# Nuclear magnetic resonance studies in a model transverse field Ising system

Y-H. Nian  Department of Physics and Astronomy, University of California
Davis, Davis, CA  I. Vinograd  Department of Physics and Astronomy, University
of California Davis, Davis, CA  C. Chaffey  Department of Physics and
Astronomy, University of California Davis, Davis, CA  Y. Li  Geballe
Laboratory for Advanced Materials and Department of Applied Physics, Stanford
University, CA 94305, USA  M. P. Zic  Geballe Laboratory for Advanced
Materials and Department of Physics, Stanford University, CA 94305, USA  P.
Massat  Geballe Laboratory for Advanced Materials and Department of Applied
Physics, Stanford University, CA 94305, USA  R. R. P. Singh  Department of
Physics and Astronomy, University of California Davis, Davis, CA  I. R. Fisher
Geballe Laboratory for Advanced Materials and Department of Applied Physics,
Stanford University, CA 94305, USA  N. J. Curro<EMAIL_ADDRESS>Department of Physics and Astronomy, University of California Davis, Davis, CA

###### Abstract

The suppression of ferroquadrupolar order in TmVO4 in a magnetic field is
well-described by the transverse field Ising model, enabling detailed studies
of critical dynamics near the quantum phase transition. We describe nuclear
magnetic resonance measurements in pure and Y-doped single crystals. The non-
Kramers nature of the ground state doublet leads to a unique form of the
hyperfine coupling that exclusively probes the transverse field
susceptibility. Our results show that this quantity diverges at the critical
field, in contrast to the mean-field prediction. Furthermore, we find evidence
for quantum critical fluctuations present near Tm-rich regions in Y-doped
crystals at levels beyond which long-range order is suppressed, suggesting the
presence of quantum Griffiths phases.

##  I Introduction

Unconventional superconductivity tends to emerge in the vicinity of a quantum
critical point (QCP), where some form of long-range ordered state is
continually suppressed to $T=0$ [1, 2, 3, 4, 5, 6, 7, 8, 9]. This observation
suggests that there may be an important relationship between the
superconducting pairing mechanism and the strong quantum fluctuations
associated with the QCP, however there are major challenges to understanding
the fundamental physics at play in these systems. In practice various
approaches can be utilized to tune the ordered state to the QCP. Hydrostatic
pressure or magnetic field are thermodynamic variables that are homogeneous
throughout the material and can be varied continuously. Doping, on the other
hand, offers a convenient method to apply ‘chemical pressure’ or introduce
charge carriers, but can introduce electronic heterogeneity at the nanoscale
which can complicate interpretation [10, 11]. In such cases it can be
difficult to disentangle what experimental observations to ascribe to
fundamental properties of a quantum phase transition versus extrinsic effects
arising from the long-range effects of the dopants.

In order to better understand the influence of doping in strongly interacting
system near a quantum phase transition, it is valuable to study a model system
in the absence of superconductivity. TmVO4 is as material that has attracted
interest recently because its low temperature properties are well-described by
the transverse field Ising model (TFIM), an archetype of quantum criticality
[12, 13]. TmVO4 exhibits long-range ferroquadrupolar order in which the Tm
$4f$ orbitals spontaneously align in the same direction, as illustrated in
Fig. 1. The Tm3+ ions ($4f^{12}$ with $L=5$, $S=1$, $J=6$) experience a
tetragonal crystal field interaction, and the ground state is well separated
by a gap of $\sim 77$ K to the lowest excited state [14, 15]. The ground state
is a non-Kramers doublet, so the first order Zeeman interaction vanishes for
in-plane fields (i.e. $g_{c}\sim 10$ while $g_{a}=g_{b}=0$). This doublet can
be described by a spin-1/2 pseudospin in which one component, $\sigma_{z}$,
corresponds to a magnetic dipole moment oriented along the $c$-axis, while the
other two components $\sigma_{x}$ and $\sigma_{y}$ correspond to electric
quadrupole moments with $B_{2g}$ ($xy$) and $B_{1g}$ ($x^{2}-y^{2}$) symmetry,
respectively [16]. The two quadrupole moments couple bilinearly to lattice
strains $\varepsilon_{xx}-\varepsilon_{yy}$ and $\varepsilon_{xy}$, which
gives rise to an effective interaction between the moments and leads to a
cooperative Jahn-Teller distortion at a temperature, $T_{Q}$ [17]. TmVO4
spontaneously undergoes a tetragonal to orthorhombic distortion with $B_{2g}$
symmetry below $T_{Q}=2.15$ K with orthorhombicity $\delta\approx 0.01$, as
illustrated in Fig. 1(b). Because there are two distinct orientations of the
quadrupolar moments, the ferroquadrupolar order has Ising symmetry that can be
described as a coupling between neighboring pseudospins. On the other hand, a
magnetic field oriented along the $c$-axis couples to the pseudospin in a
direction that is transverse to the ferroquadrupolar order [18]. This field
mixes the two degenerate ground state quadrupolar states, enhancing the
fluctuations of the pseudospins and suppressing $T_{Q}$ at a quantum phase
transition with critical field $H_{c}^{*}\approx 0.5$ T [12]. This
interpretation has been strengthened by the recent observation of a quantum
critical fan emerging from the QCP that extends to temperatures above $T_{Q}$
[19].

Figure 1:  (a) Crystal structure of TmVO4 ($I41/amd$) with Tm atoms in blue, V
atoms in green, and oxygen atoms in red. For the studies discussed here, the
magnetic field, $\mathbf{H}_{0}$, was rotated in the $ac$-plane, with an angle
$\theta$ between $\mathbf{H}_{0}$ and the $c$ axis. The projection of the
field along the $c$-axis is $H_{0}\cos\theta$. (b) Schematic phase diagram of
TmVO4 as a function of magnetic field $H_{c}$ along the $c$-axis, illustrating
the $B_{2g}$ orthorhombic distortion in the ferroquadrupolar state. (c) Phase
diagram for Tm1-xYxVO4, reproduced from [20]. The dashed line represents the
mean-field result expected purely from dilution.

LiHoF4 is another important material whose physics is well described by the
TFIM [21]. There are important differences, however, between LiHoF4 and TmVO4.
Although the physics of both systems derives from non Kramers doublets, the
former is a ferromagnet with Ho moments ordering along the $c$-axis, whereas
the latter has ferroquadrupolar order with quadrupolar moments ordering in the
plane. As a result, the transverse field direction for LiHoF4 is perpendicular
to the $c$-axis, whereas in TmVO4 the transverse field direction is parallel
to $c$. This fact is crucial for TmVO4 because it also has profound
consequences for the hyperfine coupling to neighboring nuclear spins and
enables unique measurements of the quantum fluctuations directly. Moreover,
since the quadrupolar moments couple to strain fields, long-range order in
TmVO4 is particularly sensitive to dopants. Therefore substituting with Y in
TmVO4 offers a unique opportunity to investigate how the quantum phase
transition changes in response to the disorder and random fields introduced by
the dopant atoms.

##  II Couplings to Non-Kramers Doublet

###  II.1 Lattice interaction

####  II.1.1 Ground state Wavefunctions

The ground state wavefunctions of the Tm in the $D_{4h}$ point group symmetry
of the TmVO4 lattice are given by:

$|\psi_{1,2}\rangle=\alpha_{1}|\pm 5\rangle+\alpha_{2}|\pm
1\rangle+\alpha_{3}|\mp 3\rangle$ (1)

in the $|J_{z}\rangle$ basis, where the $\alpha_{i}$ coefficients are
determined by the details of the crystal field Hamiltonian [15, 18]. Is is
straightforward to show that $J_{x,y}$ operators vanish in the subspace
spanned by these states. On the other hand, there are three other operators
that do not vanish:

$J_{x}^{2}-J_{y}^{2}\sim\sigma_{x}\text{, \hskip
56.9055pt}J_{x}J_{y}+J_{y}J_{x}\sim\sigma_{y}\text{, \hskip 56.9055pt and
}J_{z}\sim\sigma_{z},$ (2)

where the $\sigma_{\alpha}$ are the Pauli matrices. Physically, the first two
operators represent quadrupolar moments with $B_{1g}$ and $B_{2g}$ symmetries,
respectively, and the third represents a magnetic moment along the $z$
direction. The conjugate fields to these moments are strain
$\epsilon_{B1g}=\epsilon_{xx}-\epsilon_{yy}$, $\epsilon_{B2g}=\epsilon_{xy}$,
and magnetic field $H_{z}$, respectively. Here the strain tensor is defined as
$\epsilon_{ij}=(\partial u_{i}/\partial x_{j}-\partial u_{j}/\partial
x_{i})/2$, where $\mathbf{u}(\mathbf{x})$ is the displacement from the
equilibrium lattice positions.

####  II.1.2 Cooperative Jahn-Teller Effect

Because the quadrupolar moments have non-uniform charge distributions, they
can interact with a strained lattice via a bilinear coupling of the form
$-\eta_{i}\varepsilon_{i}\sigma_{i}$, where $\eta_{i}$ is an electron-lattice
coupling constant. This coupling renormalizes the elastic constant, leading to
a softening in both the $B_{1g}$ and $B_{2g}$ channels, but is strongest for
the $B_{2g}$ channel for TmVO4. It can be shown that this leads to an
effective coupling between the quadrupolar moments:

$\mathcal{H}_{ex}=\sum_{l\neq
l^{\prime}}J(l-l^{\prime})\sigma_{y}(l)\sigma_{y}(l^{\prime})$ (3)

where the sum is over the lattice sites, and $J(l-l^{\prime})$ is an Ising
interaction between the Tm quadrupolar moments [16, 17]. The coupling depends
on the details of the lattice, and because it is mediated by strain fields, it
can extend well beyond just nearest neighbor sites. This interaction leads to
long-range order in the three-dimensional TmVO4 lattice below a temperature
$T_{Q}=2.15$ K, with finite expectation values of
$\pm\langle\sigma_{y}\rangle$. This ferroquadrupolar order is accompanied by a
$B_{2g}$ lattice distortion as illustrated in Fig. 1(b) [22].

###  II.2 Zeeman interaction

The interaction between a non-Kramers doublet in a tetragonal environment and
a magnetic field is given by:

$\mathcal{H}_{Z}=g_{z}\mu_{B}H_{z}\sigma_{z}+\frac{1}{2}(g_{J}\mu_{B})^{2}b\left[(H_{x}^{2}-H_{y}^{2})\sigma_{x}+2H_{x}H_{y}\sigma_{y}\right]$
(4)

where $H_{x,y}$ is a magnetic field along the $(x,y)$ direction, $g_{J}=7/6$
for Tm3+ and $g_{c}$ and $b$ depend on the crystal field Hamiltonian [23].
These parameters have been measured for TmVO4 to be $g_{c}=10.21$ and
$b/k_{B}=0.082K^{-1}$ [15]. Note that $\mathbf{H}$ couples quadratically in
the $x$ and $y$ directions, rather than linearly for a Kramers doublet. A
field in the $z$ direction splits the doublet linearly, and acts as a
_transverse_ field for the Ising interaction in Eq. 3.

####  II.2.1 Induced moments for perpendicular fields

The Zeeman interaction can also be written as
$\mathcal{H}_{Z}=\mathbf{\mu}\cdot\mathbf{H}$, where the magnetic moment along
$z$ is $\mu_{z}=g_{||}\mu_{B}\sigma_{z}$, and the perpendicular fields
$H_{x,y}$ can couple with quadrupolar moments giving rise to effective
magnetic moments:

$\mu_{x,y}=\frac{1}{2}(g_{J}\mu_{B})^{2}b(H_{x}\sigma_{y,x}\pm
H_{y}\sigma_{x,y}).$ (5)

For sufficiently low perpendicular fields, $H_{x,y}\leq 3$ T, the second order
Zeeman interaction in the perpendicular direction will be less than
$0.1k_{B}T_{Q}$, and can be safely ignored. At higher fields, $H_{x}$ and
$H_{y}$ can also act either longitudinal or transverse fields for the Ising
order, and can in fact be used to detwin the ferroquadrupolar order [24].

