# Evaporating black holes and late-stage loss of soft hair

Peng Cheng<EMAIL_ADDRESS>Institute for Theoretical Physics, University of
Amsterdam, 1090 GL Amsterdam, Netherlands

###### Abstract

We present a paradox for evaporating black holes, which is common in most
schemes trying to avoid the firewall by decoupling early and late radiation.
At the late stage of the black hole evaporation, the decoupling between early
and late radiation can not be realized because the black hole has a very small
coarse-grained entropy, then we are faced with the firewall again. We call the
problem hair-loss paradox as a pun on losing black hole soft hair during the
black hole evaporation and the situation that the information paradox has put
so much pressure on researchers.

##  I Introduction

Black holes are fascinating objects in the universe, which have brought us
many theoretical puzzles at the same time. The black hole information paradox
(BHIP), as an example, was firstly put forward by Stephen Hawking Hawking1976
and has been confusing researchers for almost half a century now.

As a milestone, the BHIP was sharpened by the Almheiri-Marolf-Polchinski-Sully
(AMPS) firewall argument Almheiri2012  in 2012. The basic idea can be
summarized as follows. For an old black hole, we can denote the early
radiation as $R$ and the partner of a late time Hawking radiation $H$ as $P$.
The unitarity requires that $H$ purifies the early radiation $R$, such that we
have the Page curve Page1993 ; Page2013  for the entropy of the overall
radiation. Let us use $R_{H}$ to denote the part of $R$ that is maximally
entangled with the Hawking radiation $H$. Furthermore, the smoothness of the
horizon requires that $P$ and $H$ are maximally entangled. However, the
unitarity and the smoothness of the horizon are not consistent with each other
because of the so-called monogamy of entanglement Terhal2004 , which claims
that $H$ can only be entangled with either $R$ or $P$. Then, the unitarity
implies the horizon is not smooth anymore.

The Harlow-Hayden-Aaronson (HHA) decoding task Harlow2013 ; Aaronson2016  was
proposed as a possible solution to avoid the firewall. The basic logic is very
similar to the black hole complementarity Susskind_1993 ; Kiem1995 ; Lowe1995
. We said that $H$ is maximally entangled with $R_{H}$, which is only a small
part of $R$. As far as no one can distill $R_{H}$ out of $R$, we can think $H$
is decoupled with the early radiation $R$. If $H$ and $R$ are decoupled, the
firewall can be avoided. The quantum computation argument claims that the task
of distilling $R_{H}$ out of $R$ is as hard as inverting a one-way function,
and the distilling time can be much longer than the evaporating time of the
black hole.

Although the decoding task provided a nice quantum computational argument,
questions like how to physically realize the decoding task and the derivation
of the Page curve was not addressed convincingly until very recently. Yoshida
considered the back-reaction of an infalling observer $O$ in solving the black
hole complexity puzzle and soon realized it could also be used to achieve the
decoupling between $H$ and $R$ Yoshida2019 . The basic idea can be summarized
as Yoshida’s decoupling theorem Yoshida2017 ; Yoshida2019 : for scrambling
black hole evolution, if the dimension of the observer’s Hilbert space
$\mathcal{H}_{O}$ is much larger than the late time Hawking radiation
$\mathcal{H}_{H}$, i.e., $d_{O}\gg d_{H}$, early and late radiation are
decoupled, and one can reconstruct the Hawking partner $P$ without using the
early radiation $R$. The inclusion of observer Hilbert space was legitimized
by gravitational dressing, and the observer degrees of freedom can be
identified with the soft hair degrees of freedom $\mathcal{H}_{S}$ of a black
hole system Hosur2016 ; Yoshida2019a ; Pasterski2020 . Here we are going to
assume the entropy of the soft hair contributes a large portion of the black
hole entropy. It has also been shown in Pasterski2020  that the soft hair
introduces an observer-dependent firewall, and the construction of $P$ can be
performed via the Petz map Petz1988 ; DenesPetz2004 . The Page curve was also
addressed in Cheng2020 .

The above argument relies on the dimension of the soft hair Hilbert space
$d_{S}$ is much larger than the Hilbert space of $H$, i.e.

$d_{S}=d_{O}\gg d_{H}\,.$ (1)

Furthermore, the error of reconstructing the interior observer is determined
by $d_{H}/d_{S}$. However, the above condition is not fulfilled at the end of
the evaporation. The reason is as follows. The coarse-grained entropy of the
black hole decreases as the black hole evaporates, and the entropy of the soft
hair can not be large than the coarse-grained entropy of the black hole. So
when the black hole entropy is relatively small, $d_{S}$ may not be much
larger than $d_{H}$. Then, the decoupling theorem fails at the end of the
evaporation, and the firewall shows up again. If the firewall shows up once,
the whole horizon would be “lighted”, and there would be a firewall all over
the horizon because of the general covariance of the general relativity. We
call the problem hair-loss paradox, as a pun on the annoyance of losing black
hole “soft hair”. The hair-loss paradox is actually a problem for most of the
arguments trying to decouple $R$ and $H$. In the HHA decoding task, if $R_{H}$
is only left with a few qubits, then the distillation of $R_{H}$ out of $R$ is
not that hard anymore, and we would have to face with the firewall again.

It’s worth to notice that a similar idea was independently considered in the
work Li2021a .

##  II Soft hair in the BHIP

In this section, we review the basic ideas of the decoupling theorem and the
role of soft hair in the BHIP. The review mainly follows Pasterski2020  (also
see Cheng2020 ). The decoupling between $R$ and $H$ can be realized by
including a large exterior observer $O$, and the measurement of soft hair by
the observer can be used to reconstruct the Hawking partner $P$ via the Petz
map.

First of all, let us describe the correlation between the exterior operator
$\mathcal{O}$ and the black hole via gravitational dressing. Any
diffeomorphism invariant operator must commute with the supertransition charge
$Q_{f}$, i.e.

$[Q_{f},\mathcal{O}_{phys}]=0\,.$ (2)

The above requirement enforces that the physical operator is dressed with
gravitational Wilson line Himwich2020

$\mathcal{W}(\omega,z^{A})=e^{-i\omega f(z^{A})}\,,$ (3)

where $z^{A}$ are the coordinates on the celestial sphere Strominger2017 , and
$\omega$ is the energy eigenvalue. So the gravitational dressing amount to add
an extra phase $f$ along the light-cone coordinate $v^{\prime}=v-f$. In other
words, in order to be physical, all operators should know the supertransition
charge of the spacetime via gravitational dressing. In an asymptotic flat
black hole background, the transition function $f$ relating the near-horizon
region and the asymptotic region can be interpreted as the soft hair of the
black hole, which can have a large contribution to the black hole entropy. In
such a sense, exterior observer has correlation with the black hole via soft
hair.

Figure 1: The system starts with $\left|{\Psi_{0}}\right>$ shown in (4), which
contains the code subspace $C$, early radiation $R$, soft hair $S$, and
exterior observer $O$. The operation $T$ maps $S$ and $C$ into a black hole
state, which then emits a Hawking radiation $H$ after the time evolution $U$.
Finally, the observer recovers the Hawking partner $P$ using the recovery map
$\mathcal{R}$. The whole process is unitary.

Now we start with the system $\left|{\Psi_{0}}\right>$ shown in Fig. 1, where
we have the code subspace of the black hole $C$ correlated with the early
radiation $R$, and the soft hair $S$ of the black hole correlated with the
observer $O$. We can write the state $\left|{\Psi_{0}}\right>$ as

$\left|{\Psi_{0}}\right>=\frac{1}{\sqrt{d_{C}d_{S}}}\sum_{f,n}\left|{f}\right>_{S}\left|{n}\right>_{C}\left|{f}\right>_{O}\left|{n}\right>_{R}\,.$
(4)

The operation $T$ embeds $S$ and $C$ onto a black hole state, which can be
represented as

$T\left|{f}\right>_{S}\left|{n}\right>_{C}=T_{f}\left|{n}\right>_{B}\,.$ (5)

We can also define the inverse mapping $T_{f}^{\dagger}$ that reverse the
above operation, which will be useful later. Then, the black hole emits an
extra Hawking radiation $H$ under the time evolution $U$. The system can be
expressed as

$\displaystyle\left|{\Psi}\right>$ $\displaystyle=$ $\displaystyle U\circ
T\left|{\Psi_{0}}\right>$ (6) $\displaystyle=$
$\displaystyle\frac{1}{\sqrt{d_{C}d_{S}}}\sum_{m,n,f}C_{m}\left|{m}\right>_{H}\otimes
T_{f}\left|{n}\right>_{B}\left|{f}\right>_{O}\left|{n}\right>_{R}\,,$

where $\left|{m}\right>_{H}$ labels the Hawking radiation $H$, and $C_{m}$ is
the Kraus operator. The recovery map $\mathcal{R}$ is expected to recover the
Hawking partner $P$ when the observer $O$ is included. We can call the process
involving $O$ “measurement”. The recovery map $\mathcal{R}$ maps the whole
system into the original state $\left|{\Psi_{0}}\right>$ and a thermo-field
double (TFD) state composing $P$ and $H$, i.e.
$\left|{\text{TFD}}\right>_{HP}$. The process can be represented as

$\displaystyle\mathcal{R}\left|{\Psi}\right>$ $\displaystyle\simeq$
$\displaystyle\left|{\Psi_{0}}\right>\otimes\left|{\text{TFD}}\right>_{HP}$
(7) $\displaystyle=$
$\displaystyle\frac{1}{\sqrt{d_{C}d_{S}}}\sum_{f,n}\left|{f}\right>_{S}\left|{n}\right>_{C}\left|{f}\right>_{O}\left|{n}\right>_{R}$
$\displaystyle~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\otimes\sum_{m}\sqrt{p_{n}}\left|{m}\right>_{P}\left|{m}\right>_{H}\,,$

with the Boltzmann weights $p_{n}$, where we have used $\simeq$ because there
is an error in the recovery map. It was shown that the Petz map can be used to
accomplish the recovery task Pasterski2020

$\mathcal{R}=\frac{1}{\sqrt{d_{C}}}T^{\dagger}C^{\dagger}_{m}\sigma^{-1/2}\,,$
(8)

with

$\sigma=\frac{1}{d_{C}}\sum_{m}C_{m}T_{f}T_{f}^{\dagger}C_{m}^{\dagger}\,.$
(9)

The process is illustrated in Fig. 1.

