help pin down the
order of the internal phase transition in this system.

_Discussion._ While the proposed mechanism of ultrasound absorption provides a
way to detect the first-order transition between the phases A and B in the
presence of sample inhomogeneity or inhomogeneous magnetic field, the non-
uniform nucleation could also be observed by other means. As mentioned
earlier, the vortex-lattice density is different in the two phases [15] and it
may be possible to track this inhomogeneity by surface scanning probes either
by observing the magnetic field or the vortex lattice on its own. A further
interesting aspect is provided by the different spin susceptibilities of the A
and B phases. Nuclear magnetic resonance (NMR) Knight-shift measurements as a
local probe would in principle be able to observe two distinct signals with a
varying volume fraction of the two domains as the magnetic field is tuned
through $H\sim H_{t}$.

This work was motivated by the heavy fermion superconductor CeRh2As2. Some
aspects of our discussion, however, might not apply straightforwardly to this
material. Recent NMR measurements indicate the presence of magnetic order
coexisting with the A phase, but not with the B phase [12, 3]. We did not
attempt here to integrate this feature into our discussion, since it is
unclear so far how this material-specific property connects to the field-
induced (first-order) transition. An interesting point we also leave open for
the time being is the study of damping mechanism. It will be interesting to
see how the DW shape and the supercurrents influence the viscous motion of
DWs. Naturally, such questions will become more urgent once the presence of
such DWs is established. Still, besides probing the physics of nucleation in a
novel, superconducting context, our efforts may help further understand the
phase diagram of CeRh2As2, where investigations are still in their early
stages.

_Acknowledgement._ We thank Elena Hassinger, Manuel Brando, Stanislaw Galeski,
and Maximilian Holst for useful discussions. A.S. and M.S. are grateful for
financial support from the Swiss National Science Foundation (SNSF) through
Division II (No. 184739). M.H.F. also acknowledges financial support from SNSF
through Division II (No. 207908).

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# UID as a Guiding Metric for Automated Authorship Obfuscation111This research
was conducted at Pennslyvania State University through an NSF funded REU. The
entire research and paper creation process took eleven weeks, starting in late
May of 2023 and ending early August 2023.

Nicholas Abegg
Saint Vincent College
<EMAIL_ADDRESS>

###### Abstract

Protecting the anonymity of authors has become a difficult task given the rise
of automated authorship attributors. These attributors are capable of
attributing the author of a text amongst a pool of authors with great
accuracy. In order to counter the rise of these automated attributors, there
has also been a rise of automated obfuscators. These obfuscators are capable
of taking some text, perturbing the text in some manner, and, if successful,
deceive an automated attributor in misattributing the wrong author. We devised
three novel authorship obfuscation methods that utilized a Psycho-linguistic
theory known as Uniform Information Density (UID) theory. This theory states
that humans evenly distribute information amongst speech or text so as to
maximize efficiency. Utilizing this theory in our three obfuscation methods,
we attempted to see how successfully we could deceive two separate
attributors. Obfuscating 50 human and 50 GPT-3 generated articles from the
TuringBench dataset, we observed how well each method did on deceiving the
attributors. While the quality of the obfuscation in terms of semantic
preservation and sensical changes was high, we were not able to find any
evidence to indicate UID was a viable guiding metric for obfuscation. However,
due to restrictions in time we were unable to test a large enough sample of
article or tune the parameters for our attributors to comment conclusively on
UID in obfuscation.

_K_ eywords Cybersecurity $\cdot$ Machine Learning $\cdot$ Authorship
Obfuscation $\cdot$ Uniform Information Density $\cdot$ Natural Language
Processing

##  1 Introduction

With recent significant advances in Artificial Intelligence (AI), it has
become possible for AI methods to automate the process of authorship
attribution (AA). AA is the process of taking a text of unknown authorship and
attributing the authorship amongst a number of known authors. These automated
AA methods are capable of attributing an author with great accuracy ([1]). As
a result, anonymity for authors has become endangered, and their ability to
release controversial text is in question. Adversarially to AAs, there has
been a rise in AI-driven authorship obfuscators (AO), which are automated
methods that take some text and obscure the original author through some
perturbation. AOs are successful if it is capable of deceiving an AA into
attributing the incorrect author of a text. AOs also need to manipulate the
text in a way that the ideas and messages originally conveyed in the text are
preserved as well as having any changes to the text be subtle enough for human
investigators not to notice. There are consistently new developments for novel
AA and AO methods, often with each trying to counter vulnerabilities exposed
by recent developments in its countering process. As a result of this
adversarial relationship, developing novel AO or AA methods is crucial for
improving both tasks. In this paper, we explore a novel obfuscation method
that is capable of obfuscating a text utilizing Uniform Information Density
(UID) metrics as a guiding measure. UID is a psycho-linguistic theory that
suggests that humans distribute information evenly throughout a message so as
to maximize efficiency and clarity. Not only do humans follow these UID
patterns, but it has been shown that language models follow their own
respective UID pattern that is separate from humans ([2]). We hypothesize that
we could utilize UID as a guiding metric in the obfuscation of an article that
results in a automated AA misattributing an obfuscated article. The alteration
of authorship classification as a result of our obfuscation technique could
indicate UID as a promising metric to be further investigated for the task of
AO. Currently, no other obfuscation method utilizes UID theory, which means
that exploring its performance and applicability could yield further
improvements in AO techniques, and eventually improvements in AA as well.

###  1.1 Research Question

##### RQ:

Explore the applicability of UID metrics in the task of obfuscation.
Specifically, investigate if UID can be used as a guiding metric to result in
successful obfuscation in which an automated authorship attributor
misattributes an obfuscated article.