###  II.3 Transverse Field Ising Model for Ferroquadrupolar Order

The low temperature degrees of the Tm electronic degrees of freedom are thus
captured by the sum $\mathcal{H}_{ex}+\mathcal{H}_{Z}$, which maps directly to
the TFIM:

$\mathcal{H}_{Tm}=\sum_{l\neq
l^{\prime}}J(l-l^{\prime})\sigma_{y}(l)\sigma_{y}(l^{\prime})+g_{z}\mu_{B}H_{c}\sum_{l}\sigma_{z}(l),$
(6)

where the sum is over the Tm lattice sites. Here we have ignored the small
contribution from the perpendicular component of the magnetic field. Mean
field theory predicts a QCP for a $c$-axis field of $T_{Q}/g_{c}\mu_{B}\approx
0.3$ T, which is close to the experimental value of $H_{c}^{*}=0.5$ T. Note
that if there is a perpendicular field oriented such that $H_{x}$ or $H_{y}$
is zero, the system can still be described by the TFIM, because
$\mathcal{H}_{Z}$ does not couple to the longitudinal order in pseudospin
space ($\sigma_{y}$). Rather, there is an effective transverse field in the
$x$-$z$ plane of pseudospin space leading to a different value of the critical
field [24].

###  II.4 Coupling to Nuclear Spins

####  II.4.1 Hyperfine Coupling to 51V

In most insulators the hyperfine coupling between a localized electron spin
and a nearby nucleus arises due to the direct dipolar interaction and can be
described as $\mathcal{H}_{hyp}=\mathbf{I}\cdot\mathbb{A}\cdot{\mathbf{J}}$,
where $\mathbf{I}$ is the nuclear spin, $\mathbf{A}$ is the (traceless)
hyperfine tensor, and $\mathbf{J}$ is the electron spin. For temperatures well
below the crystal field excitations, $\mathbf{J}$ should be replaced by the
ground state pseudospin operators and $\mathbb{A}$ should be renormalized. For
a non-Kramers doublet, there can be no coupling along the $x$ or $y$
directions because the magnetic field of the nucleus does not interact with
the doublet. Rather, the hyperfine coupling has the form:

$\mathcal{H}_{hyp}=A_{zz}I_{z}\sigma_{z}+C(H_{x}I_{x}-H_{y}I_{y})\sigma_{x}+C(H_{x}I_{y}+H_{y}I_{x})\sigma_{y},$
(7)

where $A_{zz}$ and $C$ are constants [23]. In the absence of magnetic field,
there is only a coupling along the $z$ direction, corresponding to the
transverse field direction. To determine the values of the coupling $C$, note
that Eq. 7 can be re-written in terms of the effective magnetic moments:

$\displaystyle\mathcal{H}_{hyp}$ $\displaystyle=$
$\displaystyle\frac{2C}{(g_{J}\mu_{B})^{2}b}(I_{x}\mu_{x}+I_{y}\mu_{y})+\frac{A_{zz}}{g_{z}\mu_{B}}I_{z}\mu_{z}$
(8) $\displaystyle=$
$\displaystyle\gamma\hbar(h_{x}I_{x}+h_{y}I_{y}+h_{z}I_{z}),$ (9)

where $h_{\alpha}$ are the hyperfine fields at the nucleus created by the Tm
moments. Using the measured values of $h_{x}/{\mu_{x}}=-0.0336T/\mu_{B}$ and
$h_{z}/{\mu_{z}}=0.0671T/\mu_{B}$ obtained by comparing the Knight shift
versus susceptibility, we can identify [25]:

$\displaystyle C$ $\displaystyle=$
$\displaystyle\frac{1}{2}\gamma\hbar(g_{J}\mu_{B})^{2}b\left(\frac{h_{x}}{\mu_{x}}\right)\approx-0.37\mu
K/T$ (10) $\displaystyle A_{zz}$ $\displaystyle=$ $\displaystyle\gamma\hbar
g_{z}\mu_{B}\left(\frac{h_{z}}{\mu_{z}}\right)\approx 368\mu K.$ (11)

####  II.4.2 Quadrupolar coupling to 51V

51V has spin $I=7/2$ and a nuclear quadrupolar moment $Q=0.052$ barns. Note
that this moment is several orders of magnitude smaller than the electronic
quadrupolar moment of the Tm $4f$ orbitals. Nevertheless, the extended charge
distribution of the latter can contribute to the electric field gradient (EFG)
tensor at the V nuclear site, which in turn couples to $Q$. As a result, the
nuclear spins can couple to the pseudospin via the nuclear quadrupolar
interaction [23]:

${\mathcal{H}_{Q}=B_{1}(I_{x}^{2}-I_{y}^{2})\sigma_{x}+B_{2}(I_{x}I_{y}+I_{y}I_{x})\sigma_{y}+P[3I_{z}^{2}-I(I+1)]\mathbf{1}}.$
(12)

Note that $B_{2}=B_{1}$, and corresponds to a 45∘ rotation of the principal
axes of the EFG. The last term, $P$, is determined by the local charge
distribution in the VO4 tetrahedra, and is independent of the $4f$ orbitals.
The EFG asymmetry parameter is given by $B_{1}\langle\sigma_{x}\rangle/P$, and
can be measured through detailed spectral measurements as a function of angle
in the ordered state. We estimate $P\approx 15$ $\mu$K and $B_{1}=B_{2}\approx
0.22$ $\mu$K [24].

Of all the terms in $\mathcal{H}_{hyp}+\mathcal{H}_{Q}$, $A_{zz}$ is several
orders of magnitude larger than any other, even for perpendicular fields of
several tesla. Thus the coupling between the 51V and the Tm $4f$ orbitals is
essentially only along the transverse field direction.

####  II.4.3 Hyperfine coupling to 169Tm

169Tm has a spin of $I=1/2$, and experiences a hyperfine coupling but no
quadrupolar interaction. By symmetry, the form of the hyperfine coupling must
also be described by Eq. 8. In this case, however, the coupling $A_{zz}\approx
160$ mK is nearly three orders of magnitude larger than that for the 51V due
to the on-site coupling [26]. As a result, the spin lattice relaxation rate in
the paramagnetic state is so fast that the 169Tm resonance has not been
observed. On the other hand, Bleaney and Wells reported 169Tm in the
ferroquadrupolar state, where they found a large shift of the resonance
frequency for fields applied in the perpendicular direction [15]. In this
case, the shift is due to the induced moments from the ordered Tm quadrupoles.
The shift exhibited a two-fold rotation symmetry as the field was rotated in
the perpendicular direction, which they attributed to the second order Zeeman
interaction and the induced magnetization. The two-fold rotation reflects the
orthorhombic crystal structure in the ferroquadrupolar state.

##  III Nuclear Magnetic Resonance Studies

Recently several studies have been conducted of the 51V NMR in TmVO4 in order
to better understand the nature of the quantum phase transition [25, 24, 19].
In principle, one could perform zero-field NMR (or nuclear quadrupolar
resonance, NQR) and gradually apply a $c$-axis field to investigate the
behavior as the field is tuned to the QCP. However, experiments below 1 MHz
are difficult because the signal-to-noise ratio varies as $f^{3/2}$, where $f$
is frequency [27]. To overcome this challenge, a perpendicular field of 3.3 T
was applied along the [100] direction of the crystal (corresponding to the $x$
or $y$ directions in Eq. 4), and the crystal was rotated to project a small
component along the $c$-axis, as illustrated in Fig. 1(a).

Spectra for several different values of $H_{c}$ are shown in Fig. 2(a). For
$H_{c}=0$, the spectra consist of seven transitions separated by a quadrupolar
interaction $P\sim 300$ kHz, as seen in Fig. 2(a). As $H_{c}$ increases, the
anisotropic Knight shift and EFG tensors alter the frequencies of the various
quadrupolar satellites in a well-controlled fashion, shown in Fig. 2(b). The
separation between the seven peaks gradually reduces and vanishes at the magic
angle (where $H_{c}=H_{0}/\sqrt{3}\approx 1.8$ T), and all the peaks shift to
higher frequency, reflecting the strong magnetic anisotropy. Surprisingly, the
integrated area of the spectra is dramatically suppressed in the vicinity of
the QCP, as shown in Fig. 2(c)). This suppression of intensity has been
interpreted as evidence for quantum critical fluctuations of the transverse
field, due to an increase in $T_{2}^{-1}$, the decoherence rate of the nuclear
spins [19]. The size of the NMR signal, $L(t)$, depends on the time evolved,
$t$, since the nuclear spins are prepared in their initial superposition
state. If $L(t)$ decays faster than the minimum time to perform an experiment,
then the signal intensity will be suppressed, or ‘wiped out’. The data in Fig.
2(c) suggests that $T_{2}^{-1}$ reaches a maximum at the QCP.

Figure 2:  (a) Spectra of 51V for several different values of $H_{c}$ as the
crystal is rotated (see Fig. 1(a)). (b) Calculated frequencies of the seven
transitions as a function of $H_{c}$. The transitions merge at the magic
angle, and then separate at higher values of $H_{c}$. The dashed red line
corresponds to the critical field, $H_{c}^{*}$. (c) The spectral area versus
$H_{c}$ for several different values of temperature. The blue diamonds
correspond to Tm1-xYxVO4 with $x=0.4$.

###  III.1 Transverse field susceptibility

In general, the decay envelope, $L(t)$, of a a spin-echo can be related to the
noise fluctuations of the environment. In TmVO4, this quantity can be written
as:

$\log[L(t)/L(0)]=-\frac{A_{zz}^{2}}{\hbar^{2}}\int_{0}^{\infty}S_{zz}(\omega)\frac{F(\omega
t)}{\pi\omega^{2}}d\omega,$ (13)

where $S_{zz}$ is the dynamical structure factor for the transverse field
fluctuations:

$S_{zz}(\omega)=\int_{0}^{\infty}\langle\sigma_{z}(\tau)\sigma_{z}(0)\rangle
e^{i\omega\tau}d\tau,$ (14)

and $F(x)=8\sin^{4}({x/4})$ is a filter function for the spin echo pulse
sequence, which takes into account the refocusing nature of the spin echo
$\pi$ pulse [28]. The spectral area, shown in Fig. 2(c), is proportional to
$L(t)$ at fixed $t$ corresponding to the pulse spacing in the spin echo
experiment. Because the hyperfine coupling in TmVO4 is solely along the
_transverse field_ direction, the nuclei are invisible to the longitudinal
degrees of freedom. Only $S_{zz}(\omega)$, the noise spectrum in the
transverse direction, contributes to the decoherence of the nuclear spins.
This anisotropic coupling is highly unusual, but it enables us to probe the
transverse fluctuations without any contamination from the longitudinal
fluctuations, which diverge strongly at the QCP. The filter function acts to
remove the static or low frequency ($\omega\leq 10^{5}$ Hz) components of the
fluctuations, which are dominated by thermal fluctuations [29, 19]. The
remaining contributions to $S_{zz}(\omega)$, and hence to the decay of $L(t)$,
is from quantum fluctuations, which exist at finite frequency. This is because
they arise from the intrinsic time evolution due to the many-body Hamiltonian,
which has a finite gap except at the QCP. The fact that $L(t)$ reaches a
minimum at the QCP indicates that these quantum fluctuations are largest here.
Importantly, these extend to finite temperature, even exceeding $T_{Q}$. These
results thus imply that there is a broad region of phase space, a ‘quantum
critical fan’, where quantum fluctuations are present.

Figure 3:  (Left) Transverse susceptibility as a function of field for a
simple cubic lattice at $T=0$ in mean-field theory and in 3D short-range
models. (Right) Temperature dependence of the transverse field susceptibility
at several different values of the transverse field calculated numerically for
small periodic clusters of the square-lattice. The dashed lines are the mean
field result, and the solid points of the same color are the results of
numerical calculations.

An open question is how does the _transverse_ susceptibility behave in the
vicinity of the quantum phase transition? In mean-field theory at $T=0$,
$\chi_{zz}$ remains constant in the ordered state, and vanishes for
$H_{c}>H_{c}^{*}$, as shown in Fig. 3(a). The NMR data are inconsistent with
the mean field picture, since the relative area under the spectra decreases
dramatically at the QCP, indicating that $\chi_{zz}$ must be strongly field-
dependent in this range. Numerical calculations that are based on high and low
field series expansions indicate that $\chi_{zz}$ diverges logarithmically on
both sides of the QCP for various 3D lattices [30]. At $T=0$ the enhancement
is in a very narrow region but it should widen into a quantum critical fan at
finite temperatures. Indeed we find significant differences between numerical
calculations for small finite clusters and mean field theory at finite
temperatures with enhancement in the general vicinity of the QCP, as seen in
Fig. 3(b). We expect the differences to be much larger and centered at the
critical point in the thermodynamic limit. These calculations, however, assume
only a nearest neighbor interaction (e.g. $J(l=l^{\prime})=0$ if
$l,l^{\prime}$ are not nearest neighbors in Eq. 6). The interaction is
expected to be long-range in TmVO4, which could tend to stabilize mean-field
behavior.