Now, by including the Hilbert space of the observer $O$, the decoupling of the
early radiation $R$ and late time radiation $H$ and the reconstruction of
Hawking partner $P$ are realized; thus, the AMPS firewall can be avoided by
the above argument. The argument can be summarized as the Yoshida’s decoupling
theorem Yoshida2019 , as already mentioned at the beginning. The mechanism of
how soft hair interacts with Hawking radiation was recently explored
Flanagan2021 ; Flanagan2021a . In paper Cheng2020 , the phase spaces of the
Hawking radiation and the measurement were evaluated, and the competition
between those two processes gives out the Page curve that is consistent with
the unitarity.

##  III Fidelity of the reconstruction

Let us sketch a proof of the decoupling theorem, from which we can see more
details about the fidelity of the reconstruction. To prove the decoupling
theorem, we need to show that the density matrix $\rho_{HR}$ can be written as

$\rho_{HR}\approx\rho_{H}\otimes\rho_{R}\,,$ (10)

for a scrambling evolution. We are going to show that $\rho_{HR}$ is very
close to a maximally mixed state in $L^{1}$ distance, namely,

$||\rho_{HR}-\frac{1}{d_{H}d_{R}}I_{H}\otimes I_{R}||_{1}^{2}\ll 1\,,$ (11)

with identity matrices $I_{H}$ and $I_{R}$. It is easy to show that

$\displaystyle||\rho_{HR}-\frac{1}{d_{H}d_{R}}I_{H}\otimes I_{R}||_{1}^{2}$
$\displaystyle\leq$ $\displaystyle||\rho_{HR}-\frac{1}{d_{H}d_{R}}I_{H}\otimes
I_{R}||_{2}^{2}$ (12) $\displaystyle=$ $\displaystyle
d_{H}d_{R}~{}\text{tr}(\rho_{HR}^{2})-1\,.$

Then, the main task left for us is to evaluate the 2nd Renyi entropy, which
can be done following the diagram technique Yoshida2017 ; Yoshida2019 . Here,
we will omit map $T$ shown in Fig. 1, which maps the code subspace $C$ and
soft hair $S$ to a black hole state, and only focus on the unitary evolution
$U$. The density matrix $\rho_{HR}$ can be expressed diagrammatically as

$\rho_{HR}=\text{tr}_{BO}\left|{\Psi}\right>\left<{\Psi}\right|=~{}\begin{matrix}\includegraphics[width=113.81102pt]{rhoHR.pdf}\end{matrix}$
(13)

where we get the reduced density matrix by tracing out the Hilbert space of
the observer $O$ and black hole $B$. Naturally, we can also illustrate
$\text{tr}(\rho_{HR}^{2})$ as follows

$\text{tr}(\rho_{HR}^{2})=\begin{matrix}\includegraphics[width=113.81102pt]{renyi.pdf}\end{matrix}$
(14)

Note that inspired by the recent discussions of replica wormholes
Penington2019a ; Almheiri2019b , there might be a different combination of the
blocks and lines corresponding to a different saddle in Euclidean path
integral, which requires further understanding. Here we would only focus on
the above diagram shown in (14). To evaluate $\text{tr}(\rho_{HR}^{2})$, we
need to recall some properties of scrambling evolution. Quantum scrambling is
related to the out-of-time-order correlators (OTOCs), and one of the
characteristics of almost perfect scrambling can be expressed as the following
decomposition Hosur2016 ; Yoshida2017

$\displaystyle\left<U^{\dagger}WU~{}Z~{}U^{\dagger}YU~{}X\right>$
$\displaystyle\approx\left<WY\right>\left<Z\right>\left<X\right>+\left<ZX\right>\left<W\right>\left<Y\right>-\left<W\right>\left<X\right>\left<Y\right>\left<X\right>\,,$

where $U$ is a scrambling evolution. Now, with four $U$s in (14),
$\text{tr}(\rho_{HR}^{2})$ can also be expressed as an OTOC of some operators,
which can be evaluated applying the above decomposition. We can get rid of
$U$s by applying the decomposition and directly calculate the correlators,
which are just some circles contracted with themselves, diagrammatically. So
for the perfect scrambling evolution $U$, we have Yoshida2017 ; Yoshida2019

$\displaystyle\text{tr}(\rho_{HR}^{2})$ $\displaystyle\approx$
$\displaystyle\frac{d_{H}}{d_{R}}(\frac{1}{d_{H}^{2}}+\frac{1}{d_{S}^{2}}-\frac{1}{d_{H}^{2}d_{S}^{2}})$
(16) $\displaystyle\leq$
$\displaystyle\frac{1}{d_{H}d_{R}}+\frac{d_{H}}{d_{R}d_{S}^{2}}\,.$

substituting the above result (16) back into the $L^{1}$ distance (12), we
obtain

$||\rho_{HR}-\frac{1}{d_{H}d_{R}}I_{H}\otimes
I_{R}||_{1}^{2}\sim\mathcal{O}\left(\frac{d_{H}^{2}}{d_{S}^{2}}\right)\,,$
(17)

and the fidelity $F$ always satisfies the following inequality

$F\leq 1-\mathcal{O}\left(\frac{d_{H}^{2}}{d_{S}^{2}}\right)\,.$ (18)

So in order to keep a high fidelity, $d_{S}$ must be much larger than $d_{H}$
such that

$\mathcal{O}\left(\frac{d_{H}^{2}}{d_{S}^{2}}\right)\ll 1\,.$ (19)

##  IV Hair-loss paradox

Figure 2: The coarse-grained entropy of an evaporating black hole decreases to
zero.

From the previous section, we have gotten an important condition to ensure the
decoupling theorem to be true. Supposing the correlations between the extra
system $O$ and the black hole are through soft hair Pasterski2020 , the
dimension of the soft hair Hilbert space $\mathcal{H}_{S}$, which equals the
dimension of the exterior observer, must be very large compared to the late
time Hawking radiation $\mathcal{H}_{H}$, and the error is proportional to

$\text{Error}\sim\mathcal{O}\left(\frac{d_{H}^{2}}{d_{S}^{2}}\right)\ll 1\,.$
(20)

So to properly complete the task, $d_{S}$ must be much larger than $d_{H}$.
This condition will bring us another paradox in the process of black hole
evaporation.

Soft hair can at most be responsible for part of the black hole micro-states,
and the coarse-grained entropy of soft hair should always be smaller than the
coarse-grained entropy of the black hole. So the soft hair Hilbert space
$\mathcal{H}_{S}$ can never be larger than the whole Hilbert space of the
black hole; thus, we have

$d_{S}\leq d_{BH}\,.$ (21)

The combination of equations (20) and (21) implies that in order to decouple
the late and early radiation, and reconstruct the interior operators with a
high fidelity, the following inequality.

$d_{BH}\gg d_{H}\,$ (22)

must be true. However, as the black hole evaporates, $d_{BH}$ is decreasing.
The decoupling theorem fails to hold once the above condition can not be
fulfilled and the firewall comes back again. In such a sense, we have not
completely wiped out the firewall at the Page time but postponed it until the
end stage of the evaporation. So, we can say that we keep losing soft hair
degrees of freedom as the black hole evaporates because the entropy of the
soft hair must be smaller than the coarse-grained entropy of the black hole.
When we do not have enough soft hair, the decoupling theorem fails. So we call
it

Hair-loss paradox: At the end stage of the black hole evaporation, the black
hole system does not have large enough coarse-grained entropy to support large
$\mathcal{H}_{S}$ to decouple the early and late radiation and construct the
Hawking partner.

The above hair-loss paradox is a paradox in a more general setting than a
paradox that only appears in Yoshida’s decoupling theorem. Most of the
attempts trying to reconstruct the interior operators using quantum
information protocol rely on a large phase space of the radiation. If the
black hole system is only left with a few qubits, even still exponentially
hard, the HHA decoding task Harlow2013 ; Aaronson2016  is not that hard. Thus,
there is no decoupling between the early and late radiation, and we always
have to face the AMPS firewall if the black hole system only has several
qubits. If the firewall shows up once on the horizon, there would be a
firewall all over the horizon because of the general covariance of the general
relativity. This paradox can be seen more explicitly by looking at the entropy
of an evaporating black hole Page1993 ; Page2013 . The Stephan-Boltzmann law
of blackbody radiation can be written as

$\frac{dM}{dAdt}\propto T^{4},$ (23)

with the area of the black hole $A$. Then, the power of the evaporation can be
written as

$\frac{dM}{dt}\propto\frac{1}{M^{2}}.$ (24)

Working out the above integral, we obtain

$M=M_{0}\left(1-\frac{t}{t_{0}}\right)^{1/3}\,,$ (25)

where $M_{0}$ is the original mass of the black hole, and $t_{0}$ is the total
time for the evaporation. Similarly, for the system’s entropy, we have

$S=S_{0}\left(1-\frac{t}{t_{0}}\right)^{2/3}\,,$ (26)

with the original entropy of the black hole $S_{0}$. The coarse-grained
entropy of the black hole system is depicted in Fig. 2. As we can see from the
figure, at the end of the evaporation, the coarse-grained entropy of the
system goes to zero, thus can not support a large number of soft hair degrees
of freedom for the purpose of decoupling between the late and early time
radiation and constructing the Hawking partner.

##  V Summary

We have presented a paradox related to the decoupling theorem of evaporating
black holes. The decoupling between the early and late Hawking radiation can
be realized by including soft hair in a black hole background. The interior
operator can also be reconstructed by the Petz map, without using the early
radiation $R$. What’s more, for scrambling evolution $U$, we can evaluate the
fidelity of the decoupling between early and late Hawking radiation. However,
in order to keep a high fidelity, the dimension of the soft hair Hilbert space
$d_{S}$ must be much larger than the one for late Hawking radiation $d_{H}$.
We argue that the condition for a high fidelity might not hold at the end
stage of the evaporation, which means the firewall would show up again even if
the decoupling theorem holds near the Page time. It is important to note that
the paradox is very common in most schemes trying to decouple the late and
early radiation to avoid firewall, for example the HHA decoding task.

