SlowGuess/ACL_2020_OCR huggingface dataset:
Transducer-Based Hard-Attention We further experiment with a transducer-based hard-attention model (Makarov and Clematide, 2018a). Unlike widely used soft-attention sequence-to-sequence models (Bahdanau et al., 2015), which predict the target tokens directly, it predicts edit action sequences to transform the input sequence into outputs, and it disposes of a hard attention mechanism. We denote the surface form change grouping in combination with this system as PCS-III-H.
To evaluate our approach in a real-world setting, we restrict our data to resources typically available to a field linguist: a small written corpus ( $\leq 100\mathrm{k}$  tokens) and a small lexicon.
For our corpora, we use the JHU Bible Corpus (McCarthy et al., 2020), which allows future work to build systems in 1600 languages. The Bible is frequently available even in low-resource languages: Ethnologue identifies 3,995 written languages, and the New Testament has been translated into 2,246. The Bible is also highly representative of a language's core vocabulary: Resnik et al. (1999) find high overlap with both the Longman Dictionary of Contemporary English (Summers and Gadsby, 1995) and the Brown Corpus (Francis and Kucera, 1964). Furthermore, the Bible is multiparallel and, thus, allows for a fair comparison across languages without confounds like domain.
For evaluation of our methods only, we additionally obtain ground-truth morphological paradigms from UniMorph (Kirov et al., 2018), which provides paradigms for over 100 languages.
From the intersection of languages in the Bible and UniMorph, we select 14 typologically diverse
9This does not result in a functional paradigm completion system, since we still lack a method to decide which surface form change to apply to realize a paradigm slot for a lemma.
$^{10}$ https://github.com/sigmorphon/conl12017/tree/master/baseline
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languages from 7 families, each of which display inflectional morphology: Basque (EUS), Bulgarian (BUL), English (ENG), Finnish (FIN), German (DEU), Kannada (KAN), Navajo (NAV), Spanish (SPA), and Turkish (TUR) as test languages, and Maltese (MLT), Persian (FAS), Portuguese (POR), Russian (RUS), and Swedish (SWE) for development. To create test data for all and development data for our development languages, we sample 100 paradigms for each set from UniMorph, then take their lemmas as our lexicon  $\mathcal{L}$ .<sup>11</sup>
5.2 Baselines and Skylines
Lemma Baseline (LB) Our first, trivial baseline predicts inflected forms identical to the lemma for all paradigm slots. We compare to one version of this baseline that has access to the ground-truth paradigm size (LB-Truth), and a second version which predicts the paradigm size as the average over the development languages (LB-Dev).
One/Ten-Shot Inflection Model Our second baseline could be seen as a skyline, since it leverages morphological information our proposed system does not have access to. In particular, we train the baseline system of CoNLL-SIGMORPHON 2017 (Cotterell et al., 2017) on one (CoNLL17-1) and ten (CoNLL17-10) paradigms. For this, we randomly sample paradigms from UniMorph, excluding those in our test data.
5.3 Hyperparameters
We choose the hyperparameters by grid search over intuitively reasonable ranges, using the development languages. No test language data is seen before final testing. Note also that only the corpus and the lexicon can be accessed by our system, and no ground-truth morphological information (including paradigm size) is given.
Our final hyperparameters are  $\lambda_{P} = 0.5$ ,  $\phi_{FC} = 0.05$ ,  $\phi_{NL} = 0.2$ ,  $\theta_{NL} = 0.5$ , and  $\lambda_{S} = 0.3$ . The window size  $2d + 1$  for feature extraction is set to 3. For CoNLL17-1, we average over the results for 10 different sampled paradigms for each language.
Systems for supervised or semi-supervised paradigm completion are commonly being evaluated using word-level accuracy (Dreyer and Eisner, 2011; Cotterell et al., 2017). However, this is not
possible for our task because our system cannot access the gold data paradigm slot descriptions and, thus, does not necessarily produce one word for each ground-truth inflected form. Furthermore, the system outputs pseudo-tags, and the mapping from pseudo-tags to paradigm slots is unknown.
