# Cultural evolution in populations of Large Language Models

Jérémy Perez Corresponding author<EMAIL_ADDRESS>Flowers Team, INRIA,
Bordeaux, France  Corentin Léger Flowers Team, INRIA, Bordeaux, France
Marcela Ovando-Tellez GIN-IMN, CNRS, Bordeaux, France  Chris Foulon GIN-IMN,
CNRS, Bordeaux, France  Joan Dussauld Independent Researcher  Pierre-Yves
Oudeyer Flowers Team, INRIA, Bordeaux, France  Clément Moulin-Frier Flowers
Team, INRIA, Bordeaux, France

###### Abstract

Research in cultural evolution aims at providing causal explanations for the
change of culture over time. Over the past decades, this field has generated
an important body of knowledge, using experimental, historical, and
computational methods. While computational models have been very successful at
generating testable hypotheses about the effects of several factors, such as
population structure or transmission biases, some phenomena have so far been
more complex to capture using agent-based and formal models. This is in
particular the case for the effect of the transformations of social
information induced by evolved cognitive mechanisms. We here propose that
leveraging the capacity of Large Language Models (LLMs) to mimic human
behavior may be fruitful to address this gap. On top of being an useful
approximation of human cultural dynamics, multi-agents models featuring
generative agents are also important to study for their own sake. Indeed, as
artificial agents are bound to participate more and more to the evolution of
culture, it is crucial to better understand the dynamics of machine-generated
cultural evolution. We here present a framework for simulating cultural
evolution in populations of LLMs, allowing the manipulation of variables known
to be important in cultural evolution, such as network structure, personality,
and the way social information is aggregated and transformed. The software we
developed for conducting these simulations is open-source and features an
intuitive user-interface, which we hope will help to build bridges between the
fields of cultural evolution and generative artificial intelligence.

Figure 1: (a) LLM agents are organized into networks wherein each agent
interacts with neighboring agents by exchanging stories. (b) Each agent is
assigned a specific personality and either initialization instructions (for
the first generation) or transformation instructions (after the first
generation), serving as prompts for generating new stories from their
neighbors’ narratives. (c) Once the network structure and agent
characteristics are defined, we simulate the cultural evolution of texts
across generations of agents. The simulation begins by prompting agents to
initialize stories, after which we allow the narratives to evolve dynamically
through interactions within the agent network

##  1 Introduction

Myths and stories are found in every human culture around the world. Research
using phylogenetic methods has revealed that myths evolve in a way analogous
to genes, progressively changing as some elements are discarded and new
elements added as they are passed through generations [44]. Some of these
myths display a surprising stability, being retained with minor modifications
though generations. For example, the Baku dream-eater demons, mythological
creatures made of various animal parts, have been part of the Japanese
folklore since at least the 15th century [31]. Moreover, myths in distinct
cultures seem to exhibit shared features, possibly pointing to convergent
evolution. This is for example the case of historical myths (i.e., myths
depicting events considered foundational for a given group), which have been
found to possess many similar elements, such as narratives featuring the
collective challenges faced in the history of the group [41]. This raises
questions regarding the factors that determine the cultural success, the
stability, and the directions of evolution of myths and stories.

More generally, providing causal explanations to the change of culture over
time is the central aim of research in cultural evolution. Contributions to
this question are generally seen as falling into two schools of thought: the
first one, referred to as the Californian school, adopts the framework of
gene-culture co-evolution [5] [7] [40] [18]. This school emphasizes how
evolved social learning mechanisms and transmission biases respectively
contribute to the stability of culture and the direction of its evolution, and
assume that the logic of natural selection applies to cultural traits as it
does for genes [40]. The second school, referred to as the Parisian school,
adopts the framework of Cultural Attraction Theory (CAT) [43][36] [31].
Disagreeing on the central role attributed to selection, this view rather
emphasizes how non-random transformations of cultural information during
transmission events can explain how cultural traits progressively evolve
toward stable forms, which are referred to as attractors. Taking inspiration
from population genetics, the Californian school has successfully employed
computational models to generate predictions, for instance about the effect of
group size [17], network structure [10] [12], or transmission fidelity [27].
As for CAT, although computational models have also been proposed [1] [30]
[8], they were mainly aimed at making conceptual points rather than to
generate testable predictions, and attraction dynamics have thus been studied
mainly through experiments [21] [33] [32] [9][9] [14] and historical data
analysis [22] [13].

