Copyright for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).

HCI SI 2023: Human-Computer Interaction Slovenia 2023, January 26, 2024,
Maribor, Slovenia

[orcid=0000-0002-7913-3839<EMAIL_ADDRESS>]
[orcid=0000-0001-9341-6088, email=<EMAIL_ADDRESS>]
[orcid=0000-0003-2691-601X<EMAIL_ADDRESS>]
[orcid=0000-0002-7784-1356<EMAIL_ADDRESS>]
[orcid=0000-0002-6988-3046<EMAIL_ADDRESS>]

# Retzzles: Do Jigsaw Puzzle Actions on Interactive Display Maps Increase the
Retention of Map Information?

Nikola Kovačević  Jordan Aiko Deja  Maheshya Weerasinghe  Klen Čopič Pucihar
Matjaž Kljun  University of Primorska, Faculty of Mathematics, Natural
Sciences and Information Technologies, Koper, Slovenia  Faculty of Information
Studies, Novo Mesto, Slovenia  De La Salle University, Manila, Philippines
University of Glasgow, Scotland, United Kingdom  Stellenbosch University,
Department of Information Science, Stellenbosch, South Africa

(2024)

###### Abstract

While maps provide upfront content, this might not always be the most
effective way for users to remember information. With the proliferation of
interactive displays for tourists and visitors in public spaces, we can create
a more playful user experience with maps than just exploring them. Adding
interactions with the map could also help users retain more information as
they use them. In this paper, we investigated whether completing a jigsaw
puzzle of a map supports users in retaining more information about a specific
map. The results of a between-subject study with a sample of $n=28$ indicate
that additional interaction helped improve mean scores of textual and spatial
recall but not visual recall. However, the results are not statistically
significant, and the topic is subject to further investigation. Our findings
contribute to discussions on using interactive touchscreen displays in similar
learning scenarios involving memory retention.

###### keywords:

knowledge retention interactive displays interactive maps tourism gamification

##  1 Introduction and Background

Throughout history, maps have been essential resources for exploration,
navigation, and communication [1]. They are often used in tourism for an
overview of points of interest since they support memory and spatial cognition
and display information quickly [2, 3]. However, traditional paper-based maps
frequently fall short in providing further resources as paper real estate is
always limited. Additional resources can be delivered either on extra paper-
based material or in a digital form [4]. For example, looking at a physical
town map on the board, one can explore additional digital information over the
phone. Fully digital maps provide the possibility of interactivity and
unlimited further resources, enabling more dynamic user interaction with the
content. Another advantage of digital maps is the possibility of showing
additional elements in the map’s context, which paper-based maps cannot
achieve. It has been observed that showing annotations linked to a target
object’s actual location (that is, right on the map) improves users’ memory
skills more than showing annotations related to an unrelated location (that
is, off the map and connected to their location through other means) [5].

Digital maps are often provided on interactive displays that are common in
tourist information offices, museums, shopping malls, train stations, and even
streets [6]. These displays open up further possibilities for making
interaction with maps playful and, in turn, help people remember more
information [7, 8, 9, 10, 11, 12]. Playing activity enables the notion of
“learning by doing” or experiential learning [13]. There are various ways to
make map interaction playful—one possibility is to use jigsaw puzzle pieces
[14, 15]. Puzzles have been observed to help make learning enjoyable [16, 17].
Specifically, the use of jigsaw elements, one of the most common puzzle games,
has been observed to help students acquire a deeper understanding of certain
concepts and terminologies [18] in the broader context of learning.

In this paper, we explored whether engaging with maps through playful elements
such as jigsaw puzzles can improve engagement and retention of information. We
hypothesise that users playing with and completing a jigsaw puzzle of a map
will retain more information about it compared to users who will start
interacting with the complete map. In summary, this research presents the
following contributions: a) an improvement of Artifact prototype Retzzles [19]
that is presented on an interactive display, and b) Empirical findings of a
user study comparing visual, spatial and textual recall between two conditions
– map interaction vs. jigsaw puzzle interaction.

##  2 Retzzles: Design and Implementation

Figure 1: User completing a jigsaw puzzle of a map on the interactive display.
When the jigsaw is completed the POIs on the map become interactive.

This section discusses the design and concept behind our prototype entitled
Retzzles. We designed our interaction following the theory of constructivism,
according to which individuals actively construct knowledge and create their
experiences [20]. While the end goal of the puzzle is the same for every user,
the path toward achieving a solution will be unique for each user. As the
puzzle is being built, the user is piecing together the knowledge as long as
they play the game. With Retzzles, users complete a jigsaw of a tourist
destination map individually; however, the final map is the same for everyone.

Retzzles is shown on an interactive touch display where users can move the
puzzle pieces and put them in the correct locations as seen in Figure 1. We
used Unity to build this prototype. Jigsaw puzzles were created using GIMP and
its pattern feature “jigsaw”. The map consisted of 20 jigsaw pieces. We opted
for this number as it was shown to be not difficult and also not easy to
complete the puzzle in the pilot study. The jigsaw puzzles are all organised
into one empty parent game object. Each piece is assigned with the DragObject
script, allowing it to be moved and dragged anywhere on the screen. This
script defines how the puzzle pieces snap into the correct position. Because
our pieces are treated as sprites in Unity, we used PolygonCollider2D to
handle the physical collisions. The collider’s shape is defined by a freeform
edge made of line segments, which is easily adjustable to cover any shape, in
our case, any jigsaw puzzle.

