REPORT

Representations of Abstract Relations in Infancy

Jean-Rémy Hochmann1,2

1CNRS UMR5229 – Institut des Sciences Cognitives Marc Jeannerod, 67 Boulevard Pinel, 69675, Bron, France
2Université Lyon 1 Claude Bernard, France

Mots clés: abstract relations, infants, language of thought

un accès ouvert

journal

ABSTRAIT

Abstract relations are considered the pinnacle of human cognition, allowing for analogical and
logical reasoning, and possibly setting humans apart from other animal species. Recent
experimental evidence showed that infants are capable of representing the abstract relations
same and different, prompting the question of the format of such representations. In a
propositional language of thought, abstract relations would be represented in the form of
discrete symbols. Is this format available to pre-lexical infants? We report six experiments
(N = 192) relying on pupillometry and investigating how preverbal 10- to 12-month-old infants
represent the relation same. We found that infants’ ability to represent the relation same is
impacted by the number of individual entities taking part in the relation. Infants could
represent that four syllables were the same and generalized that relation to novel sequences
(Experiments 1 et 4). Cependant, they failed to generalize the relation same when it involved
5 ou 6 syllables (Experiments 2–3), showing that infants’ representation of the relation
same is constrained by the limits of working memory capacity. Infants also failed to form a
representation equivalent to all the same, which could apply to a varying number of same
syllables (Experiments 5–6). These results highlight important discontinuities along cognitive
development. Contrary to adults, preverbal infants lack a discrete symbol for the relation same,
and rather build a representation of the relation by assembling symbols for individual entities.

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Citation: Hochmann, J.-R. (2022).
Representations of Abstract Relations
in Infancy. Open Mind: Discoveries in
Sciences cognitives, 6, 291–310. https://
doi.org/10.1162/opmi_a_00068

EST CE QUE JE:
https://doi.org/10.1162/opmi_a_00068

Reçu: 29 Janvier 2022
Accepté: 21 Octobre 2022

Intérêts concurrents: The author
declares no conflict of interest.

Auteur correspondant:
Jean-Rémy Hochmann
hochmann@isc.cnrs.fr

droits d'auteur: © 2022
Massachusetts Institute of Technology
Publié sous Creative Commons
Attribution 4.0 International
(CC PAR 4.0) Licence

La presse du MIT

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INTRODUCTION

How do young infants think, before they have words to express their thoughts? Thoughts can
be characterized in terms of content (what they are about) and format (what they are like). Of
cours, the two issues are not independent; certain format favour certain content, and certain
content may require certain format. The present work aims at improving our characterization
of infants’ thought format, focusing on the case of abstract relations.

A discussion about the format of mental representations typically begins with the opposition
between perceptual-like, iconic images and language-like, symbolic propositional representa-
tion (Paivio, 1971; Bruner, 1964; Fodor, 1975, 2008). While Piaget (1954) thought young
infants initially lack mental representations altogether, the idea that infants possess perceptual
or perceptual-like mental representations is not controversial anymore. Such representations
can account for object recognition ( Wilcox & Baillargeon, 1998), visuospatial operations such
as mental rotation (Moore & Johnson, 2008, 2011; Quinn & Liben, 2008, 2014) and mental
simulation (Téglás et al., 2011). Some researchers have even proposed that, early in life, all of

Abstract Relations in Infancy Hochmann

mental representations consist in “impoverished perceptual-like images” (Bruner, 1964;
Amandes, 1992; Amandes & Cánovas, 2014).

Do infants also possess a propositional language of thought (Fodor, 1975; Macnamara,
1972; Pylyshyn, 1973)? Components of such language of thought are discrete abstract symbols
referring to entities and their relations, which are combined to form propositions, much like
words are combined to form sentences. Discrete symbols that enter propositional representa-
tions are thus particularly efficient to represent abstract relations (Hochmann & Bouffe, 2021;
Premack, 1983). Evidence that infants possess abstract concepts (Carey, 2009) y compris
abstract relations (Hochmann, 2021) and precursors of logical operators (Cesana-Arlotti,
Kovács, & Téglás, 2020b; Hochmann & Toro, 2021) could indicate that infants possess prop-
ositional representations, but alternative accounts of these data remain possible (Leahy &
Carey, 2020; Hochmann, 2020).

To progress in our understanding of what it is like to think without words, as an infant, nous
sought to characterize the format of the representation of an abstract relation, the relation
same. Results show that infants are capable of representing same and suggest that the format
of that representation is inherently different from the adults’, challenging the view that infants
possess a propositional language of thought.

The Relation Same

Children learn the words “same” and “different”, as applied to pairs of individuals (par exemple., △ and
△ are the same; △ and ◻ are different), in the fourth year of life (Christie & Gentner, 2014;
Hochmann et al., 2017; Hochmann et al., submitted). Cependant, there is now substantial evi-
dence that even young infants are already able to represent the relation same between two
individuals (see Hochmann, 2021 for review). Neonates exhibit a specific neural response to
sequences of syllables containing two identical syllables (Gervain et al., 2008, 2012). Infants as
young as 3 months habituate to exemplars of the relation same (Addyman & Mareschal, 2010;
Anderson et al., 2018; Ferry et al., 2015; Tyrrell et al., 1991) et 6- to 18-month-olds can
condition behavioral responses to the perception of two identical stimuli (Hochmann et al.,
2011, 2016, 2018b; Kovács, 2014; Walker & Gopnik, 2014, 2017).

Going beyond the question of whether infants represent the relation same, in the present
travail, we ask how infants represent such relation. In the studies reviewed above, infants gen-
eralized the conditioned response to novel pairs of items that instantiated the relation same.
Evidence for generalization denotes abstraction, suggesting that infants’ representation of same
cannot be reduced to a perceptual-like image (Premack, 1983). Does generalization also
imply that, like adults, infants represent the relation same with a discrete symbol dissociated
from the representation of entities? Not necessarily.

Extensive research suggests that the representation of the relation same might not be adult-
like before 4–5 years of age. While infants succeed in a simple match-to-sample task (par exemple.,
matching △ to △) (Hochmann et al., 2016), children below 4 ou 5 years fail in a relational
match-to-sample task (RMTS), where they have to match pairs of stimuli that instantiate the
relations same or different (par exemple., △ △ matches ◻ ◻; △ (cid:1) matches ◻ X) (Premack, 1983;
Hochmann et al., 2017). Despite a handful of successes by parrots, crows and highly-trained
monkeys (see Smirnova et al., 2021 for review), this task also remains extremely difficult for
non-human animal species (Flemming & Thompson, 2021; Gentner et al., 2021). De plus,
children younger than 4 and animals do not spontaneously categorize arrays of 16 pictures as
all the same vs. not all the same or all the same vs. all different, whereas older children and
adults do (Hochmann et al., 2017; Fagot et al., 2001). Those failures suggest that the infants’

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Abstract Relations in Infancy Hochmann

(and animal) representation of the relation same differs from that of older children and adults. Il
has been proposed that the acquisition of the word “same” plays a role in the transition
between the two types of representation. Even though a causal link between these abilities
has yet to be demonstrated, those children who understand the word “same” or spontaneously
produce the words “same” and “different” tend to succeed in RMTS and to categorize arrays as
all the same vs. not all the same (Christie & Gentner, 2014; Hochmann et al., 2017). De la même manière,
among great apes, those who have acquired symbols for the relations same and different per-
form better in RMTS (Premack, 1983, Thompson et al., 1997). In sum, children may not possess
an adult-like representation of same before they acquire a symbol like the word “same”1.