This prevalence of experimental and historical methods is likely attributable
to the difficulty in capturing factors of attraction—such as evolved
psychological mechanisms—that influence cultural evolution within agent-based
or formal models. Here, we propose that this limitation of agent-based models
can be overcome by using generative artificial agents. In particular, using
Large Language Models (LLMs) to simulate the evolution of linguistic culture
appears fruitful, as we can expect those models to transform cultural
information in realistic ways.

On top of allowing to generate hypotheses about the causes of cultural change
in humans societies, studying the evolution of culture in populations of
generative agents is also crucial to understand the dynamics of AI-generated
cultural evolution. Indeed, although technology has long influenced cultural
evolution, for example with the invention of the printing press, some authors
have argued that the recent advances in generative algorithms are likely to
result in an unprecedented shift in cultural evolution. The fact that
algorithms are now participating in the creation of cultural traits sets us at
the very beginning of an era of “machine culture”, defined as “culture
mediated or generated by machines” [6]. Therefore, studying the dynamics of
machine-generated culture becomes highly important. Applying paradigms from
Cultural Attraction theory to study LLMs has already began to generate
precious insights about the bias exhibited by LLMs when transmitting
linguistic content [2].

Overall, it appears that there is much to gain by using LLMs as agents to
simulate the evolution of culture. So far, the fields of cultural evolution
and generative artificial intelligence have remained quite disconnected, and
facilitating exchanges between these fields seems promising for generating
important findings. Some parallel works have investigated the use of Large
Language Models as agents in multi-agent simulations, although these studies
were not specifically designed to model cultural evolution [38][47].

Here, we propose an open-source software for simulating the transmission and
evolution of linguistic culture in populations of Large Language models. This
software features an intuitive interface that allows to manipulate many
variables of interest, such as the structure of the social network, the ways
in which different sources of information are aggregated, or the personalities
of the different agents. We also introduce several visualizations and measures
that are useful for tracking the results of the simulations. We hope that this
tool will pave the way for more interaction between the fields of cultural
evolution and generative artificial intelligence. This software is open source
and accessible at this link.

Figure 2: Visualization of the evolution of the texts generated along a chain
of 50 agents (i.e. 50 generations of one agent per generation). (a) The
similarity matrix represents the semantic similarity between all stories
generated. The color of the cell at row i, column j corresponds to the
similarity of the stories i and j, which here corresponds to the stories
generated at generation i and generation j. (b) The similarity graph is
another way of visualizing the similarity between all generated stories. Each
node corresponds to one story, and the distance between node is proportional
to the semantic distance between corresponding stories. Stories generated at
successive generations are linked by a wider edge and arer assigned similar
colors. (c) We also visualize the words used at each generation. Words are
along the x-axis, and generation along the y-axis. A dot at position (x,y)
means that the word x was used in a story at generation y. A line means that
the corresponding word was used by two successive generations. We only display
the first half of the figure here. The complete figure can be found in the
Fig. 15 of Appendix.

##  2 Methods

###  2.1 Description of the model

The model presented here simulates the cultural evolution of linguistic
content in a population of large language models (LLMs). Each agent can be
seen as an independent instance of a LLM. The agent are arranged according to
a specified social network structure (Fig. 1.a). Network structures that can
currently be generated with the software are detailed in the Appendix A. At
the first generation, all agents are prompted with an Initialization Prompt.
This prompt describes what kind of content the agents should generate. For
example, one could chose “Tell me a story” as the initialization prompt. All
agents then output an answer by passing the initialization prompt to their
respective instance of the LLM. The agents then transmit stories to their
neighbors (according to the specified network structure): each agent receives
a new prompt, which is the concatenation of a Transformation Prompt and the
list of stories produced by its neighbors at the previous generation (Fig.
1.b). An example of a Transformation Prompt could be “Here are some stories.
Make up a new one by combining two of them”. Agents can additionally be
provided with a personality, which is always added at the top of their prompt.
For example, a personality prompt could be “You are very imaginative”. Agents
may either all have the same personality or have different personalities.

