# CONCEPTUAL REVIEW ARTICLE
# Learning Additional Languages as Hierarchical Probabilistic Inference: Insights From First Language Processing
a b c
Bozena Pajak, Alex B. Fine, Dave F. Kleinschmidt,
c
and T. Florian Jaeger
aDuolingo, Inc.,bHebrew University of Jerusalem, andcUniversity of Rochester
We present a framework of second and additional language (L2/L*n*) acquisition motivated by recent work on socio-indexical knowledge in first language (L1) processing.
The distribution of linguistic categories covaries with socio-indexical variables (e.g.,
talker identity, gender, dialects). We summarize evidence that implicit probabilistic
knowledge of this covariance is critical to L1 processing, and propose that L2/L*n* learning uses the same type of socio-indexical information to probabilistically infer latent
hierarchical structure over previously learned and new languages. This structure guides
the acquisition of new languages based on their inferred place within that hierarchy
and is itself continuously revised based on new input from any language. This proposal
unifies L1 processing and L2/L*n* acquisition as probabilistic inference under uncertainty over socio-indexical structure. It also offers a new perspective on crosslinguistic
influences during L2/L*n*learning, accommodating gradient and continued transfer (both
negative and positive) from previously learned to novel languages, and vice versa.
**Keywords** second language acquisition; hierarchical probabilistic inference; statistical
learning; speech adaptation
We would like to thank four anonymous reviewers, whose comments and suggestions have been
extremely helpful in revising the manuscript. We are especially grateful to Lourdes Ortega, who
went far beyond her duty in providing invaluable insights and assisting us with the revisions.
This research was supported by an NIH postdoctoral fellowship to BP (NIH Training Grant T32-
DC000035 awarded to the Center for Language Sciences at University of Rochester), an NSF
Graduate Research Fellowship to DK, an NIH postdoctoral fellowship to AF (NIH Training Grant
T32-HD055272), and by the Eunice Kennedy Shriver National Institute of Child Health & Human
Development of the National Institutes of Health under Award Number R01HD075797 to TFJ.
The content is solely our responsibility and does not necessarily represent the official views of the
National Institutes of Health.
Correspondence concerning this article should be addressed to Bozena Pajak, Duolingo, Inc.,
5533 Walnut Street, 3rd floor, Pittsburgh, PA 15232. E-mail: bozena@duolingo.com
---
## Introduction
Infants are born with the ability to learn any of the world’s languages.
Additional languages can be acquired throughout the life span, but the ability
to achieve nativelike proficiency declines with age of first exposure (Hakuta,
Bialystok, & Wiley, 2003; Stevens, 1999). What then are the constraints on
second and third (or additional) language (L2/L*n*) acquisition in adulthood?
One known constraint is that learning new languages as an adult is plagued
by negative transfer from the native language (L1), which occurs when the
L1 and the target language differ with respect to specific linguistic properties,
and the learner incorrectly applies the L1 norm to the L2/L*n*. However, prior
native language knowledge has also been found to facilitate learning: At least
for some grammatical features, learners have an easier time acquiring L2/L*n*
properties that already are present in their L1. Standard approaches, from both
the emergentist and the nativist traditions, generally agree that L1 knowledge
plays an important role in learning subsequent languages (for overviews, see
O’Grady, 2008; Odlin, 2013; White, 2012). Therefore, understanding precisely
how and when prior language knowledge leads to interference or facilitation is
a pressing question in research on L2/L*n* acquisition.
In this article, we outline a unified framework of both L1 adaptation and
L2/L*n* learning as continuous probabilistic inference in response to language
input. This framework, we argue, helps reconceptualize the nature of transfer
(or crosslinguistic influences) from prior language knowledge. On the one
hand, L2/L*n* learning is known to be extremely difficult: Learners struggle with
pervasive interference from previously learned languages and rarely approach
native-speaker levels of proficiency. On the other hand, there is a growing
literature, as we describe below, demonstrating the astonishing flexibility of
adults to learn the statistical properties of languages that they are exposed to
in the lab. The theoretical framework we propose brings a new perspective to
bear on these seemingly contradictory findings.
At the heart of the proposed framework lie the hypotheses that (a) adult
language learners perform continuous probabilistic/statistical inference on their
language input and that (b) this inference process is sensitive to the underlying
socio-indexical structure of their linguistic environment, by which we mean
talker identity and linguistic generalizations across talkers (e.g., by gender,
age, dialect, foreign accent). The first hypothesis is shared with many previous
proposals (discussed below), though, as we argue, some of its consequences
are still underappreciated. The second insight—that probabilistic inference
and learning should take into account learners’ probabilistic, hierarchically structured implicit beliefs about the socio-indexical structure of their linguistic
1
environment—is underexplored in research on L2/L*n* acquisition.
We distinguish variability due to socio-indexical structure from variability
due to linguistic context, such as surrounding sound segments or syllable position. Such linguistic context has received comparatively more attention in L1
and L2/L*n*processing and learning (e.g., McMurray & Jongman, 2011; Nearey,
1990, 1997; Nearey & Assmann, 1986; Nearey & Hogan, 1986; Smits, 2001a,
2001b). Here, we are interested in dependencies beyond the linguistic context
defined in this sense. Specifically, talkers differ in their realization of phonetic
contrasts (e.g., Peterson & Barney, 1952), as they do in their lexical, syntactic,
and other preferences (e.g., Weiner & Labov, 1983). Crucially though, talkers
tend to not vary randomly. Instead, there is structure in the variability across
talkers: Some of the variability across talkers is predicted by talkers’ physiological properties (which in turn are correlated with age, gender, etc.) or by their
language background (e.g., Great Lakes vs. Texan American English). This
structured variability is what we refer to as *hierarchical indexical structure*
2
(following Kleinschmidt & Jaeger, 2015).
As we describe below, L1 processing requires listeners to overcome—and,
in fact draw on—variability between talkers and groups of talkers in order to
achieve robust language understanding. We propose that L2/L*n* learning can be
seen as an extreme case of the same inference problem. In this view, learning to
understand a L2/L*n* constitutes the same fundamental computational problem
as adapting to a new L1 dialect or accent. Differences between L1 adaptation
and L2/L*n* learning, as well as differences between L2/L*n* learning of different
languages, are then primarily attributed to two factors: (a) differences in the
strength of the learner’s prior beliefs about the L*n* based on previous exposure
to other languages (L1 to L*n*–*1*) and (b) the similarity between these prior
beliefs and those required to robustly process the L*n.* Two critical contributions
of our framework are therefore that (a) it provides a unified view of both L1
processing and L2/L*n* learning as involving the same types of probabilistic
inferences and that (b) it helps reconceptualize the nature of transfer in L2/L*n*
acquisition by viewing it as learners’ inferences about the target language based
on their current total language knowledge. This includes rich knowledge about
talker- and group-specific distribution of linguistic categories (i.e., knowledge
about how linguistic structure is conditioned on socio-indexical structure).
Before launching into the stepwise development of our arguments, we outline our proposal and the structure of the article. The development of our
argument falls into three parts. In the first part, we discuss why implicit distributional knowledge of the covariance between linguistic and socioindexical structure is critical for robust L1 understanding. We then summarize
some of the key pieces of evidence that L1 processing, indeed, critically relies
on socio-indexical knowledge. With this background established, the second
part of our argument turns to L2/L*n* acquisition and to the exposition of the
framework we propose. We argue that L2/L*n* learners engage in probabilistic inference over the environment-specific “mini-grammars” they induced for
L1 (and other languages previously exposed to), which in turn guides their
learning of the target language. Learning a new language thus involves inferring its relationship with previously established patterns. In the final part
of our argument, we describe how this reconceptualization of L2/L*n* acquisition naturally captures aspects of L2/L*n* learning that currently lack a unifying
explanation. In particular, the proposed framework accounts for the following
five well-documented properties of L2/L*n* acquisition: (a) L2/L*n* development
is gradual, rather than being limited to an initial transfer from previously
acquired languages, and highly variable, as it involves simultaneous maintenance of multiple options for some linguistic properties; (b) transfer can apply
from any previously learned language, not only L1; (c) transfer is affected by
(actual and perceived) structural similarities between the source language and
the target language; (d) transfer is multidirectional in that it can affect previously acquired language knowledge, including the learner’s L1; and (e) transfer
involves drawing not only on the specific categories that exist in the source
language, but also on the statistical distributions over those categories.
All throughout the article, we illustrate the proposed framework within
a normative probabilistic approach that can be naturally interpreted in terms
of Bayesian inference. The central ideas behind our proposal are, however,
compatible with a few other distributional frameworks, such as, for example,
associative learning (e.g., Bates & MacWhinney, 1987; Ellis 2006a, 2006b;
MacWhinney, 1983), episodic (Goldinger, 1998) and exemplar-based approaches (Johnson, 1997; Pierrehumbert, 2003; van den Bosch & Daelemans,
2013). We discuss links to and differences from these accounts where appropriate. In developing our proposal, our primary goal is to help readers unfamiliar
with this type of framework to develop intuitions about it. We therefore avoid
mathematical notation. There are, however, computational implementations
of the proposed framework for L1 speech perception (Kleinschmidt & Jaeger,
2015; Nielsen & Wilson, 2008) and L1 sentence processing (Fine, Qian, Jaeger,
& Jacobs, 2010; Mysl´ın & Levy, 2016). Detailed development of the formal
inference framework applied to L2/L*n*processing can be found in Pajak (2012).