###  III.2 Fidelity Susceptibility

Understanding the mechanisms of decoherence is a key problem for quantum
computing, and the behavior of a central spin coupled to a well-controlled
environment is an important theoretical model that has been studied
extensively [31, 29]. In the case where the central spin (or qubit) is coupled
to a 1D TFIM via a hyperfine coupling along the transverse field direction,
the decoherence of the qubit can be elegantly expressed in terms of the
overlap of the wavefunction of the environment at different times and values
of the transverse field. In fact, the 51V spins coupled to the
ferroquadrupolar ordering in TmVO4 maps well to this model, but with a 3D
lattice for the environment [19]. Thus, TmVO4 offers a unique opportunity to
experimentally study the central spin model.

Importantly, this connection offers a new approach to understanding NMR
decoherence in terms of the quantum fidelity of the environment, which is
defined as the modulus of the overlap between two states:
$F=|\langle\Psi^{\prime}|\Psi\rangle|$. In the case of the central spin model,
the two states are $\Psi^{\prime}_{\lambda}(t=0)$ and
$\Psi_{\lambda+\epsilon}(t)$, where $\lambda$ corresponds to the transverse
field, and $\epsilon$ corresponds to the small hyperfine field. Two ground
states of the TFIM at different values of the transverse field may initially
be very similar, but will evolve strongly away from one another in the
vicinity of the QCP. At $T=0$, the intensity of the NMR free induction decay
is proportional to $F^{2}$, thus the qubit experiences a strong decoherence as
the transverse field approaches the critical value. This tendency can be
captured by the fidelity susceptibility:
$\chi_{F}=-{\partial^{2}F}/{\partial\epsilon^{2}}$. At finite temperatures,
the fidelity can be expressed in terms of the density matrix [29]. A related
quantity is the Quantum Fisher Information which quantifies the sensitivity of
density matrices to small changes in parameters [32]. Because the fidelity
susceptibility tends to diverge at a QCP, this quantity has been exploited
theoretically to identify quantum and topological phase transitions [33, 34].

On the surface, this picture differs from the conventional NMR picture in
which decoherence arises due to the presence of stochastic fluctuations of the
hyperfine field, which can be quantitatively measured via Bloch-Wangsness-
Redfield theory: $T_{2}^{-1}=A_{zz}^{2}S_{zz}(\omega=0)/2\hbar^{2}$ [35, 36,
37]. However, $\chi_{F}$ in fact can be related to the transverse field
susceptibility, $\chi_{zz}=S_{zz}/k_{B}T$ [38]. This remarkable connection
offers new insights and connections between NMR and quantum information
theory. For example, NMR wipeout is ubiquitous in strongly correlated systems,
and has been observed in the high temperature superconducting cuprates and the
iron based superconductors [39, 40, 41, 42, 43]. In these cases, this
phenomenon has been attributed to electronic inhomogeneity introduced because
of the dopant atoms. However, the behavior in TmVO4 suggests that it might be
valuable to considering the wipeout in these other systems as a consequence of
their proximity to a QCP.

##  IV NMR studies of Y substitution

Replacing Tm with Y suppresses the long range ferroquadrupolar order in
Tm1-xYxVO4 to zero at $x_{c}\approx 0.22$, as illustrated in Fig. 1(c) [20]. Y
has no $4f$ electrons and thus lacks any magnetic or quadrupolar moments, so
it acts to dilute the interactions between the Tm quadrupolar moments. The
rapid suppression with doping is surprising because mean-field theory predicts
a much weaker doping dependence: $T_{Q}\sim 1-x$. Y doping also suppresses
ferromagnetic order in LiHoF4, however in this case long-range order persists
until $x=0.95$ [44]. The reason for the difference between the TmVO4 and
LiHoF4 is that the Y creates strain fields that couple to the ferroquadrupolar
order in the former. Y is slightly larger than Tm, thus it creates local
distortions in the lattice that couple to the Tm quadrupolar moments [20].
This behavior is similar to that of a random field Ising model (RFIM), and
causes $T_{Q}$ to be suppressed much faster with Y doping [45]. The local
strain fields may have components with $B_{1g}$ symmetry, which couples to
$\sigma_{x}$ and is a transverse field, as well as fields with $B_{2g}$
symmetry, which couples to $\sigma_{y}$ and is a longitudinal field.

Y substitution offers an opportunity to test whether the decoherence observed
in the pure TmVO4 is due to quantum critical fluctuations. Fig. 2(c) shows
that for $x=0.40$, which has no long-range ferroquadruplar order, the relative
spectral area does not change significantly at $H_{c}^{*}$, in contrast to
$x=0$. This observation indicates that the quantum fluctuations are suppressed
in the $x=0.40$ sample.

Figure 4:  (a) Spectra for several values of $x$ measured in an external field
$H_{0}=1$ T oriented perpendicular to the c-axis at 1.8 K for all but the
$x=1$ case. For YVO4 the spectrum was measured at 4.5 T and 10 K, but has been
shifted to lower frequency by $\gamma\Delta H$ ($\Delta H=3.9$ T) to coincide
with the other spectra. The red dotted lines are fits as described in the
text. (b) and (c) Histograms of the hyperfine coupling constants, $A_{aa}$ and
$A_{cc}$, respectively, for a series of Y dopings for simulations as described
in the text. (d) Average $\langle A_{aa}\rangle$ and standard deviation,
$\sigma$, of the distributions shown in (b) as a function of Y doping, $x$.
(e) The measured Gaussian linewidth of the spectra shown in (a) as a function
of Y doping. The dashed red line was computed using the computed standard
deviation, as discussed in the text.

###  IV.1 NMR Spectra

NMR spectra in doped systems are generally broader than in undoped materials
because the dopants generally give rise to inhomogeneity. As seen in Fig.
4(a), the spectra of the pure TmVO4 and YVO4 consist of seven clear resonances
with small linewidths, but these resonances grow progressively broader with
doping. Each of the seven resonances broadens equally between $0\leq x\leq
0.1$. This behavior indicates that the broadening mechanism is not quadrupolar
inhomogeneity, but rather a Knight shift inhomogeneity. The red dotted lines
in Fig. 4(a) are fits to the spectra, and the data in panel (e) show how the
Gaussian width, $\sigma$, varies with doping for the spectra that can be
clearly fit. It is surprising that even though random strain fields are
clearly present and rapidly suppressing $T_{Q}$, they apparently do not
significantly alter the local EFG at the V sites. In many other strongly-
correlated systems, doping usually causes significant quadrupolar broadening
[46, 47, 48, 49]. In Tm1-xYxVO4, the larger Y atoms slightly displace the O
and V in their vicinity [20]. On the other hand, it is possible that the VO4
tetrahedra may not be significantly distorted upon Y substitution. Also, there
are two main contributions to the EFG: a lattice term arising from the
arrangement of charges, and an on-site term that is determined by the
electronic configuration of the local electronic orbitals [37]. It is
reasonable that the latter term dominates the EFG at the V, and that the
electronic configuration of the V and O orbitals remain relatively unperturbed
by Y doping.

Figure 5:  (a) Spectra of Tm1-xYxVO4 with $x=0.40$ for several different
values of $H_{c}$. For $H_{c}\gtrsim 1.5$ T, three peaks are discernable,
labelled $A$, $BA$, and $C$. (b) Computed spectra based on the histograms of
hyperfine couplings shown in Fig. 4(b,c) for several different values of
$H_{c}$ for $x=0.40$.

####  IV.1.1 Numerical simulations

To investigate the inhomogeneity of the magnetic environments, we computed the
direct dipolar hyperfine couplings, $A_{aa}$ and $A_{cc}$, to the V sites in a
$9\times 9\times 9$ superlattice in which a fraction of the Tm sites are
randomly removed. Histograms of these couplings are shown in Fig. 4(b,c) for
different Y concentrations. The sum is dominated by the two nearest neighbor
Tm sites along the c-axis direction (see Fig. 1(a)). The distribution for the
perpendicular direction ($A_{aa}$) broadens with doping, but does not exhibit
any structure. Fig. 4(d) shows how the mean, $\langle A_{aa}\rangle$, and
standard deviation, $\sigma_{hist}$, of the histograms vary with Y
concentration. The standard deviation increases linearly with doping, which
agrees with the experimental observation of the linewidth. The dashed red line
in Fig. 4(e) represents the expected magnetic linewidth in a field of
$H_{0}=1$ T, as in the experiment. This quantity is given by
$\sigma(x)|K|\gamma H_{0}/\langle A_{aa}\rangle$, where $K=-0.66\%$. Here we
have subtracted (in quadrature) the standard deviation of the histogram of the
pure TmVO4 case, which includes boundary effects:
$\sigma(x)=\sqrt{\sigma_{hist}^{2}(x)-\sigma_{hist}(0)^{2}}$. The simulated
linewidth agrees well with the measured linewidth, indicating that for low Y
concentrations the magnetic environment of the remaining Tm is not
significantly altered, despite the presence of the strain fields surrounding
the Y sites. At higher doping levels, the magnetic broadening becomes
comparable to the quadrupolar splitting, and the spectra become too broad to
extract any information.

####  IV.1.2 Effect of $c$-axis field

Fig. 5(a) shows how the spectra for the $x=0.40$ sample vary as the crystal is
rotated in a fixed field, similar to the data shown in Fig. 2(a) for the $x=0$
case. As $H_{c}$ increases, there is no significant wipeout at $H_{c}^{*}$, as
expected since there is no long range order at this doping level and therefore
no quantum critical behavior. The integrated area for these spectra are shown
in Fig. 2(c) as a function of $H_{c}$. However, there are three peaks that
emerge as $H_{c}$ increases beyond $\sim 1.5$ T, labelled $A$, $B$, and $C$,
that are not present in the undoped sample. In fact, these extra peaks are
consistent with the simulated histograms of the $c$-axis hyperfine couplings
shown in Fig. 4(c). The three peaks correspond to V sites with 0, 1 or 2
nearest neighbor Tm atoms, respectively.

As seen in Fig. 4(b) these different V sites should not be discernible for a
field $H_{0}\perp c$. On the other hand, as $\mathbf{H}_{0}$ rotates towards
the $c$-axis, three distinct peaks should emerge. This behavior is
demonstrated in Fig. 5(b), which displays the histograms of the Knight shift,
$K(\theta)=A_{aa}\chi_{aa}\sin^{2}\theta+A_{cc}\chi_{cc}\cos^{2}\theta$, for
several different values of $H_{c}=H_{0}\cos\theta$. Here
$\chi_{\alpha\alpha}$ is the static susceptibility, and we assume
$\chi_{cc}/\chi_{aa}=3$ for concreteness. The three sites are indeed
discernible for sufficiently large $H_{c}$, which agrees well with the
observations shown in panel (a). Moreover, the relative intensity of the peaks
($A:B:C=0.32:0.49:0.18$) also agrees well with the observed spectra
($0.33:0.51:0.16$). We therefore conclude that site $A$ corresponds to V with
2 n.n. Tm, site $B$ with 1 n.n. Tm, and site $C$ with 0 n.n. Tm. This property
enables us to learn about the electronic inhomogeneity by measuring the
relaxation at the different sites.

Figure 6:  (a) $(T_{1}T)^{-1}$ versus temperature for several different Y
doping levels, measured at $H_{0}=1$ T (except for the 100%, measured at 4.5
T), for $\theta=90^{\circ}$. In this case, all three sites overlap. This data
corresponds to the magnetic relaxation channel, as described in [50]. (b)
$(T_{1}T)^{-1}$ versus the c-axis field component, $H_{c}$, for the pure
TmVO4, and for the $A$ and $B$ sites in the 40% sample.

###  IV.2 Spin Lattice Relaxation Rate

Fig. 6(a) displays $(T_{1}T)^{-1}$ versus temperature for several different
doping levels, measured for field perpendicular to the $c$-axis. Note that for
this field orientation the resonance frequencies of sites $A$, $B$, and $C$
overlap, and thus we are unable to discern if these spin fluctuations are
spatially inhomogeneous. There is a clear peak for the pure TmVO4 at $T_{Q}$
reflecting the critical slowing down at the thermal phase transition. As the
doping level increases this peak is suppressed to lower temperatures, yet
$(T_{1}T)^{-1}$ increases and reaches a broad maximum around $x\approx 0.10$.
In fact, the spin fluctuations appear to be enhanced near the vicinity of the
critical doping level, $x_{c}$, possibly reflecting quantum critical
fluctuations at this doping. At higher doping levels, the fluctuations
gradually are suppressed and eventually disappear. For the pure YVO4, there
are no magnetic moments present anymore, and $(T_{1}T)^{-1}$ is several orders
of magnitude smaller.

