Spontaneous Lexicon Change 
Luc Steels ¢1,2) and Fr6d6ric Kaplan (1,3) 
(1) Sony CSL Paris - 6 Rue Amyot, 75005 Paris 
(2) VUB AI Lab - Brussels 
(3) LIP6 - 4, place Jussieu 75232 Paris cedex 05 
Abstract 
The paper argues that language change can 
be explained through the stochasticity observed 
in real-world natural language use. This the- 
sis is demonstrated by modeling language use 
through language games played in an evolv- 
ing population of agents. We show that the 
artificial languages which the agents sponta- 
neously develop based on self-organisation, do 
not evolve even if the population is changing. 
Then we introduce stochasticity in language use 
and show that this leads to a constant innova- 
tion (new forms and new form-meaning associ- 
ations) and a maintenance of variation in the 
population, if the agents are tolerant to varia- 
tion. Some of these variations overtake existing 
linguistict conventions, particularly in changing 
populations, thus explaining lexicon change. 
1 Introduction 
Natural language evolution takes place at all 
levels of language (McMahon, 1994). This is 
partly due to external factors such as language 
contact between different populations or the 
need to express new meanings or support new 
modes of interaction with language. But it 
is well-established that language also changes 
spontaneously based on an internal dynam- 
ics (Labov, 1994). For example, many sound 
changes, like from/b/to/p/, /d/ to/t/, and 
/g/ to /k/, which took place in the evolution 
from proto-Indo-European to Modern Germanic 
languages, do not have an external motivation. 
Neither do many shifts in the expression of 
meanings. For example, the expression of fu- 
ture tense in English has shifted from "shall" 
to "will", even though "shall" was perfectly 
suited and "will" meant something else (namely 
"wanting to"). Similarly, restructuring of the 
grammar occurs without any apparent reason. 
For example, in Modern English the auxiliaries 
come before the main verb, whereas in Old En- 
glish after it ('he conquered be would' (Old 
English) vs. 'he would be conquered' (Mod- 
ern English)). This internal, apparently non- 
functional evolution of language has been dis- 
cussed widely in the linguistic literature, lead- 
ing some linguists to strongly reject the possi- 
bility of evolutionary explanations of language 
(Chomsky, 1990). 
In biological systems, evolution takes place 
because \[1\] a population shows natural varia- 
tion, and \[2\] the distribution of traits in the 
population changes under the influence of selec- 
tion pressures present in the environment. Note 
that biological variation is also non-functional. 
Natural selection acts post .factum as a selecting 
agent, pushing the population in certain direc- 
tions, but the novelty is created independently 
of a particular goal by stochastic forces oper- 
ating during genetic transmission and develop- 
ment. Our hypothesis is that the same applies 
to language, not at the genetic but at the cul- 
tural level. We hypothesise that language for- 
mation and evolution take place at the level of 
language itself, without any change in the ge- 
netic make up of the agents. Language recruits 
and exploits available brain capacities of the 
agents but does not require any capacity which 
is not already needed for other activities (see 
also (Batali, 1998), (Kirby and Hurford, 1997)). 
The present paper focuses on the lexicon. It 
proposes a model to explain spontaneous lexi- 
con evolution, driven solely by internal factors. 
In order to have any explanatory force at all, 
we cannot put into the model the ingredients 
that we try to explain. Innovation, mainte- 
nance of variation, and change should follow 
as emergent properties of the operation of the 
model. Obtaining variation is not obvious, be- 
1243 
cause a language community should also have a 
natural tendency towards coherence, otherwise 
communication would not be effective. An ade- 
quate explanatory model of lexicon change must 
therefore show \[1\] how a coherent lexicon may 
arise in a group of agents, \[2\] how nevertheless 
the lexicon may remain internally varied and ex- 
hibit constant innovation, and \[3\] how some of 
this variation may be amplified to become dom- 
inant in the population. These three quite dif- 
ficult challenges are taken up in the next three 
sections of the paper. 