---
## L1 Processing as Hierarchical Probabilistic Inference Under Uncertainty
We begin by introducing two fundamental computational challenges to language understanding: (a) the speech signal is perturbed by noise, causing the
mapping between signal and linguistic categories to be nondeterministic, and
(b) this nondeterministic mapping varies between talkers. We then review what
properties a speech perception system must have in order to achieve robust language understanding despite these two challenges and what this can tell us about
the structure of the implicit linguistic knowledge underlying L1 processing.
## Recognition as Inference Under Uncertainty
There is now broad agreement that language comprehension is sensitive to
the statistics of the input (for recent reviews, see Kuperberg & Jaeger, 2015;
MacDonald, 2013). This sensitivity to linguistic distributions is evident at all
levels of linguistic organization. Even the earliest moments of speech processing exhibit sensitivity to implicit knowledge about the distributions of linguistic
categories (Feldman, Griffiths, & Morgan, 2009). The recognition of phonological categories and words is similarly sensitive to distributional knowledge (e.g.,
Bejjanki, Clayards, Knill, & Aslin, 2011; Dahan, Magnuson, & Tanenhaus,
2001; Luce & Pisoni, 1998; McClelland & Elman, 1986; Norris & McQueen,
2008). Beyond word recognition, the incremental integration of information
during sentence processing relies heavily on implicit beliefs about lexical and
syntactic distributions (e.g., Arai & Keller, 2013; MacDonald, Pearlmutter, &
Seidenberg, 1994; McDonald & Shillcock, 2003; Dikker & Pylkkanen, 2013; ¨
Tabor, Juliano, & Tanenhaus, 1997; Tanenhaus, Spivey-Knowlton, Eberhard,
& Sedivy, 1995; Trueswell, Tanenhaus, & Kello, 1993).
Drawing on the statistics of the input has, in fact, been shown to be a rational
solution to the problem of inferring linguistic categories from the speech signal
3
(e.g., Bejjanki et al., 2011; Feldman et al., 2009; Norris & McQueen, 2008).
Even in a cognitively bounded system that makes rational use of its finite
resources (e.g., including time; Griffiths, Vul, & Sanborn, 2012; Lewis, Howes,
& Singh, 2014), prediction based on the statistics of the input is a crucial
component of language understanding (for discussion, see Kuperberg & Jaeger,
2015). The speech signal is perturbed by noise from multiple sources, including
errors during speech planning, muscle noise during production, ambient noise
from the environment, and noisy neuronal responses in the perceptual system.
Although these types of noise differ in many important aspects, they have a
common consequence: Noise makes the mapping between linguistic categories
---
**Figure 1** Bayes’ rule provides a link between the probability distribution over acousticphonetic cues given categories and the classification function. We illustrate this relation
for the categories /b/ and /p/, and the voice onset time (VOT) cue, which is one of
the primary cues to voicing in English. For a given VOT value, the probability that it
corresponds to, say, a /b/ is proportional to the probability of producing that particular
VOT value given the talker intended to produce /b/.
and the acoustic signal nondeterministic and, thus, the inverse mapping from the
signal to the categories is also nondeterministic. This makes the recognition of
linguistic categories—and language understanding more generally—a problem
of *inference under uncertainty*.
Specifically, each linguistic category can be thought of as a probability distribution, a function specifying how likely each possible cue value is, given a
particular category. The rational solution to the problem of recognizing phonological categories—as examples of linguistic categories—relies on knowledge
of these distributions. Bayes’ rule describes the exact relationship between the
cue distributions and the categorization function of a rational listener. Figure 1
depicts this for the relation between voice onset time (VOT)—one of the primary cues to voicing in English—and the phonological categories /b/ and /p/.
The classification function predicted by Bayes’ rule, as shown in Figure 1,
provides a good qualitative and quantitative fit against human behavior in phonetic categorization tasks (e.g., Clayards, Tanenhaus, Aslin, & Jacobs, 2008;
Kleinschmidt & Jaeger, 2015).
The problem of inference under uncertainty is not limited to the recognition
of phonological categories, but extends across all levels of linguistic organization. Although many important questions remain about the mechanisms that
underlie such inferences, rational models have been found to provide good
qualitative and quantitative fits against human language processing at these
higher levels of linguistic organization as well (e.g., Boston, Hale, Kliegl, Patil,
& Vasishth, 2008; Demberg & Keller, 2008; Norris & McQueen, 2008; Smith
& Levy, 2013; for further references, see Kuperberg & Jaeger, 2015). Beyond
---
**Figure 2** Visualization of between-talker variability in /b/–/p/ production: distributions
of voice onset time (VOT) values for /b/ and /p/ in English (left panel) and rational
classification curves of sound tokens along the [b]–[p] continuum (right panel) given
the distributions shown on the left. The depicted data are hypothetical but plausible (for
comparison, see Allen et al., 2003).
$$
\ /{\mathfrak{b}}/{/\ \ {\mathfrak{p}}}/
$$
$$
/\mathbf{p}/
$$
robustly inferring the intended message from noisy input, implicit probabilistic
knowledge can also increase processing speed, for instance, through efficient
allocation of attentional resources (Smith & Levy, 2013).
In summary, there is converging evidence that (a) the computational systems
underlying language comprehension involve implicit probabilistic knowledge
about the statistical distributions of linguistic categories and that (b) this knowledge plays a crucial role in language understanding. However, as we discuss
next, reliance on implicit probabilistic knowledge is only beneficial to the
extent that this knowledge reflects the actual statistics of linguistics distributions. This turns out to be critical, as the probabilistic mapping between the
signal and linguistic categories is variable, changing depending on the local
environment.
## Variability in Mapping Between Signal and Linguistic Categories
Linguistic distributions change depending on the talker, genre, and other socioindexical variables. This makes linguistic distributions nonstationary, at least
from the perspective of language users. In research on speech perception, this
problem is known as lack of invariance although this term was originally used
to refer to variability in linguistic distributions due to linguistic (rather than
socio-indexical) context, such as differences in the realization of onset consonants depending on the following vowel (Liberman, Cooper, Shankweiler, &
Studdert-Kennedy, 1967; see also Nearey, 1990; Smits, 2001a, 2001b). Different talkers produce instances of the same category differently, using different
acoustic-phonetic cues or cue values (e.g., Allen, Miller, & DeSteno, 2003;
McMurray & Jongman, 2011; Newman, Clouse, & Burnham, 2001). Figure 2 illustrates this for the VOT example from Figure 1 (for further examples and
discussion, see Weatherholtz & Jaeger, 2016).
As can be seen in Figure 2, the rational solution discussed in the previous
section is only rational as long as the listener makes the correct assumption
about the mapping between acoustic-phonetic cues and linguistic categories. If
a listener assumes that the probabilistic mapping between signal and linguistic
categories is stationary, this will systematically and negatively affect language
understanding. Imagine, for example, a listener with the implicit probabilistic
beliefs corresponding to the solid blue line in Figure 2. If that listener receives
input from a talker, who produces /b/ and /p/ according to the distributions
corresponding to the dashed orange line in Figure 2, the listener will frequently
hear /p/, when the talker in fact intended to produce a /b/.
Between-talker variability thus has two immediate consequences. First,
listeners might need to adapt whatever implicit phonetic beliefs they hold
when they encounter a novel talker that deviates from previously encountered
talkers. We can think of this as learning a language model, specifying a set
of probabilistic mappings between the signal and linguistic categories for the
novel talker—essentially, a probabilistic mini-grammar for that particular talker
(Kleinschmidt & Jaeger, 2015). And second, even if a particular talker has previously been encountered, listeners are never quite certain which previously
learned language model is appropriate in the current circumstances. Put differently, between-talker variability makes language understanding a problem
of inference under uncertainty not only about linguistic categories, but also
about the appropriate language model for the current local environment. The
consequences of between-talker variability are not limited to speech perception
(although they are perhaps starkest in this domain). Rather, the logic outlined
above for speech perception extends to lexical and syntactic processing: Reliance on implicit knowledge of linguistic distribution only facilitates efficient
sentence processing if language users’ implicit beliefs sufficiently closely reflect the actual statistics of the current local environment (see Fine, Jaeger,
Farmer, & Qian, 2013; Mysl´ın & Levy, 2016; Yildirim, Degen, Tanenhaus, &
Jaeger, 2015).
## Overcoming Variability: Evidence From L1 Processing
Now that we have established the conceptual framework of inference under
uncertainty about both linguistic categories and the appropriate language model
for the current local environment, we summarize some of the key findings from
research on L1 language processing that illustrate how listeners overcome
the challenge raised by between-talker variability. We split this summary into two sections, corresponding to the two consequences of variability introduced
above. This will establish the conceptual framework that we then extend to
L2/L*n* learning.