###  2.2 Analysis

####  2.2.1 Similarity

The main metric we use to analyze our results is the similarity between texts.
To compute this metric, we first use TfidfVectorizers from scikit-learn [39]
to convert texts into meaningful numerical representations. We then compute
the cosine similarity [16] between all the texts generated, resulting in a
similarity matrix of size $(N_{agents}$*$N_{generations})$ X
$(N_{agents}$*$N_{generations})$, where the color of the cell (i,j) represents
the similarity between story i and story j.

From this similarity matrix, we extract more interpretable measures. The first
one is the within-generation similarity, which captures how similar are the
texts generated at a given generation with each other. The second one is the
successive similarity, which represents the average similarity between the
texts generated at a given generation and the texts generated at the previous
generation. The last one is the similarity with the first generation, which is
the average similarity between the texts generated at a given generation and
the texts generated at the first generation.

####  2.2.2 Visualization

We also provide two visualization techniques that offer qualitative insights
into the generated data.

##### Word chains

We extract the key words from each text and represent their evolution though
generations. To extract keywords from texts, we tokenize the text into words,
remove common stopwords and non-alphanumeric tokens, calculate the frequency
distribution of the remaining words, and select the top keywords based on
their frequency. This allows to visualize which words are the most frequent,
the most stable, or the most often reinvented.

##### Similarity network

We also represent the similarity between generations using a graph network,
where each node represents a generation of texts. The positioning of nodes is
determined by a layout algorithm provided by the NetworkX library [15],
arranging them based on their similarities and interconnections. Generations
with the highest similarity are positioned closer together, and successive
generations, represented by similar colors, are linked by thicker edges. This
approach provides an intuitive depiction of the evolutionary dynamics of the
generated content.

##  3 Preliminary Results

Figure 3: Effect of network structure : Cultural dynamics of a population of
10 agents over 10 generations for three different types of network structures.
(a), (b), (c) Similarity matrices for a fully-connected network, a caveman
network with 2 cliques, and a circle network. The index of a story is defined
as the agent’s index (here between 0 and 10) + $N_{agents}$ * generation-
index. For example, the story 3 belongs to the first generation, and story 13
to the second generation. The color of the cell at row i and column j
represents the semantic similarity between stories i and j. Black lines mark
the separation between generations. (d) Evolution of the average similarity
between stories produced at a generation and stories at the generation just
before.(e) Evolution of the average similarity between each pair of stories
produced at a given generation.(f) Evolution of the average similarity between
stories produced a given generation and stories produced at the first
generation. Lines represent averages over 5 simulations, and the filled areas
represent the standard deviations.

The results presented in this paper are preliminary, and are mainly meant to
illustrate how one can manipulate with the different variables to see their
effects on the measures described above. However, they do already offer some
interesting insights.

###  3.1 Transmission chain

We first illustrate the dynamics of the model using a linear transmission
chain of 50 agents (i.e one agent per generation for 50 generations). The
initialization and transmission prompts used are provided in the Section A of
Appendix. The agents were not assigned any personality for this experiment
(personality prompt is empty). Fig. 2.a shows the similarity matrix for this
chain. We can notice that stories seem to evolve in a punctuated manner: there
is an alternation of phases where stories are transmitted with no
modifications, and phases where stories are modified. These dynamics recall
previous observations from experiments and modelling work in cultural
evolution [24] [46] [35] [34], where cultural information was found to evolve
in a sequence of bursts and stasis. The transition matrix also suggests the
existence of hierarchically structured clusters of stories that are not
identical but share some degree of similarity. Fig. 2.b shows the graph of
similarity of this chain, which allows to visualize how stories progressively
evolve through a semantic space. Looking at this graph suggests that stories
got ”trapped” in a specific part of the semantic space for a while (from
generation 14 to 41), possibly indicating the presence of an attractor. Fig.
2.c shows the chain-of-words representation for this chain. This visualization
allows to notice that some words are very stable, being kept almost throughout
the chain, such as the word ”magic”, while some words only last for the first
few generations before being lost, such as the word ”learn”.

