Sharp transition towards shared vocabularies in multi-agent systems

TLDR: A microscopic model of communicating autonomous agents performing language games without any central control is introduced and it is shown that the system undergoes a disorder/order transition, going through a sharp symmetry breaking process to reach a shared set of conventions.

Abstract: What processes can explain how very large populations are able to converge on the use of a particular word or grammatical construction without global coordination? Answering this question helps to understand why new language constructs usually propagate along an S-shaped curve with a rather sudden transition towards global agreement. It also helps to analyse and design new technologies that support or orchestrate self-organizing communication systems, such as recent social tagging systems for the web. The article introduces and studies a microscopic model of communicating autonomous agents performing language games without any central control. We show that the system undergoes a disorder/order transition, going through a sharp symmetry breaking process to reach a shared set of conventions. Before the transition, the system builds up non-trivial scale-invariant correlations, for instance in the distribution of competing synonyms, which display a Zipf-like law. These correlations make the system ready for the transition towards shared conventions, which, observed on the timescale of collective behaviours, becomes sharper and sharper with system size. This surprising result not only explains why human language can scale up to very large populations but also suggests ways to optimize artificial semiotic dynamics.

Figures

Figure 2. Temporal evolution: we report here time evolution curves of a Naming Game played by N = 1000 agents. Without loss of generality (see text) we consider M = 1 objects. Bold curves are obtained averaging 3000 runs, while the light ones are obtained by a single run. (a) Total number of words in the system Nw(t) vs. t (t here denotes the number of games played) ; (b) Number of different words in the system Nd(t), whose average maximum is N/2; (c) Success rate S(t), calculated by assigning 1 to a successful interaction and 0 to a failure and averaging over many realizations. In the inset it is shown that, up to the disorder/order transition, the success rate is well described by the relation S(t) = 3t/N2.

Figure 3. Scaling relations: (a) scaling of the time where the total number of words reaches a maximum (tmax) as well as of the convergence times (tconv) with the population size N . Both curves exhibit a power law behavior with exponent 3/2. Statistical error bars are not visible on the scale of the graph. An interesting feature emerges from the ratio between convergence and maximum times, which exhibits a peculiar oscillating trend on the logarithmic scale (mainly due to convergence times oscillations). (b) scaling of the maximum number of words that the system stores during its evolution with the population size N . The curve exhibits a power law behavior with exponent 3/2. Statistical error bars are not visible on the scale of the graph. It must be noted that the values represent the average peak height for each size N , and this value is larger than the peak of the average curve. (c) Curves of the success rate S(t) are reported for various systems size. The time is rescaled as t → (t/tS(t)=0.5) so that the crossing of all the lines at t/tS(t)=0.5 = 1 is an artifact. The increase of the slope with system size is evident, showing that the disorder/order transition becomes faster and faster for large systems, when the dynamics is observed on the system time scale N3/2. The form of the rescaling has been chosen in order to take into account the deviations from the pure power-law behaviour in the scaling of tconv, rescaling each curve with a self consistent quantity (tS(t)=0.5). (d) Bottom right: Success rate S(t) for various systems size. The curves collapse well after time rescaling t → (t− tS(t)=0.5)/(t2/3S(t)=0.5)5/4, indicating that the characteristic time of the disorder/order transition scales as N5/4.

Figure 4. Single words ranking: The ranking of single words is presented for different times for a population size of N = 104. The histograms are progressively well described by a power law function. For times close to convergence the most popular word (i.e. that ranked as 1st) is no more part of the power law trend and the whole distribution should be described with eq. (3).

Figure 1. Inventory dynamics: Examples of the dynamics of the inventories in a failed and a successful game, respectively. The speaker selects the word highlighted in yellow. If the hearer does not possess that word he includes it in his inventory (top). Otherwise both agents erase their inventories only keeping the winning word.