## Learning Between-Talker Variability
Imagine a situation in which a listener encounters a novel talker whose acoustic realizations of linguistic categories (e.g., her pronunciations) deviate from
previously encountered talkers. In this situation, listeners need to adapt their im-
4
plicit beliefs about linguistic distributions for the current environment. Indeed,
a growing body of work suggests that L1 speech perception in such situations
relies on continuous, implicit statistical learning. In situations with which they
have little prior experience, listeners appear to rapidly adapt to the statistics of
the acoustic cues associated with different phonetic categories. The main source
of evidence for this comes from phonetic recalibration (or phonetic perceptual
learning) studies, where listeners hear a sound that is acoustically ambiguous
between, say, /b/ and /p/. If a listener hears this sound in a context which implies that it was intended to be a /b/ (e.g., a word that can end in /b/ but not /p/,
like *stub*), then they will recalibrate their /b/ category, classifying more sounds
on a [b]-to-[p] continuum as /b/ after exposure (e.g., Bertelson, Vroomen, &
de Gelder, 2003; Eisner & McQueen, 2006; Kraljic & Samuel, 2005; Norris,
McQueen, & Cutler, 2003; for further references, see Kleinschmidt & Jaeger,
2015).
There are two reasons to think that this adaptation is a form of probabilistic inference. First, as listeners in perceptual recalibration experiments are
exposed to more and more evidence from a particular talker, their behavior
gradually changes in ways predicted both qualitatively and quantitatively by
rational inference under uncertainty about the mapping between linguistics
cues and categories (Clayards et al., 2008; Kleinschmidt & Jaeger, 2011, 2012,
2015). The type of learning behavior that such a model predicts is illustrated
schematically in Figure 3.
Second, listeners seem to adapt not just to differences in the mean cue
values for a category, but also the variance of these category-specific cue
distributions (e.g., Bejjanki et al., 2011; Clayards et al., 2008; Kleinschmidt &
Jaeger, 2012; for further discussion, see Kleinschmidt & Jaeger, 2015). This
follows readily under a rational inference account of between-talker variability,
in which adaptation results in changes to listeners’ probabilistic beliefs about the
shape of the relevant distributions, including their variance (see Kleinschmidt
& Jaeger, 2015). Although questions remain about the precise mechanisms,
it is now clear that adaptation also occurs in more complex pronunciation
---
**Figure 3** Illustration of implicit statistical learning during perceptual recalibration
(based on Kleinschmidt & Jaeger, 2015): changes to the beliefs about the categoryspecific cue distributions based on different amounts of exposure to the recalibration
stimuli, shown as vertical dashes on the *x*-axis (left panel) and resulting changes to
the classification function (right panel). A model based on the principles of Bayesian
(or normative) inference provides a good fit against recalibration and other phonetic
adaptation behavior (Clayards et al., 2008; Kleinschmidt & Jaeger, 2011, 2012).
shifts, for example, when encountering a dialect- or foreign-accented talker
(Baese-Berk, Bradlow, & Wright, 2013; Bradlow & Bent, 2008; Weatherholtz,
2015; but see Best et al., 2015, for limitations). Further, there is evidence that
adaptation is not just specific to the linguistic input that has been observed
from a talker. Rather, adaptation can generalize to other sounds (Kraljic &
Samuel, 2006) and words (Maye, Aslin, & Tanenhaus, 2008; McQueen, Cutler,
& Norris, 2006; Weatherholtz, 2015) not heard previously from the novel
talker.
Similar adaptation to novel talkers has been observed for deviation from previously encountered phonotactics (Kraljic, Brennan, & Samuel, 2008), prosody
(Kurumada, Brown, Bibyk, Pontillo, & Tanenhaus, 2014), lexical usage (e.g.,
Metzing & Brennan, 2003; Creel, Aslin, & Tanenhaus, 2008; Grodner & Sedivy,
2011; Yildirim et al., 2015), and even syntactic distributions (Fine et al., 2013;
Farmer, Fine, Yan, Cheimariou, & Jaeger, 2014; Farmer, Monaghan, Misyak,
& Christiansen, 2011; Hanulikova, Van Alphen, Van Goch, & Weber, 2012;
Kamide, 2012). For example, Fine et al. (2013) demonstrated that listeners can
rapidly and implicitly learn the statistics of a novel local environment. Participants read sentences that had either a matrix verb or relative clause structure,
as illustrated in the following two examples:
The experienced soldiers warned about the dangers . . .
a. before the midnight raid. (*warned* as a matrix verb)
b. conducted the midnight raid. (*warned* as a participle in a relative clause)
---
At *warned about the dangers*, these sentences are temporarily ambiguous:
Participants so far do not know whether the sentence they are reading will have
the structure in (a) or in (b). This ambiguity is resolved at the underlined material
in (a) and (b), allowing participants to discover the structure of the sentence they
are reading. Therefore, reading times at the disambiguating region (underlined
in the example) provide an index of how unexpected the observed structure was
for subjects. Indeed, reading times at disambiguation are higher for subjectively
less probable structures (in this case, relative clauses) than for more probable
structures (here, matrix verbs; e.g., MacDonald, Just, & Carpenter, 1992).
If listeners are adapting to the distribution of main verbs and relative clauses
in the local environment, their implicit beliefs about these probabilities should
change. This change should be reflected in changes in the reading times for
the disambiguation region. This is indeed what Fine et al. (2013) found. For
example, when relative clauses were locally highly probable, subjects became
better at reading relative clause sentences and worse at reading main verb
sentences. In fact, fewer than 30 relative clauses were necessary to override
the expectation for matrix verbs. Evidence that these changes in reading times
indeed reflect changes in probabilistic beliefs about the distribution of syntactic
structures comes from anticipatory eye movements during spoken language
understanding (Kamide, 2012) and from event-related potentials (Hanulikova
et al., 2012). Related modeling work by Fine and colleagues suggests that
syntactic adaptation of this kind can be successfully captured using the same
Bayesian approach described above for speech perception (Fine et al., 2010;
Kleinschmidt, Fine, & Jaeger, 2012).
In summary, research on L1 processing suggests that listeners can learn
the statistics of novel local environments (e.g., a novel talker). The evidence
summarized so far leaves open whether listeners have a single language model
that they continuously adapt to adequately reflect the statistics of their recent
experience, readapting every time these statistics change. As we discuss next,
this does not seem to be the case. Rather, there is evidence that listeners
can represent several different language models as part of their implicit L1
knowledge.
## Representing Between-Talker Variability
A substantial part of the variability in the linguistic signal is systematic—it
is predictable based on socio-indexical variables like talker identity, sociolect,
dialect, accent, and so on. A comprehension system that merely relies on
continuous adaptation would fail to take advantage of this structure. Instead,
a rational solution to a world in which listeners encounter the same talker
---
**Figure 4** Schematic visualization of a hypothetical listener’s structured, uncertain beliefs about different language models (mini-grammars). Each node in the graph corresponds to a set of beliefs about language models. Dotted nodes/edges indicate uncertainty arising from the possibility of inducing new group or individual talker representations or reclassifying a representation (LJoe) across levels.
$$
\left(\mathrm {L} _ {\mathrm {J o e}}\right)
$$
repeatedly is to remember what one has learned about that talker (see
Kleinschmidt & Jaeger, 2015). Further, a rational listener should aim to learn
generalization over similar previously encountered talkers, allowing the listener
to more effectively adapt to novel talkers based on similar previous experiences.
In short, a rational listener should represent knowledge about the covariation
between linguistic features and socio-indexical features (e.g., talker identity
or talker groups), thereby capturing the systematic aspects of between-talker
variability. This idea is illustrated in Figure 4, where each node corresponds to
a language model (or mini-grammar) for a particular talker (terminal nodes) or
group of talkers.It is in this sense that a rational listener is expected to have rich
5
beliefs about the socio-indexical structure underlying the linguistic signal.
Indeed, research on speech perception provides compelling evidence in
support of this view. The most basic evidence comes from studies that have
found adaptation to a novel talker to persist over time, even after listeners
are exposed to other talkers. For example, Eisner and McQueen (2006) had
participants adapt to a novel talker and then tested them either immediately
after exposure or with a 12-hour delay. Although the latter group of participants
left the lab and received input from other talkers, Eisner and McQueen found
no difference in the strength of talker-specific adaptation between the two
participant groups (see also Goldinger, 1996). Similar evidence is beginning to emerge for sentence processing (Wells, Christiansen, Race, Acheson, &
MacDonald, 2009).
There is also evidence that listeners form novel generalizations across talkers, for instance, based on dialect- or foreign-accented speech (Baese-Berk
et al., 2013; Bradlow & Bent, 2008; Weatherholtz, 2015). Critically, listeners
draw on these generalizations during speech perception (e.g., Johnson, Strand,
& D’Imperio, 1999; Niedzielski, 1999; Strand, 1999; Walker & Hay, 2011).