When each jigsaw piece is dragged over the correct location and dropped, it
snaps automatically in its spot. As the user solves the puzzle, POIs become
revealed when the suitable puzzles are pieced together. After completing the
jigsaw, the POIs buttons become interactive. Tapping on them reveals
additional information about the touristic location they are placed at on the
map (Figure 3 bottom right). For this study, we put ten abstract symbols on
the map as POIs, as done in [5]. The two reasons behind this decision were to
avoid the familiarity with symbols usually used on maps and to not correlate
the symbols with the information they revealed when tapped on. The symbols
were created using the online graphic design platform
Canva111https://www.canva.com/. The map was created using the Snazzy
Maps222https://snazzymaps.com/ and the “No label, Bright Colors” layout as it
provided a map with fewer distractions. For the map, we used the city of
Lancaster, California, as users were likely not familiar with its layout, as
seen in Figure 2 left. For the same reason, we used 10 POIs users were likely
unfamiliar with.

Figure 2: The map and interact-able Points of Interest (POI) of the Retzzles:
Oxford Suites Hotel, Alderbrook Nursing Facility, Red Salmon Restaurant,
U-Haul Moving Supplies, Sun Flower Caffe, Target Grocery Store, Bowlero
bowling, Sunnydale School, The Tire Store, Costco Grocery Store and Sunnydale
School.

We have added some automated mechanisms to log data within the prototype for
more efficient data collection. We tracked the number of moves/clicks for each
puzzle piece, activated POIs, calculated the time needed to solve the puzzle,
and opened and read the POIs’ information. We also recorded and saved every
movement of each piece.

##  3 User Study

For this study, we proposed the following hypothesis: $H_{0}$: Puzzle
interactions aid in improved visual, spatial and textual recall of map
information.

figure[t]  Different Views of Retzzles. Top Left: Map Condition with 10 points
of interest (POI) displayed. Top right: Puzzle Condition where the map needs
to be assembled first before POIs can be interacted with. Bottom Left: One
piece left in the puzzle condition before the map becomes interactive. Bottom
Right: Point of Interest opened showing additional information.

Figure 3: Different conditions and stages of Retzzles. Top Left: the initial
stage of the puzzle condition. Top right: One piece left; when it will be
placed in the map will become interactive as in bottom left. Bottom Left: the
initial stage of the map-only condition. Bottom Right: The information card
opened when tapped on the corresponding POI.

We conducted a between-subject study design to validate our hypothesis with
$n=28$ participants recruited through convenience sampling. We recruited
participants who either have experience with 2D games or have prior experience
in solving puzzles. For the study, an unfamiliar tourist place, such as the
city of Lancaster, was used as the subject of the map in the prototype across
both conditions. The study involved three phases: 1) Orientation and Informed
Consent, 2) Interaction Task and 3) Wrapping phase. In 1), the moderator of
the study provided a brief introduction to the experiment and the prototype
Retzzles. Next, the participants were invited to read and sign the consent
form. At the beginning of 2), the moderator explained the task in more detail.
We used two conditions, namely (1) Map condition (Figure 3 bottom left) and
(2) Puzzle condition (Figure 3) top left). Symbols and information used
between both conditions were the same. However, the interaction amount
differed as the latter condition required puzzle assembly before unlocking the
touch-screen map interactions. After interacting with the prototype,
participants answered different questionnaires to measure visual, spatial and
textual recall.

The aim in both conditions was to memorise as much information as possible
after engaging with the prototype. The participants were first given a module
that instructed them on utilising the prototype. When they were ready, they
proceeded to the actual task based on the conditions set for them.
Participants in both conditions were instructed to interact with the prototype
while remembering as much information as possible. Interaction for the Map
condition consisted of engaging with a map as the POIs were already
interactive. Interaction with the Puzzle condition required participants to
solve the jigsaw puzzle of a map before being able to interact with the POIs
and review the information provided.

##  4 Results and Discussion

Table 1: Overview of NASA-TLX Cognitive Scores

| cond | MD | PD | TD | P | E | F
---|---|---|---|---|---|---|---
mean | puzzle |  ▼36.1 |  ▼8.21 |  ▲24.6 |  ▼28.6 |  ▼37.5 |  ▼12.1
map | 49.3 | 8.57 | 19.3 | 29.6 | 45.0 | 14.3
std dev | puzzle | 26.3 | 05.04 | 22.5 | 16.0 | 25.9 | 6.71
map | 19.2 | 06.02 | 16.0 | 18.0 | 24.3 | 14.9
Shapiro-Wilk $W$ | puzzle | 0.899 | 0.697 | 0.792 | 0.906 | 0.850 | 0.879
map | 0.958 | 0.672 | 0.785 | 0.915 | 0.962 | 0.697
Shapiro-Wilk $p$ | puzzle | 0.109 | <.001 | 0.004 | 0.139 | 0.022 | 0.057
map | 0.686 | <.001 | 0.003 | 0.185 | 0.750 | <.001
Mann-Whitney $U$ | $p$ | **0.122 |  | **0.758 | **0.871 | **0.309 |
|  $H_{a}$ $\mu_{puzzle}\neq\mu_{map}$ ,**no sign. diff.

Legend: Cond: Condition, MD: Mental Demand, PD: Physical Demand, D: Temporal
Demand, P: Performance, E: Effort, F: Frustration

###  4.1 Information Recall

Table 2: Overview of Metrics Used. Green arrow meaning better performance compared to the map condition, red arrow meaning worse performance. Legend: Cond: Condition, VR: Visual Recall, NS-VR: Negative Symbol Recall, SR: Spatial Recall, N-TR: Name Textual Recall, C-TR: Category Textual Recall | cond | VR | NS-VR | SR | N-TR | C-TR
---|---|---|---|---|---|---
| puzzle |  ▼75.7 |  ▼7.14 |  ▲68.6 |  ▲50.7 |  ▲68.6
mean | map | 80.7 | 6.43 | 60.7 | 47.1 | 57.9
| puzzle | 18.7 | 8.25 | 26.3 | 25.3 | 11.7
std dev | map | 18.6 | 11.5 | 29.2 | 17.7 | 21.9
| puzzle | 0.915 | 0.767 | 0.880 | 0.956 | 0.936
Shapiro-Wilk $W$ | map | 0.876 | 0.638 | 0.882 | 0.948 | 0.928
| puzzle | 0.184 | 0.002 | 0.059 | 0.661 | 0.370
Shapiro-Wilk $p$ | map | 0.051 | <.001 | 0.062 | 0.525 | 0.289
Mann-Whitney $U$ | $p$ | **0.452 |  | **0.328 | **0.693 | **0.116
|  $H_{a}$ $\mu_{puzzle}\neq\mu_{map}$ ,**no sign. diff.

