Efficient Semiring-Weighted Earley Parsing

This paper provides a reference description, in the form of a deduction system, of Earley's (1970) context-free parsing algorithm with various speed-ups. Our presentation includes a known worst-case runtime improvement from Earley's $O (N^3|G||R|)$, which is unworkable for the large grammars that arise in natural language processing, to $O (N^3|G|)$, which matches the runtime of CKY on a binarized version of the grammar $G$. Here $N$ is the length of the sentence, $|R|$ is the number of productions in $G$, and $|G|$ is the total length of those productions. We also provide a version that achieves runtime of $O (N^3|M|)$ with $|M| \leq |G|$ when the grammar is represented compactly as a single finite-state automaton $M$ (this is partly novel). We carefully treat the generalization to semiring-weighted deduction, preprocessing the grammar like Stolcke (1995) to eliminate deduction cycles, and further generalize Stolcke's method to compute the weights of sentence prefixes. We also provide implementation details for efficient execution, ensuring that on a preprocessed grammar, the semiring-weighted versions of our methods have the same asymptotic runtime and space requirements as the unweighted methods, including sub-cubic runtime on some grammars.

UniMorph 4.0: Universal Morphology

The Universal Morphology (UniMorph) project is a collaborative effort providing broad-coverage instantiated normalized morphological inflection tables for hundreds of diverse world languages. The project comprises two major thrusts: a language-independent feature schema for rich morphological annotation and a type-level resource of annotated data in diverse languages realizing that schema. This paper presents the expansions and improvements made on several fronts over the last couple of years (since McCarthy et al. (2020)). Collaborative efforts by numerous linguists have added 67 new languages, including 30 endangered languages. We have implemented several improvements to the extraction pipeline to tackle some issues, e.g. missing gender and macron information. We have also amended the schema to use a hierarchical structure that is needed for morphological phenomena like multiple-argument agreement and case stacking, while adding some missing morphological features to make the schema more inclusive. In light of the last UniMorph release, we also augmented the database with morpheme segmentation for 16 languages. Lastly, this new release makes a push towards inclusion of derivational morphology in UniMorph by enriching the data and annotation schema with instances representing derivational processes from MorphyNet.

Exact Paired-Permutation Testing for Structured Test Statistics

Significance testing -- especially the paired-permutation test -- has played a vital role in developing NLP systems to provide confidence that the difference in performance between two systems (i.e., the test statistic) is not due to luck. However, practitioners rely on Monte Carlo approximation to perform this test due to a lack of a suitable exact algorithm. In this paper, we provide an efficient exact algorithm for the paired-permutation test for a family of structured test statistics. Our algorithm runs in $\mathcal{O}(GN (\log GN )(\log N ))$ time where $N$ is the dataset size and $G$ is the range of the test statistic. We found that our exact algorithm was $10$x faster than the Monte Carlo approximation with $20000$ samples on a common dataset.

Efficient Sampling of Dependency Structures

Probabilistic distributions over spanning trees in directed graphs are a fundamental model of dependency structure in natural language processing, syntactic dependency trees. In NLP, dependency trees often have an additional root constraint: only one edge may emanate from the root. However, no sampling algorithm has been presented in the literature to account for this additional constraint. In this paper, we adapt two spanning tree sampling algorithms to faithfully sample dependency trees from a graph subject to the root constraint. Wilson (1996)'s sampling algorithm has a running time of $\mathcal{O}(H)$ where $H$ is the mean hitting time of the graph. Colbourn (1996)'s sampling algorithm has a running time of $\mathcal{O}(N^3)$, which is often greater than the mean hitting time of a directed graph. Additionally, we build upon Colbourn's algorithm and present a novel extension that can sample $K$ trees without replacement in $\mathcal{O}(K N^3 + K^2 N)$ time. To the best of our knowledge, no algorithm has been given for sampling spanning trees without replacement from a directed graph.

