F}}}{2\pi^{2}}\left(1+\ln\frac{16}{{{\tilde{E}}^{\rm sq}_{\rm F}}}\right)+\\\
+\left(A_{I3}-\frac{41}{6\pi}\right)\tau^{3}+\frac{{{\tilde{E}}^{\rm sq}_{\rm
F}}}{2\pi^{2}}\left(\frac{\left({{\tilde{E}}^{\rm sq}_{\rm
F}}\right)^{2}}{576}\left(-2+3\ln\frac{16}{{{\tilde{E}}^{\rm sq}_{\rm
F}}}\right)+\frac{\tau{{\tilde{E}}^{\rm sq}_{\rm
F}}}{8}\left(1-2\ln\frac{16}{{{\tilde{E}}^{\rm sq}_{\rm
F}}}\right)+2\tau^{2}\ln\frac{16}{{{\tilde{E}}^{\rm sq}_{\rm
F}}}\right)+o((|\tau|+|{{\tilde{E}}^{\rm sq}_{\rm F}}|)^{4}).$ (200)

We substitute this result in Eq. (184), where, for convenience, the parameter
$w=\tau/{{\tilde{E}}^{\rm sq}_{\rm F}}$ is introduced, which results in the
equation

$w=w_{0}({{\tilde{E}}^{\rm sq}_{\rm F}})\\\ +\frac{\left({{\tilde{E}}^{\rm
sq}_{\rm
F}}\right)^{2}}{8}\left[\frac{1}{576}\left(-2+3\ln\frac{16}{{{\tilde{E}}^{\rm
sq}_{\rm F}}}\right)+\frac{w}{8}\left(1-2\ln\frac{16}{{{\tilde{E}}^{\rm
sq}_{\rm F}}}\right)+2w^{2}\ln\frac{16}{{{\tilde{E}}^{\rm sq}_{\rm
F}}}+2(A_{I3}\pi-41/6)\pi w^{3}\right]=0.$ (201)

The leading-order solution of this equation yields the expression (77) of the
main text. So we have up to subleading order

$w({{\tilde{E}}^{\rm sq}_{\rm F}})\simeq w_{0}({{\tilde{E}}^{\rm sq}_{\rm
F}})+\gamma\left(w_{0}\left({{\tilde{E}}^{\rm sq}_{\rm
F}}\right)\right)\left({{\tilde{E}}^{\rm sq}_{\rm F}}\right)^{2},$ (202)

where

$\gamma(w)=\frac{1}{8}\left(Bw^{3}-4w^{2}+5w/12-5/576\right),$ (203)

and $B=2A_{I3}\pi^{2}-41\pi/3+16=7.11111$.

Analogous program can be implemented for Eq. (186)

$\mathcal{E}_{\rm sq}(\tau,{{\tilde{E}}^{\rm sq}_{\rm F}})=\mathcal{E}_{\rm
bnd}(\tau)+\mathcal{E}_{0}(\tau)+\mathcal{E}_{\rm sing}(\tau,{{\tilde{E}}^{\rm
sq}_{\rm F}}),$ (204)

where

$\mathcal{E}^{\rm sq}_{\rm
bnd}(\tau)=\int\limits_{\varepsilon_{1}(\tau)}^{\varepsilon_{1}}\varepsilon\rho(\varepsilon,\tau)d\varepsilon,\\\
\mathcal{E}^{\rm
sq}_{0}(\tau)=\int\limits_{\varepsilon_{1}}^{0}\varepsilon\rho(\varepsilon,\tau)d\varepsilon,\\\
\mathcal{E}^{\rm sq}_{\rm sing}(\tau,{{\tilde{E}}^{\rm sq}_{\rm
F}})=\int\limits_{0}^{{{\tilde{E}}^{\rm sq}_{\rm
F}}}\varepsilon\rho(\varepsilon,\tau)d\varepsilon.$ (205)

We get analogously to the derivation (191) and (192)

$\mathcal{E}^{\rm sq}_{\rm
bnd}(\tau)=\frac{8\tau}{\pi}+\frac{4\tau^{2}}{\pi}+\frac{14\tau^{3}}{\pi}+\frac{265\tau^{4}}{6\pi}+O\left(\tau^{5}\right)$
(206) $\mathcal{E}^{\rm sq}_{\rm sing}(\tau,{{\tilde{E}}^{\rm sq}_{\rm
F}})=\frac{\left({{\tilde{E}}^{\rm sq}_{\rm
F}}\right)^{2}}{2\pi^{2}}\left(\frac{1+2\ln\frac{16}{{{\tilde{E}}^{\rm
sq}_{\rm F}}}}{4}\right.\\\ \left.+\frac{\left({{\tilde{E}}^{\rm sq}_{\rm
F}}\right)^{2}}{1024}\left(-3+4\ln\frac{16}{{{\tilde{E}}^{\rm sq}_{\rm
F}}}\right)+\frac{\tau{{\tilde{E}}^{\rm sq}_{\rm
F}}}{18}\left(2-3\ln\frac{16}{{{\tilde{E}}^{\rm sq}_{\rm
F}}}\right)+\frac{\tau^{2}}{2}\left(-1+2\ln\frac{16}{{{\tilde{E}}^{\rm
sq}_{\rm F}}}\right)\right)+o(\text{4th order}).$ (207) $\mathcal{E}^{\rm
sq}_{0}(\tau)=\mathcal{E}_{0}(0)+A_{\mathcal{E}1}\tau+A_{\mathcal{E}2}\tau^{2}+A_{\mathcal{E}3}\tau^{3}+A_{\mathcal{E}4}\tau^{4}+o(\tau^{4}),$
(208)

where $\mathcal{E}_{0}(0)=-8/\pi^{2}$,

$A_{\mathcal{E}n}=\frac{1}{n!}\int\limits_{\varepsilon_{1}}^{0}\varepsilon\left.\frac{\partial^{n}\rho(\varepsilon,\tau)}{\partial\tau}\right|_{\tau=0}d\varepsilon,$
(209)

and numerical calculation yields

$\displaystyle A_{\mathcal{E}1}$ $\displaystyle=$ $\displaystyle 2-8/\pi,$
(210) $\displaystyle A_{\mathcal{E}2}$ $\displaystyle=$
$\displaystyle-1.81362,$ (211) $\displaystyle A_{\mathcal{E}3}$
$\displaystyle=$ $\displaystyle-14/\pi,$ (212) $\displaystyle
A_{\mathcal{E}4}$ $\displaystyle=$ $\displaystyle-14.455.$ (213)

Summing all contributions we have

$\mathcal{E}_{\rm sq}(\tau,{{\tilde{E}}^{\rm sq}_{\rm
F}})=-8/\pi^{2}+2\tau+\left(A_{\mathcal{E}2}+\frac{4}{\pi}\right)\tau^{2}+\left(A_{\mathcal{E}4}+\frac{265}{6\pi}\right)\tau^{4}\\\
+\frac{\left({{\tilde{E}}^{\rm sq}_{\rm
F}}\right)^{2}}{2\pi^{2}}\left(\frac{1+2\ln\frac{16}{{{\tilde{E}}^{\rm
sq}_{\rm F}}}}{4}+\frac{\left({{\tilde{E}}^{\rm sq}_{\rm
F}}\right)^{2}}{1024}\left(-3+4\ln\frac{16}{{{\tilde{E}}^{\rm sq}_{\rm
F}}}\right)+\frac{\tau{{\tilde{E}}^{\rm sq}_{\rm
F}}}{18}\left(2-3\ln\frac{16}{{{\tilde{E}}^{\rm sq}_{\rm
F}}}\right)+\frac{\tau^{2}}{2}\left(-1+2\ln\frac{16}{{{\tilde{E}}^{\rm
sq}_{\rm F}}}\right)\right).$ (214)

We now substitute $\tau=w{{\tilde{E}}^{\rm sq}_{\rm
F}}=\left(w_{0}+\gamma\left({{\tilde{E}}^{\rm sq}_{\rm
F}}\right)^{2}\right){{\tilde{E}}^{\rm sq}_{\rm F}}$ to obtain