2 How a coherent lexicon may arise 
To investigate concretely how a lexicon may 
originate, be transmitted from one generation 
to the next, and evolve, we have developed a 
minimal model of language use in a dynam- 
ically evolving population, called the naming 
game (Steels, 1996). The naming game has 
been explored through computational simula- 
tions and is related to systems proposed and 
investigated by (Oliphant, 1996), (MacLennan, 
1991), (Werner and Dyer, 1991), a.o. It has even 
been implemented on robotic agents who de- 
velop autonomously a shared lexicon grounded 
in their sensori-motor experiences (Steels and 
Vogt, 1997), (Steels, 1997). The naming game 
focuses on associating form and meaning. Ob- 
viously in human natural languages both form 
and meaning are non-atomic entities with com- 
plex internal structure, but the results reported 
here do not depend on this internal complexity. 
We assume a set of agents .A where each 
agent a E ,4 has contact with a set of ob- 
jects O = {o0, ..., on}. The set of objects 
constitutes the environment of the agents. A 
word is a sequence of letters randomly drawn 
from a finite alphabet. The agents are all as- 
sumed to share the same alphabet. A lexicon £ 
is a time-dependent relation between objects, 
words, and a score. Each agent a E A has 
his own set of words W~,t and his own lexicon 
La,t C Oa × Wa,t × J~, which is initially empty. 
An agent a is therefore defined at a time t as a 
pair at =< W~,t, La,t >. There is the possibil- 
ity of synonymy and homonymy: An agent can 
associate a single word with several objects and 
a given object with several words. It is not re- 
quired that all agents have at all times the same 
set of words and the same lexicon. 
We assume that environmental conditions 
identify a context C C O. The speaker selects 
one object as the topic of this context fs E C. 
He signals this topic using extra-linguistic com- 
munication (such as through pointing). Based 
on the interpretation of this signalling, the 
hearer constructs an object score 0.0 < eo <_ 1.0 
for each object o E C reflecting the likelihood 
that o is the speaker's topic. If there is absolute 
certainty, one object has a score of 1.0 and the 
others are all 0.0. If there is no extra-linguistic 
communication, the likelihood of all objects is 
the same. If there is only vague extra-linguistic 
communication, the hearer has some idea what 
the topic is, but with less certainty. The mean- 
ing scope parameter am determines the number 
of object candidates the hearer is willing to con- 
sider. The meaning focus parameter Cm deter- 
mines the tolerance to consider objects that are 
not the center of where the speaker pointed to. 
In the experiments reported in this paper, the 
object-score is determined by assuming that all 
objects are positioned on a 2-dimensional grid. 
The distance d between the topic and the other 
objects determines the object-score, such that 
1 eobject 
-- 1 + (¢_~)2 (1) 
) 
Cm is the meaning focus factor. 
To name the topic, the speaker retrieves from 
his lexicon all the associations which involve fs. 
This set is called the association-set of fs. Let 
o E O be an object, a E ¢4 be an agent, and t a 
time moment, then the association-set of o is 
Ao,a,t = {< o,w,u >l< o,w,u >e La,t} (2) 
Each of the associations in this set suggests a 
word w to use for identifying o with a score 
0.0 _< u _< 1.0. The speaker orders the words 
based on these scores. He then chooses the as- 
sociation with the largest score and transmits 
the word which is part of this association to the 
hearer. 
Next the hearer receives the word w trans- 
mitted by the speaker. To handle stochasticity 
the hearer not only considers the word itself a 
set of candidate words W related to w. These 
are all the words in the word-set of the hearer 
Wh,t that are either equal to w or related with 
some distance to w. The form scope parameter 
1244 
a/determines how far this distance can be. A 
score is imposed over the members of the set of 
candidate words: 
1 = 1 + (3) 
¢I is the form-focus factor. The higher this 
factor, the sharper the hearer has been able to 
identify the word produced by the speaker, and 
therefore the less tolerant the hearer is going to 
be to accept other candidates. 
For each word wj in W, the hearer then 
retrieves the association-set that contains it. 
He constructs a score-matrix which contains 
for each object a row and for each word- 
form a column. The first column contains the 
object-scores eo, the first row the form-scores 
m~. Each cell in the inner-matrix contains the 
association-score for the relation between the 
object and the word-form in the lexicon of the 
hearer: 
Wl W2 ... 
mw I mw2 ... 
O1 eol u(o\] ,Wl > U~Ol ,w2   ... 
02 Co2 U<o2,w\] > U<o2,w2> ... 
Obviously many cells in the matrix may be 
empty (and then set to 0.0), because a certain 
relation between an object and a word-form may 
not be in the lexicon of the hearer. Note also 
that there may be objects identified by lexicon 
lookup which are not in the initial context C. 