Figure 4: Effect of transmission prompts : Cultural dynamics of a population
of 10 agents over 10 generations for four different transmission prompts. (a),
(b), (c), (d) Similarity matrices for the ”CombineTwo”, ”MinorChanges”,
”Repeat” and ”MaximizeDifference” transformation prompts. (e) Evolution of the
average similarity between stories produced at a generation and stories at the
generation just before.(f) Evolution of the average similarity between each
pair of stories produced at a given generation.(g) Evolution of the average
similarity between stories produced a given generation and stories produced at
the first generation. Lines represent averages over 5 simulations, and the
filled areas represent the standard deviations.

###  3.2 Effect of network structure

We first manipulated the network structure by running 5 simulations of 10
agents for 10 generations, for each network structure (Fig .3). We compared
three network structures: a fully-connected network, a circle network, and a
caveman network with 2 cliques (see Fig .S1 of the Appendix). We only show one
of the five similarity matrices for each network structure, and provide all
matrices in Appendix C.2. Qualitatively, the similarity matrices reveals
distinct patterns for each network structure: while similarity appears to
increase homogeneously for the fully-connected network, it does so in a
clustered manner for the caveman and circle networks. Looking at the evolution
of the similarity measures, we observe that for all structures, stories get
more and more similar to stories of the same generation and of the previous
generation, indicating a progressive homogenisation of the population. We also
observe that stories get more and more dissimlar with stories from the first
generation. For all measures, these dynamics seem to happen at a faster rate
for the fully-connected structure than for the caveman network, itself faster
than the circle network. These results replicate findings from previous work
in network science and cultural evolution, where models and experiments reveal
that more efficient networks (that is, networks with smaller average path
length) lead to quicker diffusion of information and thus lower diversity [11]
[12] [37] [26].

###  3.3 Effect of transformation prompt

We then manipulated the transformation prompt by running 5 simulations of 10
agents for 10 iterations (Fig. 4). We compared the effect of four different
transformation prompts referred to as ”Combine2”, ”MinorChanges”, ”Repeat” and
”MaximizeDifference”. The exact content of these prompts is provided in
Appendix A. These dynamics reveal that clear differences can be observed, and
those differences are aligned with what would be expected. For example, the
Repeat prompt leads to high within- and between- generation similarity, while
these metrics are low for the MaximizeDifference prompt. Apart for the
MaximizeDifference condition, all conditions show a gradual increase in the
simlilarity with previous generation and within-generation, indicating a
progressive homogenisation of the cultural content. Lastly, for all conditions
but the Repeat condition, similarity with the initial generation appears to
decrease over time. This is in particular interesting for the
MaximizeDifference condition, as the second generation was already instructed
to maximize the difference with the first generation.

###  3.4 Effect of different personalities

Figure 5: Effect of personalities : Cultural dynamics of a population of 10
agents over 10 generations for four different personnalities. (a), (b), (c),
(d) Similarity matrices for ”NoPersonality”, ”Creative”, ”NotCreative” and
Mixed population of ”Creative” and ”NotCreative”. (e) Evolution of the average
similarity between stories produced at a generation and stories at the
generation just before.(f) Evolution of the average similarity between each
pair of stories produced at a given generation.(g) Evolution of the average
similarity between stories produced a given generation and stories produced at
the first generation. Lines represent averages over 5 simulations, and the
filled areas represent the standard deviations

We then manipulated the personality assigned to agents by running 5
simulations of 10 agents for 10 generations (Fig. 5). We compared 4 different
conditions. In the first one, agents were not assigned any personality. In the
second one, all agents were assigned the personality ”Creative”. In the third
one, all agents were assigned the personality ”NotCreative”. In the fourth
one, half of the agents were assigned the personality ”Creative” and the other
half was assigned the personality ”NotCreative”. Details of the personality
prompts can be found in Appendix A. Although performing more simulations would
be necessary to draw conclusions, it does seem that different personalities
differentially impact cultural dynamics. In particular, our results suggest
that agents in the Creative condition generate more variation than agents in
the NotCreative condition: indeed, the NotCreative appears to exhibit higher
similarity with the first generation, between successive generations, and
within generations compared to the Creative condition. Also interesting is the
fact the the MixedPopulation condtion seems to be more similar to the Creative
condition than to the NotCreative condition, even though it contains Creative
and NotCreative agents in equal proportions. This suggests that the cultural
dynamics of an heterogeneous population may not reflect the proportions of the
different personalities it contains.