Therefore, we propose to use best-match accuracy (BMAcc), the best accuracy among all mappings from pseudo-tags to paradigm slots, for evaluation. Let  $\Gamma = \{\gamma_i\}_{i=1}^N$  and  $\hat{\Gamma} = \{\hat{\gamma}_j\}_{j=1}^M$  be the set of all paradigm slots in the ground truth and the prediction, respectively, with transformation functions  $f: \Sigma^* \times \Gamma \to \Sigma^* \cup \{\emptyset\}$  and  $\hat{f}: \Sigma^* \times \hat{\Gamma} \to \Sigma^*$ ,<sup>12</sup> where  $f_\gamma(\ell) = \emptyset$  if the corresponding inflection is missing in the ground truth.<sup>13</sup> We define two types of BMAcc:
Macro-averaged BMAcc This is the average per-slot accuracy for the best possible matching of slots. For any  $\gamma_{i},\hat{\gamma}_{j}$ , we define  $g_{t}(\mathcal{L},\gamma_{i},\hat{\gamma}_{j})$  as the number of correct guesses (true positives) if  $\hat{\gamma}_j$  maps to  $\gamma_{i}$ ,  $g_{a}(\mathcal{L},\gamma_{i})$  as the number of ground truth inflections for  $\gamma_{i}$ , and  $\mathrm{acc}(\mathcal{L},\gamma_i,\hat{\gamma}_j)$  as the per-slot accuracy:
$$
\begin{array}{l} g _ {t} (\mathcal {L}, \gamma_ {i}, \hat {\gamma} _ {j}) = | \{\ell \in \mathcal {L} \mid f _ {\gamma_ {i}} (\ell) = \hat {f} _ {\gamma_ {j}} (\ell) \neq \emptyset \} | \\ \left. g _ {a} \left(\mathcal {L}, \gamma_ {i}\right) = \left| \left\{\ell \in \mathcal {L} \mid f _ {\gamma_ {i}} (\ell) \neq \emptyset \right\} \right|, \right. \tag {16} \\ \end{array}
$$
$$
\operatorname {a c c} \left(\mathcal {L}, \gamma_ {i}, \hat {\gamma} _ {j}\right) = \frac {g _ {t} \left(\mathcal {L} , \gamma_ {i} , \hat {\gamma} _ {j}\right)}{g _ {a} \left(\mathcal {L} , \gamma_ {i}\right)}. \tag {17}
$$
Then, we construct a complete bipartite graph with  $\Gamma$  and  $\hat{\Gamma}$  as two sets of vertices and  $\mathrm{acc}(\mathcal{L},\gamma_i,\hat{\gamma}_j)$  as edge weights. The maximum-weight full matching can be computed efficiently with the algorithm of Karp (1980). With such a matching  $\mathcal{M} = \{(\gamma_m,\hat{\gamma}_m)\}_{m = 0}^{\min \{N,M\}}$ , the macro-averaged BMAcc is defined as:
$$
\begin{array}{l} \operatorname {B M A c c} - \operatorname {m a c r o} (\mathcal {L}, \Gamma , \hat {\Gamma}) \tag {18} \\ = \frac {\sum_ {(\gamma_ {m} , \hat {\gamma} _ {m}) \in \mathcal {M}} \operatorname {a c c} (\mathcal {L} , \gamma_ {m} , \hat {\gamma} _ {m})}{\max \{N , M \}} \\ \end{array}
$$
The normalizing factor  $\frac{1}{\max\{N,M\}}$  rewards predicting the correct number of paradigm slots. In the case when  $\mathrm{acc}(\mathcal{L},\gamma_m,\hat{\gamma}_m) = 1$  for all  $(\gamma_{m},\hat{\gamma}_{m})\in$ $\mathcal{M}$ , BMAcc-macro  $(\mathcal{L},\Gamma ,\hat{\Gamma})$  reaches its maximum if and only if  $N = M$ .
12These are equivalent to our definition in §3, since the system does not need to predict the inflectional features.
13 In practice, we merge paradigm slots that are identical for all lemmas in both the predictions and gold standard before evaluating.
<sup>11</sup>For Basque, Kannada, and Maltese, we only take 20 paradigms for each set, due to limited availability.