To explore this problem, we designed three algorithms known as Synonym Swap,
UID Word Swap (UWS) and UID Paraphrase (UP). Synonym Swap and UWS involves
selecting a word roughly in each sentence and swapping it out for a suitable
synonym amongst a list of candidate synonyms. UP involves using diversity beam
search for word replacement based on UID metrics. We will explore the design,
implementation, and results of all three algorithms later in this paper.

####  1.1.1 Limitations: Addressing Scope

It is important to note that due to restrictions on time, this research will
mainly focus on investigating the application of our novel AO technique using
a small number of articles from the TuringBench dataset. Therefore, it is
essential to consider that our results and findings could be subject to errors
and warrant further investigation and exploration to draw more definitive and
concrete conclusions about the efficacy of UID as a metric for obfuscation.

Another limitation we faced was the lack of accurate and easy to use detectors
for the articles. Our first experiments, those done on Synonym Swap, used
OpenAI’s detector which was taken down on July 20, 2023. As a result of the
detector being removed, we were forced to utilize two open-source
implementations of models Detect GPT and ZeroGPT out-of-the-box with no
tuning.

###  1.2 Literature Overview

####  1.2.1 Authorship Attribution

The ability to attribute an author of some text to a specific author amongst a
pool of authors has been accomplished in a multitude of ways. With the rise of
machine generated text, there have been AA models that are capable of
achieving near-perfect accuracy in identifying the language model (LM) behind
a given text ([3]). There are also methods of deobfuscation, which is the
process of reducing the impact obfuscation processes have on AA’s ability to
successfully attribute the correct author ([4]). Yet, the quality and
sophistication of modern LMs mean they are capable of producing text of human-
level quality that confuses machine authorship classifiers ([1]). There have
also been successful efforts at AA for code. One particular study identified
differentiating characteristics in programming style between ChatGPT and
human-generated code. This allowed for significantly accurate classification
of code authorship between human-authored and ChatGPT generated code ([5]).
For a more comprehensive overview of the state of AA and its literature, there
are two recent and in-depth surveys ([6]) ([7])

####  1.2.2 Authorship Obfuscation

##### Rule-Based Obfuscation

The task of authorship obfuscation is typically approached in two ways. There
are rules-based methods in which rule(s) or guideline(s) are set and the
method attempts to alter the text through some perturbation that results in
the rule(s) or guideline(s) being satisfied. An example of rule based
obfuscation is utilizing a general stylometric average of specific stylometric
characteristics such as punctuation, word frequency, part of speech frequency,
etc., to push an author’s stylometric metrics in line with these averages. The
hope would be that the changes push an author’s text towards this general
average and would obfuscate an author’s identifiable style and preserve their
anonymity ([8]). Another rule-based method employed an approach very similar
to the methods we devised for this paper. Observing the words that appeared
most frequently in an author’s text, the obfuscation method attempted to
select a synonym to replace the word in order to mask an author’s word choice
and frequency stylometric signature. Using WordNet to generate these synonyms
and calculating the Wu and Palmer similarity score of each synonym to find the
most suitable replacement for a given word. This resulted in obfuscated text
that still retained much of the quality of the original text as at most only
one word per sentence was changed ([9]). A notable novel obfuscation technique
takes a heuristic approach to the AO task for the first time. The approach
involves modeling style using Jensen-Shannon distance. Then obfuscating the
text through a heuristic paraphrasing operation that greedily maximizes
obfuscation at each step. Specifically, aiming to distance the style of the
obfuscated text from the author’s style and move towards a more generic style
[10].

##### Internal AA Obfuscation

The other approach involves accessing an AA classifier so as to guide the task
of obfuscation. Methods such as Mutant-X ([11]), A4NT ([12]), and ParChoice
([13]) utilize a classifier to ensure successful obfuscation. Mutant-X assumes
black-box knowledge, which means it has access to the adversary’s trained
classifier as well as its input features for reference. Mutant-X involves
employing a fitness function which considers both the attribution probability
from the adversary classifier as well as semantic similarity. A notable
advantage is that it requires no text previously written by the author for
training, making it significantly easier to use ([11]). A4NT obfuscates an
author’s text by imitating specific target classes, such as converting a
female-authored text to emulate a male-authored text instead. The imitation is
achieved by referencing the target classifier to guide the changes that would
result in a male classification instead ([12]). Parchoice takes a piece of
text, paraphrases it to generate multiple paraphrase candidates, and then
selects the most appealing candidate. For document-level obfuscation, the
method is rather similar to Mutant-X, as ParChoice paraphrases a random
sentence in the document and selects the candidate that would be most likely
to cause misclassification by the classifier ([13]).

###  1.3 Psycho-linguistics and Uniform Information Density

Uniform Information Density (UID) theory suggests that humans optimize their
speech and text so as to uniformly distribute information over an entire
message ([14]). Essentially humans tend to prefer communicating with others in
a way that spreads information throughout the sentence in a balanced manner.
Furthermore, information content in sentences can be quantified so as to
measure and represent the UID of different messages ([15]). Recently, it has
also been found that not only do humans demonstrate and follow particular
patterns for UID, but decoding algorithms follow their own patterns as well
([2]). The ability to to quantify UID and the fact that both humans and
machines demonstrate unique patterns of UID, indicate the possibility that UID
could be a useful metric in emulating the authorship of specific LMs or a
human author.