A possible way of avoiding this problem is that there might be a large
modification of the black hole entropy at the end stage of the evaporation,
such that the condition (22) is always held. This has a strong flavor of the
black hole remnants Aharonov1987 ; Adler2001 . However, a more precise
solution to the hair-loss paradox needs further studies.

###### Acknowledgements.

We would like to thank Yang An, Jan de Boer, Diego Hofman, Ran Li, and Pujian
Mao for inspirational discussions. PC is financially supported by China
Scholarship Council (CSC).

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# Exploiting Emotion-Semantic Correlations for
Empathetic Response Generation

Zhou Yang1,2, Zhaochun Ren3, Yufeng Wang1,2, Xiaofei Zhu4, Zhihao Chen1,2,
Tiecheng Cai1,2, Yunbing Wu1,2, Yisong Su1,2, Sibo Ju1,2, Xiangwen Liao1,2
1College of Computer and Data Science, Fuzhou University; 2Digital Fujian
Institute of Financial Big Data, Fuzhou, China
3Leiden University, Leiden, The Netherlands
4College of Computer Science and Technology, Chongqing University of
Technology, Chongqing, China
{200310007, 211027083, n180320046, 210310002, 221010003<EMAIL_ADDRESS>
<EMAIL_ADDRESS><EMAIL_ADDRESS>{wyb5820<EMAIL_ADDRESS>
Corresponding author.

###### Abstract

Empathetic response generation aims to generate empathetic responses by
understanding the speaker’s emotional feelings from the language of dialogue.
Recent methods capture emotional words in the language of communicators and
construct them as static vectors to perceive nuanced emotions. However,
linguistic research has shown that emotional words in language are dynamic and
have correlations with other grammar semantic roles, i.e., words with semantic
meanings, in grammar. Previous methods overlook these two characteristics,
which easily lead to misunderstandings of emotions and neglect of key
semantics.

To address this issue, we propose a dynamical Emotion-Semantic Correlation
Model (ESCM) for empathetic dialogue generation tasks. ESCM constructs dynamic
emotion-semantic vectors through the interaction of context and emotions. We
introduce dependency trees to reflect the correlations between emotions and
semantics. Based on dynamic emotion-semantic vectors and dependency trees, we
propose a dynamic correlation graph convolutional network to guide the model
in learning context meanings in dialogue and generating empathetic responses.
Experimental results on the EMPATHETIC-DIALOGUES dataset show that ESCM
understands semantics and emotions more accurately and expresses fluent and
informative empathetic responses. Our analysis results also indicate that the
correlations between emotions and semantics are frequently used in dialogues,
which is of great significance for empathetic perception and expression.111Our
code is available at
https://github.com/zhouzhouyang520/EmpatheticDialogueGeneration_ESCM

##  1 Introduction

Attracting an increasing amount of attention, empathetic response generation
aims to generate empathetic responses by perceiving the speaker’s emotional
feelings Rashkin et al. (2019); Zhong et al. (2021, 2020); Liang et al.
(2021); Zheng et al. (2021); Liu et al. (2021); Wang et al. (2021).

Early methods perceive the speaker’s feelings by understanding the holistic
semantics and emotions expressed in the language of the context Rashkin et al.
(2019); Lin et al. (2019); Majumder et al. (2020). These methods are prone to
generate trivial and uninformed responses, ascribed to the neglect of nuances
of human emotion in dialogues Li et al. (2020). To address this issue, recent
methods detect emotional words in the language of the communicators and build
them as static vectors to perceive subtle emotions Li et al. (2020); Sabour et
al. (2022); Kim et al. (2021); Gao et al. (2021); Li et al. (2022); Kim et al.
(2022).

Figure 1:  Examples from the EMPATHETIC-DIALOGUES dataset. Sentence 1 shows
the variability of emotional words. Sentence 2 shows the correlations of
emotional words with semantic roles.

However, according to linguistic research Foolen et al. (2012); Dirven (1997);
Osmond (1997); Radden (1998), focusing on emotional words while ignoring their
characteristics in the expression process leads to emotional misunderstandings
and the neglect of words with important semantic information. As an important
theory of emotional expression in linguistics, the conceptualization of
emotions Foolen et al. (2012) suggests that emotional words have two important
characteristics in the expression process: variability and relevance.
Variability is that the affection of emotional words changes dynamically
during the expression process. For example, “well” generally carries a
positive meaning, but in sentence 1 (shown in Figure 1), it is used as an
interjection to express a neutral emotion. Using static vectors (such as
Embedding Pennington et al. (2014); Mikolov et al. (2013) or VAD Mohammad
(2018)) to represent this dynamic emotion, previous methods are prone to
misunderstand this sentence as positive.

Relevance refers to the grammatical correlations between emotional words and
words carrying semantic meaning, which plays an important role in
understanding emotions and semantics. For example, as shown in Figure 1,
sentence 2 expresses the “exciting” emotion due to the victory of “team”.
“Team” is the primary subject described in the sentence, carrying key semantic
information. Through the “[ADJ]-CCOMP-[NOUN]” correlation, the emotional word
“exciting” directly modifies “team”. Compared to previous work that did not
consider such correlations, the model is more likely to identify key semantic
words that are directly associated with emotional words through these types of
syntax-meaningful relationships. Therefore, focusing on the variability and
relevance of emotional words can promote the correct recognition of emotions
and the detection of important semantics.

Therefore, we propose a dynamical Emotion-Semantic Correlation Model (ESCM)
for empathetic dialogue generation. ESCM dynamically constructs emotion-
semantic vectors through the interaction of context and emotions. By encoding
emotion-semantic vectors, the model dynamically adjusts emotions and semantics
in the context to capture the variability of emotional words. To reflect the
correlations between emotions and semantics clearly, we introduce a dependency
tree. Based on the dynamic emotion-semantic representation and the dependency
tree, ESCM proposes a dynamic correlation graph convolutional network to guide
the model to capture the correlations between emotions and semantics clearly.
By learning dynamic emotion-semantic representations and their correlations,
ESCM accurately understands the emotions of the dialogue and captures
important semantics to generate more empathetic responses.

We conduct experiments on the EMPATHETIC-DIALOGUES dataset Rashkin et al.
(2019). The results show that the ESCM model accurately understands the
dialogue and generates grammatically fluent and informative empathetic
responses. Furthermore, we extract and statistically analyze the common
correlation structures in dialogues from the Empathetic-Dialogue dataset. The
results indicate that the correlations between emotion and semantics are
frequently and extensively utilized in expressing emotions during
conversations. Additionally, the results of our analysis of correlation
structures are consistent with linguistic conclusions Foolen et al. (2012).

To sum up, our contributions are as follows:

  * •

We introduce the expressive characteristics of emotions in linguistics,
including the variability of emotions and the correlations between emotions
and semantics, to enhance the understanding of the meaning in conversations.

  * •

We propose the ESCM model, which constructs dynamic emotion-semantic vectors
to adjust the dynamics of emotions, and leverages a dependency tree-based
dynamic correlation graph convolutional network to learn correlations, in
order to generate empathetic responses.

  * •

Experiments on the EMPATHETIC-DIALOGUE dataset demonstrate the effectiveness
of ESCM. Furthermore, additional statistical and analytical experiments show
that the correlations in dialogue are consistent with psychological research.

##  2 Related Work

Empathetic response generation refers to empathetically responding by
perceiving emotional feelings in the language of the speaker Rashkin et al.
(2019).

Early approaches explore the overall emotions of the conversation. Rashkin et
al. (2019) introduce emotion representation generated by a pre-trained emotion
classifier to learn and express specific types of emotions in the
conversation. However, emotions expressed in responses are often diverse
rather than specific Lin et al. (2019). Therefore, Lin et al. (2019) utilize
multiple professional emotion listeners to express various appropriate
emotions. Majumder et al. (2020) group multiple conversation emotions by
polarity and simulate the speaker’s emotions to generate empathetic responses.

These methods focus on the overall emotions of the conversation and ignore
nuanced emotions Li et al. (2020). To capture nuanced emotions, Li et al.
(2020) extract emotional words through the NRC Emotion Lexicons Mohammad and
Turney (2013) and integrate them into the model. Gao et al. (2021) and Kim et
al. (2021) introduce emotional cause detection models to capture emotional
words and perceive nuanced emotions. Li et al. (2022) enhance emotional
representation in the context with additional knowledge, which helps detect
emotional words. Sabour et al. 2022 use commonsense reasoning knowledge to
infer nuanced emotions in the conversation. Kim et al. 2022 employ pre-trained
models to detect word-level emotion and keywords to detect the nuanced emotion
in dialogues. These methods detect emotional words with nuanced emotions in
the language of the conversation and use static vectors such as word
embeddings or VAD to represent emotional words.

Overall, early approaches ignore emotional words with nuanced emotions. Recent
methods ignore two major characteristics of emotional words in linguistic
expression: variability and correlation. Unlike these methods, we consider the
two characteristics of emotional words and propose a dynamic emotion-semantic
correlation model to better understand the conversation.

Figure 2:  An overview of ESCM. ESCM consists of three main key modules: (1) a
context encoder (Section 3.3), which encodes the semantic of context. (2) a
dynamic correlation encoding module (Section 3.4), which learns the
correlations between emotions and semantics. (3) emotion and response
predicting module (Section 3.5), which predicts dialog emotion categories and
generates empathetic responses.

##  3 Method

###  3.1 Task Formulation

Given a dialogue context $D$ = [$U_{1},U_{2},...,U_{M}$] of two interlocutors,
our model needs to accurately perceive the emotions and semantics in the
dialogue context and generate empathetic responses $Y$ = [$y_{1}$, $y_{2}$,
…,$y_{j}$, $y_{N}$]. Here, $U_{i}$ = [$w^{i}_{1},w^{i}_{2},...,w^{i}_{m_{i}}$]
represents the i-th utterance containing $m_{i}$ words. $Y$ is a response
containing N words.