##  4 Discussion

We introduced a framework for modelling cultural evolution in population of
LLMs agents, along with several metrics and visualizations that allows to
extract qualitative and quantitative insights about the resulting cultural
dynamics. We presented how this framework allows to manipulate several
variables known to impact cultural evolution, namely the network structure,
the way of transforming previous social information, and agents’
personalities. Although the results presented in this paper are still
preliminary, they already reveal several insights. First, the fact our
simulations replicate several findings from empirical and theoretical work in
cultural evolution confirms that LLMs-based multi-agent models are an adequate
tool for generating hypotheses about the dynamics of human culture. It also
suggests that results from studies of human-generated culture may apply to
machine-generated culture. Moreover, we found that manipulating personality
and social information transformation appears to have significant impact on
the observed dynamics. This suggests that using LLMs to study cultural
evolution is promising, as these variables have so far been difficult to model
using traditional modelling tools. It also indicates that the dynamics of
machine-generated culture will likely be influenced by the specific way in
which generative agents are instructed to use pre-existing social information,
and which personality traits to emulate.

These results were preliminary and should mainly be seen as proof of concept.
Future work will involve performing more systematic and rigorous analyses of
the effect of the different variables on cultural evolution. It would also be
interesting to compare how different groups, all starting with the same story,
evolve over time.

Although Large Language models are a useful proxy of human behavior, some
precautions must be taken when generalizing results of such simulation to
human behavior. First, because of the biases in their training set, LLMs are
mainly representative of western culture [3]. As such, they may not be able to
capture the specific dynamics of other cultures. A potential way to alleviate
that is to use models that were trained on more representative datasets, such
as the BLOOM model whose training data includes 46 different languages [49].
More generally, precisely evaluating to what extent current models miss some
aspects of non-western cultures is a major direction for future work on
machine-generated cultural evolution. A second limitation to keep in mind is
that in some situations, LLMs may struggle to role-play and impersonate
specific characters [25]. Better understanding to what extent they take into
account their assigned personality when creating cultural content is a crucial
step in order to derive hypotheses about human culture using such models.

Another important difference between this model and human cultural evolution
is that the latter is grounded in a physical environment. As such, the success
of cultural traits not only depend on the cognitive mechanisms of the agents
transmitting it, but also on their relationship with the environment of the
agents [45]. For example, beliefs in moralizing gods have been found to be
predicted with high accuracy by the ecological and historical context [4].
Extending this model to include interaction with a physical environment
therefore seems like a very promising direction.

Finally, the current model assumes that personalities are fixed and stable
through time. However in humans, there are feedback loops between the cultural
traits expressed in a group and the personalities, values and preferences of
its member [42] [19]. Including such interactions would be fruitful to model
phenomena such as opinion dynamics and polarization.

More generally, although we here focused on the dynamics of collective
creation, this framework is suited to explore other questions related to
collective behavior, including opinion dynamics, collective innovation and the
evolution of language.

Overall, we have sketched how using generative agents to simulate cultural
evolution may be promising, both for generating hypotheses about human
cultural evolution and for better understanding the dynamics of machine-
generated culture. We hope that making this tool easy to use (see usage
details in Appendix B) and accessible to the scientific community will foster
more exchanges between the fields of cultural evolution and generative
artificial intelligence.

## Acknowledgements

This research was partially funded by the French National Research Agency
(ANR, project ECOCURL, Grant ANR-20-CE23-0006). This work benefitted from
access to the Jean Zay (Idris) supercomputer associated with the Genci grant
A0151011996. This research originated as a project from the Hackathon
Hack1Robo. We also thank Maxime Derex for participating in helpful
discussions.

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##  Appendix A Simulation details

##### LLM used

The results presented in this paper were generated using MistralOrca [28],
which is a version of openAI’s Mistral-7B Model, instruct-tuned on Filtered
OpenOrcaV1 GPT-4 Dataset. We used a quantized GGUFv2 version, quantized using
the method ”GGML-TYPE-Q4-K”.