We evaluated visual, spatial, and textual recall and measured participants’
subjective cognitive load using the NASA-TLX questionnaire. To test visual
recall, participants were presented with 20 abstract symbols (10 symbols were
present on the map while the others were not) and asked to identify which 10
were on the map. The results are in the percentage of correct symbols recalled
(Visual Recall [VR]) or the percentage of incorrect symbols recalled (Negative
Symbol Recall [NS-VR]). Spatial recall was assessed by asking users to
remember the positions of the abstract symbols on the map and to place them in
their correct locations on a separate blank map [SR]. Finally, for textual
recall, users were shown ten symbols on the map and asked to provide
information about each POI, including its name (Name Textual Recall [N-TR])
and category (Category Textual Recall [N-TR). For example, they might provide
the name “Costco” and the category “grocery store”.

The main goal of the analysis was to compare map and puzzle conditions. We
used the Shapiro-Wilk test to explore the normality of data distribution. We
found that the data is normally distributed ($p\geq 0.05$) for all but the
visual recall. We decided to run all statistical tests using the Mann-Whitney
U test, a form of independent samples t-test used when the normal distribution
requirement is unmet.

Based on the participants’ mean scores alone (in percentages), the puzzle
condition performed better in all metrics except for the visual recall
($SR:68.6,N-TR:50.7,C-TR:68.6$) Figure 4. Likewise, for the cognitive load, we
can see that the puzzle condition was less mentally demanded than the map-only
condition ($MD:36.1$, see Table 1). We conducted the Mann-Whitney U test, a
form of independent samples t-test, to further test the significance of the
different metrics. However, based on our sample size of 28 participants, we
found no significant difference ($p\geq 0.05$) across all variables. Thus, we
rejected our null hypothesis despite better results of the puzzle condition
for the spatial and textual recall.

Our sample size may not have been large enough to reach a more conclusive
result based on the participants’ mean scores in the puzzle condition, which
were higher for spatial and textual memory than the map condition. Other
factors may have contributed to the effects on visual recall as well. One is
that users in the Puzzle condition were using the prototype longer than users
in the map condition, which was expected. For example, several participants
mentioned associating symbols with the colours used in the POIs, which our
study did not consider a variable.

###  4.2 Time and Interaction

As participants used the system, an internal logging mechanism took note of
the usage times with the prototype (from opening the scene until solving the
puzzle). From here, we collected information such as how much time they
interacted with the prototype overall and per puzzle piece. The overall
duration from the start of the interaction to completing the condition varied
greatly. The shortest duration recorded in the puzzle condition was 157
seconds, while the longest was 778 seconds, with an average of 329.21 seconds.
In the map condition, the shortest time was 110 seconds, the longest was 622
seconds, and the average time was 316.35 seconds.

Furthermore, the quantity of POI clicks varied, providing a better sense of
participant engagement. In the puzzle condition, the lowest number of POI
clicks was 21, the maximum number was 82, and the average was 41.31. In the
map condition, the lowest number of clicks was 20, the maximum number was 72,
and the average was 35.5.

###  4.3 Puzzle Specific Findings

This section reports on participants’ puzzle-solving behaviour. To better
understand the following findings a clear view of starting and ending
positions of puzzle is needed, which is visible in Figure 4.

  * •

Patterns in piece completion: We noticed that certain parts were consistently
completed by the majority of participants early on, indicating their
attractiveness or perceived importance in the puzzle-solving process. These
were the pieces: j23 (4 out of 14 participants), j25 (4 out of 14
participants), and j1 (3 out of 14 participants). The parts that took the
least time to complete were j21 (24 seconds), j25 (24 seconds), j10 (26
seconds), and j1 (30 seconds). The pieces with the fewest pickups were j1, j2,
j5, j10, j15, j23 and j25, which all have 14 pickups. This indicates that each
participant chose them only once when solving the puzzle.

  * •

Varied completion times: The fastest completion time was 98 seconds. The
slowest completion time was 255 seconds. This tells us that participants
exhibited different levels of efficiency when solving puzzles. On the other
hand, the average completion time was: 133 seconds.

  * •

Troublesome pieces: Certain pieces appeared to cause difficulty for multiple
participants, as evidenced by longer completion times or frequent
backtracking. These pieces may warrant further investigation for potential
design improvements. The most often completed parts were j12 (4 out of 14
participants) and j9 (3 out of 14 participants). These are the centre parts
and have no POI components on them. The sections that took the longest to
complete were: j14 (99 seconds), j4 (81 seconds), j19 (77 seconds), and j20
(74 seconds). Here we have border pieces j4 and j20, as well as middle parts
j14 and j19. All of them have POI elements on them. We can gain more
information into this by examining how many chunk instances of parts exist
across all participants. The top three sections in terms of the number of
pickups are: j14 (24 chunks), j17 (23 pickups), and j18 (22 pickups).

  * •

Participant-specific strategies: Each participant demonstrated distinct
puzzle-solving approaches, emphasising individuality and creativity in
problem-solving behaviours. Each participant took a different approach to
solving the puzzle.

(a) The starting positions of the puzzle pieces.

(b) The ending positions of the puzzle pieces.