Sites $A$, $B$ and $C$ can be discerned when there is a finite $H_{c}$
component present. Fig. 6(b) compares $(T_{1}T)^{-1}$ versus $H_{c}$ in pure
TmVO4 with Tm0.6Y0.4VO4 for the $A$ and $B$ sites. The strong field dependence
of the pure system reflects the growth of the gap as the system is tuned away
from the QCP at $H_{c}^{*}$: $(T_{1}T)^{-1}\sim\exp(-\Delta(H_{c})/T)$ [19].
As $H_{c}$ is tuned beyond the QCP, the gap increases and $(T_{1}T)^{-1}$
decreases. It is surprising that in the $x=0.40$ sample, which has no long
range order, the $A$ and $B$ sites exhibit behavior that is qualitatively
similar to that in the pure system. This behavior suggests that there are
still localized clusters of Tm which continue to exhibit behavior reminiscent
of the undoped lattice. Statistically there are regions of the disordered
lattice with connected Tm atoms, and these may continue to exhibit
correlations despite the absence of long-range order, giving rise to Griffiths
phases [51]. An interesting open question is how such disconnected clusters
may be affected by the presence of random strain fields.

Inhomogeneous dynamics in the disordered lattice may also explain the fact
that the spectra in Fig. 5(a) appear to exhibit an increasing intensity for
$H_{c}\gtrsim 1.5$ T once the $A$ and $B$ peaks emerge. If local clusters of
Tm continue to exhibit quantum critical fluctuations at these sites, then
$T_{2}^{-1}$ will be large, suppressing the signal from these sites. In other
words, the $A$ and $B$ sites may experience partial wipeout in the vicinity of
$H_{c}^{*}$. Overall these sites contribute $84\%$ of the total area, and the
relative area under the spectra decreases by approximately the same value near
$H_{c}^{*}$ in Fig. 2(c). These observations further support the argument that
the $A$ and $B$ sites are locally unperturbed by the Y dopants, and may
exhibit behavior consistent with quantum Griffiths phases.

##  V Conclusions

TmVO4 offers a unique new experimental platform to investigate quantum
critical phenomena, and to investigate the effects of doping. The unique
properties of the non-Kramers doublet in this system not only gives rise to
the unusual Ising ferroquadrupolar order, but also ensures that the nuclear
spins in this system only couple to the transverse field degrees of freedom.
Studies of the Tm1-xYxVO4 uncovered several unexpected results. First, despite
the presence of random strain fields, the EFG at the V sites remains
unperturbed, at least for low doping concentrations. As the doping level
increases and the long range ferroquadrupolar order vanishes, the spin lattice
relaxation rate for the V sites is enhanced, before decreasing for doping
levels that exceed the critical concentration. However, we find evidence that
quantum critical fluctuations remain present for V sites that belong to Tm-
rich clusters, even beyond the critical doping level, suggesting the presence
of quantum Griffiths phases in the Y-doped system. It is unclear whether such
isolated Tm clusters also experience random transverse or longitudinal strain
fields. Further studies of this doped system will shed important light on how
quantum fluctuations are destroyed by disorder.

## Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential
conflict of interest.

## Author Contributions

All crystals were synthesized by Y.L., M.Z. and I.R.F. NMR measurements were
conducted by Y-H.N, I.V. and C.C. Data analysis was carried out by I.V. and
N.J.C., and numerical calculations were carried out by R.R.P.S. The manuscript
was written by N.J.C. and edited by all co-authors.

## Funding

Work at UC Davis was supported by the NSF under Grants No. DMR-1807889 and
PHY-1852581, as well as the UC Laboratory Fees Research Program ID
LFR-20-653926. Crystal growth performed at Stanford University was supported
by the Air Force Office of Scientific Research under award number
FA9550-20-1-0252.

## Acknowledgments

We thank P. Klavins for support with cryogenic operations at UC Davis, and A.
Albrecht and R. Fernandes for enlightening discussions.

## References

  * Balakirev  _et al._ [2003] F. F. Balakirev, J. B. Betts, A. Migliori, S. Ono, Y. Ando, and G. S. Boebinger, Signature of optimal doping in Hall-effect measurements on a high-temperature superconductor, Nature 424, 912 (2003).
  * Coleman and Schofield [2005] P. Coleman and A. J. Schofield, Quantum criticality, Nature 433, 226 (2005).
  * Park  _et al._ [2006] T. Park, F. Ronning, H. Q. Yuan, M. B. Salamon, R. Movshovich, J. L. Sarrao, and J. D. Thompson, Hidden magnetism and quantum criticality in the heavy fermion superconductor CeRhIn5, Nature 440, 65 (2006).
  * Park  _et al._ [2008] T. Park, V. A. Sidorov, F. Ronning, J.-X. Zhu, Y. Tokiwa, H. Lee, E. D. Bauer, R. Movshovich, J. L. Sarrao, and J. D. Thompson, Isotropic quantum scattering and unconventional superconductivity, Nature 456, 366 (2008).
  * Shibauchi  _et al._ [2014] T. Shibauchi, A. Carrington, and Y. Matsuda, A quantum critical point lying beneath the superconducting dome in iron pnictides, Annu. Rev. Condens. Matter Phys. 5, 113 (2014).
  * Kuo  _et al._ [2016] H.-H. Kuo, J.-H. Chu, J. C. Palmstrom, S. A. Kivelson, and I. R. Fisher, Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors, Science 352, 958 (2016).
  * Lederer  _et al._ [2015] S. Lederer, Y. Schattner, E. Berg, and S. A. Kivelson, Enhancement of superconductivity near a nematic quantum critical point, Phys. Rev. Lett. 114, 097001 (2015).
  * Schuberth  _et al._ [2016] E. Schuberth, M. Tippmann, L. Steinke, S. Lausberg, A. Steppke, M. Brando, C. Krellner, C. Geibel, R. Yu, Q. Si, and F. Steglich, Emergence of superconductivity in the canonical heavy-electron metal YbRh2Si2, Science 351, 485 (2016).
  * Paschen and Si [2020] S. Paschen and Q. Si, Quantum phases driven by strong correlations, Nature Review Physics 3, 9 (2020).
  * Alloul  _et al._ [2009] H. Alloul, J. Bobroff, M. Gabay, and P. J. Hirschfeld, Defects in correlated metals and superconductors, Rev. Mod. Phys. 81, 45 (2009).
  * Seo  _et al._ [2014] S. Seo, X. Lu, J.-X. Zhu, R. R. Urbano, N. Curro, E. D. Bauer, V. A. Sidorov, L. D. Pham, T. Park, Z. Fisk, and J. D. Thompson, Disorder in quantum critical superconductors, Nat. Phys. 10, 120 (2014).
  * Massat  _et al._ [2022] P. Massat, J. Wen, J. M. Jiang, A. T. Hristov, Y. Liu, R. W. Smaha, R. S. Feigelson, Y. S. Lee, R. M. Fernandes, and I. R. Fisher, Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO4, Proc. Natl. Acad. Sci. 119, e2119942119 (2022).
  * Sachdev [2001] S. Sachdev,  _Quantum Phase Transitions_ (Cambridge University Press, 2001).
  * Knoll [1971] K. D. Knoll, Absorption and fluorescence spectra of Tm3+ in YVO4 and YPO4, Physica Status Solidi (B) 45, 553 (1971).
  * Bleaney and Wells [1980] B. Bleaney and M. R. Wells, Radiofrequency studies of TmVO4, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 370, 131 (1980).
  * Melcher [1976] R. L. Melcher, The anomalous elastic properties of materials undergoing cooperative Jahn Teller phase transisions (Elsevier, 1976) Chap. The anomalous elastic properties of materials undergoing cooperative Jahn Teller phase transisions, pp. 1–77.
  * Gehring and Gehring [1975] G. A. Gehring and K. A. Gehring, Co-operative Jahn-Teller effects, Rep. Prog. Phys. 38, 1 (1975).
  * Maharaj  _et al._ [2017] A. V. Maharaj, E. W. Rosenberg, A. T. Hristov, E. Berg, R. M. Fernandes, I. R. Fisher, and S. A. Kivelson, Transverse fields to tune an Ising-nematic quantum phase transition, Proc. Natl. Acad. Sci. 114, 13430 (2017).
  * Nian  _et al._ [2023] Y.-H. Nian, I. Vinograd, T. Green, C. Chaffey, P. Massat, R. R. P. Singh, M. P. Zic, I. R. Fisher, and N. J. Curro, Spin-echo and quantum versus classical critical fluctuations in TmVO4, arXiv:2306.13244 [cond-mat.str-el] (2023).
  * Li  _et al._ [2024] Y. Li, M. P. Zic, L. Ye, W. J. Meese, P. Massat, Y. Zhu, R. M. Fernandes, and I. R. Fisher, Disorder-induced local strain distribution in Y-substituted TmVO4, arXiv:2402.17049 [cond-mat.str-el] (2024).
  * Bitko  _et al._ [1996] D. Bitko, T. F. Rosenbaum, and G. Aeppli, Quantum critical behavior for a model magnet, Phys. Rev. Lett. 77, 940 (1996).
  * Melcher  _et al._ [1973] R. L. Melcher, E. Pytte, and B. A. Scott, Phonon instabilities in TmV${\mathrm{O}}_{4}$, Phys. Rev. Lett. 31, 307 (1973).
  * Washimiya  _et al._ [1970] S. Washimiya, K. Shinagawa, and S. Sugano, Effective Hamiltonian for non-Kramers doublets, Phys. Rev. B 1, 2976 (1970).
  * Vinograd  _et al._ [2022] I. Vinograd, K. R. Shirer, P. Massat, Z. Wang, T. Kissikov, D. Garcia, M. D. Bachmann, M. Horvatić, I. R. Fisher, and N. J. Curro, Second order Zeeman interaction and ferroquadrupolar order in TmVO4, npj Quantum Materials 7, 68 (2022).
  * Wang  _et al._ [2021] Z. Wang, I. Vinograd, Z. Mei, P. Menegasso, D. Garcia, P. Massat, I. R. Fisher, and N. J. Curro, Anisotropic nematic fluctuations above the ferroquadrupolar transition in TmVO4, Phys. Rev. B 104, 205137 (2021).
  * Schwab and Hillmer [1975] G. Schwab and W. Hillmer, Epr of non-kramers rare-earth ions in tetragonal crystals, physica status solidi (b) 70, 237 (1975).
  * Hoult and Richards [1976] D. Hoult and R. Richards, The signal-to-noise ratio of the nuclear magnetic resonance experiment, Journal of Magnetic Resonance (1969) 24, 71 (1976).
  * Cywiński  _et al._ [2008] Ł. Cywiński, R. M. Lutchyn, C. P. Nave, and S. D. Sarma, How to enhance dephasing time in superconducting qubits, Phys. Rev. B 77, 174509 (2008).
  * Chen  _et al._ [2013] S.-W. Chen, Z.-F. Jiang, and R.-B. Liu, Quantum criticality at high temperature revealed by spin echo, New J. Phys. 15, 043032 (2013).
  * Weihong  _et al._ [1994] Z. Weihong, J. Oitmaa, and C. J. Hamer, Series expansions for the 3D transverse Ising model at T=0, J. Phys. A: Math. Gen. 27, 5425 (1994).
  * Quan  _et al._ [2006] H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, Decay of Loschmidt echo enhanced by quantum criticality, Phys. Rev. Lett. 96, 140604 (2006).
  * Philipp Hauke and Zoller [2016] L. T. Philipp Hauke, Markus Heyl and P. Zoller, Measuring multipartite entanglement through dynamic susceptibilities, Nature Physics 12, 778 (2016).
  * König  _et al._ [2016] E. J. König, A. Levchenko, and N. Sedlmayr, Universal fidelity near quantum and topological phase transitions in finite one-dimensional systems, Phys. Rev. B 93, 235160 (2016).
  * Tang  _et al._ [2021] H.-K. Tang, M. A. Marashli, and W. C. Yu, Unveiling quantum phase transitions by fidelity mapping, Phys. Rev. B 104, 075142 (2021).
  * Wangsness and Bloch [1953] R. K. Wangsness and F. Bloch, The Dynamical Theory of Nuclear Induction, Phys. Rev. 89, 728 (1953).
  * Redfield [1957] A. G. Redfield, On the Theory of Relaxation Processes, IBM J. Res. Dev. 1, 19 (1957).
  * Slichter [1992] C. P. Slichter,  _Principles of Nuclear Magnetic Resonance_ , 3rd ed. (Springer-Verlag, 1992).
  * Gu [2010] S.-J. Gu, Fidelity approach to quantum phase transitions, Int. J. Mod Phys B 24, 4371 (2010).
  * Curro and Hammel [2000] N. Curro and P. Hammel, The Cu NMR echo decay in stripe ordered La1.65Eu0.2Sr0.15CuO4, Phys. C 341, 1797 (2000).
  * Curro  _et al._ [2000] N. Curro, P. Hammel, B. Suh, M. Hücker, B. Büchner, U. Ammerahl, and A. Revcolevschi, Inhomogeneous low frequency spin dynamics in La1.65Eu0.2Sr0.15CuO4, Phys. Rev. Lett. 85, 642 (2000).
  * Hunt  _et al._ [1999] A. Hunt, P. Singer, K. Thurber, and T. Imai, ${}^{63}Cu$ NQR measurement of stripe order parameter in La2-xSrxCuO4, Phys. Rev. Lett. 82, 4300 (1999).
  * Julien  _et al._ [2001] M.-H. Julien, A. Campana, A. Rigamonti, P. Carretta, F. Borsa, P. Kuhns, A. P. Reyes, W. G. Moulton, M. Horvatić, C. Berthier, A. Vietkin, and A. Revcolevschi, Glassy spin freezing and NMR wipeout effect in the high-$T_{c}$ superconductor La1.90Sr0.10CuO4 critical discussion of the role of stripes, Phys. Rev. B 63, 144508 (2001).
  * Dioguardi  _et al._ [2013] A. P. Dioguardi, J. Crocker, A. C. Shockley, C. H. Lin, K. R. Shirer, D. M. Nisson, M. M. Lawson, N. apRoberts Warren, P. C. Canfield, S. L. Bud’ko, S. Ran, and N. J. Curro, Coexistence of cluster spin glass and superconductivity in Ba(Fe1-xCox)2As2 for $0.060\leq x\leq 0.071$, Phys. Rev. Lett. 111, 207201 (2013).
  * Babkevich  _et al._ [2016] P. Babkevich, N. Nikseresht, I. Kovacevic, J. O. Piatek, B. Dalla Piazza, C. Kraemer, K. W. Krämer, K. Prokeš, S. Mat’aš, J. Jensen, and H. M. Rønnow, Phase diagram of diluted ising ferromagnet ${\mathrm{liho}}_{x}{\mathrm{y}}_{1-x}{\mathrm{f}}_{4}$, Phys. Rev. B 94, 174443 (2016).
  * Nattermann [1997] T. Nattermann, Theory of the random field ising model, in  _Spin Glasses and Random Fields_ (World Scientific, 1997) pp. 277–298.
  * Imai  _et al._ [1993] T. Imai, C. P. Slichter, K. Yoshimura, and K. Kosuge, Low frequency spin dynamics in undoped and Sr-doped La2CuO4, Phys. Rev. Lett. 70, 1002 (1993).
  * Lang  _et al._ [2010] G. Lang, H.-J. Grafe, D. Paar, F. Hammerath, K. Manthey, G. Behr, J. Werner, and B. Büchner, Nanoscale electronic order in iron pnictides, Phys. Rev. Lett. 104, 097001 (2010).
  * Kissikov  _et al._ [2016] T. Kissikov, A. P. Dioguardi, E. I. Timmons, M. A. Tanatar, R. Prozorov, S. L. Bud’ko, P. C. Canfield, R. M. Fernandes, and N. J. Curro, NMR study of nematic spin fluctuations in a detwinned single crystal of underdoped Ba(Fe2-xCox)2As2, Phys. Rev. B 94, 165123 (2016).
  * Menegasso  _et al._ [2021] P. Menegasso, J. C. Souza, I. Vinograd, Z. Wang, S. P. Edwards, P. G. Pagliuso, N. J. Curro, and R. R. Urbano, Hyperfine couplings as a probe of orbital anisotropy in heavy-fermion materials, Phys. Rev. B 104, 035154 (2021).
  * Vinograd  _et al._ [2021] I. Vinograd, S. P. Edwards, Z. Wang, T. Kissikov, J. K. Byland, J. R. Badger, V. Taufour, and N. J. Curro, Inhomogeneous Knight shift in vortex cores of superconducting FeSe, Phys. Rev. B 104, 014502 (2021).
  * Vojta [2019] T. Vojta, Disorder in quantum many-body systems, Annu. Rev. Conden. Ma. P. 10, 233 (2019).