##### Prompts used for the experiments

For the chain of 50 agents (Section 3.1), the initialization prompt used was
”Imagine that you are telling a story to your kid. What would that story be?
Just output the story, nothing else.” The transformation prompt used was ”Here
is one or more stories you were told as a kid. It is now your turn to tell a
story at your kid. Tell that story. Write only one story. Do not output
anything else.”.

For all other simulations, the initialization prompt was ”Tell me a story”.
Except when manipulating the transformation prompt, the transmission prompt
for all simulations was CombineTwo. Here is the complete list of
transformation prompts used in our experiments :

  * •

CombineTwo (default):

> ”You will receive stories. Pick the two stories you prefer, and create a
> story that is combination of these two stories. Just output your story,
> don’t write anything else.”

  * •

MinorChanges:

> ”You will receive a list of one or more stories. Create a new story by
> making some minor changes to one of those stories. Just output one story, do
> not output anything else.”

  * •

Repeat:

> ”You will receive stories. Select only one of these stories, and repeat it.
> Just output the story, don’t write anything else.”

  * •

MaximizeDifference:

> ”You will receive stories. Create a story that is as different as possible
> from the stories you received. Just output your story, nothing else.”

Except when manipulating the personality, the personality prompt was an empty
string for all simulations. When manipulating the personalities, the prompts
were:

  * •

Creative:

> ”For what follows, pretend that you are a very creative person.”

  * •

NotCreative:

> “For what follows, pretend that you are not a very creative person.”

##### Network structure

Unless the network structure was the manipulated variable, the default
structure was a fully-connected network (Supplementary Fig .1.a). We also used
a chain network (Supplementary Fig .1.d) in Section 3.1, as well as circle
(Supplementary Fig .1.b) and caveman (Supplementary Fig .1.d) networks in
Section 3.2.

Supplementary Figure 1: Different types of networks used in our experiments
with 10 agents. In a fully connected network (a), every agent is directly
connected to every other agent, enabling efficient dissemination of
information. In a circular network (b), agents are connected in a circular
fashion, thereby forming a closed loop where stories flow sequentially around
the circle. The caveman network (c) consists of agents organized into cliques,
with our example showcasing two cliques of 5 agents each. In the chain network
(d), agents are arranged linearly, and content generation happens
sequentially, meaning that agents only generate a story after receiving the
story of the previous agent in the chain.

##  Appendix B User Interface

Supplementary Figure 2: Screenshot of the Graphical User Interface

To allow researchers to easily use our model, we developed an intuitive user
interface that allows to manipulate the variables of interest and generate
figures (see Supplementary Figure 2 ) . In the Simulation panel, users can set
these variables. Starting from the top of the panel, users can select how many
agents they wish to simulate (“Number of agents”), how many generations to
simulate (“Number of generations”), and how many times to repeat the
simulations (”Number of seeds”). Users can also select which initialization
prompt and transformation prompt to use (“Initialization prompt” and
“Transformation prompt”). Users may add a new prompts by clicking on the “Add
prompt…” button. This opens a new window in which they can set the name and
content of the prompt. Users can also select which network structure to use
for the simulation. When “sequence” is selected, agents are arranged in a
chain, and each agents waits to receive the output of the previous agent in
the chain before generating its own output. The other options are ”Circle”,
which creates a cyclic graph, ”Caveman”, which creates a connected-caveman
network [48] (in which case the user must also select the number of cliques),
and a ”Fully-Connected”, which creates a fully-connected network. The
structure of the chosen graph is displayed on the right side of the window.
Finally, users can also select the personalities to assign to the agents. A
checkbox allows to indicate whether all agents should have the same
personality. If it is the case, users can select the corresponding personality
in the drop-down menu. Like for the prompts, users can add new personalities
to the list. If agents have different personalities, the users can assign each
agent its personality in the corresponding list. On top of these parameters,
users should give a name to the simulation, which will be the name of the
folder in which results are saved. Users should also specify the URL to send
the request to in order to get answers from the LLM. We generated such an URL
using a library from oogabooga (https://github.com/oobabooga/text-generation-
webui), and provide details of this procedure in the README file of our github
repository. Once all of these parameters have been set, users can run the
simulations by clicking on ”Run”. Once the simulation has terminated, figures
will be generated and displayed in the Figures tab of the GUI, as well as
being stored in the result folder.