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Method	Test
Test Ave.	EUS	BUL	ENG	FIN	DEU	KAN	NAV
LB-Truth	4.94 / 5.25	0.03 / 0.05 (1659)	1.89 / 2.16 (56)	20.40 / 20.40 (5)	0.96 / 0.96 (141)	15.66 / 15.68 (29)	1.18 / 1.19 (85)	2.89 / 5.39 (50)
LB-Dev	2.22 / 2.53	0.03 / 0.05 (48)	1.89 / 2.16 (48)	2.13 / 2.15 (48)	0.96 / 0.96 (48)	9.46 / 9.47 (48)	1.18 / 1.19 (48)	2.89 / 5.39 (48)
CoNLL17-1	18.70 / 18.70	0.00 / 0.00 (1659)	12.34 / 12.24 (56)	59.92 / 59.92 (5)	3.52 / 3.52 (141)	26.71 / 26.73 (29)	5.74 / 5.82 (85)	0.00 / 0.00 (50)
CoNLL17-10	35.58 / 35.56	0.00 / 0.00 (1659)	43.75 / 43.58 (56)	70.58 / 70.58 (5)	24.51 / 24.51 (141)	35.75 / 35.77 (29)	34.53 / 34.51 (85)	0.00 / 0.00 (50)
PCS-I	16.09 / 16.39	0.11 / 0.11 (51)	18.01 / 19.18 (39)	56.17 / 56.17 (6)	3.40 / 3.40 (23)	18.28 / 18.30 (19)	14.29 / 14.15 (209)	2.19 / 3.74 (8)
PCS-I+II-A	17.60 / 17.89	0.11 / 0.11 (51)	22.72 / 23.87 (52)	56.17 / 56.17 (6)	5.70 / 5.70 (71)	20.57 / 20.56 (32)	12.60 / 12.48 (237)	2.19 / 3.74 (19)
PCS-I+II-B	17.60 / 17.89	0.11 / 0.11 (51)	22.72 / 23.87 (57)	56.17 / 56.17 (6)	5.70 / 5.70 (71)	20.57 / 20.56 (32)	12.60 / 12.48 (237)	2.19 / 3.74 (18)
PCS-I+III-C	15.90 / 16.19	0.07 / 0.10 (27)	16.18 / 17.24 (16)	63.20 / 63.20 (5)	3.58 / 3.58 (15)	5.19 / 5.18 (14)	17.82 / 17.82 (162)	2.19 / 3.74 (8)
PCS-I+III-H	17.45 / 17.67	0.04 / 0.04 (27)	16.95 / 18.16 (16)	62.20 / 62.20 (5)	3.78 / 3.78 (15)	19.98 / 19.96 (14)	15.83 / 15.85 (162)	2.55 / 4.78 (8)
PCS-I+II+III-C	19.10 / 19.41	0.07 / 0.10 (27)	16.77 / 17.94 (16)	72.80 / 72.80 (4)	3.51 / 3.51 (15)	23.28 / 23.31 (13)	18.03 / 17.90 (161)	2.16 / 3.81 (7)
PCS-I+II+III-H	18.76 / 19.06	0.06 / 0.08 (27)	17.39 / 18.65 (16)	74.00 / 74.00 (4)	3.77 / 3.77 (15)	18.87 / 18.89 (13)	17.90 / 17.90 (161)	2.0 / 3.41 (7)
Method	Test	Development
SPA	TUR	Dev. Ave.	MLT	FAS	POR	RUS	SWE
LB-Truth	1.43 / 1.43 (70)	0.00 / 0.00 (120)	7.94 / 7.87	9.21 / 7.69 (24)	2.04 / 2.04 (136)	6.53 / 6.53 (76)	5.47 / 5.17 (55)	16.44 / 17.91 (11)
LB-Dev	1.43 / 1.43 (48)	0.00 / 0.00 (48)	4.33 / 4.18	4.25 / 3.55 (52)	2.04 / 2.04 (33)	6.53 / 6.53 (43)	5.47 / 5.17 (47)	3.35 / 3.65 (54)
CoNLL17-1	60.07 / 60.07 (70)	0.00 / 0.00 (120)	33.68 / 34.73	11.82 / 12.08 (24)	46.68 / 46.68 (136)	82.87 / 82.87 (76)	7.75 / 10.98 (55)	19.30 / 21.03 (11)
CoNLL17-10	76.23 / 76.23 (70)	34.88 / 34.88 (120)	49.3 / 53.02	13.07 / 13.33 (24)	64.26 / 64.26 (136)	89.54 / 89.54 (76)	19.22 / 36.75 (55)	60.41 / 61.22 (11)
PCS-I	25.04 / 25.04 (30)	7.40 / 7.40 (186)	18.72 / 21.66	12.21 / 12.00 (25)	6.36 / 6.36 (35)	36.47 / 36.47 (45)	8.24 / 20.98 (22)	30.31 / 32.47 (20)
PCS-I+II-A	31.03 / 31.03 (39)	7.33 / 7.33 (237)	17.06 / 20.77	8.45 / 8.50 (38)	6.50 / 6.50 (52)	37.14 / 37.14 (92)	12.56 / 30.66 (53)	20.65 / 21.06 (33)
PCS-I+II-B	31.03 / 31.03 (39)	7.33 / 7.33 (237)	17.02 / 20.80	7.83 / 7.88 (41)	6.51 / 6.51 (52)	37.14 / 37.14 (92)	12.95 / 31.42 (55)	20.65 / 21.06 (33)
PCS-I+III-C	24.10 / 24.10 (29)	10.73 / 10.73 (91)	22.43 / 23.78	15.79 / 11.54 (17)	6.24 / 6.24 (30)	27.22 / 27.22 (29)	11.56 / 20.48 (15)	51.36 / 53.43 (11)