Figure 4: Look at puzzle positions in the prototype Retzzles.

table[t] Overview of Metrics Used. Green arrow meaning better performance
compared to the map condition, red arrow meaning worse performance. Legend:
Cond: Condition, VR: Visual Recall, NS-VR: Negative Symbol Recall, SR: Spatial
Recall, N-TR: Name Textual Recall, C-TR: Category Textual Recall cond VR NS-VR
SR N-TR C-TR mean puzzle ▼76.3 ▼8.75 ▲70.0 ▲56.3 ▲65.0 map 81.3 7.50 62.5 53.8
51.3 std dev puzzle 23.3 9.91 27.8 28.3 12.0 map 21.0 13.9 24.9 20.7 17.3
Shapiro-Wilk $w$ puzzle 0.904 0.736 0.900 0.937 0.897 map 0.863 0.628 0.841
0.941 0.849 Shapiro-Wilk $p$ puzzle 0.313 0.006 0.287 0.581 0.274 map 0.128
<.001 0.077 0.622 0.094 Mann-Whitney U p **0.668 **0.489 **0.750 $H_{a}$
$\mu_{puzzle}\neq\mu_{map}$ ,**no sign. diff.

##  5 Conclusion and Future Work

In this paper, we explored whether engaging with maps in the form of jigsaw
puzzle pieces can help users remember more information from the map. We
present our prototype, Retzzles, used to test this. In one condition, users
first had to solve jigsaw puzzles on a map before being able to interact with
points of interest displaying essential information. In another condition, the
interactive map was already present. Results of our between-subject study,
involving $n=28$ participants, showed better mean scores for spatial and
textual recall; however, no significant difference between these conditions
was found. Our initial analysis also found no observable differences in the
time spent interacting with the puzzle. Despite this, the puzzle condition has
shown a slight advantage. While this might be simply because users spent more
time with the puzzle, which they found playful, it adds to the knowledge that
active learning has advantages.

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# ALIFE2024

Seth Bullock  Conor Houghton,
Intelligent Systems Laboratory, University of Bristol, United Kingdom
<EMAIL_ADDRESS>
# Modeling language contact with the Iterated Learning Model

Seth Bullock  Conor Houghton,
Intelligent Systems Laboratory, University of Bristol, United Kingdom
<EMAIL_ADDRESS>
###### Abstract

Contact between languages has the potential to transmit vocabulary and other
language features; however, this does not always happen. Here, an iterated
learning model is used to examine, in a simple way, the resistance of
languages to change during language contact. Iterated learning models are
agent-based models of language change, they demonstrate that languages that
are expressive and compositional arise spontaneously as a consequence of a
language transmission bottleneck. A recently introduced type of iterated
learning model, the Semi-Supervised ILM is used to simulate language contact.
These simulations do not include many of the complex factors involved in
language contact and do not model a population of speakers; nonetheless the
model demonstrates that the dynamics which lead languages in the model to
spontaneously become expressive and compositional, also cause a language to
maintain its core traits even after mixing with another language.

## Introduction

Iterated Learning Models (ILMs) are agent-based models in which languages
evolve as they are transmitted from generation to generation. They were
proposed as a description of how languages become compositional and expressive
(Kirby,, 2001; Kirby and Hurford,, 2002). Here, the Semi-Supervised ILM, a
specific version of the model recently introduced in Bunyan et al., (2024), is
used to simulate the effect on a language of contact with another language.

The continuous processes required to produce the vast array of languages
currently in use seems to indicate that languages are extremely mutable and
unstable. Languages certainly change. For example, since Jonathan Swift’s
novel Gulliver’s Travels was published less than three hundred years ago on 28
October 1726, the English lexicon has expanded enormously to provide a
vocabulary for the many novel objects, behaviours and social structures that
have resulted from the Industrial Revolution, the Age of Revolution and the
Computer Age. However, for all that, the language has not changed that much:
though unarguably ‘old-fashioned’ in its phrasing, Gulliver’s Travels is
perfectly comprehensible to the contemporary reader.

This is striking. Between Swift’s era and the present day, English has become
a lingua franca, spoken for periods as the language of administration in
countries within which it was not native and used as a second language by more
people than use it as a first language. Consequently, it might be expected
that it would have changed dramatically with a huge number of words from other
languages crowding out older words and rendering the novel incomprehensive.
Indeed the idea that English continually adds new words by taking them from
other languages is something of a cliche.

However, it is not really true. Taking the example of English and Irish
(endonym: Gaeilge, ISO 639-3: gle); Jonathon Swift was among the first
prominent Irish writers writing in English and there has been a rich history
of interaction between speakers of Irish and of English in the period since
Gulliver’s Travels was written. Ultimately an English language has replaced
Irish as the main language of Ireland and the descendants of the substantial
Irish diaspora are for the most part English speakers. Nonetheless only a
handful of words derived from Irish are in common use in English. Indeed,
while it is claimed that the aboriginal Celtic languages of Great Britain and
Ireland form a language substrate for English (Filppula et al.,, 2008), even
in Ireland any more recent influence of Irish on the grammar, pronunciation
and lexicon of the language now spoken is apparent only in small, though
valued, ways. In fact, as in the example of the word ‘oxter’ for ‘armpit’,
many of the lexical difference between Irish-English and other Englishes
represent the preservation in Irish-English of English words that have fallen
out of use elsewhere, rather than the influence of Irish.

Of course, the dynamics of language contact is complex and it is certainly not
invariably true that one language retreats while leaving the other unchanged.
Indeed, in the case of English, the Norman Conquest and the influence of Old
French (ISO 639-3: fro) caused substantial changes, marked by the transition
from Old English (ISO 693-3: ang) to Middle English (ISO 693-3: enm). Old
French in turn showed considerable influences from Old Frankish (ISO 639-3:
frk), though this is a salutary example; the main effect of Old Frankish was
to change stress pattern in pronunciation, disrupting the grammatical
information in word endings that Vulgar Latin relied on, leading to a shift
from a synthetic to an analytic language. In other words, although contact
with Old Frankish was important in the change from Vulgar Latin to Old French,
these changes did not mean Old French resembled Old Frankish any more than
Vulgar Latin did Rickard, (2003); Lodge, (2013).