###  3.2 Overview

We propose ESCM, which takes into account the dynamic emotions and semantics
in the dialogue and their correlations. The proposed model is a transformer-
based model with encoder-decoder architecture. To accurately perceive the
content of the dialogue, we mainly reconstruct the encoder. As shown in Figure
2, ESCM mainly consists of three parts: (1) a context encoder (Section 3.3),
which is a standard encoder structure and is used to understand the semantics
of the dialogue; (2) a dynamic correlation encoding module (Section 3.4),
which includes the construction of dynamic correlation vectors and the
encoding of a dynamic correlation graph convolutional network. It learns the
correlations between emotions and semantics; (3) emotion and response
predicting module (Section 3.5), which completes the functions of emotion
prediction and response generation.

###  3.3 Context Encoder

As with previous methods Li et al. (2020, 2022); Sabour et al. (2022), we
concatenate the utterances of the dialogue context and prepend $[CLS]$ as the
whole sequence token to form the context input $C$ = = $[CLS]\oplus
U_{1}\oplus U_{2}\oplus...\oplus U_{M}$. Here, $\oplus$ denotes the
concatenation symbol. To input the context $C$ into the model, we convert $C$
into context word embeddings $E_{c}$. Then, we sum up the word embeddings
$E_{c}$, position embeddings, and state embeddings to form the semantic
embeddings $\widetilde{E}_{c}$. The state embeddings are used to distinguish
between speaker or responder types and are randomly initialized. To understand
the semantics of the dialogue, we feed the semantic embeddings
$\widetilde{E}_{c}$ into the context encoder $Enc_{ctx}$ to obtain the context
semantic representation $H_{k}$:

$\displaystyle H_{ctx}=Enc_{ctx}(\widetilde{E}_{c})$ (1)

where $H_{ctx}\in R^{L\times d}$, L is the length of the context sequence, and
d represents the hidden size of the encoder.

###  3.4 Dynamic Correlation Encoding Module

Dynamic correlation encoding consists of two sub-modules: (1) Dynamic emotion-
semantic vectors. It brings the model the ability to flexibly adjust emotions
and semantics, making the representation of context more reasonable. (2)
Dynamic correlation graph convolutional network. This module uses emotions,
semantics, part-of-speech, and dependency types to guide the model to discover
and aggregate words with strong correlations, in order to more accurately
understand the emotions and semantics of the conversation.

Dynamic Emotion-Semantic Vectors. Context has a significant impact on words,
and understanding words without context may lead to errors. For example,
without context, the word “well” is generally considered to have a positive
emotion, but in sentence 1 (shown in Figure 1), it functions as an
interjection to enhance the tone. This usage does not indicate a positive
meaning. Therefore, it is necessary to dynamically adjust emotions and
semantics to adapt to the context.

Regarding semantics, we utilize weighted adjustments of context word
embeddings with semantics.

$\displaystyle E_{ds}=w_{s}E_{c}+b_{s}$ (2)

where $w_{s}$ and $b_{s}$ are trainable parameters, and $E_{ds}\in R^{L\times
d_{s}}$. $d_{s}$ is the hidden size of the dynamic semantic vector $E_{ds}$.

Regarding emotions, we interact context word embeddings $E_{c}$ with emotion
embeddings $E_{e}$ to obtain dynamic emotion vectors $E_{de}$. Emotion
embeddings refer to emotion categories represented in word form, which are
converted into vector embeddings.

$\displaystyle E_{dot}=(w_{c}E_{c}+b_{c})\cdot(w_{e}E_{e}+b_{e})^{T}$ (3)
$\displaystyle E_{de}=w_{ce}E_{dot}+b_{ce}$ (4)

where $w_{c},b_{c},w_{e},b_{e},w_{ce},b_{ce}$ are trainable parameters.
$E_{dot},E_{de}\in R^{L\times d_{e}}$, and $d_{e}$ is the number of emotional
categories.

We then feed the combined emotion and semantic vectors into the encoder to
learn emotion-semantic representations. In this way, the model can take into
account both emotion and semantics simultaneously during training to more
comprehensively understand words in context.

$\displaystyle V_{des}=E_{de}\oplus E_{ds}$ (5) $\displaystyle
H_{des}=Enc_{des}(V_{des})$ (6)

where $V_{des}$, $Enc_{des}$, and $H_{des}$ refer to the dynamic vectors,
encoder, and representations for emotion-semantics, respectively. And
$V_{des},H_{des}\in R^{L\times(d_{s}+d_{e})}$.

Dynamic Correlation Graph Convolutional Network. The next problem is how to
focus on and learn grammatical correlations. Dependency trees clearly reflect
the grammatical dependency relationships between related words Kuncoro et al.
(2016); Kiperwasser and Goldberg (2016); Chen and Manning (2014); Dozat and
Manning (2016). Therefore, we use dependency trees to reflect the correlations
between words. However, words with correlations in the dependency tree are not
always important for understanding emotions and semantics. For example,
“exciting” and “team” are more important, while “exciting” and “is” are
relatively unimportant. To distinguish these correlations, we consider
multiple aspects of correlation guidance, including dynamic emotion-semantic
representation, part-of-speech of related words, and the dependency types
between them.

We list two examples to illustrate the validity of the above correlation
guidance. In sentence 2 (shown in Figure 1), the part-of-speech (ADJ and
NOUN)222ADJ: adjective, NOUN: noun and the dependency type (CCOMP)333CCOMP:
clausal complement indicate that “exciting” is closely related to the key
semantic “team”. Conversely, the part-of-speech (ADJ and AUX)444AUX: auxiliary
and dependency type (COP)555COP: copula indicate that the correlation between
“exciting” and “is” is trivial and unimportant.

Therefore, we consider the above multiple aspects and concatenate the emotion-
semantic representation, part-of-speech, and dependency type to form the
guiding vector $V_{qk}$.

$\displaystyle V_{qk}=H_{des}\oplus V_{p}\oplus V_{r}$ (7)

where $V_{p}$, $V_{r}$ respectively denote part-of-speech embeddings ,
dependency type embeddings, which are randomly initialized. And
$V_{p},V_{r}\in R^{L\times L\times(d_{pr})}$, $V_{qk}\in R^{L\times
L\times(d_{s}+d_{e}+2d_{pr})}$. $d_{pr}$ is the embedding size of $V_{p}$ or
$V_{r}$.

By assigning probabilities to each correlated neighbor, we aggregate the
neighboring nodes that are associated in the dependency tree. Subsequently, we
obtain the correlation representation $H_{cor}$.

$\displaystyle p_{i,j}=\frac{a_{i,j}\cdot exp(V_{qk}[i]\cdot
V_{qk}[j])}{\sum^{L}_{j=1}{a_{i,j}\cdot exp(V_{qk}[i]\cdot V_{qk}[j])}}$ (8)
$\displaystyle H_{cor}=ReLU(\sum^{L}_{j=1}{p_{i,j}(W_{v}V_{des}[j]+b_{v})})$
(9)

where $p_{i,j}\in R^{L\times L\times 1}$, $H_{cor}\in
R^{L\times(d_{s}+d_{e})}$. $a_{i,j}$ is the value of the adjacency matrix
about the dependency tree. When node i and node j have a direct relationship
in the dependency tree, $a_{i,j}$ is 1, otherwise it is 0. $V_{qk}[i]$ and
$V_{qk}[j]$ represent the guiding vectors of node i and node j, respectively.
$W_{v}$ and $b_{v}$ are trainable parameters, and $ReLU$ is the ReLU
activation function.

###  3.5 Emotion and Response Predicting

Based on the context semantics and the correlations between emotions and
semantics, we predict the emotions of the conversation and generate empathetic
responses.

Emotion Predicting. To understand the context semantics and capture important
correlations, we use two aggregation networks with the same structure but
different parameters to process the context semantic representation $H_{ctx}$
(Eq. 1) and correlation representation $H_{cor}$ (Eq. 9). We take the
processing of the context representation as an example.

We first calculate the weights of the words in the context semantic
representation $H_{ctx}$ and sum them up according to their weights to obtain
the hidden layer representation $H^{2}$.

$\displaystyle H^{1}_{a}=Tanh(w^{1}_{a}H_{ctx}+b^{1}_{a})$ (10) $\displaystyle
P_{s}=Softmax(w^{1}_{s}H^{1}_{a}+b^{1}_{s})$ (11) $\displaystyle
H^{2}=\sum^{L}_{j=1}P_{s}[j]\cdot H_{ctx}[j]$ (12)

where $H^{1}_{a}\in R^{L\times d}$, $P_{s}\in R^{L\times 1}$, $H^{2}\in
R^{d}$. $w^{1}_{a},b^{1}_{a},w^{1}_{s},b^{1}_{s}$ are learnable parameters,
and $Tanh$ is the tanh activation function.

Then we feed the hidden layer representation into a non-linear layer to learn
and generate context semantic emotion probabilities $P^{e}_{ctx}$.

$\displaystyle H^{2}_{a}=Tanh(w^{2}_{a}H^{2}+b^{2}_{a})$ (13) $\displaystyle
P^{e}_{ctx}=Softmax(w^{2}_{s}H^{2}_{a}+b^{2}_{s})$ (14)

where $H^{2}_{a}\in R^{d}$, $P^{e}_{ctx}\in R^{d}_{e}$,
$w^{2}_{a},b^{2}_{a},w^{2}_{s},b^{2}_{s}$ are learnable parameters.

Similarly, we use the same structure to construct an aggregation attention
network about the correlations and obtain emotion probabilities
$P^{e}_{cor}\in R^{d}_{e}$. We add the two types of emotion probabilities
together as the overall emotion probability $P_{e}\in R^{d}_{e}$.

$\displaystyle P_{e}=P^{e}_{ctx}+P^{e}_{cor}$ (15)

To ensure that important information in semantics and correlations is not
affected by each other, we set loss functions for them separately. We employ
log-likelihood loss to optimize the parameters during the training phase based
on the emotion category and the ground truth label.

$\displaystyle\mathcal{L}^{e}_{ctx}=-log(P^{e}_{ctx}(e^{*}))$ (16)
$\displaystyle\mathcal{L}^{e}_{cor}=-log(P^{e}_{cor}(e^{*}))$ (17)

Response Predicting. Similarly, our decoder generates responses based on the
context semantics and the correlations between emotion and semantics. This
module takes the context semantic representation $H_{ctx}$ and the correlation
representation $H_{cor}$ as input and predicts the next word at each time step
t. Similar to Li et al. (2022), we use a point generator network to capture
key vocabulary in the context and correlations.