$\mathcal{E}_{\rm sq}(\tau,{{\tilde{E}}^{\rm sq}_{\rm
F}})=-8/\pi^{2}+2\tau+\sum_{k=2,4}\sum_{n=0}^{k}a^{\rm
sq}_{kn}w^{n}_{0}({{\tilde{E}}^{\rm sq}_{\rm F}})\left({{\tilde{E}}^{\rm
sq}_{\rm F}}\right)^{k},$ (215)

where coefficients $a^{\rm sq}_{kn}$ read

$\displaystyle a^{\rm sq}_{20}$ $\displaystyle=$
$\displaystyle-1/(8\pi^{2})=-0.0126651,$ (216) $\displaystyle a^{\rm sq}_{21}$
$\displaystyle=$ $\displaystyle 2/\pi^{2}=0.202642,$ (217) $\displaystyle
a^{\rm sq}_{22}$ $\displaystyle=$ $\displaystyle
A_{\mathcal{E}2}+{4}/{\pi}=-0.54038,$ (218) $\displaystyle a^{\rm sq}_{40}$
$\displaystyle=$ $\displaystyle-7/(2048\pi^{2})=-0.000346313,$ (219)
$\displaystyle a^{\rm sq}_{41}$ $\displaystyle=$
$\displaystyle-5A_{\mathcal{E}2}/2304+(89-5\pi)/(576\pi^{2})=0.0168282,$ (220)
$\displaystyle a^{\rm sq}_{42}$ $\displaystyle=$ $\displaystyle
5A_{\mathcal{E}2}/48+(5\pi-17)/(12\pi^{2})=-0.199828,$ (221) $\displaystyle
a^{\rm sq}_{43}$ $\displaystyle=$ $\displaystyle
4(1-\pi)/\pi^{2}-A_{\mathcal{E}2}=0.945664,$ (222) $\displaystyle a^{\rm
sq}_{44}$ $\displaystyle=$ $\displaystyle\frac{1}{4}A_{\mathcal{E}2}B+2\pi
A_{I3}+A_{\mathcal{E}4}+\frac{361-82\pi}{6\pi}=-1.35695.$ (223)

Sc lattice. We expand the free energy per one spin projection

$\mathcal{E}_{\rm sc}(\tau)=\frac{1}{N}\sum_{\mathbf{k}}t^{\rm
sc}_{\mathbf{k}}\theta({E^{\rm sc}_{\rm F}}-t^{\rm sc}_{\mathbf{k}}(\tau)),$
(224)

for sc lattice with electron spectrum

$t^{\rm sc}_{\mathbf{k}}(\tau)=[-2(\cos k_{x}+\cos k_{y}+\cos
k_{z})+4\tau(\cos k_{x}\cos k_{y}+\cos k_{y}\cos k_{z}+\cos k_{x}\cos
k_{z})]t.$ (225)

where the Fermi energy ${E^{\rm sc}_{\rm F}}$ is determined from the equation

$I_{\rm sc}(\tau)=\frac{1}{N}\sum_{\mathbf{k}}\theta({E^{\rm sc}_{\rm
F}}-t^{\rm sc}_{\mathbf{k}}(\tau))=1/2.$ (226)

Below we omit the argument of $t^{\rm sc}_{\mathbf{k}}$ for brevity. We
directly differentiate Eq. (226) with respect to $\tau$ to obtain

$\frac{1}{N}\sum_{\mathbf{k}}\partial_{\tau}({E^{\rm sc}_{\rm F}}-t^{\rm
sc}_{\mathbf{k}})\delta({E^{\rm sc}_{\rm F}}-t^{\rm
sc}_{\mathbf{k}}(\tau))=0,$ (227)

so we obtain

$\partial_{\tau}{E^{\rm sc}_{\rm F}}=\rho^{\rm sc}_{1}({E^{\rm sc}_{\rm
F}})/\rho^{\rm sc}_{0}({E^{\rm sc}_{\rm F}}),$ (228)

where the partial DOS

$\rho^{\rm sc}_{n}(E;\tau)=\frac{1}{N}\sum_{\mathbf{k}}[\partial_{\tau}t^{\rm
sc}_{\mathbf{k}}(\tau)]^{n}\delta(E-t^{\rm sc}_{\mathbf{k}}(\tau))$ (229)

is introduced and $\rho^{\rm sc}_{0}(E;\tau)=\rho_{\rm sc}(E,\tau)$. We expand
$\mathcal{E}_{\rm sc}(\tau)$ in powers of $\tau$ to calculate

$\frac{\partial\mathcal{E}_{\rm
sc}}{\partial\tau}=\frac{1}{N}\sum_{\mathbf{k}}[t^{\rm
sc}_{\mathbf{k}}\partial_{\tau}({E^{\rm sc}_{\rm F}}-t^{\rm
sc}_{\mathbf{k}})\delta({E^{\rm sc}_{\rm F}}-t^{\rm
sc}_{\mathbf{k}})+\partial_{\tau}t^{\rm sc}_{\mathbf{k}}\theta({E^{\rm
sc}_{\rm F}}-t^{\rm sc}_{\mathbf{k}})].$ (230)

Due to Eq. (226) the first term vanishes. Using the bipartite character of the
lattice, $E_{\rm F}(0)=0$, $\partial_{\tau}t^{\rm
sc}_{\mathbf{k}+\mathbf{Q}}=\partial_{\tau}t^{\rm sc}_{\mathbf{k}}$, $t^{\rm
sc}_{\mathbf{k}+\mathbf{Q}}(\tau=0)=-t^{\rm sc}_{\mathbf{k}}(\tau=0)$, we
shift summation momentum $\mathbf{k}\rightarrow\mathbf{k}+\mathbf{Q}$ in the
latter formula at $\tau=0$ and obtain

$\left.\frac{\partial\mathcal{E}_{\rm
sc}}{\partial\tau}\right|_{\tau=0}=\frac{1}{N}\sum_{\mathbf{k}}\partial_{\tau}t^{\rm
sc}_{\mathbf{k+\mathbf{Q}}}\theta({E^{\rm sc}_{\rm F}}-t^{\rm
sc}_{\mathbf{k}+\mathbf{Q}}(\tau=0))]=0.$ (231)

From the Eq. (230) we get

$\frac{\partial^{2}\mathcal{E}_{\rm
sc}}{\partial\tau^{2}}=\sum_{\mathbf{k}}\partial_{\tau}t^{\rm
sc}_{\mathbf{k}}\cdot\partial_{\tau}({E^{\rm sc}_{\rm F}}-t^{\rm
sc}_{\mathbf{k}})\delta({E^{\rm sc}_{\rm F}}-t^{\rm
sc}_{\mathbf{k}})=(\partial_{\tau}{E^{\rm sc}_{\rm F}})\rho_{1}({E^{\rm
sc}_{\rm F}};\tau)-\rho_{2}({E^{\rm sc}_{\rm F}};\tau).$ (232)

Using Eq. (228) we obtain

$\frac{\partial^{2}\mathcal{E}_{\rm
sc}}{\partial\tau^{2}}=\frac{\left(\rho^{\rm
sc}_{1}(E;\tau)\right)^{2}}{\rho_{\rm sc}(E;\tau)}-\rho^{\rm sc}_{2}(E;\tau).$
(233)

We calculate $\rho^{\rm sc}_{n}({E^{\rm sc}_{\rm F}}=0)$, that corresponds to
the case of half-filling,

$\rho_{n}({E^{\rm sc}_{\rm
F}}=0)=\frac{4^{n}}{2t}\int\frac{d\mathbf{k}}{(2\pi)^{3}}(\cos k_{x}\cos
k_{y}+\cos k_{y}\cos k_{z}+\cos k_{x}\cos k_{z})^{n}\delta(\cos k_{x}+\cos
k_{y}+\cos k_{z}).$ (234)

Since for the integration domain $\cos k_{z}=-\cos k_{x}-\cos k_{y}$,

$\rho_{n}({E^{\rm sc}_{\rm
F}}=0)=\frac{(-4)^{n}}{2t}\int\frac{d\mathbf{k}}{(2\pi)^{3}}(\cos^{2}k_{x}+\cos^{2}k_{y}+\cos
k_{x}\cos k_{y})^{n}\delta(\cos k_{x}+\cos k_{y}+\cos k_{z}).$ (235)

Introducing $r_{a}=\cos k_{a}$, $a=x,y,z$ we have

$\rho_{n}({E^{\rm sc}_{\rm
F}}=0)=\frac{(-4)^{n}}{2t\pi^{3}}\int\limits_{-1}^{+1}\frac{dr_{x}}{\sqrt{1-r_{x}^{2}}}\int\limits_{-1}^{+1}\frac{dr_{y}}{\sqrt{1-r_{y}^{2}}}\int\limits_{-1}^{+1}\frac{dr_{z}}{\sqrt{1-r_{z}^{2}}}(r_{x}^{2}+r^{2}_{y}+r_{x}r_{y})^{n}\delta(r_{x}+r_{y}+r_{z}).$
(236)

We take into account that the regions $r_{x}<0,r_{y}>0$ and $r_{x}>0,r_{y}<0$
yield the same contributions; the same takes place also for $r_{x},r_{y}<0$
and $r_{x},r_{y}>0$ (we account this by adding the factor of 2).