##  2 Preliminary & Framework

###  2.1 TuringBench Dataset

The dataset we utilized is the TuringBench dataset which consists of 200k news
articles with 20 labels. One label is human, which represents human generated
articles from media outlets such as CNN, The Washington Post, and Breitbart.
The 19 others are different neural text-generators such as GPT-3, GROVER,
FAIR, etc. that generate articles utilizing headlines as the generation
prompts.([16]). The dataset is specifically designed for the “Turing Test”
problem, which involves being able to differentiate machine generated text and
human generated text. This makes the dataset a perfect source for longer form
article content that are pre-labeled allowing us to compare the classification
labels to the ground truth labels.

###  2.2 Semantic Cosine Similarity Score

To select a proper alternate article for obfuscation, we needed to calculate
the semantic similarity score of the new articles produced by UID Word Swap.
We utilized Scikit Learn’s Pairwise submodule cosine similarity function to
calculate the cosine similarity between an obfuscated article and the original
unaltered article. We decided to compare the semantic similarity of entire
articles rather than individual sentences.

###  2.3 UID Score

Uniform Information Density (UID) is defined as the preference for humans to
distribute information within a sentence uniformly, maximizing efficiency in
communication [15]. To select a proper candidate, we needed to calculate the
UID score of each probable obfuscated article to determine which resulted in
the greatest difference of UID from the original. For all articles, we
calculated four different UID metrics and selected the two that seemed to have
the most variation. The two UID metrics we decided to utilize were the UID
score variance and UID score ${difference}^{2}$. To calculate both of these
scores, we first computed the surprisal of the tokens in the article.
Surprisal is defined as the negative log probability of a token given the
previous tokens in the context of the article. The UID score $variance$ is
obtained by calculating the $variance$ of the surprisals for all tokens within
the article. To obtain the UID score ${difference}2$, we calculate the average
of the squared differences in surprisals for every two consecutive tokens
within the article.

###  2.4 Authorship Attributors

To test how our obfuscation methods affect an automated authorship attributor,
we utilized two attributors, ZeroGPT([17]) and DetectGPT([18]), to test the
effects on our data. Out first experiment utilized OpenAI’s detector which was
retired as of July 20, 2023.

##  3 Synonym Swap: A Simple Test of Obfuscation

###  3.1 Design and Implementation Overview

Prior to the creation of the UWS algorithm, we designed and tested a more
primitive obfuscation technique that we called Synonym Swap. Synonym Swap
centered around taking some number of articles and attempting to obfuscate
each sentence of each article. The obfuscation technique consisted of swapping
out a target word within a sentence for a synonym that was calculated to be
the most probable next token by the GPT-2 language model. To select the target
word, Synonym Swap would start in the middle of a sentence and check each word
from there to the end of the sentence, until it found the first suitable
candidate. The criteria for selecting a suitable candidate consists of the
word not being a stop word, having at least one synonym, not being labeled as
a proper noun, and has more than 2 characters. Stop words are highly frequent
words that are avoided as target words as they lack significance within a
sentence concerning informational content. Once a suitable candidate has been
selected, Synonym Swap pools all of the synonyms for the target word using the
WordNet corpus from NLTK and calculates which one is most probable to appear
as the next token in the sentence given the previous tokens of the sentence.
Once the most probable synonym replacement has been selected, the sentence is
then altered to contain this new word and the process is repeated until the
end of the article. If a sentence was too short or did not have a suitable
candidate then it is left untouched by Synonym Swap.

###  3.2 Experiments

To test the effectiveness of Synonym Swap we used 100 articles from the
TuringBench dataset, with 50 being human articles and the other 50 being
generated by GPT-3. Each article obfuscated by Synonym Swap and then
classified by a binary Authorship Attributor, OpenAI Detector222As of July 20,
2023, OpenAI’s detector has been taken down due to poor accuracy in
detection.. The classifier takes a piece of text and generates the probability
that a given text is written by a machine as well as assigning a label to the
article. There are 5 different possible labels that the classifier can assign
to a piece of text: very unlikely, unlikely, unclear if it is, possibly, or
likely. We had the classifier label both the original 50 human and 50 GPT-3
generated texts and the Synonym Swap obfuscated texts to compare the effect
that the obfuscation had on the classifier.

###  3.3 Results

The results indicated that the simple Synonym Swap was capable of confusing
the classifier and causing it to generate different labels as a result of the
obfuscation. Furthermore, the simple Synonym Swap was capable of producing
semantically similar and reasonable sentences, but would also generate
unreasonable or nonsensical changes to the text. Often these unreasonable
results were a result of WordNet, which was caused by it grabbing all possible
synonyms for a word which often did not fit the specific context in which the
swap was occurring. For example, when targeting the word “may” in the context
such as “May I leave the room?,” synonyms generated would include words
related to the month of May and various kinds of flowers.

###  3.4 Graphs for Synonym Swap

Figure 1: Unaltered Human: Synonym Swap Labels for Original Results (unlikely
and very unlikely refer to if the text was generated by an AI) Figure 2:
Altered Human: Synonym Swap Labels for Original Results (unlikely and very
unlikely refer to if the text was generated by an AI) Figure 3: Unaltered
Machine: Synonym Swap Labels for Alternate Article Results (unlikely and very
unlikely refer to if the text was generated by an AI) Figure 4: Altered
Machine: Synonym Swap Labels for Alternate Article Results (unlikely and very
unlikely refer to if the text was generated by an AI)

These plots provided us with some evidence that even a simple of obfuscation
like Synonym Swap was capable of altering the labels produced by the detector.
Specifically, Figure 1 and Figure 2 show a drastic change in the articles
marked very unlikely AI generated. It seems our changes made it more unclear
to the detector on whether the text was AI generated or not. Figure 3 and 4
also show a similar pattern of making it more unclear to the detector if a
text is AI generated or not. While it is a very small experiment, with only
100 articles being used, it still indicates some promise to the method of
obfuscation via single word swapping per sentence.

