Fig 3 reports the average proportion of selection of each test item by Trial Type (Gap vs. Gap+Intervention trials) and Experiment (1A or 1B).

For Gap trials (Fig 3Aa and 3Ab), we replicate the minimal category effect seen in previous results (i.e., [12]) showing that participants are more likely to select a test item belonging to the category which is minimally consistent with the exemplars (middle-small-gap, border-large-gap, middle-large-gap) than a test item outside of this category (out), both for Experiment 1A (β = -3.75, z = -12.20, p < .001) and Experiment 1B (β = -5.17, z = -11.46, p < .001; We Helmert-coded the predictor Test Item to compare the choice of out to the choice of the rest of the test items as a group). Crucially, the size of the gap between learning exemplars modulated participants’ responses. That is, participants selected middle-small-gap items more than middle-large-gap items both in Experiment 1A (M_{middle-large-gap} = 0.59, M_{middle-small-gap} = 0.98; β = 3.72, z = 7.53, p < .001) and in Experiment 1B (M_{middle-large-gap} = 0.44, M_{middle-small-gap} = 0.94; β = 3.45, z = 10.38, p < .001). Participants were sensitive to the distribution of the learning exemplars with natural stimuli but also with unfamiliar stimuli. This latter case shows that familiarity with the categories (e.g., mammals, carnivores, animals) and possible existing labels for them cannot fully explain the results.

For Intervention trials (Fig 3Ba and 3Bb), we first replicate the effect described above: participants were sensitive to the size of the gap between the exemplars, that is, they selected middle-small-gap more than middle-large-gap in Experiments 1A (M_{middle-large-gap} = 0.43, M_{middle-small-gap} = 0.97; β = 3.95, z = 9.75, p < .001) and in Experiment 1B (M_{middle-large-gap} = 0.32; M_{middle-small-gap} = 0.82; β = 2.70, z = 10.32, p < .001). Crucially, we expected that the presence of an intervening item would increase participants’ violation of a convexity constraint on word forms.

Indeed, in Experiment 1A, participants selected middle-large-gap less in Gap+Intervention trials than in Gap trials (β = -0.72, z = -3.80, p < .001). Yet, the presence of an intervening lexical item did not affect the choice of any other test items (all ps > 0.4) leading to an interaction effect: the difference between the selection rate of middle-small-gap and middle-large-gap was greater in Gap+Intervention trials than in Gap trials (β = 0.68, z = 2.51, p < .01).

In Experiment 1B, participants similarly selected middle-large-gap less in Gap+Intervention trials than in Gap trials (β = -0.61, z = -2.40, p < .05). But we should pause and note that the same was true for middle-small-gap items (β = -1.40, z = -3.96, p < .001; here the intercept reflected selection of middle-small-gap in Gap trials). This was because the intervening exemplar leX was sometimes close to middle-small-gap (and even closer than it was to middle-large-gap), thus introducing an independent reason not to select middle-small-gap in these intervention trials.

Overall, we did observe that intervening labels block the extension of a word to the minimal category including all observed exemplars, even though this effect was polluted for artificial stimuli.

We highlighted two factors that disturb the association of a word form to the single category that minimally includes all its learning exemplars: a) the size of the gap between the exemplars; b) the presence of intervening lexical items. There may be three potential interpretations for these results:

Experiment 2 was designed to distinguish between these three interpretations.

The results are presented in Fig 6. The pairs (le1, le2) and (le1’, le2’) played symmetric roles, we accordingly collapsed responses for middle-small-gap and middle-small-gap’ and responses for border-small-gap and border-small-gap’ (practically ignoring the prime sign in the report).

First, the results confirm the existence of a gap effect. Participants showed sensitivity to the sampling distribution of the exemplars, in that they selected more middle-small-gap than middle-large-gap in both the also-condition (β = 2.20, z = 11.26, p < .001) and the plural-condition (β = 1.70, z = 8.59, p < .001).

Interestingly, the minimum path (in terms of number of branches) between the learning exemplars le1 and le2 was smaller in Experiment 1A (mean for d(le1, le2) = 3.65), compared both to (le1, le2) and (le1’, le2’) in Experiment 2 (mean for d(le1,le2) = 7.16) (see S1 Supplemental material). Accordingly, we found a cross-experiment gap effect such that middle-small-gap was less selected in Experiment 2 (M = 0.75) than in Experiment 1A (M = 0.95).