$\rho_{n}({E^{\rm sc}_{\rm
F}}=0)=\frac{(-4)^{n}}{\pi^{3}t}\left[\int\limits_{0}^{+1}\frac{dr_{x}}{\sqrt{1-r_{x}^{2}}}\int\limits_{0}^{+1}\frac{dr_{y}}{\sqrt{1-r_{y}^{2}}}\frac{(r_{x}^{2}+r^{2}_{y}+r_{x}r_{y})^{n}}{\sqrt{1-(r_{x}+r_{y})^{2}}}\theta(1-r_{x}+r_{y})+\right.\\\
\left.+\int\limits_{0}^{+1}\frac{dr_{x}}{\sqrt{1-r_{x}^{2}}}\int\limits_{0}^{+1}\frac{dr_{y}}{\sqrt{1-r_{y}^{2}}}\frac{(r_{x}^{2}+r^{2}_{y}-r_{x}r_{y})^{n}}{\sqrt{1-(r_{x}-r_{y})^{2}}}\right].$
(237)

Direct numerical calculation yields $\rho^{\rm sc}_{0}(0;0)=0.142127$,
$\rho^{\rm sc}_{1}(0;0)=-0.353038$, $\rho^{\rm sc}_{2}(0;0)=1.023248$ then the
formula (233) yields at $\tau=0$,

$a^{\rm sc}_{2,\rm PM}\equiv\frac{\left[\rho^{\rm
sc}_{1}(0;0)\right]^{2}}{\rho_{\rm sc}(0;0)}-\rho^{\rm
sc}_{2}(0;0)=-0.146317.$ (238)

Therefore we get to the leading order the free energy per one spin projection

$\mathcal{E}_{\rm sc}(\tau)\approx\mathcal{E}_{\rm sc}(0)+{a^{\rm sc}_{2,\rm
PM}}\tau^{2}/2.$

## References

  * (1) R.J. Jelitto, J. Phys. Chem. Solids 30, 609 (1969).
  * (2) S. Katsura and T. Horiguchi, J. Math. Phys. 12, 230 (1971).


[affiliation=1,2]ConorAtkins [affiliation=1,2]IanWood [affiliation=1,2]Mohamed
AliKaafar [affiliation=1]HassanAsghar [affiliation=1,2]NardineBasta
[affiliation=1,2]MichalKepkowski

# ConvoCache: Smart Re-Use of Chatbot Responses

###### Abstract

We present ConvoCache, a conversational caching system that solves the problem
of slow and expensive generative AI models in spoken chatbots. ConvoCache
finds a semantically similar prompt in the past and reuses the response. In
this paper we evaluate ConvoCache on the DailyDialog dataset. We find that
ConvoCache can apply a UniEval coherence threshold of 90% and respond to 89%
of prompts using the cache with an average latency of 214ms, replacing LLM and
voice synthesis that can take over 1s. To further reduce latency we test
prefetching and find limited usefulness. Prefetching with 80% of a request
leads to a 63% hit rate, and a drop in overall coherence. ConvoCache can be
used with any chatbot to reduce costs by reducing usage of generative AI by up
to 89%.

###### keywords:

semantic similarity, cache, conversational service, open domain conversation,
chit chat.

##  1 Introduction

A significant problem in providing spoken chatbot systems is the cost and
latency. While recent large language models (LLMs) and voice synthesis have
become more realistic, they have also become slower and more expensive. Using
GPT-4-turbo and ElevenLabs, for example, can cost around $ 0.01 USD per
utterance of 10 words111Assuming 150 tokens of prompt$+$dialogue history,
using public price as of 3rd March 2024., which will scale with every user and
every utterance. The user perceived latency of such a service can be 1–2s,
based on systems developed by the authors, while research shows humans prefer
a 200–500ms delay with a limit around 1.1s [1, 2]. Humans typically take
100–350ms to respond [1, 3]. This limits the believably of spoken chatbots due
to slow responses.

We propose ConvoCache to reduce the cost and latency of chatbot systems.
ConvoCache can rapidly reuse responses from past conversation for most
requests (Figure 1).

Not all conversations will fit responses that have been generated before.
ConvoCache generates multiple response candidates which are evaluated using a
fast automatic dialogue evaluation model such as UniEval [4]. If there are no
good responses available (a cache-miss), then a new response will be generated
and saved to our cache. A turn-taking filler word like ``um'' could be used to
reduce the perceived delay naturally during a cache-miss [1].

While the dialogue quality may be impacted by caching, we find in this paper
that the impact is minor. We promote the use of ConvoCache in applications
that allow for less accuracy such as generic chit chat and small talk,
especially low latency voice chatbots. Creating a phone call chatbot that is
as believable as a human requires low latency and very realistic voice
synthesis—which can be slow. Our approach makes this possible and makes
deployment at scale cheaper per user. At Apate.AI, we deploy such a chatbot to
talk to scammers. Believability, latency and cost are more important than
conversation quality. A customer service chatbot would be a similar use case
but with more emphasis on accuracy.

Figure 1: Overview of ConvoCache.

To test our conversational caching concept, we focus on the textual dialogue
coherence as this relates to a response fitting the conversation [4, 5, 6].
The voice in our system is unchanged as response audio is saved in the cache.
We simulate our system responding to the chit chat dialogue set DailyDialog
[7]. We report the hit/miss rate of our cache given a 90% UniEval coherence
threshold, our system latency and G-Eval scores of the dialogue produced.

We make the following contributions:

  * •

We propose ConvoCache, a conversational caching system that implements
dialogue evaluation to control for quality. Our source code is available
online222https://github.com/RoshanStacker/ConvoCache.

  * •

We tested our system with several encoder models and encoding techniques. We
provide a benchmark of ConvoCache with G-Eval scores [6].

  * •

We measure the impact of prefetching on the hit rate and response quality of
ConvoCache.

##  2 Background

###  2.1 Related work

Caching responses has been investigated before. In cloud computing literature,
ChatCache [8] observed semantic redundancy in practical conversations and
built a similar system using voice and textual encoder models. The focus of
ChatCache was on voice assistants responding to commands and questions on low
power edge computers. They showed that textual and spoken semantic models are
both able to find this semantic redundancy. Other work [9] focuses on question
answering and using a cache instead of a chatbot, showing significant
improvements to latency. Our work is different as it focuses on generic chit
chat conversations which have more room for imperfect responses, and have
important context that we use in our embeddings. Following these previous
works, we have access to more effective semantic similarity models in SimCSE
[10] and AnglE [11], and we evaluate the coherence of the dialogue generated
by the cache, not just the hit rate.

The end of speech can be quickly detected using voice activity, but speech
transcription into text has a longer delay before the whole utterance is
transcribed. This impacts the delay of responses. Previous work has focused on
reducing this delay [3], while others have implemented prefetching to generate
a response before the end of speech [12]. We experiment with incomplete
utterances to simulate prefetching as a way to further reduce the latency of
ConvoCache.