###  3.5 Text Generation Quality

Below we provide some samples of the text generated by synonym swap compared
to the original articles.

##### Human Generated Text (Previous Label: Very Unlikely AI generated, New
Label: Unclear if it is)

Human Text (Original): “a look at some of donald trump’s early activity as
president: – 24: executive orders and memoranda signed. that includes to
withdraw the nited states from trade deal, impose federal hiring freeze reduce
regulations related health care law enacted under former president barack
obama. 1: blocked. an order ban travelers…”

Synonym Swap Text: "a look at some of donald trump’s early activity as
President_of_the_United_States – 24: executive orders and memoranda signed.
that includes to withdraw the nited states from trade deal, impose federal
hiring stop_dead reduce regulations related health care law enacted under
former president barack obama. 1: hinder an order ban travelers…”

The above examples showcase the text quality generated by Synonym Swap on a
human generated piece of text which was able to successfully deceive the AA
after its changes. The red colored text are the target words with the top part
of the text representing the original and the bottom part showing the
obfuscated version. As shown in the text, the quality of the Synonym Swap
alterations can range from acceptable to wholly unreasonable. The first swap,
"president" to "President_of_the_United_States" is an example of a swap that
is satisfactory. An example of a incorrect swap that Synonym Swap can make is
the swap "freeze" to "stop_dead". While the phrase is a synonym to freeze, it
fails to fit the context of the sentence and is considered a incorrect swap.

##### Machine Generated Text (Previous Label: Very Unlikely AI generated, New
Label: Unlikely AI generated)

Machine Text: ”and tensions in the middle east?curtis’ heartachethe .k. is
sadly one of leading countries dealing with coronavirus, as another 14 cases
have been confirmed now country. total, there 20 incidents april 4, 2014, none
it’s ended death.on itv’s show this morning, gloria hunnisett talks a parent
who lost their daughter at 21 days old due to virus. curtis’ story haunting
absolutely heartbreaking.they didn’t think was anything wrong her until few
later when she admitted hospital.” Synonym Swap Text: “and tensions in the
middle east?curtis’ heartachethe .k. is sadly one of leading countries dealing
with coronavirus, as some_other 14 cases have been confirmed now country.
total, there 20 incidents april 4, 2014, none it’s ended death.on itv’s show
this morn gloria hunnisett talks a parent who lost their daughter at 21 days
old due to virus. curtis’ story haunting absolutely heartbreaking.they didn’t
think was anything haywire her until few later when she admitted hospital.”

In the above example, the swaps showcase more of synonym swaps capabilities to
make changes to text. The first swap, "another" to "some_other" is reasonable
and correct swap that fits within the context of the sentence. However, the
second swap, "wrong" to "haywire", is entirely unreasonable and completely
fails to capture the original idea and content of the original sentence.

###  3.6 Discussion

Synonym Swap allowed us to get an idea of the effectiveness of simply swapping
single words in a sentence on an automated authorship attributor. Our results
indicated that even a technique that randomly swaps words with no logical
process behind its target selection can still influence an AA’s labels on the
text. It also informed us of the need to implement a new method for selecting
replacement words for obfuscation. For Synonym Swap, we were limited to the
Wordnet corpus and its ability to generate likely synonyms for a target word,
which often proved insufficient. We also relied on GPT-2’s ability to select
the most probable word from these selected synonyms, given only the previous
tokens of the current sentence. Thus, it was unable to consider any
information contained in the sentence after its location had been determined,
which further limited Synonym Swap’s ability to preserve semantics. With these
lessons in mind, we decided to design a new obfuscation technique to correct
many of these faults as well as further enhance its ability to select target
candidates in sentences more logically. This technique, UID Word Swap (UWS),
utilizes DistilBERT, a compressed version of BERT, instead of GPT-2.
DistilBERT is a large language model that is specifically trained to excel at
masked language modeling which is precisely the task that we are undertaking
when swapping a word to obfuscate the text. Not only does DistilBERT fix our
problem with only having the context of the sentence up to and not after the
target word, but it also removes the need for using the Wordnet corpus. Since
DistilBERT is specifically trained for masked language modeling, it is capable
of selecting semantically similar and reasonable words without referring to a
corpus such as Wordnet.

##  4 UID Word Swap & Paraphrase

Following our preliminary algorithm, Synonym Swap, we developed two more
algorithims for obfuscation. The first is UWS, which utilizes DistilBERT to
generate the probable words in a masked language model format. The second is
UID Paraphrase, which uses diverse beam search to generate diverse paraphrased
versions of the articles. Both methods generated 10 new articles for each of
the 100 articles in our small data set. We will go into further specific
details about the implementation and results for both next.

###  4.1 UID Word Swap

####  4.1.1 Implementation and Design

UID Word Swap (UWS) is a further iteration on Synonym Swap that was designed
from the ground up with the goal of improving on the aspects in which Synonym
Swap failed. Mainly, poor word choice in relation to the context of the
sentence. Using DistilBERT to generate the candidate words for a particular
target word, UWS not only generates higher quality results that are more
semantically similar, but also does so significantly faster. Below we will
provide a pseudo code algorithm of UWS to demonstrate the general process of
the algorithm.