Our critical expectation concerned the comparison between linguistic presentations. Test items in the gap between (le1, le2) and (le1’, le2’) were selected more often in the plural-condition than in the also-condition: this was true both for middle-large-gap (β = 0.73, z = 2.24, p < .05) and border-large-gap (β = 0.64, z = 2.13, p < .05), resulting in an interaction effect: the difference between the selection rate of middle-small-gap (serving as a baseline) and the combined selection rate of middle-large-gap and border-large-gap was greater in the plural-condition than in in the also-condition (β = 0.46, z = 2.02, p < .05; We Helmert coded the predictor Test Item to compare the choice of middle-small-gap to the choice of the middle-large-gap and border-large-gap as a group).

When presented with a plural construction (e.g., “These are blickets”), participants were more likely to associate the word to a category that spans over all the exemplars than when they were presented with a construction compatible with homophony (e.g., “This is a blicket and this is also a blicket”). This effect suggests that the gap effect documented in Experiment 1 is the footprint of homophony mapping two words with the same phonological form onto two convex concepts and not of the association of a single word to a discontinuous category.

Certainly, in line with previous results (e.g.,[21], participants were guided in part by similarity: they extended a label more to an object close to the exemplars (middle-small-gap) than to an object further away (middle-large-gap) and they extended the label less to middle-small-gap in Experiment 2 than they did in Experiment 1 due to a greater distance between the learning exemplars in Experiment 2 (Note that this is also compatible with the size principle documented by Xu and Tenenbaum (2007) [12]: since the boundaries of the categories defined by the pairs of exemplars (le1, le2) and (le1’, le2’) were less sharp than in Experiment 1A, the correct level of generalization was more uncertain in Experiment 2 than in Experiment 1A.). Yet, such similarity effects cannot explain the main result of Experiment 2 since the linguistic manipulation is realized holding constant similarity relations among learning exemplars and test items. The amount of similarity-driven generalization in participants’ responses could be quantified (see [12] for a model comparison of rule- vs. similarity-based model), but it is sufficient for our purposes to note that it cannot account for the entirety of the present effects, which are driven by linguistic manipulations alone in Experiment 2. Note that while we demonstrate that participants are sensitive to the linguistic constructions in which the words enter, we cannot tell whether the also construction alters the results in one direction (towards homophony), or whether the plural construction pushes in the opposite direction (against homophony), or both.

One may also ask whether the plural/also effect is linked to the very specific linguistic constructions involved or whether it is merely driven by the visual, two-part presentation that co-varies with these constructions in our experiments. Importantly, a visual effect (i.e., a visual “zeugma”) would make the same point as a more specific linguistic construction effect: all that matters for our argument is that there is room for two tokens of the same phonological form, either because two tokens are indeed present, or simply because the presentation introduces different labeling events.

The study of homophony allowed us to examine the existence of a convexity constraint over concepts/words. We started by defining that a concept is convex if its members form a group that share a common set of properties that holds them to be contiguous in conceptual space. The notion of contiguity in conceptual space is meaningful as long as the conceptual space is equipped with a metrical structure such as the one we defined throughout this study. One worry however is that there may not be a stable metric between abstract entities across contexts [22], such that two entities can be made arbitrarily similar by changing the dimension under consideration. For instance, one may consider that a Ferrari and a VW Beatle are closer to one another than a Ferrari and a diamond, but this similarity relation may reverse if the context involves paying attention to the value of entities. As a result, one may wonder whether the notion of conceptual similarity may not be too fragile to sustain word learning. This is an important challenge that needs to be looked at carefully, as the current results are incorporated into word learning algorithms. We submit however that in the long run this variability could be controlled if we accept that some “conceptual dimensions” are privileged: they are more stable across contexts, by default, and infants are biased to pay more attention to them (e.g., [23]). For instance, animacy may be a property that is privileged in that sense, over say color, to categorize objects. It does not always have to be the case, but on average this will create the basis for a stable set of privileged features to (partly) provide a structure for conceptual space (see also [24] for the notion of ad hoc categories and [25], [26] for the idea of concept naturalness).