###  2.2 Sentence encoders

We investigate the use of two encoders that have been effective in semantic
textual similarity (STS) tasks; SimCSE [10] and AnglE [11]. These models are
designed to encode a single phrase and cluster semantically similar phrases
based on cosine similarity.

SimCSE [10] uses a RoBERTa [13] language model and contrastive learning to
train semantic similarity. This produces embeddings of 1024 dimensions. AnglE
[11] introduces angle optimisation which avoids problematic areas of the
cosine similarity curve with gradients close to zero. The authors report that
this helps AnglE learn subtle semantic differences, and show improvement over
SimCSE making AnglE a new state of the
art333https://paperswithcode.com/task/semantic-textual-similarity. AnglE uses
a Llama 2 [14] language model which provides a significant performance gain
over RoBERTa, producing embeddings of 4096 dimensions. AnglE outperforms
SimCSE slightly when both are using a Llama 2 model [11]. Llama 2 is slower
than RoBERTa, so we use SimCSE with
RoBERTa444https://huggingface.co/princeton-nlp/sup-simcse-roberta-large and
AnglE with Llama 2 7B555https://huggingface.co/SeanLee97/angle-
llama-7b-nli-20231027 to compare the encoders and language models.

###  2.3 Automatic dialogue evaluation

Conversations often allow for a wide range of valid responses, especially chit
chat conversations. This is known as the one-to-many problem [15], and it
makes it difficult to evaluate dialogue with automated systems. This has lead
to the trend of using larger language models to perform reference free
evaluation [16].

Recent advancements make use of multi-dimension evaluation [4, 17]. These
evaluate dialogue responses on dimensions such as: engagingness, naturalness,
groundedness, understandability and coherence, then combine these scores for
one measure of quality. In this work we focus only on the coherence evaluation
for two reasons. Firstly, coherence represents how well a response fits into a
conversation and the context. Since we reuse a response from a different
context this very important. Secondly, the other dimensions are not applicable
to our experiments as they measure how well a response includes external
information, or how fluent the response is without taking into account
context. Since all of our responses are taken from a fluent dataset, they
would all score the same regardless of our cache.

UniEval [4] implements boolean questions and a T5 [18] language model with
continual training on each evaluation dimension. Since UniEval does not use an
LLM it is much faster compared to more recent models, while maintaining
similar results for coherence. We use the coherence question from the paper
[4]: ``question: Is this a coherent response given the dialogue history?''

G-Eval [6] uses the GPT-3.5 or GPT-4 LLM with a detailed prompt for each
dimension of evaluation. LLMs have been shown to be effective evaluators [19,
20]. G-Eval makes use of multiple response candidates, and their probability,
to generate a more fine-grained score by calculating the weighted sum of the
candidates. We were unable to obtain the original coherence prompt for
dialogue from the authors, so we created our own coherence prompt using the
template of the dialogue engagingness prompt from G-Eval [6]. We provide this
prompt in our code repository alongside our evaluation code.

##  3 ConvoCache system design

Input: Number of utterances $n$, dialogue history
$D=(U_{1},U_{2},\ldots,U_{n})$, decay parameter $\lambda$, number of cache
results $k$, coherence threshold $t$

1 for  _$i=1$ to $n$_ do

$\mathbf{e}_{i}\leftarrow\text{Encode}(U_{i})$

// embeddings

2

$\mathbf{s}=\mathbf{0}$

// query vector

3 for  _$i=1$ to $n$_ do

$w_{i}=\frac{e^{-\lambda i}}{\sum_{j=1}^{n}e^{-\lambda j}}$

// exponential decay

4 $\mathbf{s}=\mathbf{s}+w_{i}{\mathbf{e}}_{i}$

$(R_{1},\ldots,R_{k})\leftarrow$ SearchCache($\mathbf{s},k$)

// find responses

5 for  _$i=1$ to $k$_ do

6 if  _$\text{UniEval}(R_{i},D) >t$_ then

return $R_{i}$

// cache-hit

7

8

9$R_{\text{new}}\leftarrow$ GenerateNewResponse($D$)

10 SaveToCache($\mathbf{s},R_{\text{new}}$)

return $R_{\text{new}}$

// cache-miss

Algorithm 1 ConvoCache response generator

To respond to a conversation with dialogue history $D$ of $n$ utterances,
ConvoCache first generates a conversation embedding $\mathbf{s}$. To do this,
we encode each utterance $U_{i}$ in the dialogue history using a model such as
AnglE or SimCSE [10], then calculate the weighted sum of these utterance
embeddings to get the conversation embedding. Our weights are given by
exponential decay $e^{-\lambda i}$ where $i=1$ is the last utterance, $i=2$ is
the 2nd last utterance, etc. The weights are normalised to ensure they sum to
$1$. Other conversation encoding methods could be used to generate
$\mathbf{s}$ from $D$.

With the conversation embedding $\mathbf{s}$, we search our cache to find the
top $k$ similar conversations and retrieve the corresponding response
candidates $(R_{1},\ldots,R_{k})$. We use cosine-similarity in the FAISS
package [21]. For larger caches, FAISS provides approximate search methods
that are faster. We use an exhaustive search in our experiments as our cache
is small.

Simply using the first response candidate $R_{1}$ generates mediocre dialogue.
We can improve this by filtering response candidates. One method of filtering
would be to use the similarity score of the cache results (inner product) as a
proxy for quality and apply a threshold. While this is fast, we found that it
is not very effective for our embeddings. Instead, we evaluate each candidate
response (we use UniEval [4]) in order of similarity until a response scores
higher then a given threshold $t$. Controlling this threshold provides a way
to adapt the system and control costs through cache-hit rate. UniEval is the
slowest part of system taking around 100ms per response evaluated (see Table
2), motivating the use of the first response to pass the threshold rather than
re-ranking all response candidates. If a model could evaluate all candidate
responses in parallel, then re-ranking should improve the system quality and
latency further.

Table 1: Percentage of test responses that use each response candidate rank, or miss. UniEval threshold $t=0.9$. Average G-Eval scores for responses skipping cache-miss. Average latency is based on Table 2, with a cache-miss equal to evaluating 5 response candidates. Model | $\lambda$ | Response Candidates |  | Average | Average G-Eval
---|---|---|---|---|---
|  | 1st | 2nd | 3rd | 4th | 5th | Miss | Latency | GPT-3.5 | GPT-4
SimCSE | 0.25 | 54.35 | 16.17 | 9.01 | 4.82 | 3.31 | 12.34 | 220ms | .666 | .759
0.50 | 56.51 | 15.52 | 8.87 | 4.75 | 3.13 | 11.22 | 214ms | .668 | .761
0.75 | 56.84 | 14.70 | 7.97 | 4.99 | 3.26 | 12.24 | 216ms | .668 | .766
1.00 | 56.38 | 13.86 | 7.92 | 4.73 | 3.44 | 13.66 | 221ms | .665 | .769
AnglE | 0.25 | 55.40 | 16.75 | 9.35 | 4.26 | 3.18 | 11.07 | 252ms | .677 | .771
0.50 | 57.72 | 15.73 | 8.55 | 4.99 | 2.72 | 10.31 | 247ms | .672 | .778
0.75 | 58.16 | 15.06 | 7.52 | 4.76 | 3.18 | 11.32 | 249ms | .676 | .785
1.00 | 57.64 | 13.95 | 7.46 | 4.75 | 3.49 | 12.72 | 254ms | .676 | .788

If we evaluate all candidate response and fail to find one above the
threshold, we consider this a cache-miss. A new response $R_{new}$ will have
to be generated using a chatbot and voice synthesis. We can make use of
fillers such as ``um'' to disguise the delay of response generation during
cache-misses, since research shows this is still natural within 1.1s [1],
while our delay is 510ms. Using fillers only during cache-misses (11% of
responses) avoids using them for every response which would be unnatural.
Every new response generated will be saved to the cache with the conversation
embedding $\mathbf{s}$. This allows the cache to grow over time and fill in
gaps, as such, the cache-hit rate would be expected to improve over time. A
limit could be placed on the size of the cache, with a strategy to remove
items that have the lowest usage. We don't investigate a dynamic cache in our
experiments, instead we load our cache with the train portion of the dialogue
dataset with 76,052 responses.