Full text

City, University of London Institutional Repository
Citation: Baronchelli, A., Felici, M., Loreto, V., Caglioti, E. and Steels, L. (2006). Sharp
transition towards shared vocabularies in multi-agent systems. Journal of Statistical
Mechanics: Theory and Experiment new, 2006(6), doi: 10.1088/1742-5468/2006/06/P06014
This is the unspecified version of the paper.
This version of the publication may differ from the final published
version.
Permanent repository link: https://openaccess.city.ac.uk/id/eprint/2672/
Link to published version: http://dx.doi.org/10.1088/1742-5468/2006/06/P06014
Copyright: City Research Online aims to make research outputs of City,
University of London available to a wider audience. Copyright and Moral
Rights remain with the author(s) and/or copyright holders. URLs from
City Research Online may be freely distributed and linked to.
Reuse: Copies of full items can be used for personal research or study,
educational, or not-for-profit purposes without prior permission or
charge. Provided that the authors, title and full bibliographic details are
credited, a hyperlink and/or URL is given for the original metadata page
and the content is not changed in any way.
City Research Online: http://openaccess.city.ac.uk/ publications@city.ac.uk
City Research Online

arXiv:physics/0509075v2 [physics.soc-ph] 26 Jun 2006
Sharp transition towards shared vocabularies in
multi-agent systems
Andrea Baronchelli, Maddalena Felici and Vittorio Loreto
Dipartimento di Fisica, Universit`a “La Sapienza” and SMC-INFM, P.le A. Moro 2,
00185 Roma, (Italy)
Emanuele Caglioti
Dipartimento di Matematica, Universit`a “La Sapienza”, P.le A. Moro 2, 00185 Roma,
(Italy)
Luc Steels
VUB AI Lab, Bruss e ls (Belgium)
Sony Computer Science Laboratory, Paris (France)
Abstract. What processes can explain how very large populations are able to
converg e on the use of a particular word or grammatical construction without global
coordination? Answering this question helps to understand why new language
constructs usually propagate along an S-shaped curve with a rather sudden transition
towards global agreement. It also helps to analyze and design new technologies that
support or orchestrate self-org anizing communication systems, such as rec ent social
tagging systems for the web. The article introduces and studies a microscopic model
of communicating autonomous agents performing language games without any central
control. We show that the system undergoes a disorder/order trans itio n, going trough
a sha rp symmetry bre aking process to reach a shared set of conventions. Before the
transition, the s ystem builds up non-trivial scale-invariant correlations, for instance
in the distribution of competing synonyms, which display a Zipf-like law. These
correla tio ns make the system ready for the transition towards shared conventions,
which, obs erved on the time-scale of collective behaviors, becomes sharper and sharper
with system size. This surprising result not only explains why human language can
scale up to very large populations but also suggests ways to optimize artificial semiotic
dynamics.

Sharp transition towards shared vocabularies in multi-agent systems 2
1. Introduction
Bluetooth, blogosphere, ginormous, greenwash, folksonomy. Lexicographers have to add
thousands of new words to dictionaries every year and revise the usage of many more.
Although precise data is hard to come by, lexicographers agree that there is a period
in which novelty spreads and different words compete, followed by a rather dramatic
transition after which almost everyone uses the same word or construction [1]. This
‘semiotic dynamics’ has lately become of technological interest because of the sudden
popularity of new web-tools (such as del.icio.us or www.flickr.com) which enable human
web-users to self-organize a system of tags and that way build up and maintain social
networ ks and share information. Tracking the emergence of new tags shows similar
phenomena of slow spreading followed by sudden transitions in which one tag overtakes
all others. There is currently also a growing number of experiments where artificial
software agents or rob ots bootstrap a shared lexicon without human intervention [2, 3].
These applications may revolutionize search in peer-to-peer information systems [4] by
orchestrating emergent semantics [5] as opposed to relying on designer-defined ontologies
such as in the semantic web [6]. They will be needed when we send groups of robots to
deal autonomously with unforeseeable tasks in largely unknown environments, such as in
the exploration o f distant planets or deep seas, hostile environments, etc. By definition it
will not be possible to define all the needed communication conventions and ontologies
in advance and robots will have to build up and negotiate their own communication
systems, situated and grounded in their ongoing activities [7]. Designers of emergent
communication systems want to know what kind of mechanisms need to be implemented
so that the ar tificial agents effectively converge towards a shared communication system
and they want to know the scaling laws to see how far the technology will carry.
2. The Naming Game
Some of the earlier work on studying the emergence of communication conventions has
adopted an evo lutionary approa ch [8, 9, 10, 11, 12, 13, 14, 15]. Roughly speaking,
the degree in which an agent’s vocabulary is similar to that of others is considered
to determine its reproductive fitness, new generations inherit some features from
their parents (vocabularies, possibly with errors due to their transmission, or learning
strategies), and natural selection drives the population towards convergence. Here we are
interested however in phenomena that happen on a much more rapid time-scale, during
the life-span of agents and without the need for successive generations. All agents will
be considered peers that have the right to invent and negotiate language use [16, 17].
We introduce and study a microscopic model of communicating agents, inspired by the
so-called Naming Game [17], in which agents have only local peer-to-peer interactions
without central control nor fitness-based selection, but nevertheless manage to reach
a global consensus. There can be a flux in t he population, but generation change
is not necessary for reaching coherence. Peer-to-peer emergent linguistic coherence