We are facing an apparent paradox: infants succeed in a number of tasks that necessitate
recognizing the abstract relation same in different pairs of stimuli (par exemple., Hochmann et al.,
2018b), but they fail at matching two pairs instantiating same in RMTS (Christie & Gentner,
2014; Hochmann et al., 2017). To account for these data, we propose that, while abstraction is
sufficient to succeed in match-to-sample, habituation and conditioned discrimination tasks,
the RMTS additionally requires that the representation of abstract relations be discrete, c'est à dire.,
distinct and fully dissociated from the representation of the entities involved in the relation.
Acquiring an external symbol such as the word “same” may trigger or facilitate the construc-
tion of such discrete representation (Premack, 1983).

Instead of a discrete symbol for the relation, we propose that the infants’ representation of
same can consist of a repeated variable (Hochmann et al., 2016; Marcus et al., 1999). If X is a
variable defined in the domain (cid:1), two same entities in that domain can be represented as X 2 (cid:1),
(X X ). Surtout, in this format of representation, there is no discrete symbol for the relation
but one symbol (one instance of the same variable) for each individual entity. Ainsi, quand
infants learn a rule exemplified with two cups, two balls, two ducks, etc., they would represent
(X X ), which means two same objects. The domain of the variable X defines the domain where
the relation applies: if X belongs to the domain of shapes, (X X ) means two same shapes; if X
belongs to the domain of colors, (X X ) means two same colors; et ainsi de suite. En outre, le
representation of the relation same is tight to a specific number of entities: (X X ) is a represen-
tation of two-same, (X X X ) is a representation of three-same, et ainsi de suite. En fait, in this format
of representation, not only isn’t there a discrete symbol for the relation, but the relation, le
domain or dimensions to which it applies, and the numerosity are all intertwined.

This format of representation relying on variables is abstract, affording the generalization of
the relation same, but lacks a discrete symbol S that is dissociated from the representation of
the entities in the relation and could be integrated in a propositional language of thought to
generate strings such as X S Y (or S(X, Oui )) meaning X is the same as Y. The format that we
propose for the infants’ and young children’s representation of same can account both for
the success in habituation and conditioned discrimination tasks (par exemple., Hochmann et al.,
2018b), and for the failure in RMTS (Christie & Gentner, 2014; Hochmann et al., 2017).
En effet, X being a variable, its value can change over time; it can refer successively to various
objets, par exemple., a duck, a cup, etc.. Infants can thus use (X X ) to represent successively (duck
duck) et (cup cup). Par conséquent, they can habituate to (X X ) (par exemple., Anderson et al., 2018)
and learn to condition a response to (X X ) (par exemple., Hochmann et al., 2018b). But X can be

1 It is also possible that the role of the word “same” is to make the relation same more relevant and more
salient. A concept that is verbally labelled may be more likely to be considered in problem solving. Kroupin
and Carey (2022un, 2022b) are investigating alternative ways to make the relation more relevant. So far, comment-
jamais, and to the best of our knowledge, there is no evidence that a child ever succeeded at the RMTS without
knowing the words “same” and “different”.

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Abstract Relations in Infancy Hochmann

assigned only one value at a given time; it cannot refer simultaneously to different objects such
as a duck and a cup. In consequence, children cannot use the (X X ) representation to match
(duck duck) et (cup cup), as is required to succeed in RMTS. Success in RMTS may require,
or be facilitated by, the acquisition of a discrete symbol S for the relation same, pour
relate both (duck duck) et (cup cup) to S, and subsequently match S to S.

The format of representation that we propose may also account for infants’ and young chil-
dren’s difficulty to represent all the same (Hochmann et al., 2017). En effet, all the same
applies equally to arrays of varying numbers of entities. With respect to quantification, tous
the same thus requires disregarding the number of elements involved in the relation to focus
on another property: exhaustivity. Représentations de, par exemple, two-same as (X X ) et
three-same as (X X X ) impede this process as each of these schemas is tight to a specific
numerosity, implicitly represented by the number of individual instances of X. For all or
exhaustivity to apply to a representation of same, that representation must be first segregated
from the representation of numerosity. The observed association between spontaneous cate-
gorization of arrays as all the same vs. not all the same and the use of the word “same” in
childhood (Hochmann et al., 2017) further suggests that representing all the same requires a
discrete symbol for the relation same, which is not only segregated from the representation of
entities, but also from the representation of numerosity.

Current Study

Ici, we tested the hypothesis that pre-lexical infants represent the relation same with the
format (X X ), c'est à dire., with an abstract symbol for each entity to which the relation same applies,
but no discrete symbol for their relation. We reasoned that, if this hypothesis is correct, le
number of same elements that can be represented as same should be constrained by the limits
of the working memory capacity. En outre, because the representation of same that we
propose is tight to a specific numerosity, representing all the same, hence disregarding the
number of same entities, should be difficult.

Working memory is a limited short-term memory system that maintains information acces-
sible for cognitive operations. In adults, working memory capacity is generally limited to about
four items (Cowan, 2001), with some variability depending on what is being represented
(Brady et al., 2016) and on interferences between individual representations (Endress & Potter,
2014; Schurgin et al., 2020). Research on infants’ working memory suggests that at 11 mois,
the working memory capacity is about three or four items (Benavides-Varela & Reoyo-Serrano,
2021; Feigenson & Carey, 2003; Feigenson et al., 2002; Ross-Sheehy et al., 2003). As previous
research found that 11-month-old infants could represent the relation same between 4 sylla-
bles (Hochmann & Toro, 2021), we expected four items (c'est à dire., syllables) to be the limit beyond
lequel 11 months infants would fail to apply the relation same.

In Experiments 1 et 4, we asked whether infants can represent the relation same between
four entities. In Experiments 2–3, we asked whether infants can represent the relation same
between a number of individuals that exceeds the alleged working memory capacity (five or
six). Enfin, we asked whether infants can ignore the number of entities involved in the relation
same, effectively representing that all items are the same, whether there are three, four or five of
eux (Experiment 5), or whether there are two, three or four of them (Experiment 6). In each
experiment, 10- to 12-month-old infants were exposed to series of sequences of syllables. Cru-
cially, even 12-month-olds are still years away from producing or understanding the word
“same” (Hochmann et al., 2017; Hochmann et al., submitted). We used syllables, which are
well represented, discriminated and categorized by the end of the first year of life (Hochmann &

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Abstract Relations in Infancy Hochmann

Bouffe, 2014; Werker & Tees, 1984). The syllables varied from one trial to another (48 different
syllables were used for each infant). In the Unbalanced group, most sequences (75%)
matched a structure defined by the relation same (Same sequences; par exemple., AAAA in Experi-
ment 1: ba ba ba ba, ko ko ko ko, mi mi mi mi). If infants were able to represent the Same
structure, they should come to expect all sequences to be composed of identical syllables,
and should be surprised by the insertion of a different syllable in 25% of sequences contain-
ing one different syllable (the Different sequences; par exemple., AAAB: nu nu nu la). The violation of
expectation was measured with pupillometry. Increase in arousal, attention or cognitive load
triggers an increase of pupil diameters (Beatty & Kahneman, 1966; Hess & Polt, 1960; Laeng
et coll., 2012). Relevant to the present study, in oddball paradigms, pupils dilate in reaction to
rare auditory stimuli in both adults (Qiyuan et al., 1985; Quirins et al., 2018) and infants
(Hochmann & Bouffe, 2014; Hochmann & Toro, 2021), most likely as a result of increased
attention or arousal due to an unexpected event.