##  4 Methodology

To assess the impact that ConvoCache has on dialogue quality, we simulate the
system responding to the DailyDialog dataset [7], which contains chit chat
conversations in English. All tests used an RTX A4000 GPU with 16GB of VRAM,
and we present computation time in Table 2. Our experiments follow these
overall steps:

  1. 1.

Establish dataset train and test splits.

  2. 2.

Seed the cache with utterances from the train split.

  3. 3.

Use the cache to respond to the test split.

  4. 4.

Evaluate the generated test conversations.

The DailyDialog dataset [7] provides many multi-turn conversations in English
(average 7.9 turns). We first take each turn/utterance and create a prompt-
response pair representing the dialogue history before this response, and the
response. A conversation of 3 utterances will generate 2 prompt-response pairs
since the first utterance has no prompt, while the others do. Using the
provided train and test splits containing 11,118 and 1,000 conversations, we
collected 76,052 prompt-response pairs for the train split, and 6,740 for the
test split.

To seed the cache, we follow the method described in Section 3 to encode the
prompts from the train split and save them to the FAISS Index [21] alongside
the response. We respond to prompts in the test split using the same method as
above. We find the top 5 response candidates ($k=5$). We experiment with
different values of exponential weight decay $\lambda$. To evaluate the
coherence of the response candidates, we use UniEval [4] and apply a coherence
threshold $t$. G-Eval [6] is used to evaluate the responses chosen by the
system for overall coherence.

##  5 Results

###  5.1 Cache hit rate and coherence

With a coherence threshold of $t=0.9$, we report our hit rates for the various
ranks of response candidates in Table 1. We find an optimal miss rate of
10.31% and 11.22% for AnglE and SimCSE respectively for $\lambda=0.5$.
ConvoCache, as described in Section 3, applies this UniEval coherence
threshold to each response candidate in order, meaning that the hit rate of
the first response candidate is the fastest possible result. We find that the
first candidate is used 56.51–57.72% of the time with a processing time of
110–148ms depending on the encoder used.

Figure 3 shows the coherence of responses from ConvoCache, using SimCSE and
$\lambda=0.5$, compared to reference responses and randomly selected train
responses. We see a similar shape to the reference with a small drop in
coherence, but significantly better than random responses. We also see that
GPT-4 scores higher than GPT-3.5 on average.

Figure 2: Percentage of all response candidates above a given coherence
threshold (colours) with various exponential decay $\lambda$.  Figure 3:
Distribution of G-Eval scores for reference responses, random cache responses,
and ConvoCache responses (black).

###  5.2 Optimising embedding weights

In our proposed approach (Section 3) we define a parameter for the exponential
decay of weights $\lambda$. Figure 2 presents values of $\lambda$ showing that
$\lambda=0.5$ and $\lambda=0.75$ are best.

###  5.3 Models and hardware

We find that AnglE performs slightly better than SimCSE in all our tests,
generating more responses with higher coherence. Table 1 and Figure 2 show
this consistent gap in performance, however this difference in performance is
small and both models could be used.

AnglE requires 15 GiB of VRAM compared to SimCSE which only requires 2.3 GiB,
15% of AnglE. Table 2 shows that when using ConvoCache with 76,052 cached
responses, SimCSE requires a total of 9.6 GiB while AnglE requires a total of
23.2 GiB. This difference is significant as ConvoCache with SimCSE can
realistically run on a 12 or 16 GiB GPU while AnglE requires a 24 GiB GPU or
multiple smaller GPUs. This impacts the costs of running the system and likely
outweighs the performance gain of AnglE discussed earlier.

Table 2: Model inference times on RTX A4000 GPU (test split). Model | Mean | $\sigma$ | Max | VRAM
---|---|---|---|---
SimCSE | 10.5 ms | 0.3 ms | 23.7 ms | 2.3 GiB
AnglE | 46.3 ms | 1.8 ms | 104.0 ms | 15.0 GiB
FAISS-SimCSE | 1.0 ms | 0.0 ms | 1.2 ms | 2.9 GiB
FAISS-AnglE | 3.3 ms | 0.0 ms | 3.5 ms | 3.8 GiB
UniEval | 98.7 ms | 6.9 ms | 159.9 ms | 4.4 GiB

Encoding with SimCSE is $4.4\times$ faster than AnglE and searching with FAISS
is faster due to using 1024 dimension vectors compared to AnglE's 4096
dimensions. However, this latency difference only has a small impact on the
total latency of the system since UniEval is the slowest model, and UniEval
executes up to 5 times. We calculate the average latency given the model
latencies in Table 2 and the proportion of responses that used each response
candidate, and include this in Table 1. We calculate a cache-miss as the same
latency as evaluating the 5th candidate. In practice, a cache-miss will
require response generation leading to a higher delay in response time.

###  5.4 Prefetching

To reduce latency further in spoken dialogue system, it is possible to start
generating a response while the user is still speaking. This is known as
prefetching [12]. We test this by truncating the last utterance in our prompts
for encoding and evaluation with UniEval to apply the threshold. Table 3 shows
a substantial drop off in hit rate when using incomplete utterances (split
$<100$%). This shows that UniEval using an incomplete dialogue history will
give low coherence scores more often. Table 3 presents G-Eval scores of the
responses (using complete dialogue history) and shows a small drop for GPT-3.5
but a significant drop in coherence measured by GPT-4.

Table 3: Partial Utterances (Prefetching). Model | $\lambda$ | Split | Hit Rate | Mean G-Eval
---|---|---|---|---
|  |  |  | GPT-3.5 | GPT-4
SimCSE | 0.5 | 100% | 88.78 | .668 | .761
90% | 71.68 | .658 | .671
80% | 63.49 | .651 | .649
70% | 58.15 | .651 | .619
60% | 53.95 | .641 | .583

##  6 Limitations

We make use of automated dialogue evaluation systems including UniEval [4] and
G-Eval [6]. These systems are not perfect evaluators and only achieve a
mediocre Spearman's correlation with human evaluators of 0.6 on the Topical-
Chat benchmark [6]. As such, we provide context to the evaluation scores in
Figure 3 and compare to evaluations of reference (good) and random (bad)
responses. We also make use of GPT-3.5 and GPT-4, which presented diverging
results for prefetching in Table 3.

Latency measurements in this work do not include the delay of Automatic Speech
Recognition (ASR), which is required for voice chatbots. ASR can increase the
user perceived latency by 200ms or more. Other work can reduce this latency
[12, 3].

##  7 Conclusion

ConvoCache allows responses to be reused between conversations and we have
shown the effectiveness of this in chit chat dialogue. This system can be
integrated with existing generative AI chatbots and provide fast responses
while maintaining quality and reducing costs for services with a large number
of requests. In the DialyDialog dataset, ConvoCache achieves a 89% hit rate
using SimCSE and responds in 110–505ms, averaging 214ms. The AnglE encoder
achieves a 90% hit rate, but is unfavourable due to the larger hardware
requirements, likely needing 2 GPUs. All responses achieve a UniEval coherence
score above 90% and evaluating our ConvoCache dialogues with G-Eval using
GPT-4, gave an average score of 3.8/5 (76%). The use of prefetching to reduce
latency further was shown to have limited effectiveness as hit rate and
coherence reduced substantially. We hope that future developments in fast
evaluation models and dialogue encoders specific to this task improve the
performance further.

##  8 Acknowledgements

This research was conducted under the support of Australian Government
National Infrastructure Defence and Industrial Research Grant (NISDRG)
NI220100105. This research was conducted in collaboration with Apate.AI,
Defeating Phone Scams with Conversational AI.

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# Evolving Semantic Communication with Generative Model

Shunpu Tang, Qianqian Yang, Deniz Gündüz, Zhaoyang Zhang S. Tang, Q. Yang, and
Z. Zhang are all with the College of Information Science and Electronic
Engineering, Zhejiang University, Hangzhou, China (email: { qianqianyang20,
tangshunpu, zhzy}@zju.edu.cn). D. Gündüz is with the Department of Electrical
and Electronic Engineering, Imperial College London, London, UK, SW7 2AZ.
(email: d.gunduz@imperial.ac.uk).