# UniMC: A Unified Framework for Long-Term Memory Conversation via Relevance
Representation Learning

Kang Zhao, Wei Liu, Jian Luan, Minglei Gao, Li Qian, Hanlin Teng, Bin Wang
XiaoMi AI Lab
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
<EMAIL_ADDRESS>

###### Abstract

Open-domain long-term memory conversation can establish long-term intimacy
with humans, and the key is the ability to understand and memorize long-term
dialogue history information. Existing works integrate multiple models for
modelling through a pipeline, which ignores the coupling between different
stages. In this paper, we propose a Unified framework for Long-term Memory
Conversations (UniMC), which increases the connection between different stages
by learning relevance representation. Specifically, we decompose the main task
into three subtasks based on probability graphs: 1) conversation
summarization, 2) memory retrieval, 3) memory-augmented generation. Each
subtask involves learning a representation for calculating the relevance
between the query and memory, which is modelled by inserting a special token
at the beginning of the decoder input. The relevance representation learning
strengthens the connection across subtasks through parameter sharing and joint
training. Extensive experimental results show that the proposed method
consistently improves over strong baselines and yields better dialogue
consistency and engagingness.

##  1 Introduction

Open-domain dialogue systems aim to establish long-term connections with users
Huang et al. (2020). Current dialogue models based on pre-training Adiwardana
et al. (2020); Roller et al. (2021); Bao et al. (2021b); Gu et al. (2022)
perform well on conversational relevance and fluency, with the advantage of
capturing domain common sense and background knowledge. However, these models
can neither handle long-term conversational context nor establish long-term
connections with users.

Many studies on persona-based dialogue Li et al. (2016a); Zhang et al.
(2018a); Qian et al. (2018); Song et al. (2019) facilitate in-depth chat by
assigning profile information. These works mainly focus on the inconsistency
of chatbot persona and context. Nevertheless, the above works can only
consider the consistency of the chatbot’s persona but ignore the memory and
utilization of the user’s persona. In addition, these methods lack the long-
term persona ability Xu et al. (2022b). This ability requires understanding
and remembering long-term dialogue history information. After interacting with
a human, the chatbot can memorize and update the personas of the user and
itself, which is used appropriately to make the response more attractive and
maintain the consistency of the dialogues.

Figure 1: Our proposed framework (UniMC) for Open-Domain Long-Term Memory
Conversation.

Recent works have made addressed this issue. Xu et al. (2022a) propose a long-
term open-domain conversation task to advance research by constructing a
dataset. It builds retrieval-augmented generative models and read-write
memory-based models for modeling long-context. Nevertheless, its stored
memories are not updated. Xu et al. (2022b) constructed a multi-turn mutual
persona dialogue dataset and proposed a long-term memory conversation task, in
which they augmented dynamic summarization and memory updating. However, it
fails to summarize dialogue into persona but merely to classify sentences.
Moreover, these methods adopt the strategy of submodule execution, which a
different model implements, and ignore the coupling between these modules.

To address the issues discussed above, we propose a unified modeling
perspective that decomposes long-term memory conversation into related
subtasks. These subtasks learn the interconnections across tasks through
multi-task learning.

In addition, we propose a method to guide the execution of each subtask and
strengthen the connection across them by learning relevance representation. As
shown in Figure 1, we decompose the main task into three stages from a unified
perspective based on probability graphs: 1) Summarization: the model inputs
the context and outputs the memory that needs to be summarized. 2) Selection:
the model retrieves the relevant memory by matching the context with the
summary in the memory pool. 3) Generation: the model generates a response
through the retrieved memory and context. We add a special token for model’s
decoder input, which corresponds to the output representation as relevance
representation. This represents the relevance between the query and memory
pool proxy, which guides subsequent decoding or classification.

In summary, the main contributions of this paper can be summarized as follows:

  * •

We propose a unified framework with multi-task learning to compact historical
dialogue into memory, judge the relevance between the present query and the
memory, and use the relevant memory to generate a response for the present
query.

  * •

We enhance the connection across subtasks by using the same relevance
judgment, which can explicitly guide model outputs.

  * •

Extensive experimental results show that the proposed method outperforms
strong baselines and yields better dialogue consistency and engagingness.

##  2 Related Work

###  2.1 Persona-based dialogue

Persona-based dialogue generates consistent and attractive responses that
utilize profile information. The critical challenge is making the chatbot
exhibit a consistent personality to gain users’ trust and their long-term
confidence Huang et al. (2020). Early work encodes personas into distributed
embeddings Li et al. (2016a), using latent variables without explicit profile
descriptions, which makes generating engaging utterances challenging. In
recent years, Zhang et al. (2018b) propose a dialogue generation task
conditioned on explicit profile information and presented the PersonaChat
dataset, which made chit-chat more engaging. Yavuz et al. (2019) enables the
model to generate responses tailored to persona descriptions by extending the
pointer generator network See et al. (2017), which allows the decoder to
engage and replicate external knowledge hierarchically. Song et al. (2019)
propose a memory-augmented architecture to exploit persona information. It
combines a conditional variational autoencoder model to address the one-to-
many problem. Madotto et al. (2019) regard persona-based dialogue learning as
a meta-learning paradigm that can generate personalized responses using only a
few dialogue samples collected from the same user. Song et al. (2021)
decompose persona-based dialogue generation into response generation and
consistency understanding tasks, augmenting coherence constraints with
additional natural language inference data. However, these persona-based
dialogue methods’ personas are static and not summarized and memorized over
the dialogue. This paper proposes a unified modelling framework to support the
model’s ability to update and memorize persona.

###  2.2 Pre-trained Dialog Models

Pre-trained language models (PLM) perform very well on many tasks Radford et
al. (2018); Devlin et al. (2019); Raffel et al. (2020); Lewis et al. (2020);
Shao et al. (2021), which proves that fine-tuning PLM can yield better
performance than training from scratch. Due to the discrepancy between the
dialogue corpus and the general document, much work on pre-trained dialog
models has recently emerged Adiwardana et al. (2020); Roller et al. (2021);
Zhou et al. (2021); Gu et al. (2022). Zhang et al. (2020) proposed DialoGPT to
overcome bland and uninformative response generation through mutual
information maximization training. Bao et al. (2020) proposed PLATO, a pre-
training dialog model based on discrete latent variables, to solve the one-to-
many problem. And then proposed to use curriculum learning Bao et al. (2021a)
and larger-scale pre-training model Bao et al. (2021b) to improve the model’s
performance. Chen et al. (2022) introduces continuous latent variables in an
enhanced transformer pre-training framework to increase the correlation and
diversity of responses. Recently, some works Thoppilan et al. (2022) have
explored models with larger parameter scales and also tried to incorporate
more external knowledge to enhance the dialogue. However, most of these models
do not possess long-term conversation capacity. In this paper, we increase the
long-term ability to interact with users based on pre-training models.

##  3 Methodology

###  3.1 Task Decomposition

Following Xu et al. (2022b), we first formalize the long-term memory
conversation task definition. Given a dialog context:
$c=\\{u_{1},b_{1},u_{2},b_{2},\dots,u_{t-1},b_{t-1}\\}$ and a query $q=u_{t}$,
where $u$ and $b$ represent the user and the chatbot, and $c$ may contain many
sessions. Long-term memory conversation aims to predict response $b_{t}$ based
on long-session dialogue, with the formula $P(b_{t}|x)$, where $x=[c;q]$.