For example, listeners’ interpretation of the very same acoustic information is
affected by top-down information about the group membership of the talker
who produced it (e.g., a male or female face: Johnson et al., 1999; Strand, 1999;
being informed that a talker is from Canada or Detroit: Niedzielski, 1999). Evidence of similar generalizations based on socio-indexical structure is beginning
to emerge for phonotactic (Staum Casasanto, 2008), lexical (Walker & Hay,
2011), pragmatic (Kurumada, 2013), and syntactic processing (Hanulikova
et al., 2012).
While it remains an open question how exactly listeners represent socioindexical structure, findings like these suggest that even L1 knowledge involves
rich implicit beliefs about the socio-indexical structure that underlies betweentalker variability. Listeners do not just adapt their language models to novel
talkers. They also represent these novel models, form generalization across
them, and draw on this knowledge to facilitate language understanding. As a
consequence, even a monolingual listener, when first exposed to a novel L2,
already has implicit beliefs about the way in which talkers differ from each other.
Overall, these implicit beliefs about the structure of the world are advantageous:
They allow recognition of previously encountered talkers (rather than learning
from scratch) and efficient generalization to similar talkers (rather than treating
all novel talkers as the same). In Bayesian terms, strong prior beliefs about what
types of talkers there are in the world mean that listeners need less evidence
from a novel talker to determine what type of language model will be adequate.
This in turn will mean that the language model used by the listener will more
quickly reflect the actual statistics of the talker (see Figure 3), reducing the risk
of misrecognition (see Figure 2).
However, with strong prior beliefs about the way in which talkers vary,
there is also a price to pay: When confronted with a novel talker that does not
follow any previously encountered pattern, adaptation becomes harder. This
is essentially a consequence of rational inference under uncertainty. In order
to deal with the noisy signal, which creates uncertainty, listeners combine
the bottom-up input with their prior beliefs; this means that prior beliefs can
change what listeners perceive (e.g., Feldman et al., 2009). When prior beliefs are particularly strong, they can therefore be difficult to overcome. As we
discuss next, this logic extends to L2/L*n* learning.
## L2/Ln Acquisition as Hierarchical Probabilistic Inference Under Uncertainty
Thus far, we have argued that L1 speaker knowledge is best understood as a set
of language models (or mini-grammars) that encode the hierarchical structure
of the listener’s linguistic environment and that are continuously being adapted
to incoming input. In this section, we extend this architecture to L2/L*n*learning.
We argue that a multilingual learner’s linguistic knowledge can be characterized
as a set of grammars that, similarly, capture the hierarchical indexical structure
of the linguistic environment and are continuously being adapted in response to
input from the additional languages being learned. This proposal views L2/L*n*
learning as in some sense an extreme version of the type of adaptation that even
L1 users need to master in order to overcome dialect, sociolect, and individual
differences in pronunciation, as well as other linguistic variation. Within this
framework, then, differences in learners’ ability to acquire additional languages
and the ability to adapt to new language properties (as well as general limitations
in the ability to learn) are at least to some extent a function of the amount
of accumulated knowledge that provides learners with strong biases about
how to interpret the incoming input. We begin with the critical assumptions
that underlie the proposed framework: (a) adults are able to perform implicit
probabilistic analyses on nonnative language input, (b) one of the main sources
of limitations on L2/L*n* acquisition is the learner’s prior language background,
and (c) the bilingual or multilingual environment of a language learner can be
characterized as an extension of hierarchically structured variability within L1.
## Statistical Learning in L2/Ln Acquisition
The justification for assuming adult sensitivity to statistical cues comes not
only from the work on L1 processing and adaptation we discussed earlier, but
also from a growing body of work on adult language learning (see Rebuschat,
2015). Adults have been shown to attend to statistical cues when learning novel
phonetic categories (e.g., Lim & Holt, 2011; Pajak & Levy, 2011; Wanrooij,
Escudero, & Raijmakers, 2013), word boundaries (Endress & Mehler, 2009;
Saffran, Newport, & Aslin, 1996), phonotactics (Onishi, Chambers, & Fisher,
2002), grammatical categories and dependencies (Reeder, Newport, & Aslin,
2013), as well as morphosyntactic and syntactic structure (Fedzechkina, Jaeger,
& Newport, 2012; Hudson Kam, 2009; Wonnacott, Newport, & Tanenhaus,
2008). Adult sensitivity to statistical cues has not only been demonstrated in learning a single new language, but also in tracking the statistics of multiple
languages within a single laboratory session (Gebhart, Aslin, & Newport, 2009;
Weiss, Gerfen, & Mitchel, 2009).
Questions about the role of statistical learning in L2/L*n* acquisition do,
however, remain. First, it is still largely an open question whether statistical
learning persists long enough to subserve L2/L*n*acquisition. While some recent
studies have found effects of distributional training to persist for months even
after relatively brief exposure (Bradlow, Akahane-Yamada, Pisoni, & Tohkura,
1999; Escudero & Williams, 2014), more work is needed to establish what type
of short-term statistical learning translates into long-lasting L2/L*n* knowledge.
Second, adults are known to have more difficulty than infants in attending
to certain statistical properties of a new language. A well-known example is
that of L1-Japanese L2-English learners, who have extreme difficulty learning
the /r/-/l/ distinction, both in perception and production (e.g., Miyawaki et al.,
1975). Similarly, adults appear to fail in some laboratory tasks, for example,
when learning some L2 phonetic categories from statistical cues alone (e.g.,
Goudbeek, Cutler, & Smits, 2008), when learning certain word orders in an
artificial language (Culbertson, Smolensky, & Legendre, 2012), or in some
cases of segmenting words from a continuous speech stream (Finn & Hudson
Kam, 2008; Newport & Aslin, 2004). However, despite the above findings,
we argue that learners are on average striving to be rational and that at least
some of these apparent failures of adult learners to successfully infer linguistic
categories from statistical cues are in fact not convincing counterexamples
to this claim. On the contrary, such counterexamples can be explained by
the proposed framework, as long as we keep in mind that the probabilistic
inferences learners need to conduct are limited by their cognitive resources.
## Sources of Limitations in L2/Ln Acquisition
Achieving nativelike proficiency in a nonnative language is extremely rare, and
certain errors tend to persist regardless of the amount of exposure, especially
in the domain of phonology (e.g., Han, 2004). Why is this the case and how is
it compatible with the approach we are advocating? Many researchers attribute
the difficulty of L2/L*n*learning relative to L1 acquisition to maturational factors
(e.g., Abrahamsson & Hyltenstam, 2008; Johnson & Newport, 1989). However, there is also evidence that neural plasticity for language learning is not
completely lost in adulthood, and nativelike attainment in L2/L*n* acquisition
might be possible (see Birdsong, 2009; Moyer, 2014). Some have argued that
the apparent limitations of L2/L*n* learning might at least in part be due to
differences in incentive and the time dedicated to the learning between infants acquiring their native language(s) and the typical adult L2/L*n* learner (e.g.,
Marinova-Todd, Marshall, & Snow, 2000). Others have argued that foreign accents and other apparent failures to converge against nativelike proficiency in
speech production could be at least in part a consequence of encoding one’s
social identity (Gatbonton, Trofimovich, & Magid, 2005; Moyer, 2007). These
arguments do not necessarily call into question that L2/L*n* acquisition is difficult, but they challenge the assumption that all deviations from the target L2/L*n*
are due to an inability to fully acquire the new language.
To the extent that the factors such as motivation or social identity do not
explain all the challenges and limitations in L2/L*n* learning, we believe that
many of the learning difficulties follow naturally from the hierarchical inference
framework that we propose here. In this framework, L2/L*n* learners implicitly
strive to behave rationally given the total knowledge they currently possess. In
particular, learners’ previously acquired language knowledge constitutes strong
implicit prior beliefs about the new target language. This prior knowledge contains useful information that allows learners to make fairly accurate implicit
guesses about many properties of the target language. At the same time, however, this prior knowledge can also hinder learning or even prevent learners
from attaining a native-speaker level of proficiency. This does not mean that
learners on average are not behaving rationally; it simply means that they are
trying to take advantage of their prior knowledge, which in some cases leads
them astray.
How are the limitations on L2/L*n* learning compatible with listeners’ often
rapid and seemingly effortless adaptation to the properties of L1 speech? In
fact, even in adaptation to novel L1 properties (e.g., accented speech), we
can sometimes observe the pervasive influence of L1-based prior beliefs. For
example, Idemaru and Holt (2011) showed that while listeners adjust their
speech categorization after hearing only five instances of an accented word, this
kind of statistical learning quickly asymptotes. Even after 5 consecutive days of
exposure to accented speech, listeners’ categorization responses did not reflect
the underlying sound distribution, but rather remained intermediate between
their long-term L1 representations and the target accent. This demonstrates
that learners’ prior language knowledge strongly guides (but therefore also
constrains) adaptation even in L1 use, to the point that prior knowledge can
even block full adaptation.
Given results like these, it is only natural to expect that prior language
knowledge may be strong enough to interfere with statistical learning of any
additional language, by which we mean a biasing role of previously learned language(s) when implicitly inferring the underlying structure of the new language.