###### Abstract

Recently, learning-based semantic communication (SemCom) has emerged as a
promising approach in the upcoming 6G network and researchers have made
remarkable efforts in this field. However, existing works have yet to fully
explore the advantages of the evolving nature of learning-based systems, where
knowledge accumulates during transmission have the potential to enhance system
performance. In this paper, we explore an evolving semantic communication
system for image transmission, referred to as ESemCom, with the capability to
continuously enhance transmission efficiency. The system features a novel
channel-aware semantic encoder that utilizes a pre-trained Semantic StyleGAN
to extract the channel-correlated latent variables consisting of serval
semantic vectors from the input images, which can be directly transmitted over
a noisy channel without further channel coding. Moreover, we introduce a
semantic caching mechanism that dynamically stores the transmitted semantic
vectors in the local caching memory of both the transmitter and receiver. The
cached semantic vectors are then exploited to eliminate the need to transmit
similar codes in subsequent transmission, thus further reducing communication
overhead. Simulation results highlight the evolving performance of the
proposed system in terms of transmission efficiency, achieving superior
perceptual quality with an average bandwidth compression ratio (BCR) of 1/192
for a sequence of 100 testing images compared to DeepJSCC and Inverse JSCC
with the same BCR. Code of this paper is available at
https://github.com/recusant7/GAN_SeCom.

###### Index Terms:

Semantic communication, wireless cache, GAN, joint source-channel coding.

##  I Introduction

Recently, there has been a growing interest in semantic communications
(SemCom) as a promising technology poised to boost communication efficiency in
the forthcoming 6G networks[1]. In contrast to conventional digital
communication systems that treat all transmitted bits uniformly and
concentrate solely on bit accuracy, semantic communication prioritizes the
transmission and reconstruction of data with more valuable semantic
information. This approach aligns well with the increasing demands of machine-
to-machine (M2M) communication, which provides significant reductions in
transmitted data and is particularly beneficial for intelligent applications
such as smart cities and extended reality (XR).

Given the remarkable success of deep learning technology, a semantic
communication system for image transmission, named DeepJSCC, was initially
investigated in [2]. In DeepJSCC, the joint source-channel encoder and decoder
are modeled as neural networks, and trained jointly to optimize the mean
square error (MSE) or the structural similarity (SSIM) between the transmitted
and reconstructed images. In a related study [3], the authors proposed
transmitting high-level semantic information, such as text descriptions, to
enhance image transmission performance, especially in bandwidth-limited
scenarios. DeepJSCC was further extended to the digital communication system
in [4], enhancing its compatibility for deployment in existing communication
systems.

A promising approach for boosting the transmission efficiency is to harness
the capabilities of recently emerged deep generative models, capable of
producing high-dimensional realistic multimedia information from low-
dimensional data. The authors in [5] utilize a deep speech generation model to
reconstruct speech from low-dimensional semantic information received, thereby
decreasing the required bandwidth to only 0.2% of that achieved by existing
works. The approach presented in [6] employs the generative adversarial
network (GAN) inversion method [7] to acquire a low-dimensional latent
representation of images. Subsequently, the image is reconstructed at the
receiver using a GAN, achieving perceptual quality comparable to existing
works while utilizing only a small fraction of the channel bandwidth. Works in
[8, 9, 10] employ a pretrained generative model at the receiver to ensure that
the receiver generates a realistic reconstruction of the source images.

While the aforementioned approaches have achieved remarkable results, SemCom
transceivers are typically trained offline and become fixed after deployment
in real-world networks. Consequently, the performance of these systems often
remains stable or may even decline when confronted with a mismatch between the
source or channel characteristics and the training data. One key advantage of
data-driven approaches is their ability to continuously improve and adapt to a
changing environment with accumulated data. Therefore, we are motivated to
design a SemCom approach that can evolve based on the accumulated transmission
experience, aiming to further reduce the transmission overhead.

In particular, we integrate wireless cache technology into the SemCom system
to store previously transmitted semantic information from the transmitter to
the receiver. This stored information is later leveraged to avoid transmitting
similar semantic data, resulting in a reduction in communication overhead.
While wireless caching has been extensively studied in digital communication
systems, such as [11, 12], its application in SemCom systems is a novel aspect
of the proposed approach. Moreover, we can extract disentangled semantic
information using existing GAN method, which enables us making cache decisions
for the disentangled semantic information in a more refined way than for the
whole source signals, making it easier to achieve potential caching gains.

In this paper, we investigate a cache-enabled ESemCom system leveraging the
pre-trained semantic StyleGAN [13] model, where both the transmitter and the
receiver are equipped with cache memories. Unlike previous works[8, 7], we
introduce a novel channel-aware GAN inversion method to extract the meaningful
semantic information from the original input and map it into the channel-
correlated latent space. This approach eliminates the need for additional
channel encoding and decoding, thereby avoiding additional training overhead
related to various channel signal-to-noise ratios (SNR). We also propose a
semantic caching mechanism that utilizes the cache memory at both the
transmitter and receiver, which stores disentangled semantic vectors at both
ends, following the first-in-first-out (FIFO) principle. When a similar
semantic vector exists in the caching memory, the transmitter sends the
corresponding index instead, thereby reducing communication overhead. To
validate our approach, we conduct simulation experiments focusing on the
transmission of face images using the CelebA-Masked dataset. Simulation
results demonstrate the effectiveness of the proposed system in terms of peak
signal-to-noise ratio (PSNR), perceptual quality and transmission efficiency.
Furthermore, the results show a continuous improvement in the transmission
efficiency of our proposed method, facilitated by the introduced caching
mechanism.

##  II Problem Statement

###  II-A System Model

In this paper, we consider the problem of transmitting images over a noisy
channel, where both the transmitter and receiver are equipped with a cache
memory of same size. The original image can be represented as
$\bm{x}\in\mathbb{R}^{3\times N_{H}\times N_{W}}$, where $3$ represents RGB
channels, while $N_{H}$ and $N_{W}$ are the height and width of the image,
respectively. The transmitter uses a GAN-based semantic encoder to extract the
latent variable $\bm{z}\in\mathbb{R}^{N_{S}\times N_{L}}$ from $\bm{x}$
through the GAN inversion method[7], which can be expressed as

$\bm{z}=G^{-1}(\bm{x}),$ (1)

where there are $N_{S}$ distinct semantic vectors in $\bm{z}$, and $N_{L}$ is
the length for each semantic vector. For example, different semantic vectors
in the latent variable of a facial image can represent different semantic
information such as eyes, eyebrows, mouth, nose, etc. Notation $G^{-1}(\cdot)$
denotes the inversion process of the generative function $G(\cdot)$. After
that, those semantic vectors that are close enough to one of the cached
semantic information in the caching memory are eliminated to reduce the
communication overhead. We refer to this process as the semantic caching
operation, given by

$\tilde{\bm{z}}=C(\bm{z}),$ (2)

where $C(\cdot)$ represent the semantic caching operation,
$\tilde{\bm{z}}\in\mathbb{R}^{n_{s}\times N_{L}}$, and $n_{s}\leq N_{S}$
depends on how many among the $N_{S}$ semantic vectors are eliminated. We
assume that the cache memory at both the transmitter and the receiver can
store $N_{C}$ realizations of each semantic vector.

To meet the average transmit power constraint, power normalization (PN) [2] is
applied to the latent variable $\tilde{\bm{z}}$, before being mapped to the
complex-valued channel input signals $\bm{z}_{c}\in\mathbb{C}^{k}$ for
transmission. We have $k=\frac{1}{2}\times n_{s}\times N_{L}$, where
$\frac{1}{2}$ comes from combining two real values to form a single complex
channel symbol. We define the bandwidth compression ratio (BCR) as $k/(3\times
N_{H}\times N_{W})$.