##  Appendix C Additional metrics and results

###  C.1 Additional metrics

##### Creativity

To obtain the creativity of a text, we compute the average semantic distance
between all pairs of words in this text. This way of measuring creativity is
supported by recent studies [23] [20].

##### Positivity and subjectivity

We used TextBlob [29] to perform sentiment analysis on the content generated.
In particular, we used their measures of positivity and subjectivity and
looked at their evolution through generations.

###  C.2 Additional results

The evolution of those additional metrics though generations is shown in
Supplementary Figure 3, Supplementary Figure 4 and Supplementary Figure 5

Supplementary Figure 3: Evolution of additional metrics for four different
network structures Supplementary Figure 4: Evolution of additional metrics for
four different transformation prompts: Combine2, MinorChanges, Repeat, and
MaximizeDifference Supplementary Figure 5: Evolution of additional metrics for
different personalities: NoPersonality, Creative, NotCreative, Mixed
population of Creative and NotCreative Supplementary Figure 6: All similarity
Matrices for the Fully-Connected Network. Supplementary Figure 7: All
similarity Matrices for the Caveman Network Supplementary Figure 8: All
similarity Matrices for the Circle Network Supplementary Figure 9: All
similarity Matrices for the MinorChanges transformation prompt Supplementary
Figure 10: All similarity Matrices for the Repeat Prompt Supplementary Figure
11: All similarity Matrices for the MaximizeDifference transformation Prompt
Supplementary Figure 12: All similarity Matrices for the Creative personality
Supplementary Figure 13: All similarity Matrices for the NotCreative
personality Supplementary Figure 14: All similarity Matrices for the Mixed
Population Supplementary Figure 15: Complete rotated word chains plot of fig
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##  Appendix A Numerical convergence

###  A.1 Numerical relaxation

We monitor the relaxation of the initial state by following reduced quantities
representative of the dynamics of the fields and of the particles in the
corona. For the former, we measure the BH net electric charge $Q_{BH}$ defined
based on the charges crossing the event horizon since the beginning of the
simulation. Since the innermost regions within the event horizon are cropped
($r_{min}>0$), charges entering the horizon can exit the simulation space.
Instead of counting the charges, we thus apply Maxwell-Gauss equation
integrated over the event horizon:

$Q_{BH}=\frac{1}{4\pi}\oiint_{EH}\boldsymbol{D}\cdot\boldsymbol{\mathop{}\\!\mathrm{d}\Sigma}.$
(39)

The electric field $\boldsymbol{D}$ is symmetric with respect to the
equatorial plane such as we can integrate over the upper hemisphere and
multiply by 2. We then compare $Q_{BH}$ to the electric charge $Q_{0}$ for
which the time-component of the 4-potential cancels out (Wald 1974):

$Q_{0}=2aB_{0}.$ (40)

In the top panel in Figure 19, we see that the net charge eventually plateaus,
which indicates that numerical relaxation is achieved in the innermost regions
of the simulation space after approximately 50$r_{g}/c$. The net charge of the
BH is negative and for $a=0.99$, its magnitude reaches almost a fourth of
$Q_{0}$. It was recently alleged by King & Pringle (2021) that if the BH was
to acquire an electric charge $Q_{0}$, the Blandford-Znajek mechanism would
not be able to operate because the 4-potential no longer contains a term
function of the BH spin. However, the correspondence of the 4-potential with
the Wald solution for a non-spinning BH does not mean that the structure of
the electromagnetic fields is the same due to the different underlying
metrics. Komissarov (2021) showed that in contrast with a Schwarzschild BH, a
maximally spinning BH with an electric charge $Q_{0}$ has a magnetosphere
where the component of the electric field parallel to the magnetic field does
not cancel: particles are susceptible to be accelerated along the magnetic
field lines.