---
Such blocking of statistical learning in L2 has in fact been modeled computationally. For example, McClelland, Thomas, McCandliss, and Fiez (1999)
showed that the inability of L1-Japanese speakers to perceptually separate the
English /r/ and /l/ categories naturally falls out of assuming the well-established
representations of the relevant phonetic category distributions in Japanese, thus
demonstrating computational validity of this explanation, which had previously
been offered by many others (e.g., Miyawaki et al., 1975; for a related approach
and the idea of L1 neural entrenchment, see MacWhinney, 2012). This means
that at least some failures to converge against native proficiency may be best
understood as the price that language learners pay for an efficient learning
system—a system in which the search through a vast hypothesis space (to
determine a grammar for a new language) is made more feasible by relying
on prior implicit beliefs about how language is structured. Similar points are
made by Ellis (2006a, 2006b), who discusses how apparent irrationalities of
L2 acquisition follow from principles of associative learning, or Flege (1999),
who notes how foreign accents may arise “not because one has lost the ability
to learn to pronounce, but because one has learned to pronounce the L1 so
well” (p. 125).
In this context, it is noteworthy that the L1 bias can—under some circumstances and at least to some degree—be overcome, thus suggesting that
learners’ difficulties are not all due to an intrinsic inability to learn some properties of a new language. The case of /r/-/l/ learning by L1-Japanese speakers is
a canonical example of the difficulty of L2 acquisition. Yet improved learning
has been shown even in this difficult case, as long as the learners were provided
with stronger support for distributional learning: either through adding more
variability to signal irrelevant phonetic dimensions (e.g., Lim & Holt, 2011;
Kondaurova & Francis, 2010) or by exaggerating the natural distributions until
some initial learning has taken place (e.g., Escudero Benders, & Wanrooij,
2011; Kondaurova & Francis, 2010). Based on these results, new L2 linguistic
structures will only be induced when the observed signal is sufficiently improbable (and thus unexpected) under the old L1 language model. The limitations
on L2/L*n* acquisition do not, therefore, argue against learners’ striving to be
rational. Some of these limitations are, in fact, the best possible outcomes given
the profound influence of prior language knowledge.
## Hierarchical Indexical Structure of a Multilingual Linguistic Environment
The linguistic environment of a multilingual learner is well captured with the
kind of hierarchical indexical structure that, as we have proposed, characterizes
---
**Figure 5** An example of a multilingual environment, where languages, dialects, and
talkers cluster based on similarity (L = language, G = language group, D = dialect,
S = speaker). Language-internal structure is shown only for L1, but similar structures
are present in all other languages. A specific example of this language environment is
as follows: G1 = Germanic, G2 = Romance, G2a = Western Romance, L1 = English,
L2 = Spanish, L3 = Italian, L4 = Romanian, L5 = German, D1 = American, D2 =
Chinese-accented, S1 = Mom, S2 = Brother, S3 = Joe, S4 = We i .
the environment of a monolingual speaker. For a monolingual speaker, the
structure includes clusters of talkers, dialects, and so on (cf. Figure 4). For a
multilingual speaker, on the other hand, the structure is far more complex. It
includes multiple different languages, where each language has its own internal
structure, as illustrated in Figure 5.
From a typological perspective, languages naturally cluster in terms of their
similarity. For example, in the hypothetical scenario illustrated in Figure 5,
the linguistic environment might include two groups of languages, such as
Germanic (G₁) and Romance (G₂), where the Romance group splits further
into West-Romance and East-Romance. It is in principle possible to find an
objective grouping of languages for any multilingual environment. However,
this objective grouping might differ from how the learner actually perceives
and represents languages, as we discuss in more detail in the next section.
Critically, the proposed hierarchical inference framework is based on the idea
that learners are able to represent in some way this socio-indexical structure of
their linguistic environment, although the perceived structure will deviate from
the actual structure throughout L*n* acquisition.
$$
\ \mathrm(\mathrm{G}_{2})
$$
## The Hierarchical Inference Framework in Multilingual Learning
After having discussed the three critical assumptions that underlie the proposed framework, we elaborate on our proposal that L2/L*n* learners engage in hierarchical probabilistic inference. In particular, we discuss two important
properties of the framework. First, learning occurs hierarchically: The learner
makes simultaneous (largely implicit) inductive inferences not only about the
properties of the target language, but also about the higher-level structure of
those properties. This includes assessing the overall similarities and differences
between languages in order to assign them to appropriate clusters, as well as
tracking the properties shared by all languages. These inferences rely on continuous, implicit statistical learning, which allows learners to keep adjusting
their implicit beliefs as a function of received language input. Second, learners’
inferences are probabilistic, which means that learners maintain implicit beliefs
about different possible language models, where each model is associated with
a certain degree of uncertainty, as reviewed for L1 earlier.
An example of a hypothetical multilingual listener’s structured beliefs is
shown in Figure 6, where Lanyrepresents “any language” that encompasses
all languages in the hierarchy (Pajak, 2012). It is the abstract knowledge that
emerges from all previously learned languages, capturing the learner’s implicit
beliefs as to what a generic language might look like. Lanyis related to the traditional concept of interlanguage (Selinker, 1972, 1992); the crucial difference
is that Lanyis not a representation of any particular language, but rather the
knowledge that emerges from all previously learned languages. The Lanyproposal parallels what we have proposed for the organization of L1 knowledge,
where higher-level nodes are distributions over the properties of individual
speakers, groups of speakers, dialects, and so on (see Figure 4). When considering the case of learning multiple languages, we build additional structure on
6
top of the structured representations of an individual’s L1.
$$
\mathrm{L}_{\mathrm{a n y}}
$$
$$
\mathrm{L}_{\mathrm{a n y}}
$$
$$
\mathrm{L}_{\mathrm{a n y}}
$$
$$
\mathrm{L}_{\mathrm{a n y}}
$$
The inferred clusters in the hierarchy reflect the perceived structural similarities between the languages. The closer two languages are in the inferred
structure, the stronger the learner’s implicit beliefs that they share many properties. For an ideal learner, the inferred structure would correspond to the
objective typological similarities between languages. For actual learners, however, the perceived similarities between languages will be distorted. In particular, learners may view languages as more similar due to learning them under
similar circumstances (e.g., classroom instruction) or due to top-down beliefs
about language relatedness. Furthermore, these inferences are also modulated
by the degree of uncertainty about previously learned languages, which is in
turn determined by language proficiency, recency and regularity of use, and
so on (see also Rothman, 2015, for a discussion of the factors that might be
involved in how L3/L*n* learners implicitly assess between-language similarity).
The role of these additional factors is expected to be particularly prominent in
---
**Figure 6** Schematic visualization of a hypothetical listener’s structured, uncertain beliefs about different language models, both within a single language (as shown for
LEnglish) and across languages. Each node in the graph corresponds to a set of beliefs
about language models. Dotted nodes/edges indicate uncertainty arising from the possibility of inducing new group or individual speaker representations or reclassifying a
representation (LJoe) across levels.
$$
\mathrm{L_{E n g l i s h}}
$$
$$
\ \mathrm(\mathrm{L}_{\mathrm{J o e}})
$$
the initial stages of acquisition, when the evidence from the target language
input is limited. Later on we discuss how these aspects of the framework relate
to empirical findings in L2/L*n* acquisition.
Most critically, the hierarchical inference framework redefines the concept
of language transfer. Instead of viewing it as a direct transfer of properties
from a known language to the target language at the outset of acquisition,
crosslinguistic influences occur in this framework indirectly via Lany,aswell
as any other intermediate clusters of languages. In many other models, learners
are assumed to begin the acquisition of a language by copying all the properties of another known language (see White, 2015, for an account from the
Universal Grammar perspective and MacWhinney, 2012, from an emergentist
perspective). In our framework, the initial state of any L*n* is viewed not as the
$$
\mathrm{L}_{\mathrm{a n y}}
$$ properties directly transferred from previously known languages, but rather as
sets of hypotheses about the L*n* grammar. These hypotheses, which are the
hierarchically structured, implicit probabilistic beliefs arising from experience
with previously learned languages, guide learners’ best guesses about what
7
the new language’s underlying grammar might look like. In other words, these
hypotheses are the possible language models that the learner entertains at the
outset of acquisition, and they include the learner’s guesses about new language’s place in the inferred hierarchy. The hypotheses might be based on (a)
the learner’s implicit prior beliefs about the specific properties of any previously learned language; (b) the learner’s inferences about Lany; (c) the learner’s
top-down beliefs, if any, about the relationship of the target language to the
known languages; and (d) any learning biases. According to this framework,
then, so-called transfer from previously learned languages is observed because,
when learners posit that the L*n* is part of a given language cluster, they assume
that it shares some properties with other languages in that cluster.
$$
\mathrm{L}_{\mathrm{a n y}},
$$
## Hierarchical Probabilistic Inference and L2/Ln Learning Data
In this section, we articulate specific predictions that follow from the hierarchical inference framework and discuss them in light of empirical findings in
different areas and aspects of L2/L*n* acquisition. We structure our discussion
around five well-known properties of L2/L*n* acquisition and crosslinguistic
influences.