Different sequences could be surprising because they violate the expected Same-sequence
in their global relational structure (par exemple., AAAB, rather than AAAA), but also because they con-
tain a local syllable change (from A to B). En outre, we may expect the effect of a local
change to increase with the number of repetitions of the same syllable (par exemple., a stronger effect is
expected for AAAAAB sequences than for AAAB sequences). To disentangle the “global
effect”, related to the violation of the relational structure, from the effect of the local change,
each experiment included a Control group, for whom 50% of sequences followed the Same
structure and 50% followed the Different structure. The effect of the local change is by defi-
nition independent from the frequency of the Different structure, and is therefore identical in
the Unbalanced and Control groups. The global effect, in contrast, should only be observed in
the Unbalanced groups.

MATERIAL AND METHODS

Participants

One-hundred-ninety-two infants (age range: 9 m 28 d – 12 m 21 d; average: 10 m 30 d) par-
ticipated in Experiments 1–6 (see Table 1 for detailed information). Fourteen additional infants
were tested but excluded for not providing a sufficient number of trials. Thirty-two infants
participated in each experiment. Half of them were included in the unbalanced group and
half in the control group. The sample size of 16 participants per group was chosen following
Hochmann and Toro (2021, Experiment 1), after a power analysis using G*Power (Faul et al.,
2009) showed this sample size to be higher than the minimal required sample size of 13 par-
ticipants for α = .05, 1 − β = .80, and d = .74. All participants were recruited through the
consultation of birth records at the city halls. Infants were tested in the babylab of Institut
des Sciences Cognitives Marc Jeannerod in Bron, France. Parents received travel reimburse-
ment and gave informed consent before participation. The study was approved by the local
ethics committee (CPP sud-est II).

Stimuli

As previously described (Hochmann & Toro, 2021), 48 syllables were created with the artifi-
cial speech synthesizer MBROLA (French voice database FR4), with phoneme duration of 120
ms and pitch of 200 Hz. Nous avons utilisé 12 consonants (/b/, /d/, /g/, /p/, /t/, /k/, /v/, /f/, /s/, /l/, /m/, /n/)
et 4 vowels (/a/, /i/, /o/, /u/). Each syllable was normalized to an intensity of 70 dB. The video
shown repeatedly on the screen of the eyetracker consisted in an animated video clip showing

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Abstract Relations in Infancy Hochmann

Tableau 1. Demographic information

Experiment
Experiment 1

Groupe
Unbalanced

Age range
10 m 6 d – 12 m 15 d

Mean age
11 m 6 d

N female
9

Contrôle

10 m 4 d – 11 m 26 d

10 m 26 d

Experiment 2

Unbalanced

10 m 12 d – 11 m 30 d

10 m 23 d

Contrôle

10 m 3 d – 12 m 0 d

10 m 25 d

Experiment 3

Unbalanced

10 m 8 d – 12 m 21 d

11 m 8 d

Contrôle

10 m 14 d – 12 m 4 d

11 m 6 d

Experiment 4

Unbalanced

10 m 3 d – 11 m 28 d

10 m 25 d

Contrôle

10 m 13 d – 11 m 24 d

11 m 1 d

Experiment 5

Unbalanced

10 m 1 d – 12 m 7 d

11 m 6 d

Contrôle

9 m 28 d – 12 m 3 d

10 m 27 d

Experiment 6

Unbalanced

10 m 6 d – 11 m 17 d

10 m 21 d

Contrôle

10 m 9 d – 11 m 30 d

11 m 2 d

7

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a smiling cartoon character jumping repeatedly. The movements in this video clip were not
synchronized to the presentation of the acoustic stimuli.

Procedure

As previously described (Hochmann & Toro, 2021), infants sat on their parent’s laps in front of
a Tobii eyetracker T60XL. The presentation of stimuli and the recording of eye-tracking data
was controlled by PsyScope X (https://psy.cns.sissa.it). All lights in the room were switched off,
except for those coming from the eyetracker screen. Each trial started automatically when
infants fixated a central blinking cross presented on the screen. The central blinking cross dis-
appeared and the jumping character appeared at the center of the screen. The pupil size is
particularly sensitive to variations of luminance. To ensure that any observed effect could
not be attributed to variations of luminance, contrast or any other visual features of the stimuli,
the exact same video was shown in all trials. The first syllable began 200 ms after the onset of
the video clip. The onsets of two successive syllables were separated by 500 ms. Un
sequence of syllables was played in each trial. All trials had the same duration: 5217 ms.

Experiments 1–3 presented below were planned. Experiments 4–6 were added after observ-

ing the results of Experiments 1–3.

Experiment 1: Half of the participants were included in the unbalanced group. The first 8
trials consisted in standard Same sequences, respecting the AAAA structure. For the rest of the
experiment, 75% of trials were standard Same sequences (AAAA; par exemple., ba ba ba ba; di di di di;
fu fu fu fu; etc.) et 25% were deviant Different sequences, which differed from the Same
sequences by ending with a different syllable (AAAB; par exemple., lo lo lo me). The experiment lasted
jusqu'à 96 additional trials were run (72 standard and 24 deviant trials), until the infant fussed out
or until the parent asked to stop the experiment. Two trials were separated by a grey screen
displaying only a central blinking cross to attract infants’ gaze. Trials were run in a pseudo-
random order, so that two deviant trials were separated by 1 à 6 standard trials. The other half

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Abstract Relations in Infancy Hochmann

of participants were included in the control group, for whom 50% of trials respected the Same
structure (AAAA) et 50% respected the Different structure (AAAB). The experiment lasted
until a total of 96 trials were run (48 Same and 48 Different trials), until the infant fussed
out or until the parent asked to stop the experiment. Two trials were separated by a grey screen
displaying only a central blinking cross to attract infants’ gaze. Trials were run in a pseudo-
random order, so that no more than four trials of the same kind could follow each other.

Experiment 2: The stimuli and procedure of Experiment 2 were identical to that of Experi-
ment 1, except for one feature: sequences of 5 instead of 4 syllables were used. The unbalanced
group heard 75% of standard Same trials (AAAAA) et 25% of deviant Different trials (AAAAB);
the control group heard 50% of Same trials (AAAAA) et 50% of Different trials (AAAAB).

Experiment 3: The stimuli and procedure of Experiment 3 were identical to that of Exper-
iment 1, except for one feature: sequences of 6 instead of 4 syllables were used. The unbal-
anced group heard 75% of standard Same trials (AAAAAA) et 25% of deviant Different trials
(AAAAAB); the control group heard 50% of Same trials (AAAAAA) et 50% of Different trials
(AAAAAB).

Experiment 4: The stimuli and procedure of Experiment 4 were identical to that of Exper-
iment 3, except for one feature: in deviant trials, instead of violating the standard structure on
the final syllable (AAAAAB in Experiment 3), the structure was violated on the fourth syllable
(AAABAA). The unbalanced group heard 75% of standard Same trials (AAAAAA; par exemple., ba ba ba
ba ba ba; di di di di di di; fu fu fu fu fu fu; etc.) et 25% of deviant Different trials (AAABAA;
par exemple., lo lo lo me lo lo); the control group heard 50% of Same trials (AAAAAA) et 50% de
Different trials (AAABAA).