The various outcomes of language contact depend on multiple factors such as
prestige, economic opportunity and the need for new words for phenomena and
objects familiar to speakers of one language but not the other (Thomason and
Kaufman,, 1988; Mufwene,, 2001; Matras and Sakel,, 2007; Sakel and Matras,,
2008). Our purpose here is to examine the, perhaps surprising, stability of
languages during asymmetric contact from the simplest possible point-of-view.
We explore whether the mechanism underpinning the development of
compositionality and expressivity in the Semi-Supervised ILM could also
account for the stability of one of the two languages in a contact situation.

### The Iterated Language Model

Languages are made easier to learn, and easier to use, by their properties of
compositionality and expressivity (Oliphant,, 1999). A compositional language
is one in which each element of meaning is encoded consistently by the same
morpheme within the signal, irrespective of context, so ‘violin’ means much
the same thing in ‘she plays the violin’ and ‘it is violin shaped’. While all
human languages exhibit compositionality of some kind, they are not completely
compositional, so, in other contexts the word ‘fiddle’ can be used: ‘Mairéad
Ní Mhaonaigh is a leading exponent in the Donegal fiddle tradition’. An
expressive language is one in which a range of different meanings are
unambiguously encoded by different signals, so the viola is called a ‘viola’
in English and can be distinguished by name from a ‘violin’. However, just as
real languages are not perfectly compositional, they are not perfectly
expressive: the ‘fiddle’ in ‘it is tempting to fiddle with it, even though it
is perfect as it is’ does not refer to a violin. Along with expressivity and
compositionality, a third simple property required from a language is
stability; while languages change, to support communication they should not
change too much from one generation to the next.

ILMs are a family of computational models designed to simulate language
change. They were originally intended to describe a mechanism by which
languages can become expressive, compositional and stable over multiple
generations of use (Kirby,, 2001; Kirby and Hurford,, 2002). In an ILM there
is a language-using ‘tutor’ agent and a language-learning ‘pupil’ agent. The
adult teaches language to the pupil by exposing it to a set of utterances. The
pupil then becomes a tutor and teaches a new pupil in the same fashion. A
language learning bottleneck is a key feature of these models: since each
tutor only presents a finite subset of the language to their pupil, when the
pupil in turn becomes an adult it will need to generate utterances that it has
not experienced before. The process of generalization inherent in the model is
thought to be critical to the behaviour of the ILM.

In the version of the ILM considered here a language consists of a set of
meaning, $\mathcal{M}$, and a set of signals, $\mathcal{S}$, both represented
by binary vectors, typically here these will be length ten vectors. In
addition the agent has an encoder map $e:\mathcal{M}\rightarrow\mathcal{S}$
and a decoder map $d:\mathcal{S}\rightarrow\mathcal{M}$ mapping signals to
meanings and vice versa, respectively:

$\mathcal{S}$$\mathcal{M}$$e$$d$

A language, in this context, corresponds to a map from meanings to signals and
so an agent’s language can be thought of as being equivalent to its encoder.
In Kirby and Hurford, (2002) the decoder $d$ is a simple neural network
whereas the encoder $e$ is a look-up table listing all possible meanings and
their corresponding signal. During learning a ‘bottleneck’ subset of meanings
$\mathcal{B}\in\mathcal{M}$ is chosen and the tutor presents this training
meaning-signal pairs $\\{(e(b),b)|b\in\mathcal{B}\\}$. This is used to train
the pupil’s decoder. At the end of training, when the pupil ‘grows up’, an
inversion process, known as obversion (Oliphant and Batali,, 1997), is used to
build an encoder for this agent, after which it can become a tutor for a newly
created naïve pupil.

During obversion, the pupil’s decoder is used to assign a probability to every
possible signal-meaning pair, the encoder map from meaning to signal is then
calculated by a process of ‘picking winners’. This is computationally
expensive to the extent that it makes simulations impractical for languages
with bit length greater than about ten. It is also unrealistic as it imagines
that a pupil is incapable of an utterances until it matures, at which point it
must consider all possible signals and all possible meaning and match them to
calculate the encoder that it will rely on in order to be able to communicate
as an adult tutor.

$\vdots$$\vdots$$\vdots$$\vdots$$\vdots$ meaning signal meaning
$m_{1}$$m_{2}$$m_{n}$$s_{1}$$s_{2}$$s_{n}$$m^{\prime}_{1}$$m^{\prime}_{2}$$m^{\prime}_{n}$$a$$d$$e$
Figure 1: Neural network. In the Semi-Supervised ILM both the encoder, $e$
(yellow), and decoder, $d$ (blue), are neural networks; in $e$ the meaning
vector forms the input, it is mapped to hidden layer and then to a signal
vector; in $d$ a signal vector forms the input, there is again a hidden layer
and the output is a meaning vector. The autoencoder, $a$, is formed by
concatenating the two neural networks, with the signal layer, green, in this
case forming a third hidden layer for the autoencoder.

In a recent paper, Bunyan et al., (2024) introduce a new ILM which is capable
of demonstrating the emergence of expressivity, compositionality and stability
under bottlenecked conditions without the need for obversion. In this ILM,
both the decoder and the encoder are neural networks. During learning the
tutor presents pairs $\\{(e(b),b)|b\in\mathcal{B}\\}$ to both the pupil’s
decoder and to its encoder. In addition, the pupil creates a third neural
network, $a=d\circ e$, by concatenating the encoder and decoder. This third
network is presented with meanings from a set $\mathcal{A}\in\mathcal{M}$ and
it learns as an autoencoder; this is intended to mimic a process of internal
learning in which a child sees objects and events and imagines how they might
be expressed in its language. This is illustrated in Fig. 1. In Bunyan et al.,
(2024) it is noted that this ILM is considerably less computationally
burdensome and it is argued that it is more realistic as a model of language
development. This new version of the ILM is used here and is referred to as
the Semi-Supervised ILM.