Sharp transition towards shared vocabularies in multi-agent systems 3
AKNORAB
SLEETS
SLEETS
ICILEF
ICILEF
OTEROL
AKNORAB
AKNORAB
Success
Speaker Speaker
SpeakerSpeaker
SLEETS
Hearer Hearer
HearerHearer
Failure
OTEROL
ITOILGAC
ITOILGAC
ITOILGAC
VALEM
VALEM VALEM
VALEM
VALEM
VALEM
VALEM
OTEROL
ICILEF
Figure 1. Inventory dynamics: Examples of the dynamics of the inventories in a
failed and a successful game, respectively. The speaker selects the word highlighted in
yellow. If the hearer do es not possess that word he includes it in his inventory (top).
Otherwise both agents erase their inventories only keeping the winning word.
has recently been studied also in [18] focusing on how a population selects among a
set of possible grammars already known to each agent, whereas here we investigate
how conventions may develop from scratch as a side effect of situated and grounded
communications. The Naming Game model to be studied here uses as little processing
power as possible and thus establishes a lower-bound on cognitive complexity a nd
performance. In contrast with other mo dels of language self-organization, agents do
not maintain information about the success rate of individual words and do not use
any intelligent heuristics like choice of best word so far or cross-situational learning.
We want to understand how the microscopic dynamics of the agent interactions can
nevertheless give rise to glo bal coherence without external intervention.
The Naming Game is played by a population of N agents trying to bootstrap
a common vocabulary for a certain number M of individual objects present in their
environment, so that one agent can draw the attention of another one to an object,
e.g. to obtain it or converse further about it. The objects can be people, physical
objects, relations, web sites, pictures, music files, or any other kind of entity for which a
population aims at reaching a consensus as far their naming is concerned. Each player is
characterized by his inventory, i.e. the word- object pairs he knows. All the agents have
empty inventories at time t = 0. At each time step (t = 1, 2, ..) two players are picked
at random and o ne of them plays as speaker and the other as hearer. Their interaction
obeys the following rules (see Fig. 1):
• The speaker selects an object from the current context;
• The speaker retrieves a word from its inventory associated with the chosen object,
or, if its inventory is empty, invents a new word;
• The speaker transmits the selected word to the hearer;
• If the hearer ha s the word named by the speaker in its invento ry and that word