They are added to the matrix, but their object- 
score is 0.0. 
The final state of an inner matrix cell of the 
score matrix is computed by taking a weighted 
sum of (1) the object-score eo on its row, (2) 
the word-form score m~ on its column, and (3) 
the association-score a<o,~> in the cell itself. 
Weights indicate how strong the agent is will- 
ing to rely on each source of information. One 
object-word pair will have the best score and 
the corresponding object is the topic fh chosen 
by the hearer. The association in the lexicon of 
this object-word pair is called the winning asso- 
ciation. This choice integrates extra-linguistic 
information (the object-score), word-form am- 
biguity (the word-form-score), and the current 
state of the hearer's lexicon (the association- 
score). 
The hearer then indicates to the speaker 
what topic he identified. In real-world language 
games, this could be through a subsequent ac- 
tion or through another linguistic interaction. 
When a decision could be made and fh = fs 
the game succeeds, otherwise it fails. 
The following adaptations take place by the 
speaker and the hearer based on the outcome of 
the game. 
1. The game succeeds This means that 
speaker and hearer agree on the topic. To re- 
enforce the lexicon, the speaker increments the 
score u of the associa~on that he preferred, and 
hence used, with a fixed quantity ~. And decre- 
ments the score of the n competing associations 
with ~. 0.0 and 1.0 remain the lower and up- 
perbound of u. An association is competing if it 
associates the topic fs with another word. The 
hearer increments by ~ the score of the associ- 
ation that came out with the best score in the 
score-matrix, and decrements the n competing 
associations with ~. An association is compet- 
ing if it associates the wordform of the winning 
association with another meaning. 
2. The game fails There are several cases: 
1. The Speaker does not know a word 
It could be that the speaker failed to re- 
trieve from the lexicon an association covering 
the topic. In that case, the game fails but the 
speaker may create a new word-form w r and as- 
sociate this with the topic fs in his lexicon. This 
happens with a word creation probability we. 
2. The hearer does not know the word. 
In other words there is no association in the 
lexicon of the hearer involving the word-form of 
the winning association. In that case, the game 
ends in failure but the hearer may extend his 
lexicon with a word absorption probability wa. 
He associates the word-form with the highest 
form-score to the object with the highest object- 
score. 
3. There is a mismatch between fh and fs. 
In this case, both speaker and hearer have 
to adapt their lexicons. The speaker and the 
hearer decrement with ~ the association that 
they used. 
Figure 1 shows that the model achieves our 
first objective. It displays the results of an ex- 
periment where in phase 1 a group of 20 agents 
develops from scratch a shared lexicon for nam- 
ing 10 objects. Average game success reaches 
1245 
. i ,,,' .,0 
6o i : ,.,~ 
| 
1 2 "~-~ 
30 ~ , ,-20 
0~.0 
Closed~em ~ One ag,ntchanges ~ On, Igl.t ©ha.ges C, eVely200 games ~ every200 games 
Figure 1: The graphs show for a population of 
20 agents and 10 meanings how a coherent set 
of form-meaning pairs emerges (phase 1). In 
a second phase, an in- and outflow of agents 
(1 in/outflow per 200 games) is introduced, the 
language stays the same and high success and 
coherence is maintained. 
a maximum and lexicon coherence (measured 
as the average spread in the population of the 
most dominant form-meaning pairs) is high (100 
%) In the early stage there is important lexi- 
con change as new form-meaning pairs need to 
be generated from scratch by the agents. Lexi- 
con change is defined to take place when a new 
form-meaning pair overtakes another one in the 
competition for the same meaning. 
Phase 2 demonstrates that the lexicon is re- 
silient to a flux in the population. An in- and 
outflow of agents is introduced. A new agent 
coming into the population has no knowledge at 
all about the existing set of conventions. Suc- 
cess and coherence therefore dip but quickly re- 
gain as the new agents acquire the existing lex- 
icon. High coherence is maintained as well as 
high average game success. Between the begin- 
ning of the flux and the end (after 30,000 lan- 
guage games), the population has been renewed 
5 times. Despite of this, the lexicon has not 
changed. It is transmitted across generations 
without change. 