## L2/Ln Development Is Gradual and Variable
In the hierarchical inference framework, L2/L*n* development is characterized
by slow changes to the learner’s implicit beliefs about the target language.
Learners begin with a set of hypotheses about the target language that are
largely based on their prior beliefs about previously learned languages and then
gradually adjust those hypotheses as they obtain more input from the target
language. Given that learners continuously entertain multiple possibilities for
the underlying language model, each with a different amount of uncertainty,
we expect to observe large variability in a beginning learner’s production and
comprehension of the target language. For example, learners might accept
two possible word orders for a given structure: one that is consistent with
the L*n* input they received and another that is consistent with the equivalent
word order in their L1. As learners receive more input from the target language, and thus accumulate more evidence for the targetlike properties, they are
expected to gradually transition to relying more on their observations in the
target language relative to their prior knowledge. This means that we expect gradual changes in learners’ beliefs about the L*n* grammar, as reflected in their
language production and comprehension, slowly reducing the influence of other
known languages.
In standard linguistic formalist approaches, transfer from L1 is assumed
to occur only at the onset of L2 acquisition, and subsequent learning consists
of stages during which the initial grammar is molded into a shape approaching the target grammar (for overviews, see White, 2009, 2015). Within these
approaches, the influence of prior language knowledge is thus a part of L*n* acquisition only to the extent that learners make use of the properties transferred
at the beginning of learning. Furthermore, there is no expectation of gradual
changes in the influence of previous language knowledge, as L*n* acquisition
is assumed to proceed in stages. Recently, several researchers have criticized
these approaches for ignoring the gradience and variability in L2 development, offering new proposals that allowed for “optionality” in the grammars of
learners throughout L2 acquisition (e.g., Multiple Grammars Theory: Amaral
& Roeper, 2014; Modular On-line Growth and Use of Language: Sharwood
Smith & Truscott, 2014).
We believe that the hierarchical inference framework is a better response to
the empirical reality of gradual development than optionality. Indeed, evidence
increasingly points to a continuous development in L2/L*n* acquisition that
is characterized not only by gradual changes, but also by large variability
in using targetlike and other-known-language-like elements (e.g., Amaral &
Roeper, 2014; Wunder, 2011). This variability persists across acquisition: from
beginning learners (e.g., Rothman & Cabrelli Amaro, 2010) to advanced L2/L*n*
users (e.g., Papp, 2000), and what changes across proficiency levels is the
frequency with which different options are produced. This is exactly what falls
out of the postulates of the hierarchical inference framework.
Relatedly, it has been found that the relative frequency of producing alternative structures in a new language (e.g., expressing vs. dropping a subject
pronoun) is affected by the number of previously learned languages that use
those structures (De Angelis, 2005). For example, L1-Spanish intermediate
learners of Italian—where, as in Spanish, subject pronouns are optional—
produce a higher rate of subject pronouns in Italian if they had previously
learned two obligatory-subject languages (L2-English, L3-French) relative to
the case of having learned only one such language (L2-English). Intuitively,
this seems to suggest that learners take individual languages as evidence, based
on which they draw inferences about new languages—an idea that is inherent
to our approach.
---
## Crosslinguistic Influences Have Multiple Sources
The hierarchical inference framework naturally extends to the acquisition of
L3 and beyond, predicting that any previously acquired language may affect
learning of a new language. Given that learners infer the underlying structure
of their total linguistic environment, they must represent this information in a
way that reflects the interconnectedness of the system. No language is a priori
privileged as the source of transfer; rather, each previously acquired language
contributes evidence toward the underlying structure of the environment. This
does not mean that every language is expected to exert equal influence on the
target L*n*, as the degree of influence will depend on other factors, such as
between-language structural similarities (see below).
The hierarchical inference framework differs in this respect from other
standard approaches to L2 acquisition, which do not have an obvious way of
capturing the acquisition of L3 and beyond. When L1 properties are assumed
to transfer to the L2 initial state at the onset of acquisition, it becomes unclear
what is predicted in the case of a multilingual learner: Should transfer occur
from L1, L2, or a combination of both? The most straightforward extension
of these approaches would be to expect that L1 should be the main (or even
only) source of transfer, just as in the case of L2 acquisition, but other interpretations are also possible (e.g., see Foote, 2009). Independent proposals
have been developed in the field of third and additional language acquisition,
investigating various factors that might determine the source of transfer, as
discussed below. The main novel contribution of our framework is providing a principled way of deriving predictions for crosslinguistic influences in
both L2 and L3/L*n* acquisition, in addition to unifying it with adaptation in
L1.
The empirical findings regarding L3 acquisition are that transfer can apply
from any previously learned language, whether native or nonnative (e.g., see de
Bot & Jaensch, 2015; Rothman, Iverson, & Judy, 2011), which is precisely the
prediction of the hierarchical inference framework. For example, beginner and
intermediate learners of L3-Brazilian Portuguese with previous Spanish exposure utilize their knowledge of Spanish object clitic pronouns when learning
similar clitic pronouns in Portuguese (whether Spanish is their L1 or L2), with
English as L2 or L1, respectively (Montrul, Dias, & Santos, 2011). Another
example comes from a large-scale study of over 50,000 learners of Dutch with
varying language backgrounds, showing independent influence of both L1 and
L2 on the attained proficiency in L3-Dutch (Schepens, Van der Slik, & Van
Hout, 2016b).
---
## Crosslinguistic Influences Are Based on Perceived Similarities
In the hierarchical inference framework, the effect of previously learned languages depends on how close a given language is to the target language in
the inferred similarity-based hierarchy and how certain the learner is about a
particular inferred relation between languages. Once a learner has observed
some similarities between two languages, further similarities are hypothesized,
because the learner has likely placed the two languages close to each other in
the inferred hierarchy. This means that we expect to observe an overextension
of properties from a known language to the target language as a function of the
perceived similarity between languages, at least at the beginning of acquisition. As already discussed, the inferred similarity between languages depends
on both the objective typological relationship and other factors that distort
learners’ perception of these similarities, such as learning two languages in
similar contexts. Therefore, we predict more pervasive influence between languages that are typologically more similar, as well as those that are alike in
other respects, such as the environments in which they were learned (e.g., two
nonnative languages). However, as learning progresses and learners uncover
the properties of the new language, we expect actual typological similarities
to play an increasingly prominent role, with other factors diminishing in their
influence. Indeed, there is evidence that L2-to-L3 influence generally diminishes with increased L3 proficiency (e.g., Wrembel, 2010).
This aspect of the hierarchical inference framework is entirely consistent
with the insights developed in a large body of research on L3 acquisition, investigating what factors—including between-language similarity—determine
which previously learned language is the source of transfer to a new language (see Giancaspro, Halloran, & Iverson, 2015; Rothman, 2015). However,
there are important differences between this previous work and our proposal.
The hierarchical inference framework predicts that all previously learned languages affect transfer to a new language, and that each of these previously
learned languages does so to the extent that learners implicitly perceive it to be
similar to the new language. The previous work, on the other hand, has largely
focused on determining a single most important factor in transfer. For example,
some research has investigated whether the source language for transfer to a
new language is always the typologically most similar language (e.g., Montrul
et al., 2011; Rothman, 2011) or always another nonnative language (e.g., Bardel
& Falk, 2007; Falk & Bardel, 2011).
The hierarchical inference framework may be able to reconcile these mixed
findings and claims by providing a principled explanation of how different factors jointly contribute to the observed crosslinguistic influences. Additionally, the hierarchical inference framework predicts that the influence of a language
will depend on the certainty that learners have in their indexical hierarchically structured implicit beliefs about this language, which is a function of the
amount of previous exposure they have had to the language. This means that
the shape of the inferred hierarchy is expected to change across L*n* acquisition.
For example, at the early stages of L*n* acquisition, learners lack sufficient data
from the target language to adequately assess its actual structural similarities to
previously learned languages, and so they may overrely on other factors, such
as presumed greater similarity between two nonnative languages (e.g., L2 and
L3, due to similarities in the environments in which they were learned) than
between the native and a nonnative language (e.g., L1 and L3). As learners
receive more for input from the target language, they are expected to increasingly take into account the actual observed between-language similarities. Our
proposal thus provides a testable guiding framework for future work on the
relative influence of different previously learned languages in learning a new
language. These predictions are shared with other accounts that emphasize the
role of perceived between-language similarities or psychotypology (e.g., Rothman, 2015) but—in the hierarchical inference framework—they necessarily
follow from the underlying architecture of hierarchical probabilistic inference.
The predictions of the hierarchical inference framework regarding
similarity-based transfer are supported by existing findings. First, there is evidence that the benefit of L1 knowledge depends gradiently on the typological
distance between L1 and L2 (Schepens, Van der Slik, & Van Hout, 2013). In
particular, Schepens and colleagues examined the proficiency scores of over
50,000 learners with varying language backgrounds in an official state exam
of Dutch and found that the scores covaried systematically with morphological
similarities between Dutch and the learners’ L1 (after controlling for other
factors, such as length of residence in the Netherlands and age of arrival): The
higher the between-language similarity, the higher the exam score. In addition,
Schepens, Van der Slik, and Van Hout (2016a, 2016b) observed similar gradient
effects of typological distance in the case of L3 acquisition when examining
the L3-Dutch proficiency scores in relation to the similarities between Dutch
and the learners’ L2 (after controlling for other factors, including the learners’
L1).