Due to the injection procedure, the relaxation of the particle distribution
takes more time. After a steep increase of the number of particles visible in
the bottom panel in Figure 19, the number of particles keeps increasing
slower, especially for simulations with higher BH spin values. A plateau is
eventually achieved after $\sim 100r_{g}/c$, once the rate at which particles
exit the simulation space equals the injection rate. The relaxation of the
outermost regions of the simulation space takes more time than the relaxation
of the innermost parts, so we typically work between $t=100r_{g}/c$ and
$t=150r_{g}/c$ to guarantee full time convergence. The total number of
particles correspond to approximately 20 particles per grid cell, with more
particles in the current sheet. It ensures a good signal-to-noise ratio by
lowering the particle shot noise.

Figure 19: (top panel) Net amount of electric charge $Q_{BH}$ within the event
horizon as a function of time for different spin values and for a thin disk
($\epsilon=5\%$) in prograde rotation. (bottom panel) Total number of
particles within the simulation space as a function of time.

###  A.2 Resolution and scale separation

We evaluated the impact of the resolution and of the scale separation on the
dissipation by computing the radial profiles for simulations with $a=0.8$,
$\epsilon=5$% and a disk in prograde rotation. Figure 20 shows the integral of
$\boldsymbol{J}\cdot\boldsymbol{E}$ over a volume bounded by the pole and the
disk in the longitudinal direction, and between the event horizon (vertical
black solid line) and a given distance $r$ to the BH in the radial direction.
Apart from the innermost regions, energy is progressively transferred from the
electromagnetic field to the particles until reaching a value of approximately
0.001$B_{0}^{2}r_{g}^{2}c$ at 26$r_{g}$, consistent with Figure 11. We compare
a simulation with the standard resolution we used in this paper (NR in Figure
20, with 2,128 and 1,120 cells in the radial and longitudinal directions
respectively) to a simulation with a resolution twice higher (HR,
4,256$\times$2,240 cells) and a high-resolution simulation like HR but with a
dimensionless magnetic field scale $\tilde{B}_{0}$ higher by a factor 4 (HB).
As emphasized by Equation (11), the Larmor radius is resolved by the same
number of cells in all 3 simulations. The profiles are averaged over
40$r_{g}/c$ after the simulations have relaxed.

The normal and high resolution cases NR and HR yield very similar profiles and
prove that the number of grid cells we use is sufficient to resolve the
magnetic reconnection process and the subsequent particle acceleration. The
simulation HB at higher magnetic field gives a profile within 15% of the NR
and HR ones. Due to our injection method (see Section 2.2.5), the higher
magnetic field produces a denser corona. The magnetization is 4 times higher
than in cases NR and HR but in the relativistic reconnection regime we
explore, this does not significantly modify the reconnection rate. Instead,
the slightly lower dissipation might be due to the higher plasma inertia.

Figure 20: Time-averaged dissipated electromagnetic energy between the event
horizon and a given radius for simulations with normal resolution (NR), high
resolution (HR) and high magnetic field (HB). The dashed and dotted black
lines show the distance to the separatrix footpoint and to the Y-point
respectively.

##  Appendix B Y-point location

We provide fitting formulas for the coordinates $(x_{Y},y_{Y})$ and the
distance $r_{Y}$ to the BH of the Y-point as a function of the spin value. We
fitted the measured median positions with the following power law:

$r=c_{1}a^{c_{2}}$ (41)

where $c_{1}$ and $c_{2}$ are the fitting parameters. The best fit parameters
for the range of spins we explore are given in Table 1. Although reasonable in
the range of BH spin values we sample, these values might lead to significant
departure from the physical ones when the power law (41) is extrapolated to
spins lower than 0.6.

Table 1: Parameters of the best fit power laws to locate the Y-point as a function of the BH spin based on Equation (41). | $r_{Y}$ | $x_{Y}$ | $y_{Y}$
---|---|---|---
$c_{1}$ | 5.21 | 4.88 | 1.81
$c_{2}$ | -2.39 | -2.34 | -2.70

##  Appendix C Synthetic images

In Figure 21, we show the synthetic images of synchrotron emission from the
current sheet for different inclinations of the line-of-sight with respect to
the BH spin axis. The BH spin is $a=0.8$ and the disk is thin and in prograde
rotation around the BH. The inclination $i=55^{\circ}$ corresponds to Figure
13.

Figure 21: Intensity maps of synchrotron emission from the current sheet for
different viewing angles.