3 How a lexicon may innovate and 
maintain variation 
So, although this model explains the forma- 
tion and transmission of a lexicon it does not 
explain why a lexicon might change. Once 
a winner-take-all situation emerges, competing 
forms are completely suppressed and no new in- 
novation arises. Our hypothesis is that innova- 
tion and maintenance of variation is caused by 
stochasticity in language use (Steels and Ka- 
plan, 1998). Stochasticity naturally arises in 
real world human communication and we very 
much experienced this in robotic experiments as 
well. Stochasticity is modeled by a number of 
additional stochastic operators: 
1. Stochasticity in non-linguistic communica- 
tion can be investigated by probabilistically 
introducing a random error as to which ob- 
ject is used as topic to calculate the object- 
score. The probability is called the topic- 
recognition-stochasticity T. 
2. Stochasticity in the message transmission 
process is caused by an error in produc- 
tion by the speaker or an error in percep- 
tion by the hearer. It is modeled with 
a second stochastic operator F, the form- 
stochasticity, which is the probability that 
a character in the string constituting the 
word form mutates. 
3. Stochasticity in the lexicon is caused by er- 
rors in memory lookup by the speaker or 
the hearer. These errors are modeled us- 
ing a third stochastic operator based on 
a parameter A, the memory-stochasticity, 
which alters the scores of the associations 
in the score matrix in a probabilistic fash- 
ion. 
The hearer has to take a broader scope into 
account in order to deal with stochasticity. He 
should also decrease the focus so that alterna- 
tive candidates get a better chance to compete. 
The broader scope and the weaker focus has also 
the side effect that it will maintain variation in 
the population. This is illustrated in figure 2. In 
the first phase there is a high form-stochasticity 
as well as a broad form-scope. Different forms 
compete to express the same meaning and none 
of them manages to become the winner. When 
form-stochasticity is set to 0.0, the innovation 
dies out but the broad scope maintains both 
variations. One form ("ludo") emerges as the 
winner but another form ("mudo") is also main- 
tained in the population. There is no longer a 
winner-take-all situation because agents toler- 
ate the variation. We conclude the following: 
1246 
0,9 ~" 
O,a I" 
0,7 5" i.U~ 
o.~ ÷ I iii; 
o,4 ~r ~ t'IUDO 
°'~+ 1 2 0,2 "t" 
0,I t 
0 
o F=0,3 ~ F=D ~ F=O 
t1~e$ 
Figure 2: Competition diagram in the presence 
of form-stochasticity and a broad form-scope. 
The diagram shows all the forms competing for 
the same meaning and the evolution of their 
score. When F = 0.3 new word-forms are 
occasionally introduced resulting in new word- 
meaning associations. When F = 0.0 the in- 
novation dies out although some words are still 
able to maintain themselves due to the hearer's 
broad focus. 
1. Stochasticity introduces innovation in the 
lexicon. There is no longer a clear winner-take- 
all situation, whereby the lexicon stays in an 
equilibrium state. Instead, there is a rich dy- 
namics where new forms appear, new associa- 
tions are established, and the domination pat- 
tern of associations is challenged. The different 
sources of stochasticity each innovate in their 
own way: Topic-stochasticity introduces new 
form-meaning associations for existing forms. 
Form-stochasticity introduces new forms and 
hence potentially new form-meaning associa- 
tions. Memory-stochasticity shifts the balance 
among the word-meaning associations compet- 
ing for the expression of the same meaning. 
2. Tolerance to stochasticity, due to a broad 
scope (high trf) and a weak focus (low  f), 
maintains variation. For example, suppose a 
form "ludo" is transmitted by the speaker but 
the hearer has only "mudo" in his lexicon. If 
the form-focus factor is low and if both forms 
refer in the respective agents to the same ob- 
ject, their communication will be successful, be- 
cause the word-score of "mudo" will not devi- 
ate that much from "ludo". Neither the hearer 
nor the speaker will change their lexicons. Sim- 
ilar effects arise when the agent broadens the 
meaning scope and weakens its meaning focus 
to deal with meaning stochasticity, caused by 
error or uncertainty in the non-linguistic com- 
munication. 