    UID_Word_Swap(masked_sentence)
    {
        sentence_tokens = tokenizer(masked_sentence)

        sentence_logits = model(sentence_tokens)

        # get 10 most probable tokens by sorting 10 highest scored tokens
        most_prob_tokens = sort(logits)[-10:]

        most_prob_words = decode(most_prob_tokens)
        for each prob_word in most_prob_words
        {
            new_sentence = masked_sentence.replace([MASK], prob_word)
            most_prob_sentences_list.append(new_sentence)
        }
        return most_prob_sentences_list
    }

    parse_sentences(article, num_of_article)
    {
        article_sentences = sentence_tokenize(article)

        for each sentence in article_sentences
        {
            sentence_words = word_tokenize(article_sentences)

            part_of_speech = get_pos(sentence_words)

            if sentence_words >= 3 words
            {
                target_word = middle word in the sentence
                target_index = middle word index in sentence
            }
            if target_index is not null
            {
                while target_word is not a stop word or punctuation  mark, does not have synonyms,
                is not alphabetical, or is a proper noun
                {
                    target_word = next word in sentence
                    target_index = next word index
                }
                masked_sentence = sentence
                masked_sentence[target_index] = [MASK] token

                probable_sentences.append(UID_Word_Swap(masked_sentence))
            }
            else
            {
                probable_sentences.append(None)
            }
        }
        return probable_sentences
    }

    human_gpt3_articles = 50 human + 50 gpt3 from TuringBench

    for each article in human_gpt3_articles
    {
        parse_sentences(article, number_of_article)
    }

As shown in the pseudo code above, we utilized a masked language modeling
approach to conduct the word swap. Specifically, on lines 351-357 is where the
target word is determined and then the [MASK] token is inserted into the
sentence. Notice the target word criteria is very similar to the target word
criteria of Synonym Swap. WordNet is even queried to check if a word has
synonyms in an effort to only pick words that would be easier to swap. At this
point, the masked sentence is given to DistilBERT which then determines the
ten most probable words for the swap. Ten alternate sentences are constructed
for every sentence in which a suitable word was located. These ten alternate
sentences are then used to construct ten new articles with each article being
made up of the ith item in the alternate sentence list constructed for each
sentence in the article. For the sentences in which no suitable word was
located, the original sentence is used for all the ten alternate articles.

##### Candidate Selection Criteria:

Following the creation of these ten alternate articles, we needed to implement
the UID score and semantic similarity scores as a guiding metric. We did this
by simply calculating the UID $variance$ and ${Difference}^{2}$ for the
original articles as well as their ten alternates. Due to the semantic
similarity scores being very high for UWS obfuscated articles, we set the
required threshold for similarity to be $>=0.98$ or 98% similar to the
original. The scores are so high as a result of the changes to each article
being at most one word swap per sentence in the article. For the two UID
scores, we calculated the difference for each alternate article’s UID scores,
compared to the original’s UID scores. For both $variance$ and
${Difference}^{2}$, the articles with the largest UID differences to the
original were inspected until one was found that satisfied the semantic
similarity score threshold. The plots for demonstrating the UID vs Semantic
Similarity Scores are shown in the following results section.

Below is a pseudo code outline of the candidate selection process used for the
UWS algorithm. any sentence

    candidate_select(num_article)
    {
        original_article = the original article
        alternate_list = ten alternate articles generated by UWS

        original_UID1 = the original UID $variance$ score
        alternate_UID1 = the ten alternate UID $variance$ scores

        original_UID2 = the original UID difference squared score
        alternate_UID2 = the ten alternate UID difference squared scores

        for each alternate article’s UID $variance$ Score
            append the difference of UID $variance$ score and original UID $variance$ score

        for each alternate article’s UID difference squared Score
            append the difference of UID difference squared score and
            original UID difference squared score

        sorted_UID1 = sorted(UID1_Difference_list)
        sorted_UID2 = sorted(UID2_Difference_list)

        for each Variacne and Difference Squared score in sorted_UID1 and sorted_UID2
            get semantic similarity score of current alternate article
            if semantic similarity >= .98:
                select given article
                break
    }

####  4.1.2 UID Word Swap Results

Below we will present the results of the experiments we ran to test the
effectivness and capabilities of the UWS obfuscation process.

#### Scatter Plots UID vs. Semantic Similarity

Figure 5: UID Word Swap utilizing UID Score ($variance$) Figure 6: UID Word
Swap utilizing UID Score (${Difference}^{2}$)

To showcase our results of UWS’s candidate selection, we generated two scatter
plots for each article that mapped the correlation of semantic similarity
score (x-axis) with the UID scores (y-axis) between the original article and
its ten alternative articles.The first scatter plot represents the UID Score 1
($variance$), while the second scatter plot corresponds to UID Score 3
(${difference}^{2}$). Notice that the Semantic Score of UWS is rather high.
This is due to the fact that only one word in each sentence at most is being
swapped. This indicates higher levels of semantic preservation, which is
expected given that the change to each article is rather small. This also
seems to result in little, but still noticeable, difference across the UID
scores for each article. Notice the original article, marked in red, has a
semantic similarity score of 1.0 as a result of being compared to itself.

##### Text Generation Quality

UWS’s results proved to generate more consistent and higher quality sentences.
While Synonym Swap only produced one new alternate sentence, which is then
generated into a new article, UWS generated 10 new sentences for each sentence
it was given. These 10 new sentences were then used to generate 10 new
alternate articles. Each of these articles then had a semantic similarity
score and four UID scores calculated. These scores were then used to generate
a plot for each article, which allows us to see which article is most
semantically similar while also being significantly different with their UID
score differences. However, due to UWS only altering one word per sentence in
each article, all articles had very similar UID scores. To address this issue,
we developed another algorithm known as UID Paraphrase that utilizes Diversity
Beam Search to generate more diverse obfuscated articles.

