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 O(H) where H is the mean hitting time of the graph. Colbourn (1996)’s sampling algorithm has a running time of O(Nˆ3), 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 O(K Nˆ3 + Kˆ2 N) time. To the best of our knowledge, no algorithm has been given for sampling spanning trees without replacement from a directed graph.
Abstract 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 with or without automatic differentiation software. We motivate the development of our framework with several cautionary tales of previous research, which has developed numerous inefficient 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 of the sentence length. We validate the implementation of our framework through runtime experiments. We find our algorithms are up to 15 and 9 times faster than previous algorithms for computing the Shannon entropy and the gradient of the generalized expectation objective, respectively.
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.
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 O(Aˆ2 Nˆ4) 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.
The success of neural networks on a diverse set of NLP tasks has led researchers to question how much these networks actually “know” about natural language. Probes are a natural way of assessing this. When probing, a researcher chooses a linguistic task and trains a supervised model to predict annotations in that linguistic task from the network’s learned representations. If the probe does well, the researcher may conclude that the representations encode knowledge related to the task. A commonly held belief is that using simpler models as probes is better; the logic is that simpler models will identify linguistic structure, but not learn the task itself. We propose an information-theoretic operationalization of probing as estimating mutual information that contradicts this received wisdom: one should always select the highest performing probe one can, even if it is more complex, since it will result in a tighter estimate, and thus reveal more of the linguistic information inherent in the representation. The experimental portion of our paper focuses on empirically estimating the mutual information between a linguistic property and BERT, comparing these estimates to several baselines. We evaluate on a set of ten typologically diverse languages often underrepresented in NLP research—plus English—totalling eleven languages. Our implementation is available in https://github.com/rycolab/info-theoretic-probing.
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.
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.
Gender stereotypes are manifest in most of the world’s languages and are consequently propagated or amplified by NLP systems. Although research has focused on mitigating gender stereotypes in English, the approaches that are commonly employed produce ungrammatical sentences in morphologically rich languages. We present a novel approach for converting between masculine-inflected and feminine-inflected sentences in such languages. For Spanish and Hebrew, our approach achieves F1 scores of 82% and 73% at the level of tags and accuracies of 90% and 87% at the level of forms. By evaluating our approach using four different languages, we show that, on average, it reduces gender stereotyping by a factor of 2.5 without any sacrifice to grammaticality.