In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

[Q]: While counter machines have received little attention in theoretical computer science since the 1960s, they have recently achieved a newfound relevance to the field of natural language processing (NLP). Recent work has suggested that some strong-performing recurrent neural networks utilize their memory as counters. Thus, one potential way to understand the sucess of these networks is to revisit the theory of counter computation. Therefore, we choose to study the abilities of real-time counter machines as formal grammars. We first show that several variants of the counter machine converge to express the same class of formal languages. We also prove that counter languages are closed under complement, union, intersection, and many other common set operations. Next, we show that counter machines cannot evaluate boolean expressions, even though they can weakly validate their syntax. This has implications for the interpretability and evaluation of neural network systems: successfully matching syntactic patterns does not guarantee that a counter-like model accurately represents underlying semantic structures. Finally, we consider the question of whether counter languages are semilinear. This work makes general contributions to the theory of formal languages that are of particular interest for the interpretability of recurrent neural networks.
[A]: We study the class of formal languages acceptable by real-time counter automata, a model of computation related to some types of recurrent neural networks.


[Q]: We investigate methods for semi-supervised learning (SSL) of a neural linear-chain conditional random field (CRF) for Named Entity Recognition (NER) by treating the tagger as the amortized variational posterior in a generative model of text given tags. We first illustrate how to incorporate a CRF in a VAE, enabling end-to-end training on semi-supervised data. We then investigate a series of increasingly complex deep generative models of tokens given tags enabled by end-to-end optimization, comparing the proposed models against supervised and strong CRF SSL baselines on the Ontonotes5 NER dataset. We find that our best proposed model consistently improves performance by $\approx 1\%$ F1 in low- and moderate-resource regimes and easily addresses degenerate model behavior in a more difficult, partially supervised setting.
[A]: We embed a CRF in a VAE of tokens and NER tags for semi-supervised learning and show improvements in low-resource settings.


[Q]: Optimal selection of a subset of items from a given set is a hard problem that requires combinatorial optimization. In this paper, we propose a subset selection algorithm that is trainable with gradient based methods yet achieves near optimal performance via submodular optimization. We focus on the task of identifying a relevant set of sentences for claim verification in the context of the FEVER task. Conventional methods for this task look at sentences on their individual merit and thus do not optimize the informativeness of sentences as a set. We show that our proposed method which builds on the idea of unfolding a greedy algorithm into a computational graph allows both interpretability and gradient based training. The proposed differentiable greedy network (DGN) outperforms discrete optimization algorithms as well as other baseline methods in terms of precision and recall.
[A]:
We propose a subset selection algorithm that is trainable with gradient based methods yet achieves near optimal performance via submodular optimization.