Conclusion	In this paper we presented a novel decoding architecture for NMT employing a hierarchical latent variable model to promote sparsity in lexical representations, which demonstrated promising application for morphologically-rich and low-resource languages. Our model generates words one character at a time by composing two latent features representing their lemmas and inflectional features. We evaluate our model against conventional open-vocabulary NMT solutions such as subword and character-level decoding methods in translationg English into three morphologically-rich languages with different morphological typologies under low to mid-resource settings. Our results show that our model can significantly outperform subword-level NMT models, whereas demonstrates better capacity than character-level models in coping with increased amounts of data sparsity. We also conduct ablation studies on the effect of feature variations to the predictions, which prove that despite being completely unsupervised, our model can in fact capture morphosyntactic information and generalize to different surface forms of words.

One drawback related to this approach, however, is that the estimation of the subword vocabulary relies on word segmentation methods optimized using corpus-dependent statistics, disregarding any linguistic notion and the translation objective, which may result in morphological errors during splitting, resulting in subword units that are semantically ambiguous as they might be used in far too many lexical contexts . Moreover, the words are generated predicting multiple subword units, which makes generalizing to unseen word forms more difficult, where some of the subword units that could be used to reconstruct a given word may be unlikely in the given context. To alleviate the sub-optimal effects of using explicit segmentation and generalize better to new morphological forms, recent studies explored the idea of extending the same approach to model translation directly at the level of characters , , which, in turn, have demonstrated the requirement of using comparably deeper networks, as the network would then need to learn longer distance grammatical dependencies . In this paper, we explore the benefit of explicitly modeling variations in the surface forms of words using methods from deep latent variable modeling in order to improve the translation accuracy in low-resource and morphologically-rich languages.

A Latent Morphology Model for Open-Vocabulary Neural Machine Translation	Translation into morphologically-rich languages challenges neural machine translation (NMT) models with extremely sparse vocabularies where atomic treatment of surface forms is unrealistic. This problem is typically addressed by either pre-processing words into subword units or performing translation directly at the level of characters. The former is based on word segmentation algorithms optimized using corpus-level statistics with no regard to the translation task. The latter learns directly from translation data but requires rather deep architectures. In this paper, we propose to translate words by modeling word formation through a hierarchical latent variable model which mimics the process of morphological inflection. Our model generates words one character at a time by composing two latent representations: a continuous one, aimed at capturing the lexical semantics, and a set of (approximately) discrete features, aimed at capturing the morphosyntactic function, which are shared among different surface forms. Our model achieves better accuracy in translation into three morphologically-rich languages than conventional open-vocabulary NMT methods, while also demonstrating a better generalization capacity under low to mid-resource settings.

Evaluation ::: Data and Languages	In order to evaluate our model we design two sets of experiments. The experiments in §SECREF8 aim to evaluate different methods under low-resource settings, for languages with different morphological typology. We model the machine translation task from English into three languages with distinct morphological characteristics: Arabic (templatic), Czech (fusional), and Turkish (agglutinative). We use the TED Talks corpora  for training the NMT models for these experiments. In §SECREF10, we conduct more experiments in Turkish to demonstrate the case of increased data sparsity using multi-domain training corpora, where we extend the training set using corpora from EU Bookshop , Global Voices, Gnome, Tatoeba, Ubuntu , KDE4 , Open Subtitles  and SETIMES . The statistical characteristics of the training sets are given in Tables TABREF16 and TABREF17. We use the official evaluation sets of the IWSLT for validating and testing the accuracy of the models. In order to increase the number of unknown and rare words in the evaluation sets we measure accuracy on large test sets combining evaluation sets from many years (Table TABREF18 presents the evaluation sets used for development and testing).

Latent variable models allow us to inject inductive biases relevant to the task, which, in our case, is word formation, and we believe that follows a certain hierarchical procedure. Our model translates words one character at a time based on word representations learned compositionally from sub-lexical components, which are parameterized by a hierarchical latent variable model mimicking the process of morphological inflection, consisting of a continuous-space dense vector capturing the lexical semantics, and a set of (approximately) discrete features, representing the morphosyntactic role of the word in a given sentence. Each word representation during decoding is reformulated based on the shared latent morphological features, aiding in learning more reliable representations of words under sparse settings by generalizing across their different surface forms. We evaluate our method in translating English into three morphologically-rich languages each with a distinct morphological typology: Arabic, Czech and Turkish, and show that our model is able to obtain better translation accuracy and generalization capacity than conventional approaches to open-vocabulary NMT.

Evaluation ::: Models	We evaluate our model by comparing it in machine translation against three baselines which constitute the conventional open-vocabulary NMT methods, including architectures using atomic parameterization either with subword units segmented with BPE  or characters, and the hierarchical parameterization method employed for generating all words in the output. We implement all architectures using Pytorch  within the OpenNMT-py framework .

Introduction	Neural machine translation (NMT) systems are conventionally trained based on the approach of maximizing the log-likelihood on a training corpus in order to learn distributed representations of words according to their sentence context, which is highly demanding in terms of training data as well as the network capacity. Under conditions of lexical sparsity, which may include the cases when the amount of training examples is insufficient to observe words in different context, and particularly in translation of morphologically-rich languages, where the same word can have exponentially many different surface realizations due to syntactic conditions, which are often rarely or ever observed in any set of collected examples, the model may suffer in learning accurate representations of words. The standard approach to overcome this limitation is to replace the word representations in the model with subword units that are shared among words, which are, in principle, more reliable as they are observed more frequently in varying context , .