4 How variation is amplified 
Although stochasticity and the agent's in- 
creased tolerance to cope with stochasticity ex- 
plain innovation and the maintenance of varia- 
tion, they do not in themselves explain lexicon 
change. Particularly when a language is already 
established, the new form-meaning pairs do not 
manage to overtake the dominating pair. To 
get lexicon change we need an additional factor 
that amplifies some of the variations present in 
the population. Several such factors are proba- 
bly at work. The most obvious one is a change 
in the population. New agents arriving in the 
community may first acquire a minor variant 
which they then start to propagate further. Af- 
ter a while this variant could become in turn 
the dominant variant. We have conducted a se- 
ries of experiments to test this hypothesis, with 
remarkable results. Typically there is a period 
of stability (even in the presence of uncertainty 
and stochasticity) followed by a period of insta- 
bility and strong competition, again followed by 
a period of stasis. This phenomenon has been 
observed for natural languages and is known in 
biology as punctuated equilibria (Eldredge and 
Gould, 1972). 
The following are results of experiments fo- 
cusing on form-stochasticity. Figure 3 shows 
the average game success, lexicon coherence, 
and lexicon change for an evolving population. 
30,000 language games are shown. It starts 
when the population develops a lexicon from 
scratch (phase 1). Form-scope is constantly 
kept at a I -- 5 in other words five forms are 
considered similar to the world heard. Initially 
there is no form-stochasticity. In phase 2 a flow 
in the population is introduced with a new agent 
every 100 games. We see that there is no lexicon 
change. Success and Coherence is maintained at 
high levels. Then form-stochasticity is increased 
to sigma/= 0.05 in phase 3. Initially there is 
still no lexicon change. But gradually the lan- 
guage destabilises and rapid change is observed. 
Interestingly enough average game success and 
coherence are maintained at high levels. After 
1247 
'00 ~ .............. V~.-,.~,-" '~ 
i : ~~~', f'i "~ " ~ " ,20 i : ',, ,~ ' ~i ~i:~, = / \] .L !~:ii~'i ,\] 
nil ¢ht L/hguige~hlfl~l(og~ulat~¢l)/-- '40 
: %.:., %::::' =2:'2,. ,o : eVtly 100 evely 100 F~)-- ~ 
: ¢*mu o,,m*, ~ .~*o.*o* ~*.~* \[ 
Figure 3: The diagram shows that change re- 
quires both the presence of uncertainty and 
stochasticity, high tolerance (due to broad scope 
and diffuse focus) and a flux in the popula- 
tion. The lexicon is maintained even in the case 
of population change (phase 2), but starts to 
change when stochasticity is increased (phase 
3). 
a certain period a new phase of stability starts. 
A companion figure (figure 4) focuses on 
the competition between different forms for the 
same meaning. In the initial stage there is 
a winner-take-all situation (the word "bagi"). 
When stochasticity is present, new forms start 
to emerge but they are not yet competitive. 
It is only when the flux in the population is 
positive that we see one competitor "pagi" be- 
coming strong enough to eventually overtake 
"bagi". "bagi" resulted from a misunderstand- 
ing of "pagi". There is a lot of instability as 
other words also enter into competition, giv- 
ing successive dominance of "kagi", then "kugi" 
and then "kugo". A winner-take-all situation 
arises with "kugo" and therefore a new period 
of stability sets in. Similar results can be seen 
for stochasticity in non-linguistic communica- 
tion and in the lexicon. 
5 Conclusions 
The paper has presented a theory that explains 
spontaneous lexicon change based on internal 
factors. The theory postulates that (1) coher- 
ence in language is due to self-organisation, i.e. 
the presence of a positive feedback loop between 
the choice for using a form-meaning pair and 
the success in using it, (2) innovation is due 
i o.~ .I- I 
J 
o~ ÷ j 
°"+ ! 1 2 
0,6 t" i I~@l 
i ', One =gent ', One agent Small 0,5 
÷ 
i Cle~d ~tm i chanties : cha;~o es St¢¢h,~icity 0,4 + wer~ 100 ,, wlrf 100 F,.O,06 
games : games 
o,z + 
0,2 ÷ 
o,I ,J- : DA61 BOO1 
" \^',1, f,'~ I~@l 
~"" ~ vaa,:', flJ 
l ; 
~i fi .1 i: I. ~*o 
, '~?LI, L:__ 
Figure 4: The diagram shows the competition 
between different forms for the same meaning. 