The next worry then is to decide how one can objectively assess what the actual, “privileged” metric in conceptual space is and derive testable predictions from there. We have seen several responses to this issue: For instance, Xu and Tenenbaum (2007) [12] gathered subjective judgments of similarities, independently from the categorization task. In our studies, we decided on a structure of conceptual space prior to using it for our test. Specifically, our notion of convexity relied on phylogenetic trees and on an arbitrary metric over a multi-dimensional space of visual features. The hope was that there would be a sufficiently good matching between these idealized conceptual spaces and what participants would actually take to be the relations between the relevant entities. Since participants had access to the entities only through visual representations, one may worry that we over-evaluated the chances that perceptual features could determine concepts. Perceptual features as such may not be the determinant of conceptual structure, since concepts may be defined by non-observable properties. Several developmental studies show that, indeed, children prefer to draw inferences based on category membership than inferences based on perceptual appearances (e.g., [27]–[29]). Nevertheless, we use perceptual similarity as a proxy to reflect conceptual structure and follow previous work in that respect (see [12], [30]–[33]). Interestingly, we note that young children may also use such a proxy in their earliest word meaning inferences [9], [34].

The current inquiry was based on the hope that conceptual space could be approximately circumscribed by objective or scientifically based properties (e.g., phylogenetic trees). There surely has to be some correlation between such an objectively based categorization and actual, subjective categorization (e.g., [35]). Most importantly, the fact that our results come out the right way suggests a posteriori that our simplifying hypotheses are acceptable to a sufficient degree: our results could not be obtained if our assumptions to approximate the underlying conceptual structure were inappropriate.

The above discussion only refers to concepts, not to words. A natural assumption is that one word would map onto one concept, but it does not have to be so. For instance, a word could map onto a set of concepts, as if there was a word meaning dog or bone (where dog and bone here are supposed to be disjoint concepts). Our study of homophones shows that this does not happen. Instead, when a word could potentially have such a disjunctive, discontinuous meaning, a homophone is created.

As we described in the introduction, convexity holds for words and not for word forms. This distinction was not and could not be investigated through previous experimental work since word learning studies focused on non-homophonous cases, for which word forms and words are confounded (e.g., [7], [8]). As a result, nothing prevented the computational implementation of these accounts to hardwire the efficient convexity constraint on word forms as a systemic property of the learning mechanism, but the current results force us to reflect on the status and consequence of this assumption. To date, word learning models capitalize on a convexity constrain on word forms, whereby word forms map onto a single meaning that ought to be convex in conceptual space, as this is the most natural version to implement for a learner who is only exposed to word forms. One possibility is that the convexity constrain on word forms is a mere heuristic, that would provide the right outcome in most word learning circumstances, where word forms and words are equivalent. Yet, the existence of homophony suggests that learners must be able to detect cues that would help them depart from their default over-simplification, and relax their word form convexity heuristic into a concept convexity constraint. Importantly, if the learner deploys such a heuristic, the system must be able to decide when to trigger and when to silence it and we documented the empirical cues under which this switch may happen. But this leaves open a fundamental question about when the system is capable of such a sophistication: should we assume that words and the abstract notion of word forms are both primitive of the learning system? This would be an interesting and striking innateness type of claim, which should be assessed carefully. We saw that by specializing on a subset of cases (neglecting homophony), current word learning accounts missed to address that discussion (and actually ended up banning homophony from the system entirely).

Let us illustrate with another example showing that the assumptions behind word learning algorithms should be scrutinized with care when they focus their attention on a subclass of phenomena. Xu and Tenenbaum (2007) [12] propose a rational use of co-occurrences of words and objects to learn the meaning of words. But this crucially applies to content words only. Function words, however, occur in all sorts of contexts and may co-occur with all possible objects, in principle. Hence, without further assumptions, the model predicts that words like “the” or “and” mean the same as “thing” or “stuff”, which also co-occur with any kind of object. Arguably, learners deploy a different strategy to learn content words and function words (see relatedly [36] for the use of a different strategy for learning numerical concepts). But how does the learning system separate hypothesis spaces and learning algorithms for content words and function words? Ideally, one would propose a device, say a sorting algorithm, which capitalizes on differences between these words to orient function words and content words to the right learning algorithms for principled reasons (see, e.g., [37] for empirical facts about the relative frequency of function and content words that could be the input of such a sorting mechanism). But until such a mechanism is exhibited, the separation of word learning into sub-algorithms which selectively apply to different classes of words comes at the cost of presupposing that learners innately expect the distinction between these classes (i.e. that languages contain both function words and content words, or that languages contain homophones and non-homophones to go back to our central case).