Experiment 5: The stimuli and procedure of Experiment 5 were identical to that of Exper-
iment 1, except for one feature: in the unbalanced group, instead of being always composed of
4 syllables, standard Same trials were composed of 3 (AAA, 25% of all trials; par exemple., ba ba ba), 4
(AAAA, 25% of all trials; par exemple., di di di di) ou 5 syllables (AAAAA, 25% of all trials; par exemple., fu fu fu
fu fu). Deviant Different trials were always composed of 4 syllables (AAAB, 25% of all trials;
par exemple., lo lo lo me); the control group heard 50% of Same trials (AAAA) et 50% of Different
trials (AAAB). Note that, in the control group, the number of syllables is fixed. The purpose of
the control group is to isolate a potential local effect in AAAB sequences. This effect can be
measured by comparing responses to AAAB and AAAA sequences, and should be by defini-
tion independent from the presence and nature of other sequences.

Experiment 6: The stimuli and procedure of Experiment 6 were identical to that of Exper-
iment 5, except for one feature: the number of syllables varied between two and four. Standard
Same trials were composed of 2 (AA, 25% of all trials; par exemple., ba ba), 3 (AAA, 25% of all trials;
par exemple., di di di) ou 4 syllables (AAAA, 25% of all trials; par exemple., fu fu fu fu). Deviant Different trials
were always composed of 3 syllables (AAB, 25% of all trials; par exemple., lo lo me); the control group
heard 50% of Same trials (AAA) et 50% of Different trials (AAB).

Analysis

Fixations were identified by PsyScope X following the dwell-time algorithm (Duchowski,
2007) with the following parameters: WindowLength = 200, MinFixationLength = 100, Dis-
tanceFromMean = 0.05. We defined an area of interest (660 pi × 432 pi) corresponding to the
surface of the video played on the screen to attract infants’ gaze. The pupil diameter for both
eyes was recorded for fixations in that area of interest. For each trial, we considered a baseline
time window beginning 500 ms before the onset of the final syllable of the sequence in

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Tableau 2.

Average numbers of trials included in the final analyses. Standard deviants from the mean are indicated in parentheses.

Experiment
Experiment 1 (4-same)

Groupe
Unbalanced 1

Total #trials
49.19 (11.18)

#good trials
29.62 (13.37)

#good same
21.75 (10.90)

#good different
7.87 (2.66)

Experiment 2 (5-same)

Unbalanced 2

70.50 (23.56)

40.50 (20.78)

29.75 (15.38)

10.75 (5.74)

Contrôle 1

45.12 (23.32)

28.56 (15.06)

14.19 (7.95)

14.37 (8.27)

Contrôle 2

64.75 (20.58)

37.94 (22.48)

18.56 (11.62)

19.37 (11.11)

Experiment 3 (6-same)

Unbalanced 3

45.19 (20.57)

27.56 (15.24)

20.56 (11.80)

7.00 (3.71)

Contrôle 3

43.56 (20.07)

26.25 (8.10)

12.94 (4.36)

13.31 (4.16)

Experiment 4 (4 of 6-same)

Unbalanced 4

72.44 (18.90)

39.94 (16.57)

30.00 (13.16)

9.94 (3.82)

Contrôle 4

78.12 (23.29)

44.94 (24.08)

22.19 (12.08)

22.75 (12.19)

Experiment 5 (all-same)

Unbalanced 5*

28.56 (12.04)

17.81 (9.26)

8.31* (4.59)

9.50 (5.05)

Contrôle 5

60.87 (26.77)

34.56 (22.71)

17.37 (11.37)

17.19 (11.54)

Experiment 6 (all-same)

Unbalanced 6**

41.56 (9.47)

22.69 (9.55)

10.81** (5.09)

11.87 (4.87)

Contrôle 6

60.19 (29.29)

30.81 (16.75)

15.25 (8.55)

15.56 (8.39)

* In the Unbalanced group of Experiments 5, only 4-syllable long standard (AAAA) and deviant (AAAB) trials were analyzed.

** In the Unbalanced group of Experiments 6, only 3-syllable long standard (AAA) and deviant (AAB) trials were analyzed.

Experiments 1–3 and 5–6, et 500 ms before the onset of the fourth syllable in Experiment 4.
The average pupil diameter in the baseline window was subtracted from all data points.

We excluded trials with less than 75% of pupil diameter information over the entire trial
duration (5217 ms) and/or less than 100 ms of pupil diameter information in the baseline time
window. The first criterion was chosen so that it would be equally stringent in all experiments;
the second criterion ensured there was reliable baseline information in all included trials.
Tableau 2 presents the average number of trials included in the final analyses for each experi-
ment. The first 8 trials in the unbalanced group constituted the familiarization with the stan-
dard structure and were not analyzed. Infants with less than 2 good trials per condition were
excluded from further analyses. Missing data for good trials were linearly interpolated.

Previous work using similar paradigms found that the effect of the violation of a sequence
structure on pupil dilation typically starts around 1250 ms after the violation onset (and can
last up to 1000 ms) (Hochmann & Toro, 2021). We thus ran repeated-measures ANOVAs com-
paring average pupil dilations in the 1250–2250 ms time window in response to Same and
Different sequences in the Unbalanced and Control groups. Bayes factors (BF) were computed
using the method in Faulkenberry (2020).

En outre, non-parametrical cluster mass permutation tests (Hochmann & Bouffe, 2014;
Maris & Oostenveld, 2007) were implemented to probe the variation of pupil dilation in
response to Same and Different sequences and the interaction of that effect with the group
(Unbalanced or Control).

In Experiments 5–6, because concurrent audio-visual stimulation attracts infants’ attention,
which in turn impacts pupil diameters, only those trials with the same number of syllables
were comparable. In Experiment 5, we thus only compared Same AAAA and Different AAAB

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Abstract Relations in Infancy Hochmann

trials. AAA and AAAAA trials were not analyzed. In Experiment 6, we thus only compared
Same AAA and Different AAB trials. AA and AAAA trials were not analyzed.

RÉSULTATS

Experiment 1: 4-Same

In Experiment 1, 10- to 12-month-old infants (N = 32) were tested on their capacity to detect
and generalize the relation same between 4 syllables (Same sequences: AAAA; Different
sequences: AAAB). Results showed that infants were not surprised by the local change of
a syllable in AAAB sequences in the Control group, but were surprised by the change of
relational structure in the Unbalanced group, demonstrating that infants could represent
the relation same between 4 elements. Detailed analyses follow.

For each group (Unbalanced, N = 16 and Control, N = 16), for each condition (Same
and Different Sequence Type), we computed the average pupil dilation between 1250 et
2250 ms after the last syllable onset, which has been identified as the critical interval for the
effect of the violation of a sequence structure on pupil dilation (Hochmann & Toro, 2021).
A repeated-measures ANOVA revealed no main effect of Sequence Type (Same, Different)
(F(1, 30) = .28; P = .60; η2 = .009; BF = .21) or Group (Contrôle, Unbalanced) (F(1, 30) = 1.49;
P = .23; η2 = .047; BF = .38), but identified a significant interaction between the two factors
(F(1, 30) = 14.12; P = .001; η2 = .320; BF = 84.66). The dilation difference was statistically
significant in the Unbalanced group (M = .040 mm, SD = .050; t(15) = 3.19; P = .003, one-tail;
BF = 19.79), but not in the Control group (M = −.030, SD = .055; t(15) = −2.18; P = .98, one-tail;
BF = 2.52).