The plots for the sample text below can be found above, figure 5 and 6.

##### Human Generated Text:

Original Article (Human): “washington ( ) at a time when president donald
trump seems to permeate nearly every aspect of american discourse, it might
come as surprise that the first movie from barack and michelle obama’s
production company, higher ground, never mentions him by name.but subtlety is
part power factory, new netflix documentary charts r ening factory in dayton,
ohio. over course two hours, movie, directed seasoned documentarians steven
bognar julia reichert, serves quiet historical political corrective, offering
their portrait state america’s industrial heartland prodding viewers rethink
who, exactly, project.american starts on december 23, 2008, crowd gathers
learn general motors plant dayton has shuttered. then fast-forwards 2015, ens
enterprise, fuyao glass america, arm shanghai-based company manufactures
automotive glass. one man makes fuyao’s expanded mission crystal clear: what
we’re doing melding cultures together: chinese culture s culture. so we are
truly global organization.as some critics have pointed out, is, important
ways, commentary unpredictability globalization; york times review frames
underscoring haves have-nots.but it’s also much more than that. arrives moment
white house continues make vociferous, bold claims about economy, particularly
manufacturing. that’s despite increasing concerns economists warnings history
recession could be horizon. there’s sobering contrast between trump’s rhetoric
how job growth ballooned during his presidency reality broader slowdown
slamming states – including ohio helped win 2016 presidential election.read”

UID Word Swap Text UID Score $variance$ & ${difference}^{2}$: “ washington ( )
at a time when president donald trump seems to permeate nearly every aspect of
american discourse , it might come as surprise that the first movie from
barack and michelle obama ’s publishing company , higher ground , never
mentions him by name.but subtlety is part power factory , new netflix
documentary charts r ening factory in dayton , ohio . over course two hours ,
movie , directed seasoned documentarians steven bognar julia reichert , serves
quiet historical political corrective , offering their portrait state america
’s industrial heartland helps viewers rethink who , exactly , project.american
starts on december 23 , 2008 , crowd gathers learn general motors plant dayton
has shuttered . then fast-forwards 2015 , ens enterprise , fuyao glass
corporation , arm shanghai-based company manufactures automotive glass . one
man makes fuyao ’s expanded mission crystal clear : what we ’re doing bringing
cultures together : chinese culture s culture . so we are truly global
organization.as some critics have pointed out , is , important ways ,
commentary upon globalization ; york times review frames underscoring haves
have-nots.but it ’s also much more than that . arrives moment white house
continues make vociferous , conflicting claims about economy , particularly
manufacturing . that ’s despite increasing concerns economists thought history
recession could be horizon . there ’s sobering contrast between trump ’s
rhetoric how job growth ballooned during his political reality broader
slowdown slamming states – including ohio helped win 2016 presidential
election.read”

Notice here some of the successful and unsuccessful word swaps that occurred.
The first swap, production being swapped for publishing, is a successful swap
as the meaning is preserved. Another example of a successful swap is prodding
being swapped for helps. However, an example of a slightly unsuccessful is the
swapping of "america" for corporation since this is altering a proper noun,
which is something that should be avoided as it alters the semantics of the
sentence in a significant way.

##### Machine Generated Text:

Machine Text (GPT-3: “’vatican city – a tribunal of senior clerics at the
vatican is about to deliver verdict in one biggest sex abuse cases it has
faced since start catholic church’s scandal.the level hypocrisy simply
appalling, vincenzo folena, an italian editorialist, networked cbs. like
osorno’s, he said, church sanctions fellow human beings employing cruel
tactics, sending them exile and punishment places for something which they do
not have feel guilty–this whilst abusers that hid behind osorno’s cassock will
never appear before court.osorno’s scandal conflicts?osorno’s appointed
bishop, juan barros, been accused snapping after priest, father fernando
karadima, was found guilty ruling launched 2011.bishop barros produced
nation’s osorno 2015, pope francis engineered his placement; delegation
prominent catholics subsequent unsuccessfully tried pit appointment down.pope
defended decision promote 2015 trip chile.the archbishop santiago, cardinal
ricardo ezzati, decorated by ? 2016. likewise walked global holocaust memorial
day events, although jewish community offended church’”

UID Word Swap Text UID Score $variance$ & difference squared: “ ’vatican city
– a tribunal of senior clerics at the vatican is about to deliver verdict in
one biggest sex abuse cases it has convened since start catholic church ’s
scandal.the level hypocrisy simply appalling , vincenzo folena , an italian
editorialist , networked cbs . like osorno ’s , he said , church sanctions
fellow human beings employing cruel tactics , sending them exile and
punishment places for something which they do not have feel guilty – this
whilst abusers that hid behind osorno ’s cassock will never appear before
court.osorno ’s scandal conflicts ? osorno ’s appointed bishop , juan barros ,
been investigated snapping after priest , father fernando karadima , was found
guilty ruling launched 2011.bishop barros produced nation ’s osorno 2015 ,
pope francis engineered his placement ; delegation prominent catholics
subsequent unsuccessfully tried pit appointment down.pope defended decision
promote 2015 trip chile.the archbishop santiago , cardinal ricardo ezzati ,
decorated by ? 2016. likewise walked global holocaust memorial day weekend ,
although jewish community offended church ’”

Here we can see some successful and unsuccessful alterations to a GPT-3
generated text. The first swap of faced being swapped for convened is rather
unsuccessful and fails to preserve the semantic idea of the original article.
A successful swap is shown with the swapping of "accused" for "investigated".
This is deemed sensible and semantically similar swap.