We consider an additive white Gaussian noise (AWGN) channel, where the
received signal at the receiver is given by

$\bm{\hat{z}}_{c}=\bm{z}_{c}+\bm{n},$ (3)

where $\bm{n}$ is the additive channel noise, consisting of independent
complex Gaussian components $\mathcal{CN}(0,\sigma^{2})$. The inverse semantic
caching operation is applied to recover the dimension of the original latent
variable, given by

$\hat{\bm{z}}=C^{-1}(\bm{\hat{z}}_{c}),$ (4)

where $\hat{\bm{z}}\in\mathbb{R}^{N_{S}\times N_{L}}$. Then, the pre-trained
GAN acts as the semantic decoder to reconstruct the image $\hat{\bm{x}}$ using
the generative function, given by

$\hat{\bm{x}}=G(\hat{\bm{z}}).$ (5)

###  II-B Metrics

We evaluate the quality of the reconstructed image $\hat{\mathbf{x}}$ using
PSNR, which can be written as

$\text{PSNR}(\bm{x},\hat{\bm{x}})=10\log_{10}\left(\frac{{255^{2}}}{{\text{MSE}(\bm{x},\hat{\bm{x}})}}\right),$
(6)

where 255 is the maximum possible pixel value in the image and
MSE$(\cdot,\cdot)$ is the mean squared error between the original and
reconstructed images. We also use the learned perceptual image patch
similarity (LPIPS)[14] to assess the reconstruction performance, which is a
metric that has been shown to closely capture the human perceptual similarity
between two images through a pre-trained VGG network, given by

$\text{LPIPS}(\mathbf{x},\hat{\mathbf{x}})=\sum_{l}\frac{1}{N_{H_{l}}N_{W_{l}}}\sum_{h,w}^{N_{H_{l}},N_{W_{l}}}||\omega_{l}\odot(y_{h,w}^{l}-\hat{y}_{h,w}^{l})||^{2}_{2}$
(7)

where $y_{h,w}^{l}$ and $\hat{y}_{h,w}^{l}$ are the $(h,w)$-th element in the
output feature map of the $l$-th VGG layer for $\bm{x}$ and $\hat{\bm{x}}$,
respectively. Besides, $N_{H_{l}}$ and $N_{W_{l}}$ denote the height and width
of the output feature map, and $\omega_{l}>0$ is the weight to control the
importance for the outputs of different layers. Given these two metrics, this
paper aims to design semantic encoding and decoding together with an efficient
semantic caching mechanism to minimize the required BCR to achieve a desired
average image reconstruction quality.

##  III Proposed Method

Figure 1: Illustration of the proposed cache-enabled evolving SemCom system

In this section, we present the details of the proposed method, including both
the channel-aware GAN-based semantic encoder and decoder, as well as the
proposed semantic caching mechanism.

###  III-A Channel-aware Semantic Encoder and Decoder

For the semantic encoder, we exploit the GAN inversion method, which is the
inversion operation of a generative function, to extract semantic information
from the given data sample. Specifically, for a given generator denoted by
$G$, which maps a latent variable to a data sample, the inversion operation
seeks the latent variable $\bm{z}$ of a data sample $\bm{x}$ by

$\bm{z}=\arg\min_{\bm{y}}||G(\bm{y})-\bm{x}||^{2}_{2}.$ (8)

In our SemCom system, the derived $\bm{z}$ can be considered as important
semantic information, given its significantly lower dimensionality compared to
the original sample $\bm{x}$. Building upon our prior research [6], we utilize
the semantic StyleGAN2[13] as the backbone generative model, which enables us
to extract the disentangled latent variable, with each semantic vector
representing a distinct semantic feature.

However, $\bm{z}$ cannot be directly transmitted over the channel as it may
not meet the average transmit power constraint. Moreover, when it gets
corrupted by the channel noise, the reconstruction performance may deteriorate
significantly. Therefore, we introduce a novel channel-aware GAN inversion
method, which incorporates the characteristics of the AWGN channel into the
GAN inversion process. Compared with the previous work [6], which applies a
channel encoder with normalizing flow to encode $\bm{z}$, the proposed method
eliminates the need for training additional channel encoder and decoder. This
both reduces the training requirements and expedites the end-to-end
transmission process. Additionally, the transmitter and receiver only require
a pre-trained generator to adapt to various channel conditions, without the
need for any re-training or fine-tuning operations.

The process of channel-aware semantic coding is illustrated in Fig. 1. We
first sample a latent variable $\bm{y}$ from the latent space. Instead of
directly feeding it into $G$, we incorporate the PN operation to control its
average power. Next, AWGN $\bm{n}$ is added to $z$ to simulate corruption from
the noisy channel. We note that here it is assumed that the transmitter has
the knowledge of the current noise power in AWGN channel. Hence, for a given
image $\bm{x}$, we want to find the latent variable $\bm{z}$ by solving the
following optimization problem,

$\bm{z}=\arg\min_{\bm{y}}||G({PN(\bm{y})+\bm{n}})-\bm{x}||^{2}_{2}.$ (9)

To preserve more perceptual quality, we replace the L2 loss in (9) with L1
loss and incorporate the LPIPS loss term, resulting in

$\displaystyle\bm{z}=$
$\displaystyle\arg\min_{\bm{y}}\lambda_{1}||G({PN(\bm{y})+\bm{n}})-\bm{x}||$
(10) $\displaystyle+\lambda_{2}\text{LPIPS}(G({PN(\bm{y})+\bm{n}}),\bm{x}),$

where $\lambda_{1}$ and $\lambda_{2}$ are positive hyper-parameters
controlling the trade-off between the two losses. Compared to the MSE loss
function, the L1 loss and LPIPS loss used here align more closely with human
perceptual characteristics. We can optimize (10) using the gradient descent
method, thus deriving $\bm{z}$ for transmission over the noisy channel.

The semantic decoder at the receiver is simply the corresponding generator $G$
to the GAN inversion $G^{-1}$ used at the transmitter. After the semantic
caching operation at the transmitter, which will be explained in more detail
in the next section, the noisy signal $\hat{z}$ is directly input into the
semantic decoder to generate the original image, without any additional
denoising operation.

###  III-B Semantic Caching Mechanism

We store a set of semantic vectors from previous transmissions in the cache
memory of both the transmitter and the receiver. Upon obtaining $\bm{z}$, the
transmitter searches within the cached semantic vectors and replaces one or
more components in the latent variables with the corresponding indices if
similar semantic vectors exist in the local cache memory. This further reduces
communication overhead.

In particular, let $\bm{z}_{i}\in\mathbb{R}^{N_{L}}$, $0\leq i<N_{S}$, denote
the $i$-th semantic vector of latent variables $\bm{z}$. For each vector,
$\bm{z}_{i}$, the transmitter searches in its local cache memory for the
closest cached semantic vector, evaluated by cosine similarity, and obtains
its index $j^{*}$ as follows

$\displaystyle j^{*}=$ $\displaystyle\arg\max_{0\leq
j<N_{C}}\mathrm{cosine}(\bm{z}_{i},\bm{c}_{i,j})$ (11) $\displaystyle=$
$\displaystyle\arg\max_{0\leq
j<N_{C}}\frac{\bm{z}_{i}\cdot\bm{c}_{i,j}}{|\bm{z}_{i}||\bm{c}_{i,j}|}.$

If the cosine similarity $\mathrm{cosine}(\bm{z}_{i},\bm{c}_{i,j^{*}})$ is
greater than a pre-defined threshold $\gamma_{i}$, we use the index $j^{*}$ to
replace the original $\bm{z}_{i}$ for transmission. This operation is executed
for all dimensions, resulting in $\tilde{\bm{z}}\in\mathbb{R}^{n_{s}\times
N_{L}}$, where

$n_{s}=\sum_{0\leq
i<N_{S}}\mathbb{I}\bigg{(}cosine(\bm{z}_{i},\bm{c}_{i,j^{*}})\geq\gamma_{i}\bigg{)},$
(12)

and $\mathbb{I}(\cdot)$ denotes the indicator function. The transmitter then
sends $\tilde{\bm{z}}$, together with the corresponding indices. We code each
index with $\log_{2}{N_{S}}+\log_{2}{N_{C}}$ bits, which is transmitted using
digital communication technique. For those components in $\bm{z}$ for which we
do not find a replacement in the cache memory, the transmitter stores them in
the cache memory. For simplicity, we employ the widely used first-in-first-out
(FIFO) principle to update the cache memory with the new latent variables.