The analysis of the time-course of pupil dilation with cluster mass permutation tests con-
firmed these results (Chiffre 1), finding no significant main effect of Sequence Type (Same,
Different), but a significant interaction between Sequence Type and Group (Experimental,
Contrôle) in the 1283–2083 ms time window; P = .006. The interaction reflected larger pupil
dilation for deviant AAAB compared to standard AAAA sequences in the Unbalanced group,
but larger pupil dilation for AAAA sequences compared to AAAB sequences in the Control
group. Two independent cluster mass permutation tests confirmed this pattern, showing larger
pupil dilation in response to deviant AAAB vs. standard AAAA sequences between 1350 et
2783 ms (P = .02) in the Unbalanced group, and larger pupil dilation in response to AAAA vs.
AAAB sequences between 1800 et 2533 ms (P = .04), et entre 2683 et 3500 ms (P =
.03) in the Control group.

In sum, when infants heard frequent AAAA sequences, they exhibited pupil dilation in
response to infrequent deviant AAAB sequences, suggesting either that infants expected only
same syllables and were surprised by the presence of a different syllable, or that infants
expected exactly four same syllables and were surprised by the absence of the fourth same
syllable. In both cases, infants could represent the relation same between 4 elements.

Experiment 2: 5-Same

In Experiment 2, we tested whether the effect observed in Experiment 1 generalized to rela-
tional structures involving five syllables. Two groups of 10- to 12-month-old infants (Unbal-
anced group: N = 16; Control group: N = 16) were exposed to Same (AAAAA) and Different
sequences (AAAAB). Results showed that infants failed to represent the relation same when it
involved five elements.

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Chiffre 1. Results of Experiments 1–3. Variation of pupil diameter in response to sequences of 4 syllables (AAAA or AAAB; Experiment 1; gauche
column), 5 syllables (AAAAA or AAAAB; Experiment 2; middle column) et 6 syllables (AAAAAA or AAAAAB; Experiment 3; right column).
The first row presents the results of the Control groups with equal distributions of same and different sequences. The second row presents the
results of the Unbalanced groups with unequal distributions of standard same (75%) and deviant different (25%) sequences. The bottom row
presents the comparison of the two groups. The grey curves show the difference between the responses to same and different sequences in the
Control group. The black curves show the difference between the responses to standard same and deviant different sequences in the Unbalanced
group. On all graphs, light colored areas denote standard errors from the mean.

A repeated-measures ANOVA analyzed the average pupil dilations between 1250 et
2250 ms and found no main effect of Sequence Type (Same, Different) (F(1, 30) = 3.23; P =
.082; η2 = .097; BF = .91), no effect of Group (Contrôle, Unbalanced) (F(1, 30) = .34; P = .56;
η2 = .011; BF = .21), and no interaction between Sequence Type and Group (F(1, 30) = .42; P =
.52; η2 = .014; BF = .22). The dilation difference was not statistically significant considering the
Unbalanced group alone (M = .025 mm; SD = .075; t(15) = 1.35; P = .098, one-tail; BF = .64) ou
the Control group alone (M = .012 mm; SD = .036; t(15) = 1.34; P = .10, one-tail; BF = .63).

Cluster mass permutation tests (Chiffre 1) analyzing the time-course of pupil dilation found
no significant interaction between Sequence Type (Same, Different) and Group (Experimental,
Contrôle), and no significant main effect of Sequence Type (all Ps > .09). Independent cluster
mass permutation tests for the Unbalanced and the Control groups found no significant dif-
ference between the response to AAAAA and AAAAB sequences (all Ps > .19).

In sum, the absence of an interaction between Sequence Type and Group supports the con-
clusion that infants in the Unbalanced group failed to represent the structure of the frequent
AAAAA sequences. They did not expect all syllables to be the same.

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Experiment 3: 6-Same

In Experiment 3, 10- to 12-month-old infants (Unbalanced group: N = 16; Control group: N =
16) were tested on their capacity to detect and generalize the relation same between 6 syllables
(Same sequences: AAAAAA; Different sequences: AAAAAB). Results showed that infants failed
to represent the relation same when it involved six elements. Plutôt, pupil dilation was evi-
denced in reaction to the local change of the last syllable in AAAAAB sequences, si
those were infrequent (Unbalanced group) ou non (Control group). Detailed analyses follow.

A repeated-measures ANOVA on the average pupil dilation values between 1250 et
2250 ms revealed a main effect of Sequence Type (Same, Different) (F(1, 30) = 8.33; P =
.007; η2 = .217; BF = 8.91), but no effect of Group (Contrôle, Unbalanced) (F(1, 30) = .07;
P = .80; η2 = .002; BF = .18), and no interaction between Sequence Type and Group (F(1,
30) = .001; P = .98; η2 = .000; BF = .18). Pupil dilatation was larger for Different than Same
sequences in both the Unbalanced group (M = .033 mm; SD = .054; t(15) = 2.40; P = .015,
one-tail; BF = 3.84) and the Control group (M = .032 mm; SD = .071; t(15) = 1.80; P = .046,
one-tail; BF = 1.28).

Cluster mass permutation tests analyzing the time-course of pupil dilation (Chiffre 1) con-
firmed the above results, revealing no significant interaction between Sequence Type (Same,
Different) and Group (Unbalanced, Contrôle), but a significant main effect of Sequence Type
entre 833 et 1900 ms (P = .006). Independent cluster mass permutation tests found
significantly larger pupil dilation for AAAAAB sequences than for AAAAAA sequences in the
Unbalanced group (N = 16) entre 833 et 1583 ms (P = .01), but no significant difference
in the Control group (N = 16) (all Ps > .30).

In sum, the absence of an interaction between Sequence Type and Group supports the con-
clusion that infants in the Unbalanced group failed to represent the structure of AAAAAA
sequences in a way that is discriminable from deviant AAAAAB sequences. They did not
expect all syllables in the sequence to be the same. The presence of a final different syllable
was surprising, but only due to a local effect.