PCS-I+III-H	24.36 / 24.36 (29)	11.69 / 11.69 (91)	21.27 / 23.13	14.69 / 9.94 (17)	4.90 / 4.90 (30)	28.36 / 28.36 (29)	7.98 / 20.12 (15)	50.40 / 52.34 (11)
PCS-I+II+III-C	24.01 / 24.01 (29)	11.35 / 11.35 (91)	22.74 / 24.79	8.55 / 6.73 (13)	6.34 / 6.34 (29)	31.71 / 31.71 (31)	12.02 / 21.74 (15)	55.07 / 57.41 (11)
PCS-I+II+III-H	24.30 / 24.30 (29)	10.54 / 10.54 (91)	23.53 / 25.43	12.94 / 11.22 (13)	6.35 / 6.35 (29)	32.43 / 32.43 (31)	13.37 / 22.05 (15)	52.58 / 55.12 (11)
Table 1: Macro- and micro-averaged BMAcc (in percentage) as well as the predicted number of paradigm slots (in brackets), for each method. Overall best scores are bold, and the best scores of our system are underlined.
Micro-averaged BMAcc Our second metric is conceptually closer to word-level accuracy. We start with the same process of bipartite graph matching, but instead use  $g_{t}(\mathcal{L},\gamma_{i},\hat{\gamma}_{j})$  as edge weights. Given the optimal matching  $\mathcal{M}$ , the microaveraged BMAcc is defined as:
$$
\begin{array}{l} \operatorname {B M A c c - m i c r o} (\mathcal {L}, \Gamma , \hat {\Gamma}) = \\ \frac {N}{\max  \{N , M \}} \frac {\sum_ {(\gamma_ {m} , \hat {\gamma} _ {m}) \in \mathcal {M}} g _ {t} (\mathcal {L} , \gamma_ {m} , \hat {\gamma} _ {m})}{\sum_ {\gamma_ {i} \in \Gamma} g _ {a} (\mathcal {L} , \gamma_ {i})}. \tag {19} \\ \end{array}
$$
5.5 Results and Discussion
Overall Results We present our experimental results in Table 1. The performance of our system varies widely across languages, with best results for ENG (74% BMAcc). On average over languages, our final system obtains  $18.76\% / 19.06\%$  BMAcc on the test set, as compared to the baseline of  $4.94\% / 5.25\%$  and skylines of  $18.70\% / 18.70\%$  and  $35.58\% / 35.56\%$ . Compared to versions of our system without selected components, our final system performs best on average for both development and test languages. Leaving out step II or step III leads to a reduction in performance.
Notably, variants of our system outperform the skyline CoNLL17-1, which has seen one training example and, thus, knows the correct paradigm size in advance, on EUS, BUL, ENG, FIN, KAN, NAV, TUR, MLT, RUS, and SWE. Moreover, it even outperforms CoNLL17-10 on EUS, ENG, and NAV,
which shows that unsupervised paradigm completion has promise even in cases where a limited number of training examples—but not large amounts—are available.
Differences between Languages We hypothesize that the large differences between languages—over  $73\%$  between EUS and ENG—can be explained in parts by the following reasons:
Intuitively, the larger the paradigm, the more difficult the task. If the number of slots is huge, each individual inflection is rare, and it is hard for any unsupervised paradigm completion system to distinguish true inflections (e.g., rise  $\rightarrow$  rises) from false candidates (e.g., rise  $\rightarrow$  arise). This could explain the high performance on ENG and the low performance on EUS, FIN, and FAS.
