After presenting a novel O(n 3 ) parsing algorithm for dependency grammar, we develop three contrasting ways to stochasticize it. We propose (a) a lexical affinity model where words struggle to modify each other, (b) a sense tagging model where words fluctuate randomly in their selectional preferences, and (c) a generative model where the speaker fleshes out each word's syntactic and conceptual structure without regard to the implications for the hearer. We also give preliminary empirical results from evaluating the three models' parsing performance on annotated Wall Street Journal training text (derived from the Penn Treebank). In these results, the generative model performs significantly better than the others, and does about equally well at assigning partof-speech tags.

The 2016 SIGMORPHON Shared Task was devoted to the problem of morphological reinflection. It introduced morphological datasets for 10 languages with diverse typological characteristics. The shared task drew submissions from 9 teams representing 11 institutions reflecting a variety of approaches to addressing supervised learning of reinflection. For the simplest task, inflection generation from lemmas, the best system averaged 95.56% exact-match accuracy across all languages, ranging from Maltese (88.99%) to Hungarian (99.30%). With the relatively large training datasets provided, recurrent neural network architectures consistently performed best-in fact, there was a significant margin between neural and non-neural approaches. The best neural approach, averaged over all tasks and languages, outperformed the best nonneural one by 13.76% absolute; on individual tasks and languages the gap in accuracy sometimes exceeded 60%. Overall, the results show a strong state of the art, and serve as encouragement for future shared tasks that explore morphological analysis and generation with varying degrees of supervision.

The CoNLL-SIGMORPHON 2017 shared task on supervised morphological generation required systems to be trained and tested in each of 52 typologically diverse languages. In sub-task 1, submitted systems were asked to predict a specific inflected form of a given lemma. In sub-task 2, systems were given a lemma and some of its specific inflected forms, and asked to complete the inflectional paradigm by predicting all of the remaining inflected forms. Both sub-tasks included high, medium, and low-resource conditions. Sub-task 1 received 24 system submissions, while sub-task 2 received 3 system submissions. Following the success of neural sequence-to-sequence models in the SIGMORPHON 2016 shared task, all but one of the submissions included a neural component. The results show that high performance can be achieved with small training datasets, so long as models have appropriate inductive bias or make use of additional unlabeled data or synthetic data. However, different biasing and data augmentation resulted in non-identical sets of inflected forms being predicted correctly, suggesting that there is room for future improvement.

Several recent stochastic parsers use bilexical grammars, where each word type idiosyncratically prefers particular complements with particular head words. We present O(n 4) parsing algorithms for two bilexical formalisms, improving the prior upper bounds of O(n5). For a common special case that was known to allow O(n 3) parsing (Eisner, 1997), we present an O(n 3) algorithm with an improved grammar constant.

Natural-language prompts have recently been used to coax pretrained language models into performing other AI tasks, using a fill-in-theblank paradigm (Petroni et al., 2019) or a few-shot extrapolation paradigm (Brown et al., 2020). For example, language models retain factual knowledge from their training corpora that can be extracted by asking them to "fill in the blank" in a sentential prompt. However, where does this prompt come from? We explore the idea of learning prompts by gradient descent-either fine-tuning prompts taken from previous work, or starting from random initialization. Our prompts consist of "soft words," i.e., continuous vectors that are not necessarily word type embeddings from the language model. Furthermore, for each task, we optimize a mixture of prompts, learning which prompts are most effective and how to ensemble them. Across multiple English LMs and tasks, our approach hugely outperforms previous methods, showing that the implicit factual knowledge in language models was previously underestimated. Moreover, this knowledge is cheap to elicit: random initialization is nearly as good as informed initialization.