$\displaystyle H=H_{ctx}\oplus H_{cor}$ (18) $\displaystyle
P(y_{t}|y<t,C)=Dec(E_{y<t},H)$ (19)

where $H\in R^{L\times(d+ds+de)}$, $P(y_{t}|y<t,C)\in R^{V}$. $V$ is the
length of the vocabulary. $Dec$ represents a decoder with a pointer network.

Subsequently, we use cross-entropy as generation loss.

$\displaystyle\mathcal{L}_{gen}(y_{t})=-\sum^{T}_{t=1}log(P(y_{t}|y<t,C))$
(20)

Total Loss. Finally, we add the loss $\mathcal{L}_{gen}(y_{t})$ and two
emotion losses $\mathcal{L}^{e}_{ctx}$ and $\mathcal{L}^{e}_{cor}$ together to
obtain the total loss $\mathcal{L}$. We optimize the training parameters in
the model using the total loss.

$\displaystyle\mathcal{L}=\mathcal{L}_{gen}(y_{t})+\mathcal{L}^{e}_{ctx}+\mathcal{L}^{e}_{cor}$
(21)

##  4 Experiments

###  4.1 Baselines

We compare recent state-of-the-art baselines with our model.

Transformer Vaswani et al. (2017) is a vanilla Seq2Seq model, including both
encoder and decoder;

EmoPrend-1 Rashkin et al. (2019) is a Transformer-based model that enhances
empathy by incorporating emotion labels from a pre-trained emotion classifier;

MoEL Lin et al. (2019) is also a Transformer-based model that softly combines
various emotions with multiple decoders to generate empathetic responses;

MIME Majumder et al. (2020) is a Transformer-based model, which consider
polarity-based emotion clusters and emotional mimicry to generate appropriate
responses;

EmpDG Li et al. (2020) emphasizes the importance of user feedback and multi-
resolution emotions. It uses a generative adversarial network to train the
model and generate empathetic responses;

KEMP Li et al. (2022) employs ConceptNet as extra knowledge to enrich the
representation of implicit emotions and captures these emotions to generate
appropriate responses;

CEM Sabour et al. (2022) takes into account both the emotional and cognitive
aspects of empathy. By incorporating reasoning knowledge, it enhances the
ability to perceive and express emotions.

###  4.2 Implementation Details

We conduct experiments on the EMPATHETIC-DIALOGUES Rashkin et al. (2019)
dataset. In the dataset, the number of emotions is $d_{e}$=32. In the model,
we use Glove Pennington et al. (2014) as the initialization vector for word
embedding, with a dimension of d=300. We set the dimension of the dynamic
emotion vector to $d_{s}$=10. At the same time, the dimensions of the part-of-
speech embedding and dependency type embedding are both set to $d_{pr}$=50. We
use Biaffine Parser Dozat and Manning (2016) to obtain dependency
relationships. For the multi-head attention networks in our model, we use a
1-layer network and set the number of heads to 2. Subsequently, we set the
batch size to 16 and use the Adam optimizer Kingma and Ba (2014) to optimize
the parameters. After training for 13500 rounds on an NVIDIA Tesla T4 GPU, the
model converged.

###  4.3 Evaluation Metrics

As with previous work, we employ both automatic and manual metrics to evaluate
the performance of the model.

Automatic Evaluation Metrics. Following Li et al. (2022); Sabour et al.
(2022), we use the following automatic metrics in our experiments: Perplexity
(PPL), Accuracy (Acc), Dist-1, and Dist-2. PPL measures language fluency,
which is of higher quality when the score is lower. Acc assesses the accuracy
of emotion perception. Dist-1 and Dist-2 Li et al. (2015) measure response
diversity at single and double granularity, respectively.

Models | Acc | PPL | Dist-1 | Dist-2
---|---|---|---|---
Transformer | - | 37.73 | 0.47 | 2.04
EmoPrend-1 | 33.28 | 38.30 | 0.46 | 2.08
MoEL | 32.00 | 38.04 | 0.44 | 2.10
MIME | 34.24 | 37.09 | 0.47 | 1.91
EmpDG | 34.31 | 37.29 | 0.46 | 2.02
KEMP | 39.31 | 36.89 | 0.55 | 2.29
CEM | 39.11 | 36.11 | 0.66 | 2.99
ESCM | 41.19 | 34.82 | 1.19 | 4.11
Table 1:  The automatic evaluation results.

Human Evaluation Metrics. Previous work scores models’ responses on a scale of
1 to 5 to assess their quality Li et al. (2020, 2022). This type of assessment
is prone to inconsistent results due to differences in individual criteria
Sabour et al. (2022). Therefore, we adopt the A/B test strategy Lin et al.
(2019); Majumder et al. (2020). Given two responses generated by the models
for the same conversation, three professional crowdsourcers are required to
assign ESCM a score of 1 on _Win_ when the response generated by ESCM is
better than the compared model. Correspondingly, when ESCM is better than or
equal to the compared model, the crowdsourcers will add points for ESCM or
_Tie_. Furthermore, three aspects are considered for evaluating models:
empathy, relevance, and fluency. Empathy evaluates whether the responses show
the right types of emotions; Relevance measures whether the reply is
consistent with the theme and semantics of the context; Fluency assesses the
response’s readability and grammatical accuracy.

Comparisons | Aspects | Win | Lose | $\kappa$
---|---|---|---|---
ESCM vs. EmpDG | Emp. | 45.4 | 24.0 | 0.48
Rel. | 52.8 | 16.3 | 0.43
Flu. | 50.1 | 5.9 | 0.45
ESCM vs. KEMP | Emp. | 44.0 | 20.0 | 0.57
Rel. | 53.3 | 21.0 | 0.46
Flu. | 35.4 | 13.4 | 0.41
ESCM vs. CEM | Emp. | 37.3 | 19.8 | 0.58
Rel. | 48.9 | 21.5 | 0.41
Flu. | 33.8 | 11.6 | 0.47
Table 2:  Results of human evaluation. For a more intuitive display, we remove
the result of the Tie and only show Win and Lose. Where $\kappa$ is the inter-
labeler agreement measured by Fleiss’s kappa Fleiss and Cohen (1973), and 0.4
$\textless$ $\kappa$ $\leq$ 0.6 indicates moderate agreement.

##  5 Results and Analysis

###  5.1 Main Results

Models | Acc | PPL | Dist-1 | Dist-2
---|---|---|---|---
ESCM | 41.19 | 34.82 | 1.19 | 4.11
w/o DESV | 39.21 | 34.10 | 1.07 | 3.52
w/o DCGCN | 39.05 | 33.52 | 1.08 | 3.69
w/o $V_{r}$ | 40.0 | 34.02 | 1.06 | 3.68
w/o $V_{p}$ | 39.41 | 34.45 | 0.99 | 3.33
w/o $V_{des}$ | 40.42 | 34.48 | 1.08 | 3.60
Table 3:  Results of the ablation experiments.

Automatic Evaluation Results. Table 1 shows the main results of the automatic
evaluation for all models. We find that early models (EmoPrend-1, MoEL, and
MIME) are not as effective as models that focus on subtle emotions (EmpDG,
KEMP, CEM). Additionally, we find that ESCM outperforms the baselines in all
metrics. In terms of diversity, ESCM significantly outperforms the baselines.
This suggests that focusing on the correlations between emotions and semantics
helps the model capture key semantics and express informative responses. ESCM
also outperforms the baselines in terms of emotion accuracy, indicating the
effectiveness of the dynamic emotion-semantic vectors. Furthermore, ESCM
achieves the best fluency, which indicates that the model combines emotions
and semantics to express more natural language.

Human Evaluation Results. As shown in Table 2, ESCM outperforms the three
strongest baselines in terms of empathy, relevance, and fluency. The
superiority in empathy indicates that the model accurately understands and
expresses emotions. The significant improvement in relevance suggests that the
model captures and expresses key semantics. The superiority in fluency
indicates that the model expresses more fluent responses by better
understanding the context.

###  5.2 Ablation Studies

To verify the effectiveness of each component, the following experiments are
conducted:

(1) w/o DESV: Dynamic emotion-semantic representations $H_{des}$ (in Eq. 6)
are replaced by context semantic representations $H_{ctx}$ (in Eq. 1);

(2) w/o DCGCN: No dynamic correlation graph convolutional network (in Eqs. 7
\- 9);

(3) w/o $V_{r}$/$V_{p}$/$V_{des}$: Without the guidance of vectors
$V_{r}$/$V_{p}$/$V_{des}$ (in Eq. 7) in the dynamic correlation graph
convolutional network.

The results of the ablation experiments are shown in Table 7. To verify the
effectiveness of the dynamic emotion-semantic vectors, we remove $DESV$. The
results show a significant decrease in emotional accuracy and diversity. The
drop in emotion accuracy suggests that dynamic emotion-semantic vectors play
an important role in capturing emotions. The changes in diversity metrics
demonstrate the crucial role of dynamic adjustment of emotions and semantics
in precise understanding and informative expression in conversations.

We remove $DCGCN$ and its various guiding vectors to verify the effectiveness
of the dynamic correlation graph convolutional network. After removing
$DCGCN$, we find a significant decrease in emotional accuracy and diversity.
This indicates that correlations have a significant impact on the perception
of emotions and semantics, and they play an important role in expressing
informative responses. We further explore the role of various guiding vectors.
When part-of-speech $V_{p}$ or dependency types $V_{r}$ are removed, the
emotional accuracy decreases significantly. This indicates that ESCM can
aggregate effective information related to emotions based on part-of-speech or
dependency types. After removing part-of-speech, dependency types, and
emotion-semantic vectors respectively, the diversity decreases significantly.
This indicates that these features affect the aggregation of semantic
information.

Furthermore, we find that removing any module improves the fluency of
responses but decreases diversity. This is mainly due to the fact that the
ablation models express responses with more fluent yet less information, such
as trivial sentences.