Evaluation ::: Results ::: The Effect of Morphological Typology	The experiment results given in Table TABREF9 shows the performance of each model in translating English into Arabic, Czech and Turkish. In Turkish, the most sparse target language in our benchmark, using character-based decoding shows to be more advantageous compared to the subword-level and hierarchical models, due to the fact that reduced granularity in the vocabulary units might aid in better predicting words under conditions of high data sparsity. In Arabic, on the other hand, using a hierarchical decoding model shows to be advantageous compared to the character-level decoder, as it might be useful in better learning syntactic dependencies, whereas it also outperforms the subword-level decoder. Using the latent morphology model provides improvements of 0.51 and 0.30 BLEU points in Arabic and Turkish over the best performing baselines, respectively. The fact that our model can efficiently work in both Arabic and Turkish suggests that it can handle the generation of both concatenative and non-concatenative morphological transformations.

Appendix ::: The Effect of Feature Dimensions	We investigate the optimal lemma and inflectional feature sizes by measuring the accuracy in English-to-Turkish translation using different feature vector dimensions. The results given in Figure FIGREF22 show that gradually compressing the word representations computed by recurrent hidden states, with an original dimension of 512, from 500 to 100, leads to increased output accuracy, suggesting that encoding more compact representations might provide the model with a better generalization capability. Our results also show that using a feature dimension of 10 is sufficient in reaching the best accuracy.

All models are trained using the Adam optimizer  with a batch size of 100, dropout rate of 0.2, learning rate of 0.0004 and learning rate decay of 0.8, applied when the perplexity does not decrease at a given epoch. Translations are generated with beam search with a beam size of 5, where the hierarchical models implement the hierarchical beam search .

Evaluation ::: Training Settings	All models are implemented using gated recurrent units (GRU) , and have a single-layer bi-RNN encoder. The source sides of the data used for training all NMT models, and the target sides of the data used in training the subword-level NMT models are segmented using BPE with 16,000 merge rules. We implement all decoders using a comparable number of GRU parameters, including 3-layer stacked-GRU subword and character-level decoders, where the attention is computed after the 1st layer  and a 3-layer hierarchical decoder which implements the attention mechanism after the 2nd layer. All models use an embedding dimension and GRU size of 512. The latent morphology model uses the same hierarchical GRU architecture, where the middle layer is augmented using 4 multi-layer perceptrons with 256 hidden units. We use a lemma vector dimension of 150, 10 inflectional features (See §SECREF21 for experiments conducted to tune the feature dimensions) and set the regularization constant to $\rho =0.4$.

Acknowledgments	This project received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreements 825299 (GoURMET) and 688139 (SUMMA).

The results in the English-to-Czech translation direction do not indicate a specific advantage of using either method for generating fusional morphology, where morphemes are already optimized at the surface level, although our model is still able to achieve translation accuracy comparable to the character-level model.

Evaluation ::: Results ::: The Effect of Data Size	The experiment conducted in the English-to-Turkish translation direction by increasing the amount of training data with multi-domain corpora demonstrates a more challenging case, where there is a greater possibility of observing rare words, either in the form of morphological inflections due to the complex agglutinative morphology of Turkish, or ambiguous terminology raising from the multi-domain characteristics. In this experiment, the character-level model experiences a drop in performance and its accuracy is much lower than the subword-level one, suggesting that its capacity cannot cope with the increased amount of sparsity. Empirical results suggest that with increased capacity, character-level models carry the potential to reach comparable performance to subword-level models . Our model reaches a much larger improvement of 0.82 BLEU points over the subword-level and 2.54 BLEU points over the character-level decoders, suggesting that it could make use of the increased sparsity in learning more accurate representations.

Evaluation ::: Results ::: Predicting Unseen Words	In addition to general evaluation using automatic metrics, we perform a more focused analysis to illustrate the performance of different methods in predicting unseen words. We sample the sentences from the development sets which contain out-of-vocabulary words, and compute the average perplexity per character on these sentences using different NMT models, as suggested by . In general, the highest perplexities are obtained using the subword-based model, suggesting that generating unseen words using subword units is indeed increasing the difficulty of prediction, compared to the character-level which obtains the lowest perplexity. This result indicates that increased granularity aids in reducing the uncertainty during prediction. Similar to the results in §SECREF8, in Czech the values are almost comparable. Due to its stochastic nature, our model yields higher perplexity values compared to the hierarchical model, whereas the values range between subword and character-based models, possibly finding an optimal level of granularity between the two solutions.

Evaluation ::: Results ::: Feature Variations	In order to understand whether the latent inflectional features in fact capture information about variations related to morphological transformations, we try generating different surface forms of the same lemma by assigning different values to the inflectional features. We use the latent morphology model based decoder to translate the English word `go', and after sampling the lemma, we fix its value and vary the values of the inflectional features at random positions for generating different outputs. Table TABREF14 presents different sets of feature values and the corresponding outputs generated by the decoder. The model generates different surface forms for different sets of features, confirming that latent variables encode information related to the infinitive form of the verb, as well as its formality conditions, prepositions, person, number and tense. We also observe that many trials based on different feature combinations may result in the same outputs, although some feature values may not be set in a single-word context. Varying the features individually does not necessarily yield distinct changes in the output, suggesting that some features may act jointly in determining the word form.

The accuracy of each model output is measured using BLEU  and chrF3  metrics, whereas the significance of the improvements are computed using bootstrap hypothesis testing .

Question: What are the three languages studied in the paper?
Answer: Arabic, Czech and Turkish