Second, the hierarchical inference framework naturally captures the rather
surprising finding that learners sometimes fail to transfer the properties that are
identical in one known language and the target language, and instead appear to
transfer nontarget properties from another language—one that is, for instance,
typologically closer. One example comes from the case of L1-English beginner learners of French in their use of subject pronouns (Rothman & Cabrelli Amaro,
2010). Both English and French are characterized by obligatory subject pronouns, and L1-English L2-French learners perform very well in their subject
pronoun use in French. At the same time, equal-proficiency L3-French learners with previous knowledge of L2-Spanish frequently accept ungrammatical null-subject sentences in French. This result can be attributed to negative
transfer from L2-Spanish, which is a language that allows subject pronoun dropping. Similar examples can be found for L1-Swedish L2-English L3-German
learners in their verb placement (Bohnacker, 2006; Hakansson, Pienemann, & ˚
Sayehli, 2002). While both Swedish and German are verb-second languages,
these learners produce fewer correct verb-second utterances in German than
L1-Swedish L2-German learners with no prior exposure to English. Again,
this can be attributed to the influence of L2-English, which—unlike other Germanic languages—is not characterized by the verb-second syntax. Within the
hierarchical inference framework, this “transfer blocking by L2” (e.g., Bardel &
Falk, 2007) is explained by learners’ inferred close relationship between French
and Spanish or German and English. There are multiple possible reasons why
learners might be expected to infer such relationship in these cases: objective
typological similarities, nonnative status of both languages, or perhaps even
top-down beliefs that both languages belong to the same language group. Once
learners establish that French and Spanish or German and English are close in
the linguistic hierarchy, they overextend the similarities to the properties that
are in fact different across the two languages.
## Crosslinguistic Influences Are Multidirectional
Another aspect of crosslinguistic influence expected within the hierarchical
inference approach is its multidirectionality, where an L*n* can affect learners’
previously acquired languages, including L1. This is because the learners’ implicit beliefs capture the whole structure of their linguistic environment in a
way that is interconnected. The interconnectedness is necessary because learners continuously adjust their inferences drawing on the total of their language
knowledge. Therefore, it must be the case that inferences about L*n* should be
able to affect previously learned languages in the same way that previously
learned languages affect L*n*. The extent of this backward (or reverse) influence (e.g., L2 to L1) depends on the same factors as the forward influence
(e.g., L1 to L2): inferred between-language similarity as well as the degree of
uncertainty about each model. It is noteworthy that well-established language
representations (e.g., L1 or other languages with near-native proficiency) should
be relatively more resistant to modifications than representations of languages about which learners have more uncertainty (e.g., low-proficiency L2 or attrited
L1).
These predictions are consistent with the existing L2/L*n* acquisition data.
First, there is evidence that a L3/L*n* can affect the learner’s L2. For example,
learning a L3 that allows null subjects influences the rate at which null subjects are accepted in the learner’s L2. In particular, Aysan (2012) found that
L1-Turkish L2-English learners accept more (ungrammatical) null-subject sentences in English when they also speak L3-Italian, which allows null subjects,
relative to the case of no L3 or L3-French, which behaves like English in not
allowing null subjects. Within the hierarchical inference framework, this can
be explained by learners’ strengthened beliefs about the optionality of subject
pronouns in languages after having been exposed to Italian, which in turn leads
to an adjustment of the previously learned grammar of English. Similarly, L1-
Cantonese L2-English L3-German learners make mistakes in the tense/aspect
use in English that can be traced back to the German grammar (e.g., using
the present perfect tense for past events without current relevance), which is
not observed for L1-Cantonese L2-English learners with no L3 or a non-Indo-
European L3, such as Japanese, Korean, or Thai (Cheung, Matthews, & Tsang,
2011). The L3-to-L2 influence can also be beneficial. For example, showing
an understanding of the perfective versus imperfective aspect distinction that
exists in all Romance languages is superior in L1-English L2-Romance learners who also know another L3-Romance language (French, Italian, or Spanish)
relative to L1-English L2-Romance learners with no L3 (Foote, 2009).
Second, the influence of nonnative languages extends even to the learner’s
L1. The extreme case of this influence is L1 attrition, which involves a simplification or an impairment of the L1 system, that is, inability to produce some L1
elements (e.g., Kopke, Schmid, Kejzer, & Dostert, 2007). Under this scenario, ¨
Lanyinferences become gradually dominated by the learners’ nonnative languages, leading to increasing adjustments to the L1 grammar, especially in cases
when the dominant nonnative language is perceived as highly similar to the L1.
However, small adjustments to L1 are also expected even when L1 is still used
on a regular basis, and indeed researchers have identified other types of L2/L*n*
influence that add to the L1 system without entailing the loss of the original
L1 knowledge. Generally, the first signs of L*n* influence on L1 involve lexical
borrowings, semantic extensions, and loan translation (see Pavlenko, 2000).
For example, adult L1-Russian L2-English learners immersed in an Englishspeaking environment were found to use Russian words with broader semantic
ranges that characterize their correspondent English equivalents (Pavlenko &
Jarvis, 2002). L*n*-to-L1 influence has also been documented in other areas,
$$
\mathrm{L}_{\mathrm{a n y}}
$$ including phonology, morphosyntax, conceptual representations, and pragmatics (e.g., Chang, 2012; Dmitrieva, Jongman, & Sereno, 2010; Mennen, 2004;
Ulbrich & Ordin, 2014). For example, Dmitrieva et al. (2010) found that monolingual L1-Russian speakers use the duration of the release and closure/frication
to distinguish voiceless and partially devoiced word-final obstruents. However,
adult L1-Russian L2-English learners immersed in an English-speaking environment use two additional cues that are also used in English to encode this
contrast. In a different domain, Tsimpli, Sorace, Heycock, and Filiaci (2004)
demonstrated L2-to-L1 influence in L1-Italian and L1-Greek learners of L2-
English immersed in an English-speaking environment for a minimum of
6 years, using both L1 and L2 on the daily basis. L1-Greek speakers were
found to produce a higher rate of overt preverbal subjects in Greek than Greek
monolinguals, and L1-Italian speakers inappropriately extended the scope of
overt pronominal subjects in Italian, both of which can be attributed to the
influence of English.
## Statistical Knowledge Affects the Content of Crosslinguistic Influences
The final point concerns the exact content of transfer. While the hierarchical
inference approach does not impose any a priori constraints in this regard, it is
very much in line with recent findings suggesting that crosslinguistic transfer
involves drawing not only on the specific categories that exist in the source
language but also on the statistical distributions over those categories.
Some evidence for this comes from studies on the initial segmentation of
words out of a continuous nonnative speech stream, showing that it is affected
by the statistical regularities of the learners’ L1. For example, during initial
exposure to a new language, L1-Korean learners tend to rely on forward transitional probabilities between syllables, while L1-English learners tend to rely on
backward probabilities (Onnis & Thiessen, 2013). This can be attributed to the
fact that forward probabilities are generally more informative in Korean given
its left-branching word order, while backward probabilities are more informative in English given its right-branching word order (see corpus analyses of both
languages in Onnis & Thiessen, 2013). In a similar vein, L1-English learners
segment words in a new language based on both transitional probabilities of the
input and generalizations over L1 phonotactics (Finn & Hudson Kam, 2008);
the influence of L1 phonotactics also extends to morphological learning (Finn
& Hudson Kam, 2015). Finally, L1-Khalkha Mongolian learners are more sensitive to nonadjacent vocalic dependencies in a new language than L1-English
or L1-French learners, which has been argued to arise from Khalkha vowel harmony patterns that are absent from English or French (LaCross, 2015). Similar results have also been observed in the domain of nonnative phonetic category
learning, where the overall informativity of acoustic or articulatory cues in L1
affects the way those cues are weighed when processing and learning nonnative
phonetic categories, either facilitating or hindering acquisition (e.g., Bohn &
Best, 2012; Pajak & Levy, 2014).
All of the above findings can be captured within the hierarchical inference
framework, because learners are expected to draw on their prior beliefs in any
way that provides them with the best possible guesses about the structure of
the new language. This means that when interpreting the L*n* statistical properties, learners should be influenced not only by the specific categories that exist
in the previously learned languages, but also by statistical distributions over
those categories. This influence will lead to interference when, for example,
the L2 statistical cues conflict with L1 properties (e.g., phonotactic constraints,
phonetic categorization cues), because learners’ expectations down-weight the
statistical regularities found in the input. On the other hand, this bias can also
lead to facilitation when the L2 statistical cues align with prior expectations.
More generally, these biases allow learners to take advantage of commonalities
between languages—including, for example, those that stem from commonalities in the use of language. The original reason for the existence of such
biases is, however, likely their necessity for robust L1 speech perception and
processing (cf. Kleinschmidt & Jaeger, 2015).