###  5.3 Correlation Analysis

To further explore the correlations, we conduct a statistical analysis of the
correlations in the EMPATHETIC-DIALOGUES dataset (see appendix A for details).
We extract 1138 correlations from the dialogue dataset, which are used a total
of 151242 times in the dialogue. This indicates that the correlation structure
is frequently and repeatedly used in the dialogue. In addition, we find that
emotions are mainly expressed through three parts of speech: adjectives,
nouns, and verbs. This is consistent with linguistic research Foolen et al.
(2012) on the parts of speech of emotional words. At the same time, we also
find that the “preposition + noun” structure is frequently used, which is also
consistent with linguistic research Foolen et al. (2012). In each emotion type
of empathetic dialogue, the frequently used correlation structures are
similar, but the frequency of use may differ.

###  5.4 Time and Resource Consumption

To further demonstrate the efficacy of the model, we conduct analytical
experiments on time and resource consumption.

Time Consumption. As shown in Table 4, we calculate the time for our model and
baselines to converge during training. The results show that our model does
not have significantly higher average per-iteration time compared to the
baselines. This is mainly because: although the intermediate variable $V_{qk}$
intuitively has higher dimensionality, in practice the dialogue context length
L is short, so the impact on time is not substantial. Meanwhile, since our
model can better understand the dialogue, it requires fewer iterations.
Therefore, the total training time is actually significantly less than the
baselines.

Resource Consumption. As shown in Table 5, we compute the GPU memory
consumption of the models. Due to the higher dimensionality of the
intermediate variable $d_{pr}$ in our model, our model requires slightly more
resources than the baselines (see last row). However, even when reducing the
GPU consumption of our model to be comparable to the baselines, our model
still significantly outperforms the baselines overall (see penultimate row).

Models | T1 (s) | T2 (s) | Num
---|---|---|---
KEMP | 0.17 | 4378.11 | 26,000
CEM | 0.22 | 4438.68 | 20,000
ESCM | 0.20 | 2733.94 | 13,500
Table 4:  Results of time consumption. T1 represents the average per-iteration time, T2 stands for the convergence time, and Num is the number of iterations needed for convergence.  Models |  PPL |  Acc |  Dist-1 |  Dist-2 |  Size(G)
---|---|---|---|---|---
KEMP |  39.31 |  36.89 |  0.55 |  2.29 |  6.02
CEM |  39.11 |  36.11 |  0.66 |  2.99 |  5.57
V1 |  33.74 |  40.21 |  0.98 |  3.17 |  4.64
V2 |  34.82 |  41.63 |  1.07 |  3.52 |  6.00
V3 |  34.82 |  41.19 |  1.19 |  4.11 |  8.10
Table 5:  Results under restricted resource consumption. ‘Size’ denotes the
GPU memory required to train the model. We list three ESCM models with
different $d_{pr}$ values, where V1, V2, and V3 represent models with
$d_{pr}=10$, $d_{pr}=20$, and $d_{pr}=50$, respectively.

###  5.5 Case Study

Emotion |  Annoyed
---|---
Conext |  I hate when my little brother throws food on the table just to annoy me
Gold |  That is a terrible waste of food, how old is your little brother?
CEM |  I would be mad too
KEMP |  I am sorry to hear that. I hope you can get it back soon.
ESCM |  That is really annoying. I hate when that happens.
Emotion |  Proud
Conext |  I am constantly amazed by my sister’s art skills. I am not sure where she got them … my brother and I can not draw to save our lives.
Gold |  What does she draw?
CEM |  That is awesome! I bet she’s a great job!
KEMP |  I am sure you will do great!
ESCM |  That is really cool. I bet you are very proud of her.
Table 6:  Case Study of ESCM and benchmarks. Words with Marked colors in the
sentence are rich in emotion.

As shown in Table 7, we select two strongest baselines and compare them with
ESCM through sample analysis. In the first case, The speaker is annoyed due to
the fact that “the younger brother threw food onto the table”. The baselines
do not accurately understand the emotional expression “annoyed” and the event
it described. However, ESCM understands and expresses “annoying” correctly,
and gives a response indicating disgust towards the event. This indicates that
ESCM is able to capture key semantics through correlations. In the second
case, the speaker expresses the emotion of “proud” using the word “amazed”
with a surprised emotion. The baselines do not understand the emotions and
semantics involved, while ESCM accurately understands the emotions and
expresses an empathetic response. This demonstrates the effectiveness of
building dynamic emotion-semantics.

##  6 Conclusion and Future Work

This paper proposes ESCM, which introduces two characteristics of emotions in
the linguistic expression process: variability and the correlations between
emotions and semantics. The proposed model constructs a dynamic emotion-
semantic vector to reflect variability and uses a dependency tree-based
dynamic correlation graph convolutional network to learn correlations. Both
automatic and manual metrics demonstrate the effectiveness of the model.
Furthermore, we conduct statistical analysis experiments. The results show
that correlations are frequently used in the dialogue. Additionally, we find
that the correlation structures in the dialogue are consistent with linguistic
research.

To further investigate the correlation between emotion and semantics, we will
take into account pre-trained knowledge, multilinguality, personalization, and
other factors in future work.

## Limitations

The limitations of our work are as follows: (1) Pre-trained models have become
the mainstream nowadays. To further explore the impact of pre-trained models,
we constructed a pre-trained ESCM model. Since the word coverage of the
EMPATHETIC-DIALOGUES dataset in the vocabulary of pre-trained models is only
51.8%, we only surpassed the baseline Emp-RFT Kim et al. (2022) on two metrics
(Acc: 42.44 (42.08), Dist-2: 9.91 (4.48)). In the future, we will further
explore the impact of pre-trained models on correlations. (2) The correlations
between emotions and semantics discussed in this paper are only applicable to
English. However, different languages may have different types of correlations
Foolen et al. (2012). Therefore, we will investigate the correlations between
emotions and semantics in multilingual contexts in the future. (3)
Intuitively, there are individual differences in the expression of emotions.
Due to data limitations, we did not consider this personalized factor. We will
involve more research on correlations and personalization in the future.

## Ethical Considerations

The potential ethical implications of our work are as follows: (1) Dataset:
EMPATHETICDIALOGUES is an open-source, publicly available dataset for
empathetic response generation. In the dataset, the original provider has
filtered information about personal privacy and ethical implications Rashkin
et al. (2019). (2) Models: Our baselines are also open source, and they have
no permission issues. Since our model is trained on a healthy dataset, it does
not generate discriminatory, abusive, or biased responses to users.

## Acknowledgments

We would like to express our sincere gratitude to the reviewers for their
diligent evaluation and constructive feedback, which helped improve the
quality of this paper. In addition, we appreciate the insightful discussions
and comments from the authors, which stimulated valuable thinking around this
work. Their diverse perspectives and experience shared through feedback have
contributed immensely to the development of this research. This work was
supported by National Natural Science Foundation of China (No.61976054).

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##  Appendix A Appendix

Figure 3:  The percentage of frequently used correlations to the total number of correlations.  Correlations/Percentage | Examples
---|---
ROOT-root-ADJ-b(7.22) |  joyful, scary
NOUN-amod-ADJ-b(6.51) | time good
VERB-dep-ADJ-b(4.66) | felt proud
ADP-pobj-NOUN-b(3.89) | into accident
ADJ-nsubj-PRON-f(3.4) |  nice it
Table 7:  Top 5 correlations that are frequently used in conversations.

Frequency Phenomenon. As shown in Figure 3, we list the correlation
statistical results. (1) As shown in “All Correlation” in Figure 3 (the
highest red line), for the overall correlations in the dataset, the top 10% of
frequently used correlations account for more than 80% of the total number of
correlations. That is, $\frac{C_{f}}{C_{total}}$=86.17%, where $C_{f}$ is the
number of frequently used correlations in the top 10%, and $C_{total}$ is the
total number of correlations used in the dataset.

(2) As shown in “Others: 32 Emotion Correlations” in Figure 3, for each type
of emotional empathetic dialogue, the top 20% of frequently used correlations
account for 80% of the total number of correlations. That is,
$\frac{C^{e}_{f}}{C^{e}_{total}}$ is approximately 80%. For example, the
number of empathetic dialogues expressing “joyful” emotion is
$C^{joyful}_{total}$=6083, and the number of frequently used associations in
the top 20% is $C^{joyful}_{f}$=4945, so $C^{joyful}_{f}/C^{joyful}_{total}$
is approximately 81.13%.