A complete long-term memory conversation model should be able to find relevant
memories, generate reasonable responses based on relevant memories, and make
timely memory updates by summarization. To model long-term chat between the
user and chatbot, we decompose the task into three stages by Bayes’ rule:

$\displaystyle P(b_{t}|x)\propto
P(m|x_{1})P(z|x_{2},m^{\prime})P(b_{t}|x_{2},m^{\prime},z),$ (1)

where $x=[x_{1};x_{2}]$ is divided into historical sessions $x_{1}$ and
current session $x_{2}$, $z$ represents the relevance between memory and
query. $m^{\prime}\in\mathrm{M}_{u}\cup\mathrm{M}_{b}$ represents query-
relevant memories. Each speaker has a corresponding memory pool $\mathrm{M}$,
consisting of a series of persona descriptions $m$. These persona descriptions
are summaries of the speaker’s historical sessions. We define
$\mathrm{M}_{u}=\\{m^{u}_{1},m^{u}_{2},\dots,m^{u}_{m}\\}$ and
$\mathrm{M}_{b}=\\{m^{b}_{1},m^{b}_{2},\dots,m^{b}_{n}\\}$ to represent the
persona memory pool of user and chatbot, respectively. We expect $z$ also to
guide the model to generate responses consistent with memory.

We interpret the first term in Eq.1 as a conversation summarization task, the
second as a memory retrieval task, and the last as a memory-augmented
generation task. Its corresponds to the three stages of summarization,
selection, and generation. The intuition behind the decomposition is that for
a complete dialogue modeling between the user and the chatbot, $x$ may contain
many rounds of conversation or multiple sessions. For long-term conversational
context, the model needs to summarize the dialogues from the current session,
recall (retrieve) them appropriately, and reply based on the retrieved
content.

Figure 2: UniMC for the conversation summarization task, the token [M] is
memory pool proxy token at the encoder. The first token [CLS] at the decoder
is used to introduce relevance representation, and the second token [CMP] is
used to generate the summary.

###  3.2 Framework

We model the long-term memory conversation task based on the Transformer
Vaswani et al. (2017), where the encoder encodes the context and memory, and
the decoder is used for three stages: Conversation Summarization, Memory
Retrieval and Memory-Augmented Generation. The three stages are unified in
form and share the same model parameters.

##### Encoder

Given the context $c$, we encode the context through the Transformer Encoder,
where the role token is inserted into each utterance to distinguish the user
and chatbot. Similarly, the input of persona memory is also distinguished by
inserting role tokens, and [M] is inserted at each starting position to
represent the memory input. The corresponding output $h^{[M]}$ of [M] at the
encoding end is called the memory pool proxy. When only [M] is encoded, it
represents a pattern of all memories. When specific memories is encoded
together, it represents the specific pattern of these memories.

We use Fusion-in-Decoder (FiD) Izacard and Grave (2020) for memory
integration, and conduct ablation for the Fusion-in-Encoder (FiE). The latter
is to concatenate the context and memory and feed it into the encoder, which
belongs to the concatenation of text.

##### Decoder

According to the task decomposition, we insert a special token [CLS] into the
starting position of each subtask to encode the relevance representation. In
order to distinguish different generation tasks, we insert special tokens
[CMP] or [GNR] to represent the decoding of summarization or response
generation.

####  3.2.1 Conversation Summarization

Figure 3: UniMC for the memory retrieval task, which the decoder input only
contain one token [CLS].

Acquiring memory from context can be viewed as a conversation summarization.
Given the context $c=\\{u_{1},b_{1},\dots,u_{t-1},b_{t-1}\\}$ and query
$u_{t}$, the model output the persona memory $m$. In Eq.1, we mentioned that
the relevance representation represents the semantic association of the query
and memory. As shown in Figure 2, we further introduce the memory pool proxy
token [M]:

$\displaystyle P(m|x)=P(z|x)P(m|x,z),$ (2)

where $z$ contains the relevance between memory pool proxy and query,
$x=\\{[\mathrm{M}];u_{1},b_{1},\dots,u_{t-1},b_{t-1},u_{t}\\}$ is model input.

The memory pool proxy token is viewed as an abstract summary that represents
the abstract pattern of all persona memories. We compute
$p(z|x,\mathrm{[M]},w_{0})=softmax(\mathrm{MLP}(h_{z}))$ as a binary
classification task by decoding the relevance representation $h_{z}$ at the
first start token $w_{0}=\mathrm{[CLS]}$ of the decoder. If the current query
$u_{t}$ is related to the pattern, then the query and context can be compacted
into a summary, in which the relevance label $y_{cs}$ is 1; otherwise, it is
0.

We start decoding the sequence at the second token
$P(m|x,z)={\textstyle\prod_{t=1}^{|m|}}p(w_{t}|x,z,w_{<t})$, where
$w_{0}=[\mathrm{CMP}]$ is interpreted as the task identifier. Finally, we
minimize the negative log-likelihood loss for conversation summarization:

$\displaystyle\mathcal{L}_{cs}=$ $\displaystyle-\mathrm{log}P(m|x).$ (3)

####  3.2.2 Memory Retrieval

In Eq. 1, the memory retrieval can be modeled as a sentence pair
classification task, which judge the relevance between the current query and
the memory. As suggested by Xu et al. (2022b), the memory in each training
sample can be divided into positive persona memory and negative persona
memory.

The positive memory is defined as the persona used in the current user’s
utterances and the bot’s responses (both bot persona and user persona observed
by the bot). In contrast, the negative memory is the remaining persona in the
current session. As shown in Figure 3, given a context $c$, query $u_{t}$ and
sample a summary $m$ from the memory pool $\mathrm{M}$, we learn the relevance
representation at the first starting token of the decoder:

$\displaystyle\mathcal{L}_{mr}=$ $\displaystyle-\mathrm{log}P(z|x,m).$ (4)

where $P(z|x,m)=P(z|x,m,w_{0})$, $w_{0}=\mathrm{[CLS]}$ is the start token of
the decoder input. Similar to the relevance judgment in conversation
summarization, the label is determined based on whether the persona $m$ is
positive or negative. Note that $m$ represents just one persona, randomly
sampled from both positive and negative personas, and the token [M] is
inserted at the starting position of each $m$.

####  3.2.3 Memory-Augmented Generation

Figure 4: UniMC for the memory-augmented generation task, the first token
[CLS] at the decoder input for modelling relevance representation, and the
second token [GNR] generates the response.

In the memory-augmented generation, we use the retrieved memory as external
information to generate a more realistic reply. Similar to what is mentioned
before, relevance representation also guides response generation. However, in
the actual situation, not all of the memories retrieved from the large-scale
memory pool may be relevant to the current conversation round. To address this
issue, we add some noise to the retrieved memories by randomly introducing
some negative memories. This allows the relevance representation to decide
whether to use these memories, which can alleviate the problem of overrecall.
The task is then constrained with a classification:

$\displaystyle P(b_{t}|x,m)=P(z|x,m)P(b_{t}|x,m,z),$ (5)

unlike the retrieval task, there may be multiple summaries $m$ introduced
here. If $m$ is all composed of negative memories, the relevance label is 0;
otherwise, it is 1. The
$P(b_{t}|x,m,z)={\textstyle\prod_{t=1}^{|b_{t}|}}p(w_{t}|x,m,z,w_{<t})$ is
then trained using a negative log-likelihood loss, and $w_{0}=[\mathrm{GNR}]$
is interpreted as the task identifier. The complete loss can be written as:
$\mathcal{L}_{mag}=-\mathrm{log}P(b_{t}|x,m)$, mag = "memory augmented
generation".

We train these three subtasks simultaneously for the entire long-term memory
conversation. Furthermore, each subtask contains the judgment between query
and summary, which strengthens the connection across different tasks during
training. Our final training loss is:

$\displaystyle\mathcal{L}=$ $\displaystyle-
logP(b_{t}|c)=\mathcal{L}_{cs}+\mathcal{L}_{mr}+\mathcal{L}_{mag}.$ (6)

###  3.3 Inference

We store all memory into a memory pool
$\mathrm{M}=\mathrm{M}_{u}\cup\mathrm{M}_{b}$ and treat it as the long-term
memory of the model. In the inference phase, the model first Retrieval the
memory pool: performs retrieval tasks based on the memory pool and the given
context and query, then takes top-k as the relevant memory according to
logits. Then, Generation: performs the memory-augmented generation based on
the context and associated memory. Finally, Summarization: perform the
conversation summarization according to the context and query, extract the
memory of the user and chatbot, respectively. The encoder encodes each memory,
and the representation corresponding to the first start token [M] is taken as
the memory vector and then written according to the cosine similarity:

$\displaystyle s=cos(h_{m_{i}}^{[M]},h_{m_{j}}^{[M]}),$ (7)

where $m_{i}\in\mathrm{M}$ and $m_{j}$ is the memory that the model summarizes
from the context. When $s>\lambda$, we replace $m_{i}$ in $\mathrm{M}$ by
$m_{j}$, otherwise store $m_{i}$ directly into $m_{j}$, where $\lambda$ is a
duplicate check threshold.

##### Explicitly Guided Decoding

The decoded tokens are implicitly influenced by relevance representation for
the conversation summarization and memory-augmented generation subtasks.
However, relevance representation can represent memory-related semantic
information of the decoded text.

To discover the role of relevance representation, we propose an explicitly
guided decoding by relevance representation method (EG), which improves the
generation performance by explicitly guiding the decoding process:

$\displaystyle w_{t}=\underset{w\in
V^{(k)}}{\arg\max}\\{p\left(w|w_{<t}\right)+\alpha\cdot p(w|h_{z})\\},$ (8)

where $p\left(w|w_{<t}\right)$ is the probability that the model generates the
next token.

##  4 Experiments

###  4.1 Datasets

Our experiments are conducted on DuLeMon Xu et al. (2022b), the largest
dataset of multi-turn Chinese mutual persona chats currently available.
DuLeMon consists of two parts, DuLeMon-SELF and DuLeMon-BOTH. In DuLeMon-SELF,
the bot only knows its persona, while in DuLeMon-BOTH, the bot also knows part
of the user’s persona.

###  4.2 Evaluation Metrics

##### Automatic evaluation Metrics

The BF1 and Rouge Lin (2004) are used to evaluate the conversation
summarization. The BF1(%) denotes the harmonic mean of the precision and
recall. It evaluates whether the model recognizes a persona in the context
that needs to be summarized. Following Xu et al. (2022b), we use AUC and
Recall@k to evaluate the ability of persona memory retrieval. The PPL, BLEU
Papineni et al. (2002), F1(%), DISTINCT-1/2 Lin et al. (2020), and the model-
based BERTScore Zhang et al. (2019) are used to evaluate generated and human-
annotated reference responses.

##### Human Evaluation Metrics

In human evaluation, we use three utterance-level measures: coherence,
consistency, and engagingness. The metrics is similar to previous research Xu
et al. (2022b), but we score coherence and consistency on a scale from 0 to 1.
For engagingness, we have a different definition. This better reflects the
plausibility of the generated responses. Four crowdsourced workers evaluate
each response, and a higher score indicates better quality.

Our discussion for these three metrics are shown in Appendix A.

Model | Backbone | BF1 | Rouge-1/2/L
---|---|---|---
UniMC | CPT-base | 86.32 | 0.675/ 0.480/ 0.663
UniMC | CPT-large | 87.40 | 0.787/ 0.658/ 0.782
Table 1: Experimental results of different summarization methods.

###  4.3 Baselines

We evaluate UniMC and several strong baselines on DuLeMon for comparison:

  * •

EVA 2.0 Gu et al. (2022): EVA2.0 is a state-of-the-art Chinese dialogue
generation model.

  * •

EVA2.0-FT: The EVA2.0 model is fine-tuned on the DuLeMon dataset.

  * •

CPT-FT: The CPT model Shao et al. (2021) fine-tuned on DuLeMon dataset. CPT is
a Chinese pre-trained unbalanced transformer model.

  * •

UniMC: UniMC is our proposed relevance representation-based unified modelling
framework for long-term memory conversation.

###  4.4 Training Details

The large-scale model (CPT-large and EVA2.0-xlarge) is first pre-trained
during training, where the pre-trained corpus is the DuLeMon-SELF training
set. Then, the model is finetuned, and the finetuned corpus is the DuLeMon-
BOTH train set. The pre-trained checkpoints are chosen based on the perplexity
of the DuLeMon-SELF validation set. More details of the model are shown in
Appendix B.