Effect of the Number of Syllables: Experiments 1, 2, et 3

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To confront the results of Experiments 1, 2, et 3, we ran a repeated-measures ANOVA on the
average pupil dilation values between 1250 et 2250 ms, with Sequence Type (Same, Different)
as within-subject factor and Group (Unbalanced, Contrôle) and Number of Syllables (4, 5, 6) comme
between-subject factors. The analysis revealed no effect of Group (F(1, 90) = .52; P = .47; η2 =
.006; BF = .13) or of Number of Syllables (F(2, 90) = 2.98; P = .056; η2 = .062; BF = .23), mais
identified a main effect of Sequence Type (F(1, 90) = 9.81; P = .002; η2 = .098; BF = 14.64), un
Sequence Type × Group interaction (F(1, 90) = 5.46; P = .022; η2 = .057; BF = 1.72) and a three-
way interaction between Sequence Type, Group and Number of Syllables (F(2, 90) = 3.16; P =
.047; η2 = .066; BF = .27). Pairwise t-tests showed that pupil dilation for Different compared to
Same sequences was larger in the Unbalanced group than in the Control group, quand
sequences involved four syllables (t(30) = 3.76; P. < .001; BF = 85.20), but not five (t(30) = .65; P = .52; BF = .22) or six syllables (t(30) = .024; P = .98; BF = .18). Note that, with respect to the three-way interaction, the frequentist and Bayesian analyses yielded contradictory results. Subsequent analyses nevertheless unambiguously support the conclusion of a stronger global effect with 4 syllables than with 5 or 6 syllables. For each experiment, for each participant in the Unbalanced group, we computed an index of the global effect (i.e., their success in representing the target structure), comparing the OPEN MIND: Discoveries in Cognitive Science 301 Abstract Relations in Infancy Hochmann participant’s pupil dilation to the averaged pupil dilation in the control group (in Different com- pared to Same sequences): for each participant s, I(s) = (PupDifferent(s) – PupSame(s)) − Average (PupDifferent − PupSame)ControlGroup. Pairwise t-tests showed that infants performed better when sequences involved four syllables than when they involved five (t(30) = 2.50; P = .018; BF = 3.65) or six syllables (t(30) = 2.64; P = .013; BF = 5.00). Performance did not differ when sequences involved five or six syllables (t(30) = .32; P = .75; BF = .19). Comparison of the Local Effect in Experiments 1, 2, and 3 The local effect, isolated in the Control groups, was expected to depend on the number of repeated syllables: the more the A syllable is repeated, the more surprising the B syllable should be. Qualitatively, this was the case. The local effect appeared stronger and more reli- able with six syllables (Experiment 3) than with five syllables (Experiment 2) than with four syllables (Experiment 1). A repeated-measures ANOVA analyzed the average pupil dilation in the Control groups, between 1250 and 2250 ms, with Sequence Type (Same, Different) as within-subject factor and Number of Syllables (4, 5, 6) as between-subject factor and found no main effect of Sequence Type (F(1, 45) = .35; P = .56; η2 = .008; BF = .17) or Number of Syllables (F(2, 45) = 2.52; P = .09; η2 = .101; BF = .27) but a significant interaction between Sequence Type and Number of Syllables (F(2, 45) = 5.11; P = .01; η2 = .185; BF = 2.83). Post-hoc t-test found that the local effect, measured as the difference of pupil dilation for Dif- ferent compared to Same sequences, was weaker in Experiment 1 with 4 syllables compared to both Experiment 2 with 5 syllables (P = .016) and Experiment 3 with 6 syllables (P = .01). The patterns in Experiments 2 and 3, with respectively 5 and 6 syllables, did not differ signif- icantly (P = .32). A cluster mass permutation test confirmed these results. It found an effect of Number of Syllables on the local effect in a time window between 1733 and 2367 ms (P = .04). In that time window, the local effect differed between sequences of 4 and 5 syllables (AAAB vs. AAAAB; t(30) = 2.41; P = .02; BF = 3.00) and between sequences of 4 and 6 syl- lables (AAAB vs. AAAAAB; t(30) = 3.07; P = .005; BF = 13.99), but not between sequences of 5 and 6 syllables (AAAAB vs. AAAAAB; t(30) = 1.16; P = .25; BF = .36). Note that in Experiment 1, we observed a reversed pattern for sequences of 4 syllables in the Control group: dilation was higher for AAAA than for AAAB, despite the two types of sequences being equally frequent. A tentative account for this finding is that the detection of the relation same between 4 syllables in AAAA sequences elicits interest that is reflected in larger pupil dilation, whereas the local change in AAAB sequences elicits no pupil dilation (as was already observed in adults; Quirins et al., 2018). Experiment 4: 4 of 6-Same Experiments 1, 2, and 3 suggest that 10- to 12-month-old infants can represent the relation same between a maximum of four elements. To obtain convergent evidence, in Experiment 4, 10- to 12-month-old infants (Unbalanced group: N = 16; Control group: N = 16) were tested on their capacity to detect and generalize the relation same between the first four syllables of a sequence of six syllables (Same sequences: AAAAAA; Different sequences: AAABAA). Results showed that infants could represent the relation same between the first four of six elements. Detailed analyses follow. A repeated-measures ANOVA over the average pupil dilation values between 1250 and 2250 ms showed no effect of Group (Control, Unbalanced) (F(1, 30) = 3.36; P = .077; η2 = .101; BF = .97), but a main effect of Sequence Type (Same, Different) (F(1, 30) = 7.06; P = .013; η2 = .190; BF = 5.20), and a significant interaction between the two factors (F(1, 30) = 6.81; P = OPEN MIND: Discoveries in Cognitive Science 302 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u o p m i / l a r t i c e - p d f / d o i / i / . / 1 0 1 1 6 2 o p m _ a _ 0 0 0 6 8 2 0 6 4 5 9 7 o p m _ a _ 0 0 0 6 8 p d / . i f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Abstract Relations in Infancy Hochmann l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u o p m i / l a r t i c e - p d f / d o i / Figure 2. Results of Experiments 4–6. Variation of pupil diameter in response to AAAAAA and AAABAA sequences (Experiment 4, left column), in response to AAAA and AAAB sequences (Experiment 5, middle column) and in response to AAA and AAB sequences (Experiment 6, right column). The top row presents the results of the control group with equal distributions of same and different sequences. The second row presents the results of the unbalanced groups with unequal distributions of standard same and deviant different sequences. The bottom row presents the comparison of the two groups. The grey curves show the difference between the responses to same and different sequences in the control group. The black curves show the difference between the responses to standard and deviant sequences in the unbalanced group. On all graphs, light colored areas denote standard error from the mean. i / . / 1 0 1 1 6 2 o p m _ a _ 0 0 0 6 8 2 0 6 4 5 9 7 o p m _ a _ 0 0 0 6 8 p d / . i f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 .014; η2 = .185; BF = 4.67). The difference in dilation was significant in the Unbalanced group (M = .062 mm, SD = .077; t(15) = 3.25; P = .003, one-tail; BF = 22.52), but not in the Control group (M = .001 mm, SD = .056; t(15) = .040; P = .48, one-tail; BF = .24). A cluster mass permutation test analyzing the time-course of pupil dilation (Figure 2) con- firmed the above results, revealing a main effect of Sequence Type (Same, Different) in the 1283–2083 ms time window; P = .05, due to larger pupil dilation for Different sequences com- pared to Same sequences. This effect was only present in the Unbalanced group, as shown by a significant interaction between Sequence Type and Group (Unbalanced, Control), in the time windows 1000–2100 ms (P = .02) and 2167–3500 (P = .02). Two independent cluster mass permutation tests confirmed the effect. In the Unbalanced group, we observed larger pupil dilation in response to deviant AAABAA sequences than to standard AAAAAA sequences between 850 and 2167 ms (P = .02). No significant difference was found in the Control group at any point in time. In Experiment 3, infants appeared to have no expectation as to the relational structure involving the sixth syllable of AAAAAA sequences. In Experiment 4 instead, infants exhibited pupil dilation in response to a different syllable in the fourth position, suggesting that infants OPEN MIND: Discoveries in Cognitive Science 303 Abstract Relations in Infancy Hochmann expected the fourth syllable to be the same as previous syllables. These results thus show that infants can represent the relation same between the first four syllables of a longer sequence. Experiment 5: All-Same Experiments 2 and 3 suggest that infants cannot represent the relation same between five and six elements, respectively. These results also suggest that infants fail at representing all the same, which would apply to any sequence of same elements, whether there are four, five or six of them. This observation is consistent with our prediction that infants should fail to disregard the number of entities involved in the relation same, as the format of representation that we propose ties together the implicit representations of numerosity and same. To further probe infants’ (in)ability to represent all the same, in Experiment 5, we asked whether 10- to 12-month-old infants (Unbalanced group: N = 16; Control group: N = 16) could detect and generalize the relation same between a varying number of syllables (Same sequences: AAA; AAAA or