### Modeling language contact

The ILM was proposed to model the way in which a language can acquire
expressivity, compositionality and stability through iterated learning with a
bottleneck. Here though, another case is considered in which there are two
pre-existing languages; the $\mathbb{A}$ language and the $\mathbb{B}$
language, each of which are both expressive and compositional. In our iterated
language model the first pupil will be taught a mixture of these two
languages, so after the training set of meanings $\mathcal{B}$ has been
selected from $\mathcal{M}$ some meanings will be encoded according to the
$\mathbb{A}$ language and some according to the $\mathbb{B}$ language:
specifically for each meaning in $\mathcal{B}$ the $\mathbb{A}$ language
signal will be selected with probability $p$ and, conversely, the $\mathbb{B}$
language meaning with probability $1-p$. This is intended to reflect a
difference in the number of exemplars presented to a child in a language
contact situation, or, more generally, $p$ is supposed to represent any
weighting, such as the fraction of $\mathbb{A}$ examplars or the authority and
emphasis with which those examples are presented. After this first initial
generation the language is evolved through the usual iterated learning process
and its similarity, $a$ and $b$, to the two original languages is quantified.
The calculation of these similarities is discussed below.

## Methods

$n_{1}$ | bit length of the meaning vectors.
---|---
$n_{2}$ | number of nodes in the hidden layers.
$n_{3}$ | bit length of the signal vectors.
$n_{1}\times n_{2}\times n_{3}$ | agent with a $n_{1}\times n_{2}\times n_{3}$ encoder
| and a $n_{3}\times n_{2}\times n_{1}$ decoder.
$\mathcal{M}$ | set of meanings.
$\mathcal{S}$ | set of signals.
$\mathcal{B}\subset\mathcal{M}$ | used for supervised learning.
$\mathcal{A}\subset\mathcal{M}$ | used for unsupervised learning.
$\mathbb{A}$ and $\mathbb{B}$ | the two initial languages.
$p$ | the language mixing parameter.
$d:\mathcal{S}\rightarrow\mathcal{M}$ | decoder map.
$e:\mathcal{M}\rightarrow\mathcal{S}$ | encoder map.
$a:\mathcal{M}\rightarrow\mathcal{M}$ | autoencoder map $a=d\circ e$.
$x$ | expressivity (blue).
$c$ | compositionality (orange).
$s$ | stability (maroon in graphs).
$a$ | similarity to language $\mathbb{A}$ (red).
$b$ | similarity language $\mathbb{B}$ (red).
Table 1: Glossary. Here a meaning is a $n_{1}$ bit length binary vector whose
components are facts or elements of meaning and a signal is a $n_{3}$ bit
length binary vector whose components are morphemes. There is a notation
clash, $a$ is used both for the encoder map and the similarity to language
$\mathbb{A}$, hopefully which is which is clear in context. Another near clash
is the use of $\mathbb{A}$ and $\mathbb{B}$ for languages and $\mathcal{A}$
and $\mathcal{B}$ for example sets, here typeface is used to make the
distinction.

The maps $d$ and $e$ are all-to-all feedforward neural networks with one
hidden layer. It is convenient to introduce a short hand for the size of each
layer of the encoder $e$: $n_{1}\times n_{2}\times n_{3}$; $n_{1}$ is the bit
length of the meaning vectors, $n_{2}$ the number of nodes in the hidden layer
and $n_{3}$ the bit length of the signal vectors, the decoder $d$, in turn, is
a $n_{3}\times n_{2}\times n_{1}$ neural network. This, and other pieces of
notation are summarized in Table 1.

Both the hidden layer and the output layer have sigmoid non-linearities. Since
$d$ and $e$ map to binary vectors the output values are binarized by setting
them to zero or one using a threshold of 0.5. However, the signal layer forms
the middle layer of the autoencoder $a$ and so the rounding step is not
performed on this layer in $a$: back-propagation requires that the values in
the hidden layer remain continuous and, in any case, the autocoder is intended
to model the child contemplating the range of different possible utterances
likely to correspond to a meaning.

All weights are initialized using the default flux.jl Xavier initialization.
The three networks are trained at the same time using stochastic gradient
descent with learning rate $\eta=5.0$. The number of epochs is $20$. For each
generation a bottleneck set, $\mathcal{B}$, and an autoencoder set
$\mathcal{A}$ are chosen randomly from $\mathcal{M}$. At the start of each
epoch two copies of $\mathcal{B}$ are made, each in a different random order;
at each iteration an item from the first copy is presented to $d$ and an item
from the other to $e$; for the $10\times 10\times 10$, $10\times 12\times 10$,
$9\times 11\times 12$ and $10\times 15\times 20$ agents $r=15$ randomly chosen
meanings from $\mathcal{A}$ are then presented to $a$, for the $20\times
30\times 20$ network $r$ is increased to 30.

Two initial languages $\mathbb{A}$ and $\mathbb{B}$ are formed by randomly
shuffling the ‘identity language’, the language in which each meaning vector
is mapped to the identical signal vector. The shuffling is done in a way that
preserves compositionality, this means that each bit in the meaning determines
a different specific bit in the signal, though, unlike in the identity
language, it will not, in general, map to a bit in the same position and ‘1’
may map to a ‘0’ rather than to ‘1’. In most simulations the meaning and
signal space are the same length. In the example where the signal space is
larger the unused bits, which after shuffling are located in specific random
positions along the signal vector, are randomly set to zero or one for all
signals, that is, they remain the same irrespective of meaning. The mixed
language used to teach the first pupil is calculated as a look up table where
for each meaning in $\mathcal{M}$ the encoded signal from the $\mathbb{A}$
language is chosen with probability $p$, otherwise the $\mathbb{B}$ language
is used.