###  4.5 Results and Discussion

####  4.5.1 Results of conversation summarization

We evaluate the models on the test set to measure the performance of different
models on conversation summarization. We use the user persona (unseen) in the
test set as a positive sample of the need to summarize and other dialogues
that do not need to summarize memory as negative cases. The samples that need
to be summarized and those that are not required are 183 and 162,
respectively.

As shown in table 1, we can see that the BF1 score exceeds 87.4%, which shows
that our method effectively identifies whether the dialogue can is compacted
into a summary. Other metrics are to evaluate how well the summary matches the
reference persona. It can be seen that the CPT-large model consistently
outperforms the CPT-based model due to the larger amount of parameters. The
experimental results show that the UniMC can effectively extract persona
information from the dialogue.

####  4.5.2 Results of Memory Retrieval

In comparing different memory retrieval models, we added the CPM baseline Xu
et al. (2022b), a rank model and reported the metrics on the test set. Table 2
shows results that comparison of different baselines on the retrieval task. We
find that the UniMC consistently outperform CPM, which UniMC(CPT-large)
outperforms CPM by 7% and 10% on AUC and Recall@5, indicating that our unified
modeling approach demonstrates significant advantages. The experimental
results show that our method efficiently retrieves context-related persona.

####  4.5.3 Results of Memory-Augmented Generation

On the memory-augmented generation, we compare UniMC and direct fine-tuning
with different baselines. Table 3 shows the comparison results of different
models, in which the results of PLATO-FT are copied from the original paper Xu
et al. (2022b). From these results, we can draw several conclusions:

Model | Backbone | AUC | Recall@5
---|---|---|---
CPM† | ERNIE | 0.76 | 0.83
UniMC | CPT-base | 0.80 | 0.91
UniMC | CPT-large | 0.83 | 0.93
Table 2: Comparison of different memory retrieval models. The result CPM
†copied from the original paperXu et al. (2022b).

1) In the experimental results of different backbone fine-tuning, it can be
seen that the performance of different backbones significantly differs. In the
perplexity metric, this cannot be compared due to the differences in
vocabulary and tokenization. However, in terms of other automatic evaluation
indicators, the dialogue generation based on CPT fine-tuning is the best. It
shows that the pre-trained model that considers understanding and generation
may be better than other pre-trained dialog models in long-term memory
conversation.

Model | Backbone | PPL | BLUE-1/2 | DISTINT-1/2 | F1 | BERTScore
---|---|---|---|---|---|---
PLATO-FT † | PLATO-2 | 9.38 | 0.194/0.087 |  0.068/0.296 | 22.61 | -
EVA2.0-FT | EVA2.0-base | 21.16 | 0.145/0.050 | 0.042/0.167 | 18.38 | 0.6215
CPT-FT | CPT-base | 15.31 | 0.230/0.096 | 0.055/0.243 | 24.63 | 0.6394
EVA2.0-FT | EVA2.0-xlarge | 13.95 | 0.179/0.088 | 0.044/0.170 | 18.69 | 0.6272
CPT-FT | CPT-large | 12.39 |  0.243/0.102 | 0.057/0.249 | 25.81 | 0.6449
UniMC | EVA2.0-xlarge | 13.61 | 0.174/0.064 | 0.065/0.259 | 20.27 | 0.6336
UniMC | CPT-base | 13.72 | 0.209/0.086 |  0.102/0.392 | 25.38 | 0.6399
UniMC | CPT-large | 9.54 |  0.217/0.090 | 0.084/0.339 | 26.14 | 0.6422
Table 3: Experimental results of the automatic evaluation for response
generation and long-term memory conversation. The first five models are fine-
tuned based on backbones without the capability of long-term memory
conversation, so these methods cannot be directly compared with other long-
term memory conversation models. We bold the best results in different
scenarios, respectively. Perplexity (PPL) is not comparable between models due
to the differences in vocabulary and tokenization. The result PLATO-FT †copied
from the original paperXu et al. (2022b).

2) In the model comparison with large-scale parameters, UniMC based on CPT-
large performs better than EVA2.0-xlarge and has fewer parameters than
EVA2.0-xlarge. This result on automatic metrics further illustrates that non-
dialog domain-specific pre-trained models seem to perform better on this task
than pre-trained dialog models. This result is somewhat similar to the
conclusion in Zheng and Huang (2021) because we insert some special tokens on
the decoder input to encode relevance representations and distinguish between
different tasks.

The experimental results in Table 3 show that UniMC based on CPT-large
performs better on most automatic metrics. Therefore, CPT-large-based UniMC is
used for our subsequent human evaluation.

###  4.6 Human Evaluation

Automatic metrics are limited in evaluating open-domain dialogue tasks Liu et
al. (2016). To further validate the model’s performance, we conduct a self-
chat evaluation. Self-chats are widely used in evaluating dialogue systems Li
et al. (2016b); Roller et al. (2021); Bao et al. (2021a); Xu et al. (2022b),
where the model plays the roles of both parties in the dialogue. Following Xu
et al. (2022b), we use the proposed UniMC as a user simulator and ask all
chatbots to chat for better control over variables. Crowdsourcing workers only
evaluate the responses generated by the chatbot and not the user simulator.
Details are as follows.

Each chatbot chats with the user simulator for ten episodes, each episode
contains four long sessions, and each session contains 16 rounds. As described
in Xu et al. (2022b), we do not impose any restrictions on a chat other than
specifying session openings. Some conversation openings are pre-selected from
the DuLeMon test set. These openings are used to start an interactive
conversation and ask the two bots to perform a chat in a given context. Table
4 presents the result, from which we can draw several conclusions:

1) The unified modeling method can significantly improve the coherence and
engagingness of the dialogue. Regarding dialogue coherence and engagingness,
the model achieves scores of 0.796 and 0.824, which are substantially better
than the baseline model EVA2.0. UniMC is 0.058 and 0.263 higher than CPT-FT on
these two metrics, which indicates that our method can improve the model’s
dialogue performance and attract users to chat for multiple rounds. In
addition, CPT-FT outperforms EVA2.0-FT on these two metrics, indicating that
non-dialogue pre-trained models may be more effective for fine-tuning.

2) The unified modeling method can significantly improve dialogue consistency.
In the evaluation, consistency needs to consider context consistency and
persona consistency. EVA2.0 is more consistent than the fine-tuned EVA2.0. It
is possible that direct fine-tuning makes it difficult for the model to
maintain persona consistency in long-term dialogue. UniMC is more consistent
than EVA2.0 and CPT-FT, showing that unified modeling of different subtasks
can improve dialogue consistency.

Model | Coherence | Consistency | Engagingness
---|---|---|---
EVA2.0 | 0.703 | 0.681 | 0.561
EVA2.0-FT | 0.672 | 0.609 | 0.638
CPT-FT | 0.738 | 0.606 | 0.647
UniMC | 0.796 | 0.740 | 0.824
UniMC w/o EG | 0.790 | 0.699 | 0.727
Table 4: Comparison of human evaluation metric results for self-chat dialogues between UniMC and baselines. The parameter sizes of EVA 2.0 and CPT are xlarge and large, respectively. The ‘EG’ represents that explicitly guided decoding strategies by relevance representation. Model | Generation | Retrieval | Summarization
---|---|---|---
F1 | BERTScore | AUC | Recall@5 | BF1 | Rouge-1 | Rouge-2 | Rouge-L
UniMC | 25.38 | 0.6399 | 0.80 | 0.91 | 86.32 | 0.675 | 0.480 | 0.663
w/o EG | 24.72 | 0.6370 | 0.80 | 0.91 | 84.49 | 0.667 | 0.491 | 0.655
w/o RR | 24.55 | 0.6364 | 0.78 | 0.90 | 82.29 | 0.638 | 0.452 | 0.629
FiD $\to$ FiE | 25.31 | 0.6370 | 0.82 | 0.92 | 80.53 | 0.668 | 0.481 | 0.656
diff [CLS] | 24.15 | 0.6348 | 0.79 | 0.90 | 85.07 | 0.663 | 0.475 | 0.651
diff decoder | 24.91 | 0.6380 | 0.82 | 0.92 | 82.92 | 0.680 | 0.482 | 0.667
Table 5: Ablation studies result of UniMC. ‘EG’ and ‘RR’ denotes explicitly
guided decoding and relevance representation, respectively. FiD$\to$ FiE
denotes the method of integrating memory is converted from Fusion-in-Decoder
to Fusion-in-Encoder. ‘diff [CLS]’ denotes different tokens are used as the
beginning of the decoder input. ‘diff decoder’ denotes decoder parameters are
not shared.

3) Explicitly guided decoding can significantly improve the performance of the
model. UniMC can achieve scores of 0.796, 0.740, and 0.824 than without EG in
coherence, consistency, and attractiveness. Experimental results show that
introduced relevance representation may contain higher-level semantic
information, which prove our proposed method’s effectiveness and potential.
Moreover, we show some cases in Appendix C to help illustrate the
effectiveness of our model.

##  5 Ablation Study

To further analyze the effectiveness of different components, we conduct
ablation studies. The results of the ablation study are shown in Table 5,
where our backbone adopts CPT-base.

First, we remove EG when decoding, which the model’s performance has decreased
to varying degrees on the memory-augmented generation and dialogue
summarization tasks. These experiments show that explicitly guided decoding
can improve the quality of model generation, especially in conversation
summarization, where it can significantly increase n-gram recall. Second, we
no longer model relevance representations and instead guide each task with a
different token. Most metrics drop significantly on the three tasks, which
illustrates the importance of relevance representation learning. Next, we
replace the memory integration method from FiD to FiE and observe that, while
the retrieval task shows some improvement, other metrics have declined. Its
shows the advantage of FiE in modelling long texts. Finally, we use different
start tokens to model the relevance representation for each task. Using the
same token is more advantageous than this method because the same token
modelling can further facilitate connections between tasks. Additionally, we
conducted different tasks with different decoders, which increased the number
of model parameters. The experimental results show that compared to the shared
decoder method, there was not much performance improvement, which shows that
our multi-task entire parameter sharing method is effective.

##  6 Conclusions and Future Work

This paper proposes a unified framework for long-term memory conversation,
mainly by introducing relevance representation for multi-task learning.
Specifically, we decompose the main task into three subtasks and model each
subtask with the same model. In addition, we insert a specific token into the
decoder input to learn a relevance representations, which is used to guide the
model’s output. Our approach can better generate appropriate responses and
enables a model to master retrieval and summarization simultaneously.
Extensive experiments demonstrate the effectiveness of UniMC. Additional human
evaluations show the advantages of UniMC. UniMC has limitations in terms of
interpretability and cannot provide reasons for why specific memories are used
when generating responses, despite the fact that we use a sampling-based
training strategy. In the future, we will attempt to fuse neural-symbolic
systems with pre-trained models, making the model logical and explainable in
dialogue.