AAAAA; Different sequences: AAAB). Results suggest that they cannot. Detailed analyses follow. A repeated-measures ANOVA on the average pupil dilation values between 1250 and 2250 ms showed no effect of Sequence Type (Same, Different) (F(1, 30) = .12; P = .73; η2 = .004; BF = .19), no effect of Group (Control, Unbalanced) (F(1, 30) = .08; P = .78; η2 = .003; BF = .18), and no interaction between Sequence Type and Group (F(1, 30) = .035; P = .85; η2 = .001; BF = .18). The difference in dilation was not significant considering the Unbalanced group alone (M = −.003 mm; SD = .111; t(15) = −.11; P = .54, one-tail; BF = .24) nor the Control group alone (M = −.010 mm; SD = .095; t(15) = −.41; P = .66, one-tail; BF = .27) (Figure 2). Cluster mass permutation tests analyzing the time-course of pupil dilation (Figure 2) con- firmed those results, showing a main effect of Sequence Type between 2400 and 3383 ms (P = .04), but no interaction between Sequence Type (Same, Different) and Group (Unbalanced, Control). Both groups showed larger pupil dilation for Same sequences compared to Different sequences, though independent cluster mass permutation tests showed that the difference between Same and Different sequences reached significance for the Control group (between 2500 and 3450 ms, P = .05) but not for the Unbalanced group. Larger pupil dilation for AAAA than for AAAB sequences, already observed in the control group of Experiment 1, may reflect greater attention to the AAAA sequences, possibly because of the local detection of the relation between 4 syllables. In any case, the important finding here is the absence of pupil dilation in response to Deviant AAAB sequences in the mist of AAA, AAAA and AAAAA sequences. In other words, infants did not perceive the structure common to the three types of Same sequences; i.e., all syllables in a sequence are the same. The variability in length of the sequences may have distracted infants, preventing them to extract the common structure. These results nevertheless converge with those of Experiments 2 and 3, where, despite a constant number of syllables, infants failed to realize that all syllables were the same. Before taking stock, we must address one last issue. Experiment 5 was designed to test infants’ ability to represent all the same when the number of syllables vary. The results suggest that infants failed. To represent the sequence structure, they may need to represent the exact number of same elements, which cannot exceed four. However, in the present experiment, one quarter of the sequences, those composed of five syllables, could not be accurately rep- resented (Experiment 2). Can infants represent all the same, when each of the sequences can be represented; i.e., when the number of syllables remains below four? In Experiment 6, we OPEN MIND: Discoveries in Cognitive Science 304 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u o p m i / l a r t i c e - p d f / d o i / i / / . 1 0 1 1 6 2 o p m _ a _ 0 0 0 6 8 2 0 6 4 5 9 7 o p m _ a _ 0 0 0 6 8 p d . / i f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Abstract Relations in Infancy Hochmann tested infants’ ability to represent all the same, when the number of syllables varied between two and four. Experiment 6: All-Same In Experiment 5, infants failed to see the common structure between AAA, AAAA and AAAAA sequences, suggesting they could not represent all the same. Experiment 6 was identical to Experiment 5, except that the number of syllables varied between two and four. We asked whether 10- to 12-month-old infants (Unbalanced group: N = 16; Control group: N = 16) could detect and generalize the relation same between two to four syllables (Same sequences: AA; AAA or AAAA; Different sequences: AAB). Results showed that they cannot. Detailed analyses follow. A repeated-measures ANOVA on the average pupil dilation values between 1250 and 2250 ms showed no effect of Sequence Type (Same, Different) (F(1, 30) = .19; P = .66; η2 = .006; BF = .20), no effect of Group (Control, Unbalanced) (F(1, 30) = .70; P = .41; η2 = .023; BF = .26), and no interaction between Sequence Type and Group (F(1, 30) = .18; P = .67; η2 = .006; BF = .19). The difference in dilation was not significant considering the Unbalanced group alone (M = .0002 mm; SD = .092; t(15) = .008; P = .50, one-tail; BF = .24) nor the Control group alone (M = .013 mm; SD = .078; t(15) = .665; P = .26, one-tail; BF = .31). Cluster mass permutation tests analyzing the time-course of pupil dilation (Figure 2) con- firmed those results, showing no main effect of Sequence Type and no interaction between Sequence Type (Same, Different) and Group (Unbalanced, Control). Both groups showed no difference in pupil dilation for Different sequences compared to Same sequences. The results of Experiment 6 converged with those of Experiment 5, suggesting that infants are unable to detect the common structure between sequences of varying length composed only of repeated syllables, even when the number of syllables remained within the range of infants’ working memory capacity. In sum, infants could not represent all the same. As of today, there is little data with respect to infants’ ability to represent a universal quantifier all (though see Téglás & Bonatti, 2009; Cesana-Arlotti et al., 2020a). Either such representa- tion and the representation of same cannot combine, or infants lack a universal quantifier altogether. The format of representation that we proposed for the relation same ties together the relation and the number of entities involved: two-same is represented as (X X ), three- same as (X X X ) and four-same as (X X X X ). In these circumstances, disregarding the number of entities to represent all-the-same appears rather difficult. DISCUSSION In six experiments, we investigated whether 10- to 12-month-olds could detect and generalize the structure of syllable sequences, based on the relation same. We exposed infants to frequent Same sequences, composed only of identical syllables (e.g., AAAA), and to rare Different sequences ending with (or containing) a different syllable (e.g., AAAB). We analyzed the pupil dilation elicited by Different sequences. Such dilation could reflect a “local effect”, i.e., responding to a local syllable change, and/or, a “global effect”, i.e., responding to the violation of the frequent relational structure of Same sequences. Control groups with equiprobable Same and Different sequences served to isolate the local effects. In Experiment 1, with 4-syllable-long sequences, pupil dilation was observed in response to rare AAAB sequences. A control group showed that this response could not be accounted for by a local effect, but rather reflected a response to the violation of the AAAA relational OPEN MIND: Discoveries in Cognitive Science 305 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u o p m i / l a r t i c e - p d f / d o i / i . / / 1 0 1 1 6 2 o p m _ a _ 0 0 0 6 8 2 0 6 4 5 9 7 o p m _ a _ 0 0 0 6 8 p d . / i f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Abstract Relations in Infancy Hochmann structure. Experiment 4 confirmed that infants could represent the relation same between four syllables: pupil dilation was observed in response to rare AAABAA sequences and a control group showed that this response could not be accounted for by a local effect. In Experiments 2, with 5-syllable-long sequences, no pupil dilation could be evidenced. In Experiment 3, with 6-syllable-long sequences, pupil dilation was observed in response to rare AAAAAB sequences, but a control group showed that this response could be accounted for by a local effect alone. Thus, there was no evidence that infants could represent the relational structure of Same sequences, beyond the fourth syllable. Overall, our results clearly show that infants could represent the abstract relation same in sequences of four syllables (Experiment 1), but there is no evidence that they can do so in sequences of five or six syllables (Experiments 2 and 3). This apparent failure is striking when considering that there is more evidence for the relation same in sequences of 5 or 6 syllables than in sequences of 4 syllables. Infants could however represent the relation same between the first four elements of longer sequences (Experiment 4). The limit of four elements suggests that, in order to represent that sequences are formed of same items, infants hold a representation of each individual item in the relation, and do not rely on quantifiers such as four, six or all. In keeping with this, we found that infants were unable to generalize the relation same when the use of a universal quantifier was encouraged, as the number of elements that were all the same varied from trial to trial (Experiments 5–6). In sum, infants only succeeded in representing the relation same, when the number of items instantiating that relation was constant and within the limit of their working memory capacity. Our findings thus reveal a discontinuity in the representation of the relation same, in the course of cognitive development. Four- to 5-year-old children, as well as adults, represent same in a format that can be integrated in a propositional language of thought and combined with quantifiers, generating concepts such as all the same, which applies to any set of same individuals, irrespective of cardinality (Hochmann et al., 2017). Such representation is likely to rely on a discrete symbol for the relation same, which, in our interpretation is missing in young infants. While the available data suggests that the discontinuity occurs sometime around the fourth