### Quantifying language properties

A Hamming similarity is used to quantify the similarity between languages. The
fraction of meanings on which they agree is calculated:

$\tilde{f}=\frac{|\\{m:e_{1}(m)=e_{2}(m)\text{ for
}m\in\mathcal{M}\\}|}{|\mathcal{M}|}$ (1)

where $e_{1}$ and $e_{2}$ are the two encoder maps. A background value,
$f_{0}$, is calculated for random pairs of languages, the similarity is then

$f=\frac{\tilde{f}-f_{0}}{1-f_{0}},$ (2)

Here $a$ is used to denote the similarity from the $\mathbb{A}$ language and
$b$ from the $\mathbb{B}$ language. In addition, expressivity,
compositionality and stability are calculated; of these, stability is the most
straightforward, it is the similarity between a language and the language for
the previous generation. Expressivity is based on the fraction of the signal
space that is employed by the language

$\tilde{x}=\frac{|\\{e(m)\text{ for }m\in\mathcal{M}\\}|}{|\mathcal{S}|}$ (3)

where $x$ is calculated from $\tilde{x}$ by removing the background value as
before. It is more difficult to define a good measure of compositionality;
roughly speaking the measure used here is based on taking each bit in the
meaning vector and calculating the conditional entropy, over all values of the
other bits in the meaning vector, of the best predicted bit in the signal.
This is described in more detail in Bunyan et al., (2024), in summary though,
$c$, is one for a perfectly compositional language and zero if the language is
no more compositional than chance.

### Simulations

For all the simulations where the meaning vector has bit length ten
$|\mathcal{B}|=80$ and $|\mathcal{A}|=240$; for the example where the meaning
vector has bit length 20 a larger bottleneck is used: $|\mathcal{B}|=185$ and
$|\mathcal{A}|=555$. Results for 50 simulations are presented for all
examples.

### Software and libraries

All code was written in Julia and run on Julia 1.9.3, neural networks were
trained using Flux v0.14.6 and plotting used Gadfly v1.3.4, Compose v0.9.5 and
Colors v0.12.10. Data was handled using DataFrames v1.5.0 and CSV v0.10.11.
The code used to produce the figures and the corresponding simulated data is
available at github.com/IteratedLM/2024$\\_$04$\\_$mix.

## Results

$p=0.5$: $\mathbb{A}$ and $\mathbb{B}$ have equal influence
---
$x$ |  $c$ |  $s$ |  $a$ |  $b$
|  |  |  |
$p=0.55$: $\mathbb{A}$ has slightly more influence than $\mathbb{B}$
$x$ |  $c$ |  $s$ |  $a$ |  $b$
|  |  |  |
$p=0.75$: $\mathbb{A}$ has much more influence than $\mathbb{B}$
$x$ |  $c$ |  $s$ |  $a$ |  $b$
|  |  |  |
generations |  generations |  generations |  generations |  generations
Figure 2: Evolution of the mixed language. Here the language is evolved for 20
generations and the results of 50 simulations are plotted for five different
language attributes. In every graph the individual simulations are plotted
with thin pale lines, the mean with a thicker, darker line. The first three
columns plot attributes of the language itself, showing its expressivity
($x$), compositionality ($c$) and the stability ($s$) of the iterated
learning. The final two columns show how similar the languages are to the
initial $\mathbb{A}$ and $\mathbb{B}$ languages, these similarities are $a$
and $b$. The three rows present results for three different values of $p$, the
fraction of the initial language taken from language $\mathbb{A}$, these are
$p=0.5$ when the new language is almost always different from either
$\mathbb{A}$ or $\mathbb{B}$, $p=0.55$ when the new language is typically
similar to $\mathbb{A}$, sometimes to $\mathbb{B}$ and sometimes to neither,
and $p=0.75$ when the new language almost always resembles $\mathbb{A}$. In
each case a $10\times 10\times 10$ agent is used.

Figure 2 shows the result of language mixing for three different values of the
mixing parameter $p$. The initial languages $\mathbb{A}$ and $\mathbb{B}$ are
perfectly expressive and compositional. However, the mixed language is not and
there is initially a low value for $x$ and $c$. Nonetheless the language
quickly recovers these properties through iterated learning: within ten
generations the languages are expressive and compositional and become stable
from generation to generation. This is true for all values of $p$, however, if
$p=0.5$ the language rarely ends up matching either $\mathbb{A}$ or
$\mathbb{B}$ while for $p=0.75$ it almost invariably matches $\mathbb{A}$.

A | B
---|---
|
Figure 3: Modeling language contact. Language contact is simulated 50 times
for $p$ values from 0.5 to 1.0 in increments of 0.05. A plots the fraction of
simulations which result in a value of $a$, upper line, or $b$, lower line,
greater than 0.9. In B $a$ is plotted vertically, although the simulations
were only run for $p\in[0.5,1.0]$ there is no distinction between the
$\mathbb{A}$ language and the $\mathbb{B}$ language, this means that the $b$
values in $p\in[0.5,1.0]$ can be used to extend the range over which $a$ is
plotted to all of $p\in[0.0,1.0]$. Each black dot corresponds to one of the 50
simulations at each $p$ value. Horizontal jitter of $\pm 0.025$ has been added
to aid visualization. The red line is the average. Both A and B describe the
same set of simulations using a $10\times 10\times 10$ agent.

This is further illustrated in Fig. 3 where the fraction of languages that
have $a>0.9$ or $b>0.9$ is plotted against the value of $p$ (see Fig. 3A) and
the average value of $a$ and $b$ is plotted, again, against $p$ (see Fig. 3B).
It is apparent that there is a very rapid transition from the behaviour near
$p=0.5$ where a new language is often formed, to the behaviour away from
$p=0.5$ where one of the two original languages is quickly reconstructed from
the elements that are present in the original mixture. What has not been
assessed is the nature of the mixed languages at $p=0.5$; although typically
they are not similar to either $\mathbb{A}$ nor $\mathbb{B}$ it is still
possible that they contains some evidence of each as is the case with mixed
languages like Maltese (ISO 639-3: mlt). However, Fig. 3B indicates that this
is rare, the low average value of $a$ is not the results of a large number of
trials in which the eventual value of $a$ is low, it is the result of a large
number of trials giving an $a$ value of zero and a smaller number where
$a=1.0$ or $a=0.5$. It will be interesting in future work to consider in more
detail the language that results whem $p$ is near 0.5 and to consider more
complicate multi-language mixing as happens in the formation of Creoles,
though, in the case of many Creoles there are other important and challenging
sociological factors involved in their formation.