###  4.2 UID Paraphrase

####  4.2.1 Implementation & Design

UID Paraphrase (UP) builds upon UWS and Synonym Swap but changes the process
of obfuscation by paraphrasing each sentence instead of swapping just a word.
To select if a sentence is eligible for obfuscation we ensured the sentence
was equal to or longer than 8 characters. The sentence is then tokenized and
entered into a diverse beam search model that attempts to generate new
sentences that are semantically similar. The diverse beam search model decodes
the sentence and considers all possible next tokens that could appear in the
sentence, scoring each with the T-5 Large Paraphraser Language model.
Utilizing the diversity penalty hyper parameter, we encourage the model to
produce more diverse outputs, so as to get more semantically unique articles.
The idea is that these unique articles are diverse enough to yield higher
variation in their UID scores while still maintaining a relatively high
semantic similarity to the original. Following a system similar to UWS, we
generate ten alternate sentences that are then used to generate the ten new
articles. From the list of ten alternate sentences for each sentence, the ith
alternate sentence is picked and used to make the ith article.

##### Candidate Selection Criteria:

Similar to UWS, after the creation of the 10 alternate articles, we then
calculate the semantic cosine similarity scores for each article compared to
the original article, as well as UID score $variance$ and UID score
${Difference}^{2}$. The candidate selection process follows a similar method
of sorting the difference in UID scores between the alternate articles and the
original articles. We then check the highest difference in UID scores until
one is found that has a semantic similarity score that passes the threshold.
Due to the greater variation in the articles for UP than in UWS, we changed
the threshold for semantic similarity to $>=0.85$ to accommodate the increased
diversity in the alternate articles. The candidate selection is shown in
pseudo code here.

####  4.2.2 UID Paraphrase Results

##### Scatter Plots UID vs. Semantic Score

Figure 7: UID Paraphrase Swap utilizing UID Score ($variance$) Figure 8: UID
Paraphrase Swap utilizing UID Score (${Difference}^{2}$)

The scatterplots help illustrate the process of selecting a proper candidate.
For this particular example, we can observe the selected articles (colored
purple) are furthest from the UID score of the original article, yet they
still satisfy the semantic similarity threshold.

##### Text Generation Quality

Below is an example of a human generated piece of text and its resulting UID
paraphrased selected articles. Notice this particular article has two separate
articles selected based on the different $variance$ and ${difference}^{2}$ UID
scores.

##### Human Generated Text:

Human Text (Original): “the nited nations has ended a campaign featuring
wonder woman as an ambassador for women and girls, two months after
announcement was met with protests petition complaining that fictional
superhero inappropriate choice to represent female empowerment. in announcing
october, said it about girls everywhere, who are their own right, men boys
support struggle gender equality. but not everyone saw way. nearly 45, 000 p
le signed protesting selection. a white of impossible proportions, scantily
clad shimmery, body suit american flag motif boots is appropriate spokeswoman
equity at nations, said. jeffrey brez, spokesman .”

UID Paraphrase UID Score variance: “A campaign involving wonder woman as an
ambassador for women and girls has ended two months after being met with
protests petition claiming that the fictional superhero inappropriate choice
to represent female liberation. Girls everywhere, who are their own right, and
men boys support gender discrimination are all in announcing october.. but not
everyone saw way. More than half of the population of nearly 45, 000 p les
have been rejected in the protesting vote. According to a white of
insignificant proportions, scantily clad shimmery, body suit american flag
motif boots, is appropriate spokeswoman equity in nations.. jeffrey brez,
spokesman .”

UID Paraphrase UID Score ${Difference}^{2}$: “Two months after being met with
protests petition claiming that the fictional superhero inappropriate choice
to represent female liberation, the nited nations has ended a campaign
starring wonder woman as an ambassador for women and girls. Girls everywhere,
who are their own right, and men boys support gender discrimination are all in
announcing october. but not everyone saw way. Over 55,000 people were rejected
in the protesting vote, with nearly 45, 000 p le signed protesting selection.
According to the author, a white of insignificant proportions, scantily clad,
body suit american flag motif boots, is appropriate spokeswoman equity in
nations. jeffrey brez, spokesman . ”

###  4.3 Authorship Attributor Labeling Results:

We then took the selected and original articles for both UWS and UP and
obtained labels for each article. We utilized two automated authorship
attributors, Zero GPT and DetectGPT, to obtain the labels. The labels were
used to compare the effectiveness of UWS and UP in obfuscating the authorship
of the articles. The detectors seemed to fair poorly at detecting machine
generated text and seemed to label almost all of the articles human, even if
they were GPT-3.

##### Note on Results:

It is important to notice that the results below are all calculated with both
UID score results combined into a list and then compared to their original
articles. This is why there are 200 altered articles as there are 100
$variance$ and 100 ${difference}^{2}$ articles and 200 original articles for
each article respectively.

Figure 9: UID Paraphrase Labels Figure 10: UID Word Swap Labels

actual
value |  | UID Word Swap GPT Zero |
---|---|---|---
| p | n | total
p′ |  True Positive 4 |  False Negative 96 | P′
n′ |  False Positive 2 |  True Negative 98 | N′
total | P | N |

actual
value |  | UID Word Swap DetectGPT |
---|---|---|---
| p | n | total
p′ |  True Positive 2 |  False Negative 98 | P′
n′ |  False Positive 0 |  True Negative 100 | N′
total | P | N |

The two confusion matrices above demonstrate the quality of the two detectors
on the UWS results. Notice the split of false negatives and true negatives is
nearly 50-50. This is due to the heavy favoring of the human label by the
detectors.