year of life, additional work is required to chart a detailed timeline of the development of the representations of same and different. In particular, the number limit identified here may be even more stringent in younger infants if their working memory is more severely limited (Káldy & Leslie, 2005). Moreover, while the data is so far compatible with the hypothesis that the acquisition of the words “same” and “different” around the fourth year of life plays a deter- mining role in the acquisition of a discrete symbol for the relation same, this hypothesis remains to be directly tested. Challenging our interpretation, one might explain the discontinuity by proposing that infants possess a discrete symbol S for same but lack quantifiers that would allow representing all the same (all S ). This account predicts that the working memory capacity constrains the number of pairs of same syllables that infants can represent, consistent with what we show in Experiments 1–4. There are reasons, however, to believe that the absence of a discrete sym- bol S for same is the most parsimonious account of available data. Considering infants’ failure in Experiment 6 is critical to address this point. We have shown that infants can represent up to 4 same syllables (Experiment 1). Presumably, they can also represent sequences of 2 same syllables and sequences of 3 same syllables. If infants possessed a discrete symbol S and use it to represent pairs of same items, they should represent 2 same syllables as S, 3 same syllables as SS and 4 same syllables as SSS. In Experiment 6, infants should thus habituate to the activation of the symbol S, or come to expect sequences that activate S. Infants should thus react to the different syllable in deviant AAB sequences. In sum, if infants possessed a OPEN MIND: Discoveries in Cognitive Science 306 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u o p m i / l a r t i c e - p d f / d o i / i / / . 1 0 1 1 6 2 o p m _ a _ 0 0 0 6 8 2 0 6 4 5 9 7 o p m _ a _ 0 0 0 6 8 p d . / i f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Abstract Relations in Infancy Hochmann discrete symbol S, we should expect pupil dilation in response to deviant sequences in Exper- iment 6. But this is not what we observed. In addition, if infants possessed S (but lack all ) they should succeed in RMTS, where quan- tifiers play no role. They would be able to represent both AA and BB as S, and match S to S. But we know that children fail at RMTS until the fifth year of life (Hochmann et al., 2017). Finally, the animal literature provides further support to the view that having a discrete symbol S—but not representing all—is crucial to succeed in RMTS: chimps initially failed at RMTS but can succeed after learning an explicit symbol for same (Thompson et al., 1997). In that study, chimps learned nothing about a universal quantifier all. In sum, given the available results from the current and previous studies, the representation of a discrete symbol S for same is unnecessary to account for infants’ successes, and can hardly accommodate their failures. We propose that infants’ representation of same is built on the aggregation of mental sym- bols that represent individual entities. These representations of entities cannot be mere percep- tual images, as infants are able to generalize the relation same to novel (perceptually different) stimuli (here, syllables). We argue that infants represent two same entities as (X X ), where X is a variable that refers to a set of properties in the domain under consideration, here the specifi- cation of a syllable. Likewise, three same entities would be represented as (X X X ) and four same entities as (X X X X ). Limited working memory capacity makes it impossible to extend this format of representation to five same entities or more. In consequence, infants can repre- sent four same entities, but have no expectation about the identity of a fifth or sixth element. Furthermore, those representations of the relation same are tight to a specific numerosity (two, three or four), which prevents infants to represent all the same, a representation that would disregard numerosity. In the present work, we used syllables, but the same format of representation is potentially applicable to other modalities and domains of cognition, provided that infants can represent a variable X in that domain. Moreover, in our experiments, same syllables were identical. Infants may be capable of representing the relation same based on only a subset of the dimensions of a given stimulus. Again, it depends on what type of variables is available to infants. If X is a variable for the vowel of a syllable (X X ) represents the relation two-same-vowel (Hochmann et al., 2011; Hochmann et al., 2018a); if X is a variable for the shape of a stimulus, (X X ) rep- resents the relation two-same-shape (Hochmann et al., 2018b). Further empirical investiga- tions should generalize our results to other modalities and define the domains in which infants can represent variables. The finding that the representation of sequences of same elements is limited by working memory capacity calls for the discussion of two findings coming from the research on infants’ working memory. First, while some studies have reported a capacity of four items at 11 months (Ross-Sheehy et al., 2003), most studies report a capacity of about three items (Benavides- Varela & Reoyo-Serrano, 2021; Feigenson & Carey, 2003; Feigenson et al., 2002). Second, when working memory is overloaded, infants sometimes (but not always) exhibit a phenom- enon called “catastrophic forgetting”: they remember fewer items than what they are capable of, sometimes even just one (Feigenson & Carey, 2005; vanMarle, 2013; Barner et al., 2007). This happens particularly when infants have to maintain independent representations for objects that have identical features, which resolves into a tendency to erroneously blend those representations (Zosh & Feigenson, 2015). Although the conditions of our study resemble the circumstances that lead to catastrophic forgetting (the same syllables had identical features), infants could encode the first four of six same syllables in Experiment 4. In fact, the detection of identical features triggered the OPEN MIND: Discoveries in Cognitive Science 307 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u o p m i / l a r t i c e - p d f / d o i / i . / / 1 0 1 1 6 2 o p m _ a _ 0 0 0 6 8 2 0 6 4 5 9 7 o p m _ a _ 0 0 0 6 8 p d / . i f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Abstract Relations in Infancy Hochmann representation of a relational structure, which results in co-dependent entities’ representations. We propose that, whereas catastrophic forgetting may be due to the difficulty to maintain inde- pendent representations for each entity, once infants learned the structure (X X X X ), they did not represent the four identical elements with independent, confusable symbols, but rather represented the second, third and fourth elements as copies of the first element. This results in a reduction of the information load, which can account for the larger working memory capacity observed here (four instead of three items; see also Alvarez & Cavanagh, 2004) and the absence of catastrophic forgetting. CONCLUSION We presented six experiments investigating the representation of the abstract relation same in infancy. We hypothesized that infants may not possess a discrete symbol to represent same that could be integrated in a propositional language of thought, but rather rely on symbols for the entities involved in the relation. Two predictions followed: infants’ representation of same should be constrained by the number of items that they could simultaneously maintain in working memory, and infants should be unable to disregard the number of involved entities, hence failing to represent all the same. As predicted, 10- to 12-month-old infants could rep- resent the relation same between four, but not more, individual entities. Neither could they represent the relation same between a variable number of entities. These results suggest that infant cognition may differ radically from adult cognition in the way it represents abstract relations. While adults possess a propositional language of thought with discrete symbols that refer to abstract relations, infants may rely instead on the juxtaposition of abstract represen- tations of individual entities. This hypothesis, set up here with the investigation of the abstract relation same, will be extended to the representation of other abstract relations. More gener- ally, the current research has laid new foundations to studying not only the content of infants’ mental representations, but also their format, in order to eventually characterize precisely not only what infants can think about, but also how infants think. ACKNOWLEDGMENTS This work was funded by a Fyssen Foundation Research Grant (2014), the Agence Nationale pour la Recherche grant ANR-16-CE28-0006 TACTIC and the collaborative McDonnell Foun- dation Grant 220020449. We thank Auriane Couderc, Emilie Serraille and Céline Spriet for their help in recruiting and testing infants; Luca Bonatti, Susan Carey, Nicoló Cesana-Arlotti and Liuba Papeo for comments on previous versions of this manuscript. REFERENCES Addyman, C., & Mareschal, D. (2010). The perceptual origins of the abstract same/different concept in human infants. Animal Cognition, 13(6), 817–833. https://doi.org/10.1007/s10071-010 -0330-0, PubMed: 20582560 Alvarez, G. A., & Cavanagh, P. (2004). 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