Figure 4: The behaviour does not change substantially when the size of hidden
layer or signal space is changed. Four different architectures are compared
here. Here the average value of $a$ is given for the $10\times 10\times 10$,
$10\times 12\times 10$ and $9\times 11\times 12$ and $10\times 15\times 20$
agents. The four curves are similar.

In Fig. 4 the performance of the $10\times 10\times 10$ Semi-Supervised ILM is
compared to three other Semi-Supervised ILMs. The Semi-Supervised ILM appears
to perform more robustly if the hidden layer has more nodes than the bit
length of the signal and meaning spaces Bunyan et al., (2024). Here, the same
set of simulations as above was performed using a Semi-Supervised ILM with a
$10\times 12\times 10$ agent. In addition, it might be suspected that the
model returns to the $\mathbb{A}$ language for $p>0.5$ because the signal
space is restricted, in a perfectly expressive language all signals are used.
With this in mind simulations, were performed using a Semi-Supervised ILM with
a $9\times 11\times 12$ agent and with a $10\times 15\times 20$. In fact,
across all these examples, the behaviour of the model was largely unchanged.

A much larger language is considered in Fig. 5; here a $20\times 30\times 20$
agent is used so the signal and meaning space both have bit length 20. The ILM
in this case produces languages which are both expressive and compositional
with values near one, as before; however the value of stability fluctuates a
lot. Stability is a measure of how many meanings map to the same signal from
one generation to the next, in other words it operates at the level of
meanings and signals, not facts and morphemes and so it is harsh test of a
compositional language: if two bits are swapped, this would reduce stability
by a half. In fact, the behaviour seems very similar to the 10-10-10 example,
the language quickly becomes expressive and compositional, for the $p=0.5$
case it generally does not resemble either the $\mathbb{A}$ or $\mathbb{B}$
language, while for $p=0.75$ it largely resembles $\mathbb{A}$.

$p=0.5$: $\mathbb{A}$ and $\mathbb{B}$ have equal influence
---
$x$ |  $c$ |  $s$ |  $a$ |  $b$
|  |  |  |
$p=0.75$: $\mathbb{A}$ has much more influence than $\mathbb{B}$
$x$ |  $c$ |  $s$ |  $a$ |  $b$
|  |  |  |
generations |  generations |  generations |  generations |  generations
Figure 5: Mixing larger languages. Here the language is evolved for 20
generations and the results of 50 simulations are plotted for the usual five
different language attributes: $x$, $c$, $s$, $a$ and $b$. The two rows give
two different values of $p$. In each case the encoder and decoder maps have a
20-30-20 layout.

## Discussion

Language contact is complex, both in its internal dynamics and in the broader
contexts in which language mixing occurs. The political and culture setting
for language contact can be extremely consequential for the populations
involved. Language loss can be traumatic and destructive and is often
accompanied by other challenging forms of loss; conversely, culture exchange
can be enriching and exciting and a useful mechanism under which languages
become capable of more efficiently expressing new ideas. None of this
complexity is included in the work presented here. The agent modeling also
ignores bilingualism and code-switching. However, what has been demonstrated
is that a mechanism which can explain the development of expressivity and
compositionality in languages can also explain the stability of languages
during language contact, even without invoking the stabilizing influence of a
population of speakers not involved in contact.

Recently, population-based versions of the ILM have been considered (Brace et
al.,, 2015; Brace and Bullock,, 2016; Sains et al.,, 2023) and a population
approach is implicit in the simulations described here in that the initial
tutor, which provides examples to the first pupil agent, draws those examples
from two different languages. However, this is an extremely restricted version
of the richer population dynamics that studying the problem of language
contact in more detail would require. In fact, because the Semi-Supervised ILM
does not have a sharp distinction between its learning and teaching phases, it
lends itself to population models and these will form the basis of further
work.

These modeling-based approaches also have a counterpart in participant studies
using artificial mini-languages, where similar issues of expressivity,
compositionality and stability are also considered, see Fedzechkina et al.,
(2016); Smith et al., (2017); Culbertson and Schuler, (2019) for reviews. A
full exploration of language contact should incorporate historical, often very
qualitatively evidence, along with simulations and matched data from
participant studies.

## Conclusion

In this paper we employed a new class of ILM to explore the outcome of contact
between two mature languages that are already expressive, compositional and
stable. The semi-supervised nature of this new iterated learning paradigm
allows the model to dispense with the computationally expensive and
unrealistic obverter mechanism that has tended to limit the size and
complexity of languages explored in previous ILM studies. Here, for the first
time we are able to model binary languages with up to $2^{20}$ possible
meanings and signals.

The results here demonstrate that when the two pre-contact languages
contribute equally to the language exposure of a naïve pupil, the resultant
language often does not resemble either of the pre-contact languages, and that
this is particularly true for larger meaning-signal spaces where recovery of
either of the original languages is very rare. However, when one language has
some degree of advantage over the other in terms of its contribution to the
learning experiences of the naïve pupil, this language or something closely
resembling it is often able to re-emerge after a period of language
destabilization during language contact. This demonstrates that the same
dynamics that drives languages to compostionality and expressivity can also
stabilize them during language contact.

## Acknowledgements

SB is supported by UKRI grant EP/Y028392/1: AI for Collective Intelligence
(AI4CI). Simulations were carried out using the computational facilities of
the Advanced Computing Research Centre at the University of Bristol,
www.bristol.ac.uk/acrc/. We are grateful to Dr Stewart whose philanthropy
supported some of the compute resource used in this project.

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