Type | Top1 | Top2
---|---|---
surprised(8281) | ROOT-root-ADJ-b(6.48) | NOUN-amod-ADJ-b(5.72)
excited(6471) | NOUN-amod-ADJ-b(8.27) | ROOT-root-ADJ-b(7.87)
annoyed(4210) | ROOT-root-ADJ-b(7.01) | ROOT-root-VERB-b(5.11)
proud(5915) | ROOT-root-ADJ-b(11.78) | NOUN-amod-ADJ-b(5.93)
angry(4859) | ROOT-root-ADJ-b(10.91) | ADJ-nsubj-PRON-f(5.97)
sad(3945) | NOUN-amod-ADJ-b(7.25) | ROOT-root-ADJ-b(5.65)
grateful(6487) | ROOT-root-ADJ-b(8.89) | NOUN-amod-ADJ-b(6.98)
lonely(3083) | NOUN-amod-ADJ-b(11.39) | ADP-pobj-NOUN-b(6.94)
impressed(5483) | ROOT-root-ADJ-b(9.5) | NOUN-amod-ADJ-b(7.5)
afraid(5276) | ROOT-root-ADJ-b(6.99) | NOUN-amod-ADJ-b(4.78)
disgusted(4326) | ROOT-root-ADJ-b(7.19) | VERB-dep-ADJ-b(5.27)
confident(4203) | VERB-dep-ADJ-b(7.52) | ROOT-root-ADJ-b(7.47)
terrified(5436) | ROOT-root-ADJ-b(5.98) | NOUN-amod-ADJ-b(4.67)
hopeful(4635) | NOUN-amod-ADJ-b(10.68) | ROOT-root-ADJ-b(7.62)
anxious(4946) | ROOT-root-ADJ-b(8.07) | VERB-dep-ADJ-b(6.29)
disappointed(3861) | NOUN-amod-ADJ-b(7.15) | ROOT-root-ADJ-b(6.81)
joyful(6083) | ROOT-root-ADJ-b(8.83) | NOUN-amod-ADJ-b(5.85)
prepared(3617) | ROOT-root-ADJ-b(6.99) | ADP-pobj-NOUN-b(6.58)
guilty(4979) | VERB-dep-ADJ-b(12.07) | VERB-acomp-ADJ-b(8.44)
furious(4978) | ROOT-root-ADJ-b(9.62) | ADJ-nsubj-PRON-f(4.74)
nostalgic(4012) | NOUN-amod-ADJ-b(9.92) | ROOT-root-ADJ-b(4.99)
jealous(5210) | NOUN-amod-ADJ-b(7.98) | ROOT-root-ADJ-b(6.93)
anticipating(4502) | NOUN-amod-ADJ-b(8.93) | ROOT-root-ADJ-b(6.13)
embarrassed(3289) | ROOT-root-ADJ-b(5.17) | VERB-dep-ADJ-b(4.68)
content(6632) | ROOT-root-ADJ-b(8.05) | NOUN-amod-ADJ-b(7.86)
devastated(3905) | ADP-pobj-NOUN-b(6.17) | ROOT-root-ADJ-b(4.87)
sentimental(3123) | NOUN-amod-ADJ-b(8.65) | ROOT-root-ADJ-b(6.56)
caring(4041) | ROOT-root-ADJ-b(6.68) | NOUN-amod-ADJ-b(5.57)
trusting(4193) | NOUN-amod-ADJ-b(6.65) | ROOT-root-ADJ-b(6.39)
ashamed(3758) | VERB-dep-ADJ-b(9.05) | NOUN-amod-ADJ-b(4.68)
apprehensive(4267) | NOUN-amod-ADJ-b(8.39) | ROOT-root-ADJ-b(7.05)
faithful(3236) | NOUN-amod-ADJ-b(8.0) | ROOT-root-ADJ-b(5.87)
Table 8:  Top 2 frequently used correlations in conversations for each
emotional dialogue. The numbers in the first column indicate the total number
of correlations for the emotional dialogue, while the numbers in the other
columns represent the percentage of times the correlations are used.

Part-of-Speech Phenomenon. As shown in Table 7, we list examples of the most
commonly used correlation structures. Taking “NOUN-amod-ADJ-b” as an example,
“NOUN-amod-ADJ” represents a noun and an adjective linked together by the
“amod” dependency type. “b” refers to the emotion word as the second word, and
“f” indicates that the emotion word is the first word. Specifically, “ROOT”
refers to the root node of the dependency tree. In the frequently used
correlations, emotions are mainly expressed through three parts of speech:
adjectives, nouns, and verbs, which is consistent with linguistic research
Foolen et al. (2012) on emotion words.

Correlation Structure Phenomenon. As shown in Table 7, we list the most
commonly used correlation structures for each type of emotion. We also find
that the “preposition + noun” method is frequently used, which is consistent
with linguistic research Foolen et al. (2012).

As shown in Table 8, we list the most commonly used correlations in various
emotional dialogues, with the numbers in parentheses indicating the
probability of their usage. In each type of emotional empathetic dialogue, the
frequently used correlation structures are similar, but the frequency of use
may vary.


Mathisorg103,org116&P.F.T. Matuokaorg120&A. Matyjaorg129,org117&C.
Mayerorg117&M. Mazzilliorg33&M.A. Mazzoniorg57&F. Meddiorg23&Y.
Melikyanorg91&A. Menchaca-Rochaorg72&E. Meninnoorg30&M. Meresorg14&S.
Mhlangaorg124&Y. Miakeorg132&L. Michelettiorg26&M.M. Mieskolainenorg43&D.L.
Mihaylovorg103&K. Mikhaylovorg64,org75&A. Mischkeorg63org*&A.N. Mishraorg70&D.
Miśkowiecorg104&J. Mitraorg140&C.M. Mituorg68&N. Mohammadiorg34&A.P.
Mohantyorg63&B. Mohantyorg85&M. Mohisin Khanorg17orgIII&M.M. Mondalorg66&C.
Mordasiniorg103&D.A. Moreira De Godoyorg143&L.A.P. Morenoorg44&S.
Morettoorg29&A. Morrealeorg113&A. Morschorg34&T. Mrnjavacorg34&V.
Mucciforaorg51&E. Mudnicorg35&D. Mühlheimorg143&S. Muhuriorg140&M.
Mukherjeeorg3&J.D. Mulliganorg145&M.G. Munhozorg120&K. Münningorg42&R.H.
Munzerorg69&H. Murakamiorg131&S. Murrayorg73&L. Musaorg34&J.
Musinskyorg65&C.J. Myersorg125&J.W. Myrchaorg141&B. Naikorg48&R.
Nairorg84&B.K. Nandiorg48&R. Naniaorg53,org10&E. Nappiorg52&M.U.
Naruorg15&A.F. Nassirpourorg80&H. Natal da Luzorg120&C. Nattrassorg129&S.R.
Navarroorg44&K. Nayakorg85&R. Nayakorg48&T.K. Nayakorg140,org85&S.
Nazarenkoorg106&R.A. Negrao De Oliveiraorg69&L. Nellenorg70&S.V. Nesboorg36&G.
Neskovicorg39&F. Ngorg125&B.S. Nielsenorg88&S. Nikolaevorg87&S.
Nikulinorg87&V. Nikulinorg96&F. Noferiniorg10,org53&P. Nomokonovorg75&G.
Noorenorg63&J.C.C. Norisorg44&J. Normanorg78&A. Nyaninorg87&J.
Nystrandorg22&M. Oginoorg81&A. Ohlsonorg102&J. Oleniaczorg141&A.C. Oliveira Da
Silvaorg120&M.H. Oliverorg145&J. Onderwaaterorg104&C. Oppedisanoorg58&R.
Oravaorg43&A. Ortiz Velasquezorg70&A. Oskarssonorg80&J. Otwinowskiorg117&K.
Oyamaorg81&Y. Pachmayerorg102&V. Pacikorg88&D. Paganoorg139&G. Paićorg70&P.
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Papikyanorg1&P. Pareekorg49&J. Parkorg60&J.E. Parkkilaorg126&S. Parmarorg98&A.
Passfeldorg143&S.P. Pathakorg125&R.N. Patraorg140&B. Paulorg58&H. Peiorg6&T.
Peitzmannorg63&X. Pengorg6&L.G. Pereiraorg71&H. Pereira Da Costaorg136&D.
Peresunkoorg87&G.M. Perezorg8&E. Perez Lezamaorg69&J. Peschekorg39&V.
Peskovorg69&Y. Pestovorg4&V. Petráčekorg37&M. Petroviciorg47&R.P.
Pezziorg71&S. Pianoorg59&M. Piknaorg14&P. Pillotorg113&L.O.D.L.
Pimentelorg88&O. Pinazzaorg53,org34&L. Pinskyorg125&S. Pisanoorg51&D.B.
Piyarathnaorg125&M. Płoskońorg79&M. Planinicorg97&F. Pliquettorg69&J.
Plutaorg141&S. Pochybovaorg144&P.L.M. Podesta-Lermaorg119&M.G.
Poghosyanorg94&B. Polichtchoukorg90&N. Poljakorg97&W. Poonsawatorg114&A.
Poporg47&H. Poppenborgorg143&S. Porteboeuf-Houssaisorg133&V.
Pozdniakovorg75&S.K. Prasadorg3&R. Preghenellaorg53&F. Prinoorg58&C.A.
Pruneauorg142&I. Pshenichnovorg62&M. Puccioorg26&V. Puninorg106&K.
Puranapandaorg140&J. Putschkeorg142&R.E. Quishpeorg125&S. Ragoniorg108&S.
Rahaorg3&S. Rajputorg99&J. Rakorg126&A. Rakotozafindrabeorg136&L.
Ramelloorg32&F. Ramiorg135&R. Raniwalaorg100&S. Raniwalaorg100&S.S.
Räsänenorg43&B.T. Rascanuorg69&R. Rathorg49&V. Ratzaorg42&I.
Ravasengaorg31&K.F. Readorg129,org94&K. Redlichorg84orgIV&A. Rehmanorg22&P.
Reicheltorg69&F. Reidtorg34&X. Renorg6&R. Renfordtorg69&A. Reshetinorg62&J.-P.
Revolorg10&K. Reygersorg102&V. Riabovorg96&T. Richertorg88,org80&M.
Richterorg21&P. Riedlerorg34&W. Rieglerorg34&F. Riggiorg28&C. Risteaorg68&S.P.
Rodeorg49&M. Rodríguez Cahuantziorg44&K. Røedorg21&R. Rogalevorg90&E.
Rogochayaorg75&D. Rohrorg34&D. Röhrichorg22&P.S. Rokitaorg141&F.
Ronchettiorg51&E.D. Rosasorg70&K. Roslonorg141&P. Rosnetorg133&A.
Rossiorg56,org29&A. Rotondiorg138&F. Roukoutakisorg83&A. Royorg49&P.
Royorg107&O.V. Ruedaorg80&R. Ruiorg25&B. Rumyantsevorg75&A. Rustamovorg86&E.
Ryabinkinorg87&Y. Ryabovorg96&A. Rybickiorg117&S. Saarinenorg43&S.
Sadhuorg140&S. Sadovskyorg90&K. Šafaříkorg34,org37&S.K. Sahaorg140&B.
Sahooorg48&P. Sahooorg49&R. Sahooorg49&S. Sahooorg66&P.K. Sahuorg66&J.
Sainiorg140&S. Sakaiorg132&S. Sambyalorg99&V. Samsonovorg91,org96&A.
Sandovalorg72&A. Sarkarorg73&D. Sarkarorg140&N. Sarkarorg140&P.
Sarmaorg41&V.M. Sartiorg103&M.H.P. Sasorg63&E. Scapparoneorg53&B.
Schaeferorg94&J. Schambachorg118&H.S. Scheidorg69&C. Schiauaorg47&R.
Schickerorg102&A. Schmahorg102&C. Schmidtorg104&H.R. Schmidtorg101&M.O.
Schmidtorg102&M. Schmidtorg101&N.V. Schmidtorg94,org69&A.R. Schmierorg129&J.
Schukraftorg34,org88&Y. Schutzorg34,org135&K. Schwarzorg104&K.
Schwedaorg104&G. Scioliorg27&E. Scomparinorg58&M. Šefčíkorg38&J.E.
Segerorg16&Y. Sekiguchiorg131&D. Sekihataorg45&I. Selyuzhenkovorg104,org91&S.
Senyukovorg135&E. Serradillaorg72&P. Settorg48&A. Sevcencoorg68&A.
Shabanovorg62&A. Shabetaiorg113&R. Shahoyanorg34&W. Shaikhorg107&A.
Shangaraevorg90&A. Sharmaorg98&A. Sharmaorg99&M. Sharmaorg99&N.
Sharmaorg98&A.I. Sheikhorg140&K. Shigakiorg45&M. Shimomuraorg82&S.
Shirinkinorg64&Q. Shouorg6,org110&Y. Sibiriakorg87&S. Siddhantaorg54&T.
Siemiarczukorg84&D. Silvermyrorg80&G. Simatovicorg89&G.
Simonettiorg103,org34&R. Singhorg85&R. Singhorg99&V.K. Singhorg140&V.
Singhalorg140&T. Sinhaorg107&B. Sitarorg14&M. Sittaorg32&T.B. Skaaliorg21&M.
Slupeckiorg126&N. Smirnovorg145&R.J.M. Snellingsorg63&T.W. Snellmanorg126&J.
Sochanorg115&C. Sonccoorg109&J. Songorg60&A. Songmoolnakorg114&F.
Soramelorg29&S. Sorensenorg129&F. Sozziorg104&I. Sputowskaorg117&J.
Stachelorg102&I. Stanorg68&P. Stankusorg94&T. M. Steinbeckorg39&E.
Stenlundorg80&D. Stoccoorg113&M.M. Storetvedtorg36&P. Strmenorg14&A.A.P.
Suaideorg120&T. Sugitateorg45&C. Suireorg61&M. Suleymanovorg15&M.
Suljicorg34&R. Sultanovorg64&M. Šumberaorg93&S. Sumowidagdoorg50&K.
Suzukiorg112&S. Swainorg66&A. Szaboorg14&I. Szarkaorg14&U. Tabassamorg15&J.
Takahashiorg121&G.J. Tambaveorg22&N. Tanakaorg132&M. Tarhiniorg113&M.G.
Tarzilaorg47&A. Tauroorg34&G. Tejeda Muñozorg44&A. Telescaorg34&C.
Terrevoliorg29,org125&J. M. Thaederorg39&D. Thakurorg49&S. Thakurorg140&D.
Thomasorg118&F. Thoresenorg88&R. Tieulentorg134&A. Tikhonovorg62&A.R.
Timminsorg125&A. Toiaorg69&N. Topilskayaorg62&M. Toppiorg51&S.R.
Torresorg119&S. Tripathyorg49&T. Tripathyorg48&S. Trogoloorg26&G.
Trombettaorg33&L. Tropporg38&V. Trubnikovorg2&W.H. Trzaskaorg126&T.P.
Trzcinskiorg141&B.A. Trzeciakorg63&T. Tsujiorg131&A. Tumkinorg106&R.
Turrisiorg56&T.S. Tveterorg21&K. Ullalandorg22&E.N. Umakaorg125&A.
Urasorg134&G.L. Usaiorg24&A. Utrobicicorg97&M. Valaorg38,org115&L. Valencia
Palomoorg44&N. Valleorg138&N. van der Kolkorg63&L.V.R. van Doremalenorg63&J.W.
Van Hoorneorg34&M. van Leeuwenorg63&P. Vande Vyvreorg34&D. Vargaorg144&A.
Vargasorg44&M. Vargyasorg126&R. Varmaorg48&M. Vasileiouorg83&A.
Vasilievorg87&O. Vázquez Doceorg116,org103&V. Vecherninorg111&A.M.
Veenorg63&E. Vercellinorg26&S. Vergara Limónorg44&L. Vermuntorg63&R.
Vernetorg7&R. Vértesiorg144&L. Vickovicorg35&J. Viinikainenorg126&Z.
Vilakaziorg130&O. Villalobos Baillieorg108&A. Villatoro Telloorg44&G.
Vinoorg52&A. Vinogradovorg87&T. Virgiliorg30&V. Vislaviciusorg88&A.
Vodopyanovorg75&B. Volkelorg34&M.A. Völklorg101&K. Voloshinorg64&S.A.
Voloshinorg142&G. Volpeorg33&B. von Hallerorg34&I. Vorobyevorg103,org116&D.
Voscekorg115&J. Vrlákováorg38&B. Wagnerorg22&M. Wangorg6&Y. Watanabeorg132&M.
Weberorg112&S.G. Weberorg104&A. Wegrzynekorg34&D.F. Weiserorg102&S.C.
Wenzelorg34&J.P. Wesselsorg143&U. Westerhofforg143&A.M. Whiteheadorg124&E.
Widmannorg112&J. Wiechulaorg69&J. Wikneorg21&G. Wilkorg84&J.
Wilkinsonorg53&G.A. Willemsorg143,org34&E. Willsherorg108&B.
Windelbandorg102&W.E. Wittorg129&Y. Wuorg128&R. Xuorg6&S. Yalcinorg77&K.
Yamakawaorg45&S. Yanoorg136&Z. Yinorg6&H. Yokoyamaorg63&I.-K. Yooorg18&J.H.
Yoonorg60&S. Yuanorg22&V. Yurchenkoorg2&V. Zaccoloorg58,org25&A. Zamanorg15&C.
Zampolliorg34&H.J.C. Zanoliorg120&N. Zardoshtiorg34,org108&A.
Zarochentsevorg111&P. Závadaorg67&N. Zaviyalovorg106&H. Zbroszczykorg141&M.
Zhalovorg96&X. Zhangorg6&Y. Zhangorg6&Z. Zhangorg6,org133&C. Zhaoorg21&V.
Zherebchevskiiorg111&N. Zhigarevaorg64&D. Zhouorg6&Y. Zhouorg88&Z.
Zhouorg22&H. Zhuorg6&J. Zhuorg6&Y. Zhuorg6&A. Zichichiorg27,org10&M.B.
Zimmermannorg34&G. Zinovjevorg2&N. Zurloorg139&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

