Modelling Verbal Morphology in Nen

We begin our description from the maximal case – transitive ambifixing verbs. Examples of this verb type include yis `to plant’ and waprs `to do' These verbs allow for full prefixing and suffixing possibilities. Evans (2016) provides the canonical paradigms for the undergoer prefixes, thematics and desinences. Suffix combinations are constructed by concatenating the corresponding thematic and the desinence. Between the undergoer prefix and verb stem is a directional prefix slot, available for all verb types. This slot is occupied by {-n-}¹¹1We follow linguistic convention with ‘{}’ denoting morphemes, and examples are italicised. to convey a `towards’, {-ng-} for ‘away’ or left empty to convey a directionally neutral semantic.

Middle verbs such as owabs `to speak' or anḡs `to return', are also ambifixing, but the prefixal slot is restricted to {n-} ($\alpha$–series), {k-} ($\beta$–series), {g-} ($\gamma$–series). These prefixes are person and number invariant, and mark the verb as being a dynamic monovalent verb. The prefix set is divided through the use of arbitrarily labels: $\alpha$, $\beta$, and $\gamma$. These dummy indices do not carry specific semantic values until they are unified with other TAM (Tense, Aspect, and Mood) markings on the verb Evans (2015).

Prefixing verbs have separate closed paradigms, tailored to the subtype. Prefixing verbs are mostly distinguished through semantics; positional verbs such as kmangr `to be lying down', the verb `to own/have' awans, the verb `to walk' tan and the copula verb m with its directional variants (be hither (i.e. come) or be thither (go)).

Inflectional prefixes for these verbs, mostly resemble the process with ambifixing verbs, yet the suffixes are limited. Of the 50 or so prefixing verbs, the vast majority are positional Evans (2020). An additional distinguishing feature of prefixing verbs, is the lack of infinitives. Both ambifixing and middle verbs form infinitives through suffixing -s to the verb stem. For the purposes of this study, we have listed the prefixing verb lemmas as the verb stem.

Methodologically, it is more convenient to segment a word as a classical bijective mapping between form to meaning. However, the Nen verbal system distributes information in a more complicated way. The prefixes (undergoer and future imperative) and suffixes (thematic and desinence) are not independent values. Nen verbal morphology is characterised by distributed exponence (DE); ``morphosyntactic feature values can only be determined after unification of multiple structural positions'' Carroll (2016).

There are two consequences for morphological parsing:

1. a)

   Provisional unspecified values occur regularly, whether

   1. (i)

      These involve partial specification that will be filled in later in the word-parse, such as the left-edge prefix {yaw-} (2|3 person non-singular undergoer), which will only be made more precise in its number value (dual, or plural) when the thematic is encountered after the verb stem: thus yaw-aka-ta-n `I see them<sup>22</sup>2Can also mean ‘I see you (more than two)’, resolved by combining with an appropriate free pronoun, bm ‘you (absolutive)’, but for present purposes we ignore this further complication. (more them two)', where the `non-dual’ marker {-ta-} eliminates the dual (them two) but yaw-akae-w-n `I see them (two)’, where the `dual thematic’{-w-} eliminates the plural (them more than two) reading.

   2. (ii)

      These involve semantically-unspecified prefix series which only acquire meaning when they are combined with suffixes at the other end of the word: thus {yaw-}, in the above example, belongs to the $\alpha$-series which, if it combines with the `basic imperfective’, will be given a (broadly) non-past reading, but when it combines with the `past perfective’ it will be given a past reading and when it combines with a ‘projected imperative’ it will be given a future meaning; a $\beta$-series form like {taw-}, by contrast, will have a `yesterday past’ interpretation when combining with the `basic imperfective’ suffixes but when combining with imperatives it will have a `now/immediate command’ meaning

2. b)

   More problematically, prefixes that normally have one reading (such as the yaw-example just discussed, which normally marks second/third-person non-singular objects) sometimes have to be given a different meaning (e.g. large plural intransitive subjects) if further parsing to the right encounters a ‘middle’ rather than a ‘transitive dynamic’ stem (Evans 2017, 2019).

   In principle that this means left-to-right morphological parsing is sometimes non-monotonic (particularly in the case of (b)), so that semantic values, as parsing proceeds, need to be sometimes held as provisionally unspecified, sometimes as partially specified, and sometimes as specified but subject to later override.