We clearly see first a rapid winner-take-all situa- 
tion with the word "bagi", then the rise of com- 
petitors until one ("pagi") overtakes the others. 
A period of instability follows after which a new 
dominant winner ("kugo") emerges. 
to stochasticity, i.e. errors in form transmis- 
sion, non-linguistic communication, or memory 
access, (3) maintenance of variation is due to 
the tolerance agents need to exhibit in order to 
cope with stochasticity, namely the broadening 
of scope and the weakening of focus, and finally 
(4) amplification of variation happens due to 
change in the population. Only when all four 
factors are present will effective change be ob- 
served. 
These hypotheses have been tested using a 
formal model of language use in a dynamically 
evolving population. The model has been im- 
plemented and subjected to extensive computa- 
tional simulations, validating the hypotheses. 
6 Acknowledgement 
The research described in this paper was con- 
ducted at the Sony Computer Science Labora- 
tory in Paris. The simulations presented have 
been built on top of the BABEL toolkit de- 
veloped by Angus McIntyre (McIntyre, 1998) 
of Sony CSL. Without this superb toolkit, it 
would not have been possible to perform the re- 
quired investigations within the time available. 
We are also indebted to Mario Tokoro of Sony 
CSL Tokyo for continuing to emphasise the im- 
portance of stochasticity in complex adaptive 
systems. 
1248 

References 
J. Batali. 1998. Computational simulations of 
the emergence of grammar. In J. Hurford, 
C. Knight, and M. Studdert-Kennedy, ed- 
itors, Approaches to the Evolution of Lan- 
guage. Edinburgh University Press, Edin- 
burgh. 
N. Chomsky. 1990. Rules and representations. 
Brain and Behavior Science, 3:1-15. 
N. Eldredge and S. Gould. 1972. Punctuated 
equilibria: an alternativeto phyletic gradual- 
ism. In T. Schopf, editor, Models in palaeobi- 
ology, pages 82-115, San Francisco. Freeman 
and Cooper. 
S. Kirby and J. Hurford. 1997. Learning, cul- 
ture and evolution in the origin of linguistic 
constraints. In P. Husbands and I. Harvey, 
editors, Proceedings of the Fourth European 
Conference on Artificial Life, pages 493-502. 
MIT Press. 
W. Labov. 1994. Principles of Linguistic 
Change. Volume 1: Internal Factors. Back- 
well, Oxford. 
B. MacLennan. 1991. Synthetic ethology: An 
approach to the study of communication. In 
C. Langton, editor, Artificial Life II, Red- 
wood City, Ca. Addison-Wesley Pub. Co. 
A. McIntyre. 1998. Babel: A testbed for re- 
search in origins of language. To appear in 
COLING-ACL 98, Montreal. 
A. McMahon. 1994. Understanding Language 
Change. Cambridge University Press, Cam- 
bridge. 
M. Oliphant. 1996. The dilemma of saussurean 
communication. Biosystems, 1-2(37):31-38. 
L. Steels and F. Kaplan. 1998. Stochasticity as 
a source of innovation in language games. In 
C. Adami, R. Belew, H. Kitano, and C. Tay- 
lor, editors, Proceedings of Artificial Life VI, 
Los Angeles, June. MIT Press. 
L. Steels and P. Vogt. 1997. Grounding adap- 
tive language games in robotic agents. In 
I. Harvey and P. Husbands, editors, Proceed- 
ings of the 4th European Conference on Arti- 
ficial Life, Cambridge, MA. The MIT Press. 
L. Steels. 1996. Self-organizing vocabularies. 
In C. Langton, editor, Proceeding of Alife V, 
Nara, Japan. 
L. Steels. 1997. The origins of syntax in vi- 
sually grounded robotic agents. In M. Pol- 
lack, editor, Proceedings of the 15th Interna- 
tional Joint Conference on Artificial Intelli- 
gence, Los Angeles. Morgan Kauffman Pub- 
lishers. 
G. M. Werner and M. G. Dyer. 1991. Evolution 
of communication in artificial organisms. In 
C. G Langton, C. Taylor, and J.D. Farmer, 
editors, Artificial Life II, Vol.X of SFI Stud- 
ies in the Sciences of Complexity, Redwood 
City, Ca. Addison-Wesley Pub. 