orgIIM.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of
Nuclear, Physics, Moscow, Russia

orgIIIDepartment of Applied Physics, Aligarh Muslim University, Aligarh, India

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

org1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

org2Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

org3Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

org5California Polytechnic State University, San Luis Obispo, California,
United States

org6Central China Normal University, Wuhan, China

org7Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

org8Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org9Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org10Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

org14Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org15COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

org18Department of Physics, Pusan National University, Pusan, Republic of
Korea

org19Department of Physics, Sejong University, Seoul, Republic of Korea

org20Department of Physics, University of California, Berkeley, California,
United States

org21Department of Physics, University of Oslo, Oslo, Norway

org22Department of Physics and Technology, University of Bergen, Bergen,
Norway

org23Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org24Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org25Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org26Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

org27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org29Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org30Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org34European Organization for Nuclear Research (CERN), Geneva, Switzerland

org35Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

org36Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

org37Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org38Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org39Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

org42Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

org44High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

org45Hiroshima University, Hiroshima, Japan

org46Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

org47Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

org48Indian Institute of Technology Bombay (IIT), Mumbai, India

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

org61Institut de Physique Nucléaire d’Orsay (IPNO), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3/CNRS), Université de
Paris-Sud, Université Paris-Saclay, Orsay, France

org62Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org63Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht,
Netherlands

org64Institute for Theoretical and Experimental Physics, Moscow, Russia

org65Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org66Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

org67Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org68Institute of Space Science (ISS), Bucharest, Romania

org69Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org70Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org71Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org72Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org73iThemba LABS, National Research Foundation, Somerset West, South Africa

org74Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org75Joint Institute for Nuclear Research (JINR), Dubna, Russia

org76Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org77KTO Karatay University, Konya, Turkey

org78Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org79Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org80Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org81Nagasaki Institute of Applied Science, Nagasaki, Japan

org82Nara Women’s University (NWU), Nara, Japan

org83National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org84National Centre for Nuclear Research, Warsaw, Poland

org85National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org86National Nuclear Research Center, Baku, Azerbaijan

org87National Research Centre Kurchatov Institute, Moscow, Russia

org88Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org89Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org90NRC Kurchatov Institute IHEP, Protvino, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

org92Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org93Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org94Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

org97Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

org101Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

org102Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org103Physik Department, Technische Universität München, Munich, Germany

org104Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org105Rudjer Bošković Institute, Zagreb, Croatia

org106Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org107Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org108School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org109Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org110Shanghai Institute of Applied Physics, Shanghai, China

org111St. Petersburg State University, St. Petersburg, Russia

org112Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org113SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org114Suranaree University of Technology, Nakhon Ratchasima, Thailand

org115Technical University of Košice, Košice, Slovakia

org116Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

org117The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org118The University of Texas at Austin, Austin, Texas, United States

org119Universidad Autónoma de Sinaloa, Culiacán, Mexico

org120Universidade de São Paulo (USP), São Paulo, Brazil

org121Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org122Universidade Federal do ABC, Santo Andre, Brazil

org123University College of Southeast Norway, Tonsberg, Norway

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Techonology of China, Hefei, China

org129University of Tennessee, Knoxville, Tennessee, United States

org130University of the Witwatersrand, Johannesburg, South Africa

org131University of Tokyo, Tokyo, Japan

org132University of Tsukuba, Tsukuba, Japan

org133Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org134Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org135Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org136 Université Paris-Saclay Centre d¿Études de Saclay (CEA), IRFU,
Department de Physique Nucléaire (DPhN), Saclay, France

org137Università degli Studi di Foggia, Foggia, Italy

org138Università degli Studi di Pavia, Pavia, Italy

org139Università di Brescia, Brescia, Italy

org140Variable Energy Cyclotron Centre, Homi Bhabha National Institute,
Kolkata, India

org141Warsaw University of Technology, Warsaw, Poland

org142Wayne State University, Detroit, Michigan, United States

org143Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

org144Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org145Yale University, New Haven, Connecticut, United States

org146Yonsei University, Seoul, Republic of Korea