Related to the last point, in a limited corpus such as the Bible, some inflected forms might not appear for any lemma, which makes them undetectable for unsupervised paradigm completion systems. For example, a FAS paradigm has 136 slots in UniMorph, but only 46 are observed.[14] Additional statistics can be found in Table 2.
Furthermore, Assumption 2 does not hold for all languages. Surface forms can be shared between paradigm slots, as, for instance, in English for he studied and he has studied. Different languages
<sup>14</sup>We had to estimate that number based on available data in UniMorph: a slot is considered observed if at least one inflected form for that slot can be found.
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Language	ET Match	Rep. Words	Absent/Total Slots
MLT	18.13	58.18	0/16
FAS	12.10	28.66	90/136
POR	56.52	30.56	4/76
RUS	24.69	25.45	4/55
SWE	72.91	13.98	0/11
Table 2: Statistics for our development languages, computed with UniMorph.  $ET$  Match is the percentage of gold  $(\ell ,w)$  pairs that can be matched to an EDIT TREE. Rep. Words denotes the percentage of inflected forms that represent multiple paradigm slots. Absent/Total Slots is the numbers of unobservable and total slots.
show different degrees of this phenomenon called syncretism.
Pipeline Effects Different combinations of components result in major performance differences. In particular, each step of our system has the potential to introduce errors. This demonstrates a pitfall of pipeline methods also discussed in McCarthy et al. (2020): the quality of individual steps, here, e.g., EDIT TREE discovery and retrieval of additional lemmas, can greatly affect the results of PCS-II and PCS-III.
Differences in Components Details of individual components also affect the results. On the one hand, applying more than one iteration of additional lemma retrieval impacts the results only slightly, as those lemmas are assigned very small weights. On the other hand, we see performance differences  $>2\%$  between PCS-III-C and PCS-III-H for DEU, MLT, and SWE.
Analysis of EDIT TREE Quality As it is the first step in our pipeline, the quality of the EDIT TREE discovery strongly affects the performance of later components. For our development languages, we show in Table 2 the percentage of  $(\ell, w)$  pairs for which the system predicts an EDIT TREE  $\psi$  such that  $\psi(\ell) = w$  appears in the gold paradigm of  $\ell$ . This corresponds to the highest possible performance after PCS-I. FAS has the worst performance  $(12.10\%)$ , while the results for SWE are high  $(72.91\%)$ . As expected, languages with lower values here also obtain lower final results.
Analysis of Syncretism We further hypothesize that syncretism could be a source of errors, due to Assumption 2. Table 2 shows the percentage of words that are the inflected forms corresponding to multiple paradigm slots of the same lemma.
We observe that SWE has a low degree of syncretism, and, in fact, our system predicts the correct paradigm size for SWE. A high degree of syncretism, in contrast, might contribute to the low performance on MLT.
We proposed unsupervised morphological paradigm completion, a novel morphological generation task. We further developed a system for the task, which performs the following steps: (i) EDIT TREE retrieval, (ii) additional lemma retrieval, (iii) paradigm size discovery, and (iv) inflection generation. Introducing best-match accuracy, a metric for the task, we evaluated our system on a typologically diverse set of 14 languages. Our system obtained promising results for most of our languages and even outperformed a minimally supervised baseline on Basque, English, and Navajo. Further analysis showed the importance of our individual components and detected possible sources of errors, like wrongly identified EDIT TREES early in the pipeline or syncretism.
In the future, we will explore the following directions: (i) A difficult challenge for our proposed system is to correctly determine the paradigm size. Since transfer across related languages has shown to be beneficial for morphological tasks (Jin and Kann, 2017; McCarthy et al., 2019; Anastasopoulos and Neubig, 2019, inter alia), future work could use typologically aware priors to guide the number of paradigm slots based on the relationships between languages. (ii) We plan to explore other methods, like word embeddings, to incorporate context information into our feature function. (iii) We aim at developing better performing string transduction models for the morphological inflection step. By substituting the current transducers in our pipeline, we expect that we will be able to improve the overall performance of our system.
We are grateful to the group of SIGMORPHON 2020 shared task organizers as well as Alexander Erdmann for discussions about our proposed task in summer 2019. Special thanks go to Mans Hulden, who was the first to suggest an initial version of the task, and to Jason Eisner, the president of SIGMORPHON. Last but not least, we also thank Clara Vania and the anonymous reviewers for their helpful comments on this work.
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