Upon receiving $\bm{\hat{z}}_{c}$ and the indices, the receiver first
transforms the complex-value latent variable back to the real-value one. Then,
the receiver identifies the corresponding semantic vector using the received
indices, thus obtaining the complete latent variable $\hat{\bm{z}}$. The
receiver also updates the cache memory with the semantic vector that have been
received, ensuring synchronization between the cache contents at the
transmitter and the receiver. We note that in this way the stored semantic
vectors in the cache memories of the transmitter and receiver would be
different due to the impact of channel noise. However, the simulation results
reveal that the proposed caching mechanism still helps in terms of
transmission efficiency..

Figure 2: BCR versus the index of the transmitted images, tested SNR=5dB.
Figure 3: Image reconstruction quality evaluated by PSNR versus SNR. Figure 4:
Image reconstruction quality evaluated by LPIPS versus SNR. Figure 5:  Visual
comparison on the reconstructed CelebAMask-HQ images under SNR of 5dB and 3dB.

##  IV Simulation

In this section, we conduct simulations to illustrate the effectiveness of the
proposed method. Firstly, we outline the simulation settings, which include
details about the dataset used and the key parameters of the transmission
model. We then assess the performance of the proposed method in comparison to
the existing SemCom system.

###  IV-A Simulation Settings

In the simulation, we set the transmit power to unity, while allowing the SNR
of the AWGN channel to vary between -5dB and 5dB. Both the transmitter and
receiver are equipped with a cache memory capable with $N_{C}=50$, and hence
can store 50 realizations of each semantic vector in latent variable $\bm{z}$.
Additionally, we assume that the transmitter has accurate knowledge of the
current channel noise power.

We employ semantic styleGAN as the backbone generative model, which has been
trained on CelebAMask-HQ[15] dataset, consisting of 30,000 high-resolution
facial images, each of size $3\times 512\times 512$. The dimension of the
latent variables $\bm{z}$ is set to $N_{S}=28$ and $N_{L}=512$. The similarity
threshold $\gamma_{i}$, is set to 0.95 for $i=6,...,13$, which represents more
semantically important facial regions such as eyes, eyebrows, mouth, and nose.
For the remaining $\gamma_{i}$ values, we set them to 0.8. We note that the
proposed model achieves a BCR of $1/110$ if $\bm{z}$ is directly transmitted
after real-to-complex value transformation mentioned earlier. This BCR value
can be further reduced with the proposed semantic caching mechanism.

We conduct simulations for the first 100 images from the testing dataset of
CelebAMask-HQ. Notably, these images are not used to pre-train the semantic
styleGAN. We compare the LPIPS performance between the proposed ESemCom with
the following methods,

  * •

DeepJSCC[2]: The classical SemCom method for image transmission.

  * •

Inverse-JSCC[8]: Extended version of DeepJSCC, which introduces the GAN
inversion method into SemCom system. We use the same semantic styleGAN as the
generative model in this method, and follow [8] to train the semantic encoder
and decoder using the loss function of
$||\bm{x}-\hat{\bm{x}}||^{2}_{2}+\text{LPIPS}(\bm{x},\hat{\bm{x}})$.

  * •

BPG+Capcaity: The upper bound performance on any digital communication system
that use the SOTA image compression algorithm named better portable graphics
(BPG)111https://bellard.org/bpg/ for source coding, which compress images at
the rate of channel capacity and assumes error-free transmission in this case.

For a fair comparison, we take into account the bandwidth cost for
transmitting the indices by the proposed method. In particular, we use channel
coding with a rate of 1/2 and binary phase-shift keying (BPSK), which can
achieve a successful transmission rate of $p=0.9$ per block under an SNR of
0dB when the block length is more than 128 according to [16]. The number of
transmissions for successfully sending indices follows a geometric
distribution with probability $p$. We then have the expected number of
transmissions to be $1/p$. Therefore, the channel use for each index is
$\frac{1}{p}\times 2\times(\log_{2}{N_{S}}+\log_{2}{N_{C}})$.

###  IV-B Simulation Results

We transmit the testing 100 images one by one under the AWGN channel with a
SNR of 5dB and 1dB, respectively. As shown in Fig. 2, for the initial
transmission with empty cache memories, the BCR for the first image by the
proposed ESemCom scheme is approximately $1/110$. As the cache memories at the
transmitter and receiver are populated with semantic vectors, the BCR by
ESemCom quickly decreases. Notably, the smallest BCR reaches $1/260$, and the
average BCR of transmitting these 100 images is about 1/192. This can be
attributed to the proposed semantic caching mechanism, by which transmitted
latent variables are cached and replaced with similar ones in subsequent
transmissions, thus avoiding redundant transmissions and improving
communication efficiency. We note that on average, 15.3 semantic vectors in
$\bm{z}$ are replaced by indices, requiring only 370 symbols on average for
transmitting these indices. We observe fluctuations in the BCR values of
ESemCom, which arise from certain images exhibiting more similarities in their
semantic vectors with respect to the images transmitted earlier. These results
demonstrate the evolving characteristics of ESemCom and emphasize the
effectiveness of the proposed semantic caching mechanism.

We then compare the performance of the proposed ESemCom, DeepJSCC, Inverse-
JSCC, and BPG+Capacity in terms of image reconstruction quality, evaluated by
PSNR and LPIPS, as shown in Fig. 3 and Fig. 4, where an AWGN channel with SNRs
ranging from 0 to 5dB is considered during testing. DeepJSCC and Inverse-JSCC
are trained with uniform SNRs from 0 to 5dB. The average BCR of ESemCom is
about 1/192, and hence we set the BCR of the other methods to be 1/192 for a
fair comparison. From these figures, the proposed ESemCom and Inverse-JSCC
achieve a lower PSNR than DeepJSCC, but outperform DeepJSCCC and BPG+Capcailty
in terms of LPIPS. This is because these methods emphasize prioritizing
semantic information while disregarding irrelevant or less critical image
details. Moreover, the proposed ESemCom achieves better LPIPS than Invese-
JSCC, and still comparable LPIPS when SNR is 0dB. These results further
validate that the proposed system effectively transmits images while
preserving perceptual quality, especially in challenging channel conditions.

We further provide a visual comparison on the reconstructed CelebAMask-HQ
images under test SNR of 5dB and 3db, respectively, in Fig. 5. From this
figure, we can find that the proposed ESemCom and Inversion-JSCC exhibit
superior human perceptual quality with the help of the generative model.
Specifically, the proposed scheme can persevere intricate facial details,
including features such as eyes, nose, and mouth, while effectively filtering
out irrelevant background information. In contrast, facial regions generated
by DeepJSCC appear blurred and even unrecognizable under this challenging
condition of low BCR and SNR. Moreover, lots of artifacts occur in the images
generated BPG+Capacity. These results further demonstrate the superiority of
the proposed ESemCom scheme.

Figure 6: Visual comparison on the reconstructed CelebAMask-HQ images under
SNR of 0dB.

Fig. 6 illustrates the visual comparison at a testing SNR of 0dB. It is
evident from this figure that the proposed ESemCom and Inverse-JSCC still
achieve comparable image quality in this challenging channel condition, while
DeepJSCC fails to perform well and BPG+Capacity is unable to transmit images.
These results demonstrate the robustness of generative model-based methods in
challenging channel conditions.

##  V Conclusion

In this paper, we explored an evolving SemCom system designed to continuously
improve its transmission efficiency by utilizing cache memory at both the
transmitter and receiver and a pretrained generative model. In particular, we
introduced a novel channel-aware semantic encoder, employing a GAN inversion
method to map input images into a channel-correlated space. This approach
allows direct transmission of the obtained latent variables over a noisy
channel without additional channel encoding, substantially improving system
robustness under diverse channel conditions. Additionally, we proposed a
semantic caching mechanism, improving communication efficiency by avoiding the
transmission of semantic vectors already present in the local cache memory.
Simulation results demonstrate the superiority of our proposed system, showing
improved perceptual quality with approximately half the BCR compared to
DeepJSCC.

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