## References

  * Adiwardana et al. (2020) Daniel Adiwardana, Minh-Thang Luong, David R. So, Jamie Hall, Noah Fiedel, Romal Thoppilan, Zi Yang, Apoorv Kulshreshtha, Gaurav Nemade, Yifeng Lu, and Quoc V. Le. 2020.  Towards a human-like open-domain chatbot.  _CoRR_ , abs/2001.09977.
  * Bao et al. (2020) Siqi Bao, Huang He, Fan Wang, Hua Wu, and Haifeng Wang. 2020.  Plato: Pre-trained dialogue generation model with discrete latent variable.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 85–96.
  * Bao et al. (2021a) Siqi Bao, Huang He, Fan Wang, Hua Wu, Haifeng Wang, Wenquan Wu, Zhen Guo, Zhibin Liu, and Xinchao Xu. 2021a.  Plato-2: Towards building an open-domain chatbot via curriculum learning.  In _Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021_ , pages 2513–2525.
  * Bao et al. (2021b) Siqi Bao, Huang He, Fan Wang, Hua Wu, Haifeng Wang, Wenquan Wu, Zhihua Wu, Zhen Guo, Hua Lu, Xinxian Huang, et al. 2021b.  Plato-xl: Exploring the large-scale pre-training of dialogue generation.  _arXiv preprint arXiv:2109.09519_.
  * Chen et al. (2022) Wei Chen, Yeyun Gong, Song Wang, Bolun Yao, Weizhen Qi, Zhongyu Wei, Xiaowu Hu, Bartuer Zhou, Yi Mao, Weizhu Chen, et al. 2022.  Dialogved: A pre-trained latent variable encoder-decoder model for dialog response generation.  In _Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 4852–4864.
  * Devlin et al. (2019) Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019.  BERT: Pre-training of deep bidirectional transformers for language understanding.  In _Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)_ , pages 4171–4186, Minneapolis, Minnesota. Association for Computational Linguistics.
  * Gu et al. (2022) Yuxian Gu, Jiaxin Wen, Hao Sun, Yi Song, Pei Ke, Chujie Zheng, Zheng Zhang, Jianzhu Yao, Xiaoyan Zhu, Jie Tang, et al. 2022.  Eva2. 0: Investigating open-domain chinese dialogue systems with large-scale pre-training.  _arXiv preprint arXiv:2203.09313_.
  * Huang et al. (2020) Minlie Huang, Xiaoyan Zhu, and Jianfeng Gao. 2020.  Challenges in building intelligent open-domain dialog systems.  _ACM Transactions on Information Systems (TOIS)_ , 38(3):1–32.
  * Izacard and Grave (2020) Gautier Izacard and Edouard Grave. 2020.  Leveraging passage retrieval with generative models for open domain question answering.  _arXiv preprint arXiv:2007.01282_.
  * Kingma and Ba (2015) Diederik P. Kingma and Jimmy Ba. 2015.  Adam: A method for stochastic optimization.  In _3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings_.
  * Lewis et al. (2020) Mike Lewis, Yinhan Liu, Naman Goyal, Marjan Ghazvininejad, Abdelrahman Mohamed, Omer Levy, Veselin Stoyanov, and Luke Zettlemoyer. 2020.  Bart: Denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 7871–7880.
  * Li et al. (2016a) Jiwei Li, Michel Galley, Chris Brockett, Georgios Spithourakis, Jianfeng Gao, and Bill Dolan. 2016a.  A persona-based neural conversation model.  In _Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 994–1003, Berlin, Germany. Association for Computational Linguistics.
  * Li et al. (2016b) Jiwei Li, Will Monroe, Alan Ritter, Michel Galley, Jianfeng Gao, and Dan Jurafsky. 2016b.  Deep reinforcement learning for dialogue generation.
  * Lin (2004) Chin-Yew Lin. 2004.  ROUGE: A package for automatic evaluation of summaries.  In _Text Summarization Branches Out_ , pages 74–81, Barcelona, Spain. Association for Computational Linguistics.
  * Lin et al. (2020) Zhaojiang Lin, Zihan Liu, Genta Indra Winata, Samuel Cahyawijaya, Andrea Madotto, Yejin Bang, Etsuko Ishii, and Pascale Fung. 2020.  Xpersona: Evaluating multilingual personalized chatbot.  _CoRR_ , abs/2003.07568.
  * Liu et al. (2016) Chia-Wei Liu, Ryan Lowe, Iulian Serban, Michael Noseworthy, Laurent Charlin, and Joelle Pineau. 2016.  How NOT to evaluate your dialogue system: An empirical study of unsupervised evaluation metrics for dialogue response generation.  In _Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, EMNLP 2016, Austin, Texas, USA, November 1-4, 2016_ , pages 2122–2132. The Association for Computational Linguistics.
  * Madotto et al. (2019) Andrea Madotto, Zhaojiang Lin, Chien-Sheng Wu, and Pascale Fung. 2019.  Personalizing dialogue agents via meta-learning.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 5454–5459.
  * Ott et al. (2019) Myle Ott, Sergey Edunov, Alexei Baevski, Angela Fan, Sam Gross, Nathan Ng, David Grangier, and Michael Auli. 2019.  fairseq: A fast, extensible toolkit for sequence modeling.  In _Proceedings of NAACL-HLT 2019: Demonstrations_.
  * Papineni et al. (2002) Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. 2002.  Bleu: a method for automatic evaluation of machine translation.  In _Proceedings of the 40th Annual Meeting of the Association for Computational Linguistics, July 6-12, 2002, Philadelphia, PA, USA_ , pages 311–318. ACL.
  * Qian et al. (2018) Qiao Qian, Minlie Huang, Haizhou Zhao, Jingfang Xu, and Xiaoyan Zhu. 2018.  Assigning personality/profile to a chatting machine for coherent conversation generation.  In _Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI-18_ , pages 4279–4285. International Joint Conferences on Artificial Intelligence Organization.
  * Radford et al. (2018) Alec Radford, Karthik Narasimhan, Tim Salimans, Ilya Sutskever, et al. 2018.  Improving language understanding by generative pre-training.
  * Raffel et al. (2020) Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, Peter J Liu, et al. 2020.  Exploring the limits of transfer learning with a unified text-to-text transformer.  _J. Mach. Learn. Res._ , 21(140):1–67.
  * Roller et al. (2021) Stephen Roller, Emily Dinan, Naman Goyal, Da Ju, Mary Williamson, Yinhan Liu, Jing Xu, Myle Ott, Eric Michael Smith, Y-Lan Boureau, and Jason Weston. 2021\.  Recipes for building an open-domain chatbot.  In _Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics: Main Volume, EACL 2021, Online, April 19 - 23, 2021_ , pages 300–325. Association for Computational Linguistics.
  * See et al. (2017) Abigail See, Peter J Liu, and Christopher D Manning. 2017.  Get to the point: Summarization with pointer-generator networks.  In _Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 1073–1083.
  * Shao et al. (2021) Yunfan Shao, Zhichao Geng, Yitao Liu, Junqi Dai, Fei Yang, Li Zhe, Hujun Bao, and Xipeng Qiu. 2021.  Cpt: A pre-trained unbalanced transformer for both chinese language understanding and generation.  _arXiv preprint arXiv:2109.05729_.
  * Song et al. (2021) Haoyu Song, Yan Wang, Kaiyan Zhang, Weinan Zhang, and Ting Liu. 2021.  Bob: Bert over bert for training persona-based dialogue models from limited personalized data.  In _Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 167–177.
  * Song et al. (2019) Haoyu Song, Wei-Nan Zhang, Yiming Cui, Dong Wang, and Ting Liu. 2019.  Exploiting persona information for diverse generation of conversational responses.  _arXiv preprint arXiv:1905.12188_.
  * Thoppilan et al. (2022) Romal Thoppilan, Daniel De Freitas, Jamie Hall, Noam Shazeer, Apoorv Kulshreshtha, Heng-Tze Cheng, Alicia Jin, Taylor Bos, Leslie Baker, Yu Du, et al. 2022.  Lamda: Language models for dialog applications.  _arXiv preprint arXiv:2201.08239_.
  * Vaswani et al. (2017) Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Ł ukasz Kaiser, and Illia Polosukhin. 2017.  Attention is all you need.  In _Advances in Neural Information Processing Systems_ , volume 30. Curran Associates, Inc.
  * Wolf et al. (2020) Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander M. Rush. 2020.  Transformers: State-of-the-art natural language processing.  In _Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations_ , pages 38–45, Online. Association for Computational Linguistics.
  * Xu et al. (2022a) Jing Xu, Arthur Szlam, and Jason Weston. 2022a.  Beyond goldfish memory: Long-term open-domain conversation.  In _Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 5180–5197.
  * Xu et al. (2022b) Xinchao Xu, Zhibin Gou, Wenquan Wu, Zheng-Yu Niu, Hua Wu, Haifeng Wang, and Shihang Wang. 2022b.  Long time no see! open-domain conversation with long-term persona memory.  In _Findings of the Association for Computational Linguistics: ACL 2022_ , pages 2639–2650.
  * Yavuz et al. (2019) Semih Yavuz, Abhinav Rastogi, Guan-Lin Chao, and Dilek Hakkani-Tur. 2019.  DeepCopy: Grounded response generation with hierarchical pointer networks.  In _Proceedings of the 20th Annual SIGdial Meeting on Discourse and Dialogue_ , pages 122–132, Stockholm, Sweden. Association for Computational Linguistics.
  * Zhang et al. (2018a) Saizheng Zhang, Emily Dinan, Jack Urbanek, Arthur Szlam, Douwe Kiela, and Jason Weston. 2018a.  Personalizing dialogue agents: I have a dog, do you have pets too? In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 2204–2213, Melbourne, Australia. Association for Computational Linguistics.
  * Zhang et al. (2018b) Saizheng Zhang, Emily Dinan, Jack Urbanek, Arthur Szlam, Douwe Kiela, and Jason Weston. 2018b.  Personalizing dialogue agents: I have a dog, do you have pets too?  In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 2204–2213.
  * Zhang et al. (2019) Tianyi Zhang, Varsha Kishore, Felix Wu, Kilian Q Weinberger, and Yoav Artzi. 2019\.  Bertscore: Evaluating text generation with bert.  _arXiv preprint arXiv:1904.09675_.
  * Zhang et al. (2020) Yizhe Zhang, Siqi Sun, Michel Galley, Yen-Chun Chen, Chris Brockett, Xiang Gao, Jianfeng Gao, Jingjing Liu, and William B Dolan. 2020.  Dialogpt: Large-scale generative pre-training for conversational response generation.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics: System Demonstrations_ , pages 270–278.
  * Zheng and Huang (2021) Chujie Zheng and Minlie Huang. 2021.  Exploring prompt-based few-shot learning for grounded dialog generation.  _arXiv preprint arXiv:2109.06513_.
  * Zhou et al. (2021) Hao Zhou, Pei Ke, Zheng Zhang, Yuxian Gu, Yinhe Zheng, Chujie Zheng, Yida Wang, Chen Henry Wu, Hao Sun, Xiaocong Yang, et al. 2021.  Eva: An open-domain chinese dialogue system with large-scale generative pre-training.  _arXiv preprint arXiv:2108.01547_.

##  Appendix A Scoring Criteria in Human Evaluation

The criteria used in human evaluation are provided in Table 6, which each
metric is at the utterance-level.

Score | Coherence
---|---
0 |  | The response is not related with the context.
---
The response simply repeats the context.
The response has conflicts with the context.
There are any logic conflicts within the response.
1 | The response is coherent with the context.
|
Score | Consistency
0 |  | The response has conflicts with the context or memory.
---
There are logic conflicts within the response.
1 | The response is consistent with context and with memory in dialogue history.
|
Score | Engagingness
0 |  | I don’t want to talk with this speaker.
---
The response is kind of perfunctory or boring.
1 | I would like to talk with the speaker for each response in the long-term conversation.
2 | The response is beyond expectations, not perfunctory, and more interesting.
Table 6: Score details of metrics used in human evaluation.

##  Appendix B Training Details

We use a sampling strategy for memory retrieval and memory-augmented
generation. In memory retrieval, a persona memory is randomly sampled from all
seen memories for each utterance, and it is labeled as 1 or 0 depending on
whether the sampled memory is positive or negative. The overall statistics of
datasets are shown in Table 7. We scaled the memory retrieval data by five
during training to balance the sample size of different subtasks. In addition,
sampling training is also performed to simulate actual usage scenarios in the
memory-augmented generation task. If there is no relevant persona for a round
of dialogue, we sample the k personas as negative examples. The model can
further judge whether the retrieved memory is valuable through such training.

For the memory of users and chatbots, we set the duplication threshold
$\lambda$ as 0.9 and the number of candidates top-k to 3. We decode with beam
search, where the beam size is set to 1 in the automatic evaluation and 4 in
the self-chat evaluation. We fixed the random seed of the experiment as 2022.
Following Xu et al. (2022b), we do not limit the memory capacity due to the
sparsity of persona dialogue and the efficiency of our persona storage.

For all models, we set the maximum context length to 256 and used the default
vocabulary of the pre-trained model. We optimize all models with the Adam
Kingma and Ba (2015) optimizer with a learning rate of 5e-5. All models were
trained using the Fairseq Ott et al. (2019) toolkit and pre-trained models
obtained from the transformers Wolf et al. (2020) library. Experiments are
conducted on NVIDIA V100 32GB and A100 40GB GPUs.

Category | SELF | BOTH
---|---|---
# Dialogues | 24500 | 3001
# Utterances | 400472 | 48522
Avg. # turns | 16.3 | 16.2
Avg. length of utterances | 19.7 | 21.2
Avg. # bot persona | 4.0 | 4.0
Avg. # user persona (seen) | 0 | 4.4
Avg. # user persona (unseen) | 4.0 | 1.3
Table 7: Statistics of DuLeMon.

##  Appendix C Case Study

To concretely demonstrate UniMC’s ability to long-term memory conversation, we
further provide a cherry-picked selected example of a single-episode dialogue
(between UniMC and EVA 2.0) in Figure 5.

Figure 5: Example of one episode conversation between UniMC and EVA2.0.