## Future Research
The hierarchical inference framework raises many new questions for future research. Here we briefly review three questions that we consider of particular interest. One question concerns the exact content and shape of Lanyinferences. We
view Lanyas a distribution over language properties, encoding the information
about the likelihood of different properties across languages. In particular, Lany
inferences may consist of a range of linguistically relevant cues across different
language domains (e.g., acoustic-phonetic features, word order, animacy, case
inflection), where each cue is accompanied by a weight (or attention strength;
cf. Bates & MacWhinney, 1987; Escudero & Boersma, 2004; MacWhinney,
1997, 2008). Within this Lanyconceptualization, learners are expected to make
inferences about possible languages that go beyond the properties of each individual language they know. However, the extent and nature of generalizations
from prior linguistic beliefs is still not very well understood (see Pajak & Levy,
2014). The same problem arises within L1, for example, when generalizing between speakers or dialects/accents (Kleinschmidt & Jaeger, 2015). Therefore,
$$
{mathrm o o f}{\mathrm{L}}_{\mathrm{a n y}}
$$
$$
\mathrm{L}_{\mathrm{a n y}}
$$
$$
\mathrm{L}_{\mathrm{a n y}}
$$
$$
\mathrm{L}_{\mathrm{a n y}}
$$ pinning down the nature of Lanyinferences will only be possible by collecting
more data pertinent to crosslinguistic generalization patterns.
$$
\mathrm{L}_{\mathrm{a n y}}
$$
Another open question of great theoretical relevance concerns the way in
which learners capture the hierarchical statistical structure of their linguistic
environment. One possibility is that it is based on the overall similarity between
languages (i.e., learners adopt the assumption that all features are either similar
or not between languages), as we proposed here. The main reason to expect
that this may be the right approach is that it is a simplifying assumption that
allows learners to pool all their data, thus leading to more confident (though
less accurate) estimates of similarity across features. This may be especially
useful at the early stages of L*n* acquisition, when evidence from L*n* input
is highly limited. However, it may be that learners capture the hierarchical
statistical structure relative to a linguistic category: for example, that L1 and
L2 are similar with regard to how they realize voicing, but differ with regard to
how they encode grammatical function assignment. Yet aiming to capture the
hierarchical statistics of every cue would quickly lead to data sparseness, which
might not allow learners to make any potentially useful generalizations. The
two possibilities outlined above are not necessarily incompatible. In fact, it is
likely that the way learners capture the statistical structure of their environment
changes across L*n*acquisition. For example, learners might begin L*n*acquisition
with a simplified measure of overall similarities between languages, which
allows them to make quick generalizations at the onset of learning. Later during
acquisition, however, when learners already have access to a larger amount of
evidence about the target L*n*, they may transition to a more refined encoding
of similarities that is based on individual linguistic categories. This would let
multilingual learners take advantage of similarities between different sets of
languages for each specific aspect of the language they try to acquire (see
Rothman, 2015).
Finally, in this article we largely focused on between-language transfer during learning. However, the way learners capture the structure of their linguistic
environment is likely to also affect their inferences during online language
production and comprehension. In fact, it might be more intuitive to think of
some aspects of transfer as happening purely during processing due to languages coexisting in the brain and being coactivated (for a review, see Kroll,
Bobb, & Hoshino, 2014), as evinced, for example, in lexical intrusions (e.g.,
Poulisse & Bongaerts, 1994) or sound productions that appear to be a mixture
of two languages (e.g., Wunder, 2011). Other processes, on the other hand,
may be more intuitively interpreted as changes to the mental representations of
each language, their mutual strengths, the relations between them, or how these representations are accessed (e.g., Amaral & Roeper, 2014). A good case
in point, for example, would be facilitation in understanding the perfective
versus imperfective aspect distinction in L3-Italian due to the knowledge of
L2-Spanish (Foote, 2009). In our view, both of these two types of crosslinguistic influence play a role, and investigating how they interact is an important area for future work.
## Conclusion
We presented a new hierarchical inference framework to investigate the role of
prior language knowledge in L2/L*n* acquisition. The framework has two crucial components: (a) statistical learning as one of the mechanisms through
which adults acquire new languages and (b) representations of language
knowledge that captures the hierarchically structured linguistic environment
of bi/multilingual learners. We proposed that, in addition to the representations of each acquired language, learners also make higher-level inferences
about what linguistic structures are likely in any language. We further proposed that learning proceeds through probabilistic inference under uncertainty.
That is, learners combine new language input with their prior language knowledge and make inferences about the underlying structure of the language they
are learning, while at the same time adjusting their beliefs about any language.
We motivated this framework in recent research on L1 perception and sentence
understanding and argued that the same architecture—hierarchically organized
language models—captures both L1 and L2/L*n* processing and learning. Our
proposal builds on a large body of prior work in different domains, bringing
together insights that, as we argued, are of great relevance to L2/L*n* research.
The hierarchical inference framework (a) provides a unified view of both L1
adaptation and L2/L*n* learning as continuous probabilistic inferences in response to language input and (b) helps reconceptualize the nature of transfer
in L2/L*n* acquisition by viewing it as learners’ inferences about the target
language based on their current total language knowledge. In this way, our
approach extends previous proposals, such as Ellis’s emergentist account (Ellis, 2006a, 2006b; Ellis, O’Donnel, & Romer, 2013) or MacWhinney’s Unified ¨
Model (MacWhinney, 2008, 2012).
Final revised version accepted 18 October 2015
## Notes
1 Throughout this article, we often use the Bayesian term “belief.” For most purposes,
belief can be substituted by “knowledge.” We use the term belief as it intuitively
highlights the uncertainty learners are expected to maintain about their
---
2
representations of linguistic and socio-indexical structures. Rather than to either
know or not know something, learners are taken to hold hypotheses about the
structure of language(s) with different degrees of certainty.
It is possible that the brain treats socio-indexical and linguistic context in similar or
even identical ways. However, the two types of variability also differ somewhat in
the computational challenge they pose for speech perception (see Kleinschmidt &
Jaeger, 2015). Depending on the answer to this question, models that were
originally intended to capture variability due to linguistic context (e.g., Nearey,
1990; Smits, 2001a, 2001b) might well be extended to capture variability due to
socio-indexical structure; indeed, this link was recognized early (Liberman et al.,
1967; see Weatherholtz & Jaeger, 2016). Below, we use the term “local
environment” to refer to the socio-indexical context, thereby highlighting the
potentially qualitative difference between linguistic and socio-indexical
context.
3 Rational here is to be understood in the sense of Anderson (1990). A rational
solution is one that makes optimal use of available information.
4 Some between-talker variability might be dealt with by listener’s prelinguistic
perceptual normalization (for references and discussion, see Weatherholtz & Jaeger,
2016). However, such normalization is insufficient to account for all systematic
variability between talkers (Johnson, 2005). Instead, some variability is idiolect-,
sociolect-, or dialect-specific and has to be learned on a talker-by-talker basis (e.g.,
Johnson, 2005, Pierrehumbert, 2003).
5 There are other models that can account for listeners’ sensitivity to some
socio-indexical variables. For instance, episodic models—where speech recognition
is mediated by detailed acoustic traces of each word token ever heard (e.g.,
Goldinger, 1998; Johnson 1997; Pierrehumbert, 2003)—can account for learning
and sensitivity to socio-indexical variables like talker identity. By storing each word
as it is perceived, information about the talker’s identity is encoded implicitly in the
detailed acoustic features of the word, and any unusual pronunciations are stored
directly. However, existing episodic models struggle with generalization to unheard
words (Cutler, Eisner, McQueen, & Norris, 2010), or to groups of talkers without
additional abstraction. It is possible to extend these models by adding such
abstraction, for instance, in the form of storing episodes at sublexical,
phonetic-category-sized granularity, or “tagging” exemplars with socio-indexical
variables (Johnson, 2013), and this moves them towards implementing the sort of
computations we propose, that is, tracking the talker- or group-specific distributions
of cues for each phonetic category (see Kleinschmidt & Jaeger, 2015).
6 For a monolingual speaker, Lanyrepresentations would be predominantly influenced
by L1, but would not be equal to L1 representations. Lanycaptures learners’ guesses
about a generic language, and these guesses will necessarily include some
properties distinct from L1, such as an expectation that languages differ in their
lexicons, sound inventories, and so on, which are possibly influenced by top-down
$$
\mathrm{L}_{\mathrm{a n y}}
$$
$$
\mathrm{L}_{\mathrm{a n y}}
$$ knowledge about the possible and likely shapes of grammars. These representations
may arise from the simple realization that there exist languages other than the
learner’s L1, or from contact with nonnative speakers, among other factors. What
exactly such Lanyrepresentations for a monolingual speaker look like is an empirical
question that we leave for future work.
$$
\mathrm{L}_{\mathrm{a n y}}
$$
7 Note that this way of looking at between-language transfer is very similar to how
transfer of knowledge is understood in hierarchical Bayesian inference (see Qian,
Jaeger, & Aslin, 2012). Learners are assumed to form hierarchically structured
representations, which then facilitate both the formation of abstract rules and
principles, and their transfer to novel problems and environments.
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