Sharp transition towards shared vocabularies in multi-agent systems 4
is associated to the object chosen by the speaker, the interaction is a success and
both players maintain in their inventories only the winning word, deleting all the
others;
• If the hearer does not have the word named by the speaker in its inventory, the
interaction is a failure and the hearer updates its inventory by adding an association
between the new word and the object.
This model makes a number of assumptions. Each player can in principle play with
all the other players, i.e. there is no specific underlying topology for the structure
of the interaction networ k. So the game can be viewed as an infinite dimension
(or “mean field”) Naming Game (an almost realistic situation thanks to the modern
communication networks). Second, we a ssume that the number of possible words is
so huge that the probability that two players invent the same word at two different
times for two different objects is practically negligible (this means that homonymy is
not taken into account here) and so the choice dynamics among the p ossible wor ds
associated with a specific object are completely independent. As a consequence, we can
reduce, without loss of generality, the environment as consisting of only one single object
(M = 1). In this perspective it is interesting noting that Komarova and Niyogi [13],
have formally proven, adopting an evolutionary game theoretic approach, that languages
with homonymy are evolutionary unstable. On the other hand, it is commonly observed
that human languages contain several homonyms, while true synonyms are extremely
rare. In [13] this apparent paradox is resolved noting that if we think of ”words in a
context”, homonymy does indeed disappears from human languages, while synonymy
becomes much more relevant. These observations match perfectly also with our third
assumption, according to which speaker and hearer are able to establish whether the
game was successful by subsequent action performed in a common enviro nment. For
example, the speaker may refer to an object in the environment he wants to obtain and
the hearer then hands the right object. If the game is a failure, t he speaker may point
or get the object himself so that it is clear to the hearer which object was intended.
3. Phenomenology
The first property of interest is the time evolution of the total number of words owned
by the population N
w
(t), of the number of different words N
d
(t), and of the success rate
S(t). In Figure (2) we report these curves averaged over 3000 runs for a population
of N = 1000 agents, along with two examples of single run curves. It is evident that
single runs originate quite irregular curves. We assume in these simulations that only
two agents interact at each time step, but the model is perfectly applicable to the case
where any number of agent s interact simultaneously.
Clearly, the system undergoes spontaneously a disorder/order transition to an
asymptotic state where global coherence emerges, i.e. every agent has the same word
for the same object. It is remarkable that this happens starting from completely empty

Frequently asked questions

Q1. What are the contributions in this paper?

The article introduces and studies a microscopic model of communicating autonomous agents performing language games without any central control. The authors show that the system undergoes a disorder/order transition, going trough a sharp symmetry breaking process to reach a shared set of conventions. This surprising result not only explains why human language can scale up to very large populations but also suggests ways to optimize artificial semiotic dynamics. 

Q2. What are the future works in this paper?

This research has been partly supported by the ECAgents project funded by the Future and Emerging Technologies program ( IST-FET ) of the European Commission under the EU RD contract IST-1940. The Commission is not responsible for any use that may be made of data appearing in this publication. 

Q3. What is the common word in the network?

An interaction in which the most common word is played will more likely lead to success, and hence the clique corresponding to the most common word will tend to increase, while other cliques will lose nodes. 

Q4. Why does the system always have the same word after a failed game?

Because two players always have the same word after a failed game, each failure at this stage corresponds to adding an edge to the graph. 

Q5. What is the effect of the word name on the hearer?

If the hearer has the word named by the speaker in its inventory and that wordis associated to the object chosen by the speaker, the interaction is a success and both players maintain in their inventories only the winning word, deleting all the others; • 

Q6. What is the purpose of the naming game?

The Naming Game is played by a population of N agents trying to bootstrapa common vocabulary for a certain number M of individual objects present in their environment, so that one agent can draw the attention of another one to an object, e.g. to obtain it or converse further about it. 

Q7. What is the first stage of the system?

Then the system enters a second stage in which it starts building correlations (i.e.multiple links connecting agents who have more than one word in common) and collective behavior emerges. 

Q8. How does the model explain the dynamics of the agents’ inventories?

The authors have explained this dynamics by observing a build up of non trivial dynamical correlations in the agents’ inventories, which display a Zipf-like distribution for competing synonyms, until a specific word breaks the symmetry and imposes itself very rapidly in the whole system. 

Q9. What is the first interesting aspect to investigate?

Since each agent is characterized by its inventory, a first interesting aspect to investigate is the time evolution of the fraction of players having an inventory of a given size. 

Q10. What is the probability that the system has not reached an absorbing state after 2k(N?

iterating this procedure, the probability that, starting from any state, the system has not reached an absorbing state after 2k(N−1) iterations, is smaller than (1−p)k which vanishes exponentially with k. 

Q11. What is the probability that the hearer possesses the word played by the speaker?

q is he probability that the hearer possesses the word played by the speaker which can be estimated as cN αN/2 (N/2 being the number of different words). 

Q12. What are the common uses of robots?

They will be needed when the authors send groups of robots to deal autonomously with unforeseeable tasks in largely unknown environments, such as in the exploration of distant planets or deep seas, hostile environments, etc.