In sum, current word learning accounts break the learning problem into manageable pieces of the puzzle, studying object labels, ambiguous words, functions words or numerical concepts separately. A reconciliation of these pieces into a single solution may be technically easy; one could say that the system “expects” these differences. But it has rich consequences because in the absence of a more complete picture, it amounts to postulating that subtle and quite specific phenomena such as the distinction between function words and content words or the existence of homophony have an innate basis.

There is a rich literature distinguishing homophony from polysemy. In short, polysemy is taken to be a form of motivated homophony, by which a word has two related meanings, with possibly systematic variation (e.g., [38]–[41]). For example, an object may take the same label as the artist who made it (e.g., Picasso / a Picasso) and this process is productive (e.g., “The museum owns a Mandela” would lead one to infer that Nelson Mandela was a painter). The current literature assumes that such productivity is caused by the presence of generative lexical or conceptual structures that allow meanings to be generated from the context (e.g., [40], [41]). As a result, the representation of polysemous words, for which different meanings are generated from a single entry, is different from the representation of homophones, for which different meanings are stored separately (e.g., [42]–[44]).

We showed that a word is more likely to yield homophony if it labels different portions of the conceptual space. In its simplest version, this would entail that learners would postulate homophony when facing polysemy, as the meanings of a polysemous word also label distant locations in conceptual space (e.g., Picasso, a human man and its painting, an artifact). Yet we know that this is not the case: Children as young as 4 years of age are able to distinguish polysemy from homophony ([45], [46]). Thus, any account of word learning must be able to explain how learners distinguish between homophony and polysemy, surely, capitalizing on the systematic link that exists between the different meanings of a polysemous word, a systematic link which exists even if the meanings are separated in conceptual space.

Depending on how we assume that polysemy is represented, the challenge may take a different form. For the sake of concreteness, assume that polysemy is underlined by Meaning Shift operations, MS, which transform the meaning of a word in systematic ways, (e.g., in the Picasso/Mandela example above, the relevant MS could be akin to “a piece of art made by…”) (see however [47], [48] for the hypothesis that the interpretation of polysemic words depends on pragmatic, gricean reasoning rather than on rule-like processes that generate an extended meaning from an existing one). Hence, polysemy does not involve a different word learning process, but the discovery of yet another layer of representation, that of the MS operations, which applies to words. Hence, Picasso really is a simple word, the name of an artist, but it can be interpreted as MS(Picasso). In practice then, if a word seems to apply to a non-convex set of examples, a learner would have three choices: (i) opt out from ambiguity altogether and postulate a broad meaning for the word, (ii) postulate ambiguity: assume that the word form corresponds to two distinct words, (iii) postulate polysemy: choose one of the meaning as primitive and postulate an MS operation to account for the rest of the examples. We have shown conditions under which learners prefer (ii) over (i), the conditions under which learners prefer (iii) remain to be studied.

Through the study of homophones, our studies uncover several factors that play an important role in revealing the existing constraints on how words associate with concepts in general. An important open question is whether these factors influence word learning during the earliest stages of word acquisition (see Dautriche, Chemla & Christophe, in press, for initial investigations with 4 year olds). While studying adults may inform us about the general strategies involved in word learning [49], children have different cognitive resources and biases and may consequently use different strategies. We discuss four factors that could lead to the emergence of homophony in children:

In this work, we showed that a word is more likely to yield homophony if: (a) it is learnt from exemplars leaving an important gap between them (in conceptual space), (b) this gap in conceptual space is occupied by other words. We submit that encountering novel words in such situations may trigger forms of word representations which comply with concept convexity. More generally, we argue that incorporating homophony and other challenging word learning phenomena into current word learning accounts, will provide a better understanding of learners’ implicit knowledge and assumptions about how word forms map onto meanings.