One of the primary motivations for choosing Nen as a case study is the phenomenon that gives rise to this combinatorial power: distributed exponence. Essentially distributed exponence is a morphological phenomenon that gives rise to some types of non-monotonicity.

In linguistics, the notion of extended exponence was first introduced by Mathews (1974) and is now commonly referred to as multiple exponence (ME). Matthews defined ME as a category that would have exponents in two or more distinct positions. Distributed exponence is a kind of ME, which involves the use of more then one morphological segment to convey meaning. It requires all relevant morphs to yield a precise interpretation of the feature value in question Carroll (2016); Harris (2017).

n-ng-owan-t-e
M:$\alpha$-VEN-set.off-ND:IPF.NP-IPF.NP.2|3SGA
\trans`You/(s)he are/is setting off.'³³3Example adapted from Evans (2020)

In the example above, no one marker marks the singular person. The information of the agent being singular is distributed across the thematic (dual/non-dual) and the desinence (single/dual/plural). If a non-dual thematic is present than the desinence cannot have dual features; the only options are singular or plural. Another morpheme present in this example is the prefix -ng- which marks the verb with the directional thither. The prefix n- marks this verb as a middle verb; it reduces the valency of the verb and yields information about the membership of the class $\alpha$. Together with the prefix, thematic and desinence, the TAM feature can be obtained.

Morphological inflection is a task of predicting a target word form from a corresponding word lemma and a set of morphosyntactic features (specifying the target slot, e.g. its part of speech (POS), tense, number, gender). For instance, a system is provided with a lemma ``to sing'' and a set of tags ``Verb; Past'' and needs to generate ``sang''. Morphological reinflection is a variation of the task when a lemma form is replaced with some other form and (optionally) its tags. The task has been traditionally solved with finite-state transducers, either hand-engineered Koskenniemi (1983); Kaplan and Kay (1994) or trainable models that rely on both expert knowledge and data Mohri (1997); Eisner (2002). In 2016 SIGMORPHON started a series of shared tasks on morphological reinflection, and neural models demonstrated superior performance when compared to finite-state or rule-based approaches, especially in high-resource languages Cotterell et al. (2016); Vylomova et al. (2020).

The data used in this study comes from a Nen verb corpus (approximately $6,000$ verb samples representing $2,231$ unique inflected forms) created by Muradoğlu (2017). This dataset is a distilled subset from the approximately 8-hour natural speech corpus for the Nen language. As such it entails a frequency sorted list of all the verb forms occurring.

The training data is a set of triples comprising a lemma, morphosyntactic features, and an inflected form (i.e. we will only focus on morphological inflection).

In the current study we conducted three experiments to address our research questions.

For our experiments, we will utilise two models that have shown superior performance in SIGMORPHON–CoNLL 2017 Shared Task on morphological reinflection in low- and medium-resource settings Cotterell et al. (2017). Both of them are essentially neural sequence-to-sequence models implemented in Dynet Neubig et al. (2017). In addition, we also compare the results with a simple non-neural baseline used in 2017–2018 tasks on morphological reinflection Cotterell et al. (2017, 2018).

The hyperparameters of the models are set to the values reported in the corresponding papers as per Table 1.

We analysed the errors produced in prediction following the taxonomy laid out by Gorman et al. (2019); Di et al. (2019).

We have taken a hierarchical approach to our error classification; whereby if more than one error is present, the category higher up is reported. For example, if a predicted form exhibits both target and allomorphy errors (error types are described in the following subsections), then only the target error is reported. The motivation for this lies in the nature of the error; free variation is technically not even an error. By contrast, misapplication of a morphophonological rule does indeed yield an incorrect form. Additionally, we have marked Target errors higher up as the system cannot be expected to correctly predict a form if the gold standard is incorrect. The hierarchy is as follows: Target$>$Stem$>$Allomorphy$>$Free Variation. 3 Table 3 summarises the types of errors across the different training sizes for each model. Overall, for both systems allomorphy errors remain relatively unimproved between the ALL and HR setting, but show a leap of reduction from the LR to MR conditions. Free variation errors are more prevalent in the ALL setting. This is probably a consequence of seeing more of the golden data and thus observing more of the systematic variations. This also explains why these errors reduce in number for the HR setting. The target errors are consistent across each experiment, as these are systematic issues with the gold data. Interestingly, stem errors reduce in the HR setting. This is despite the use of hallucinated data.