On Finding the $K$-best Non-projective Dependency Trees

The connection between the maximum spanning tree in a directed graph and the best dependency tree of a sentence has been exploited by the NLP community. However, for many dependency parsing schemes, an important detail of this approach is that the spanning tree must have exactly one edge emanating from the root. While work has been done to efficiently solve this problem for finding the one-best dependency tree, no research has attempted to extend this solution to finding the $K$-best dependency trees. This is arguably a more important extension as a larger proportion of decoded trees will not be subject to the root constraint of dependency trees. Indeed, we show that the rate of root constraint violations increases by an average of $13$ times when decoding with $K\!=\!50$ as opposed to $K\!=\!1$. In this paper, we provide a simplification of the $K$-best spanning tree algorithm of Camerini et al. (1980). Our simplification allows us to obtain a constant time speed-up over the original algorithm. Furthermore, we present a novel extension of the algorithm for decoding the $K$-best dependency trees of a graph which are subject to a root constraint.

Higher-order Derivatives of Weighted Finite-state Machines

Weighted finite-state machines are a fundamental building block of NLP systems. They have withstood the test of time -- from their early use in noisy channel models in the 1990s up to modern-day neurally parameterized conditional random fields. This work examines the computation of higher-order derivatives with respect to the normalization constant for weighted finite-state machines. We provide a general algorithm for evaluating derivatives of all orders, which has not been previously described in the literature. In the case of second-order derivatives, our scheme runs in the optimal $\mathcal{O}(A^2 N^4)$ time where $A$ is the alphabet size and $N$ is the number of states. Our algorithm is significantly faster than prior algorithms. Additionally, our approach leads to a significantly faster algorithm for computing second-order expectations, such as covariance matrices and gradients of first-order expectations.

Please Mind the Root: Decoding Arborescences for Dependency Parsing

The connection between dependency trees and spanning trees is exploited by the NLP community to train and to decode graph-based dependency parsers. However, the NLP literature has missed an important difference between the two structures: only one edge may emanate from the root in a dependency tree. We analyzed the output of state-of-the-art parsers on many languages from the Universal Dependency Treebank: although these parsers are often able to learn that trees which violate the constraint should be assigned lower probabilities, their ability to do so unsurprisingly de-grades as the size of the training set decreases. In fact, the worst constraint-violation rate we observe is 24%. Prior work has proposed an inefficient algorithm to enforce the constraint, which adds a factor of n to the decoding runtime. We adapt an algorithm due to Gabow and Tarjan (1984) to dependency parsing, which satisfies the constraint without compromising the original runtime.

Efficient Computation of Expectations under Spanning Tree Distributions

We give a general framework for inference in spanning tree models. We propose unified algorithms for the important cases of first-order expectations and second-order expectations in edge-factored, non-projective spanning-tree models. Our algorithms exploit a fundamental connection between gradients and expectations, which allows us to derive efficient algorithms. These algorithms are easy to implement, given the prevalence of automatic differentiation software. We motivate the development of our framework with several cautionary tales of previous research, which has developed numerous less-than-optimal algorithms for computing expectations and their gradients. We demonstrate how our framework efficiently computes several quantities with known algorithms, including the expected attachment score, entropy, and generalized expectation criteria. As a bonus, we give algorithms for quantities that are missing in the literature, including the KL divergence. In all cases, our approach matches the efficiency of existing algorithms and, in several cases, reduces the runtime complexity by a factor (or two) of the sentence length. We validate the implementation of our framework through runtime experiments. We find our algorithms are up to 12 and 26 times faster than previous algorithms for computing the Shannon entropy and the gradient of the generalized expectation objective, respectively.

SIGMORPHON 2020 Shared Task 0: Typologically Diverse Morphological Inflection

A broad goal in natural language processing (NLP) is to develop a system that has the capacity to process any natural language. Most systems, however, are developed using data from just one language such as English. The SIGMORPHON 2020 shared task on morphological reinflection aims to investigate systems' ability to generalize across typologically distinct languages, many of which are low resource. Systems were developed using data from 45 languages and just 5 language families, fine-tuned with data from an additional 45 languages and 10 language families (13 in total), and evaluated on all 90 languages. A total of 22 systems (19 neural) from 10 teams were submitted to the task. All four winning systems were neural (two monolingual transformers and two massively multilingual RNN-based models with gated attention). Most teams demonstrate utility of data hallucination and augmentation, ensembles, and multilingual training for low-resource languages. Non-neural learners and manually designed grammars showed competitive and even superior performance on some languages (such as Ingrian, Tajik, Tagalog, Zarma, Lingala), especially with very limited data. Some language families (Afro-Asiatic, Niger-Congo, Turkic) were relatively easy for most systems and achieved over 90% mean accuracy while others were more challenging.