Below are the F1 scores for paraphrase swaps.

[H]  Model F1 Score GPT Zero 0.54 DetectGPT 0.5

Table 1: UID Paraphrase F1 Scores for GPT Zero and DetectGPT

actual
value |  | UID Paraphrase Zero GPT |
---|---|---|---
| p | n | total
p′ |  True Positive 8 |  False Negative 92 | P′
n′ |  False Positive 0 |  True Negative 100 | N′
total | P | N |

actual
value |  | UID Paraphrase DetectGPT |
---|---|---|---
| p | n | total
p′ |  True Positive 0 |  False Negative 100 | P′
n′ |  False Positive 0 |  True Negative 100 | N′
total | P | N |

Once again, there is a similar split of false and true negatives that is due
to the favoring of the human label by the detectors.

[H]  Model F1 Score GPT Zero 0.51 DetectGPT 0.51

Table 2: UID Word Swap F1 Scores for GPT Zero and DetectGPT

Below is one of the examples where the attributor’s labels between the two
articles were different between the original label and the selected label. It
seems that the diverse beam search had some problem generating a proper
paraphrased article, leading to the nonsensical output shown in the selected
article. It is possible that due to the beginning of the selected article
being a sensical paraphrase of the original, it retained a high enough
semantic similarity score. At the same time, the nonsensical ending of the
paraphrased article resulted in a substantially different UID score, causing
its score to be drastically different from the original’s. Both of these
events led to its selection as the paraphrased article. The nonsensical ending
of the article is then likely the reason why the attributor altered its label
to machine.

##### Original Article:

’the plan for mandatory debt-market defaulting in the life of dealer during
first year rbi may postpone its to make compulsory all defaults debt market
when it is launched, chief economic adviser arvind subramanian today said he
told reporters that not be feasible have default one yearmarket expectations
rs 50 rate cut soon; raghuram rajan’s wish list yet revealed: shah - business
standardreserve bank governor rajan india and philip clarke, ceo tesco k
expectation a basis points next monetary policy meets with consensus,
according standard report as growth known, participants eagerly wait
decisionrbi set 1 2 2% over five years: shaktikanta das linerbi line ’s key
variable repo rate, which displayed an increasing trend period 2011-14
declined 2015 following easing : reserve moneycontrol.comrbi displayed’

##### UID Paraphrase Variance Selected Article:

According to a shakti bank governor’s mandatory debt-market defaulting in the
first year of the bank’s life, the plan for mandatory debt-market defaulting
in the life of the dealer during the first year rbi’s first year may
postponed, but the main variable repo rate, which increased trend rate in
2015, remains unchanged, according to reserve moneycontrol.comrbi’s forecast,
rising trend rate remains unchanged, with increasing trend rate declines
rajan rbi a rajan rajan rajan rajan rajan rbi rbi rajan rajan rajan rajan rbi
rbi rbi’s first year rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi
rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi
rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi
rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi
rbi rbi rbi rbi rbi rbi rbi rbi rbi rbi

##  5 Conclusion & Discussion

From the results we gathered, there is no indication that UID is a metric that
can be used in the process of obfuscation. A number of factors could be the
reason for the results failing to provide any interesting evidence. These
factors could be the poor accuracy of the detectors, using a rather small
sample of 100 articles, and a lack of fine tuning for the parameters for UP’s
diverse beam search. The quality of text generated by both UWS and UP were
rather promising and were capable of producing semantically similar results
that had rather varied UID results.

###  5.1 Future Work

While our results failed to indicate much about the effectiveness of UID as a
metric for obfuscation, further investigation is needed as much of our results
can be deemed erroneous as a result of the poor detectors and small dataset
size.

Future work would firstly involve the tuning of an AA that would provide
accurate labels on the original articles. The AAs we used for our experiments
in this paper failed to properly label the original articles. In fact, the AAs
seemed heavily biased towards labeling nearly every article as human-
generated. Thus, to make any conclusive remarks about the success and
capabilities of both UWS, UP, and UID scores as a metric entirely would
require further investigation. Tuning certain parameters for the current AAs,
Detect GPT and ZeroGPT, or using a different detector could yield better
results.

While UID is calculated for each article, it is not directly used within the
obfuscation process. Further work on both UWS and UP in which we utilize the
scores to guide the changes within the article could prove more successful.
For instance, currently UWS uses DistilBERT to pick the ten most probable
words for each sentence in the article. Ten articles are then created and then
after the UID scores are calculated. Possibly involving the UID scores in the
creation of the alternate articles or in the selection of the ten probable
words could yield more impactful results on the labeling of the articles.

Other improvements we could make to our research would be as follows:

  * •

Increase number of articles as well as number of authors (other than human or
GPT-3)

  * •

Increase sophistication of both UWS and UP

  * •

Further implement UID as a guiding metric within the obfuscation process

## Acknowledgments

I want to thank Dr. Dongwon Lee (Penn State University) for providing advice
and guidance on conducting research. Furthermore, I would also like to thank
Saranya Venkatraman (Penn State University & New York University) who provided
much advice and assistance while conducting the research. Saranya also
conducted the test on the Authorship Attributors which provided me with the
results used in this paper. This paper would not have been possible without
the assistance of both Dr. Lee and Saranya.333This research was conducted at
Pennslyvania State University through an NSF funded REU. The entire research
and paper creation process took eleven weeks, starting in late May of 2023 and
ending early August 2023.

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