In Experiment 2, we tested the effects of training set composition; in other words, the informative nature of each verb type.

As mentioned above, the ambifixing verb class has the largest combinatorial space, reducing in size as we consider middle and prefixing verbs, respectively. Another way to consider this would be by providing comprehensive lists of the morphemes in a given language (such as Bickel and Nichols (2005); Shosted (2006)). Thus, the complexity of an inflectional system is measured by enumerating the number of inflectional categories and the range of available markers for their realisation (i.e. E-complexity). The bigger the number, the more complex the resulting system is.⁷⁷7Although more recent works have explored the issues with E-complexity Ackerman and Malouf (2013), we use it here as a guiding principle and acknowledge that further work is required to make a more nuanced statement. With this in mind, we would expect that, given the same training size for each verb type, the ambifixing would perform the worst,⁸⁸8The combinatorial space for a transitive verb is $1,740$ cells Muradoglu et al. (2020) then the middle followed by the prefixing verbs. Our results, shown in Table 4, confirm this hypothesis.

More revealing than the overall accuracy for each set and model combination, is a decomposition of accuracy according to the verb class. Table 5 summarises the performance for each category according to verb class. Unsurprisingly, when the training set contains only one type of verb, it performs best for the type of verb seen in the training data.

From a linguist perspective, with principle parts from the middle verbs (mainly the suffixal system, recall that the middle verb takes a dummy prefix to reduce valency) and prefixing verbs (prefixal paradigm) we can construct the full paradigm available to ambifixing verbs. The results presented here show no such compositionality; instead, we see a simple correspondence to verb type observed.

As expected, we see the weak leaking or overlap between ambifixing and middle verbs, with very little transferability from prefixing to other verb types. It highlights the importance of tag choice; middle verbs have a [M] tag for the undergoer prefix, to mark the dummy prefix. If this tag were absent, would we see more transferability between ambifixing and middle verbs? Linguistically, no information would be lost as the absence of this tag still allows for the middle verbs to be clustered together.

Experiment 3, entailed testing the systems with an unseen feature bundle and analysing the predicted forms, to gauge whether the models learnt syncretic behaviour.

As can be seen by the suffixal paradigm found in Evans (2016),⁹⁹9Table 23.14 (pg 563) and Table 23.16 (pg 565) where both numbers are available, almost all the TAM categories exhibit syncretism across the second and third-person singular actor. The past perfective slot is the only case with distinct forms for the second and third singular person numbers. We are testing the prediction of an exception. The second singular is formed with {-nd-$\emptyset$-} and the third-person singular with the {-nd-a} suffix. We note the similarity between the second singular and dual forms, where the second dual is {-a-nd}. This becomes particularly pertinent when a vowel is inserted between consonants for ease of articulation but must also adhere to vowel harmony. In such cases, the second dual and second singular may appear the same.

Using the Aharoni and Goldberg (2017) architecture, the model incorrectly predicts 81 out of the 100 test forms as the third singular perfective category with the suffix {-nd-a} instead of {-nd–$\emptyset$-}. Four forms predicted correctly (likely due to the similarity between the surface forms of the second-person dual and singular tags) and the remaining fifteen distributed across second-person dual and plural actor of the same TAM category, second/third singular for the imperfective non-prehodiernal TAM category, and several instances of nonce inflections such as {-ngt} or {-ngw}.

Similarly, the Makarov and Clematide (2018) system overwhelmingly predicts the unseen second singular form to be syncretic with the third singular (90 out of the 100 forms are predicted as such). Of the remaining ten instances three are correct, four are incorrectly modelled as the imperfective imperative (yet given the prefixing series is $\alpha$, the future imperative prefix is absent) and one of each: second/third imperfective non-prehodiernal, second/third neutral preterite or second dual past perfective.

From these results, it is clear that such systems not only observe patterns that are directly stipulated through annotation but also others that may be inferred from the data. It is important to note this behaviour, particularly in cases such as the one presented here as the verb corpus only entails two instances of the second singular past perfective.