Abstract: This paper is concerned with open-domain question answering (i.e., OpenQA). Recently, some works have viewed this problem as a reading comprehension (RC) task, and directly applied successful RC models to it. However, the performances of such models are not so good as that in the RC task. In our opinion, the perspective of RC ignores three characteristics in OpenQA task: 1) many paragraphs without the answer span are included in the data collection; 2) multiple answer spans may exist within one given paragraph; 3) the end position of an answer span is dependent with the start position. In this paper, we first propose a new probabilistic formulation of OpenQA, based on a three-level hierarchical structure, i.e., the question level, the paragraph level and the answer span level. Then a Hierarchical Answer Spans Model (HAS-QA) is designed to capture each probability. HAS-QA has the ability to tackle the above three problems, and experiments on public OpenQA datasets show that it significantly outperforms traditional RC baselines and recent OpenQA baselines.

Introduction: Open-domain question answering (OpenQA) aims to seek answers for a broad range of questions from a large knowledge sources, e.g., structured knowledge bases BIBREF0 , BIBREF1 and unstructured documents from search engine BIBREF2 . In this paper we focus on the OpenQA task with the unstructured knowledge sources retrieved by search engine. Inspired by the reading comprehension (RC) task flourishing in the area of natural language processing BIBREF3 , BIBREF4 , BIBREF5 , some recent works have viewed OpenQA as an RC task, and directly applied the existing RC models to it BIBREF6 , BIBREF7 , BIBREF3 , BIBREF8 . However, these RC models do not well fit for the OpenQA task. Firstly, they directly omit the paragraphs without answer string. RC task assumes that the given paragraph contains the answer string (Figure 1 top), however, it is not valid for the OpenQA task (Figure 1 bottom). That's because the paragraphs to provide answer for an OpenQA question is collected from a search engine, where each retrieved paragraph is merely relevant to the question. Therefore, it contains many paragraphs without answer string, for instance, in Figure 1 Paragraph2. When applying RC models to OpenQA task, we have to omit these paragraphs in the training phase. However, during the inference phase, when model meets one paragraph without answer string, it will pick out a text span as an answer span with high confidence, since RC model has no evidence to justify whether a paragraph contains the answer string. Secondly, they only consider the first answer span in the paragraph, but omit the remaining rich multiple answer spans. In RC task, the answer and its positions in the paragraph are provided by the annotator in the training data. Therefore RC models only need to consider the unique answer span, e.g., in SQuAD BIBREF9 . However, the OpenQA task only provides the answer string as the ground-truth. Therefore, multiple answer spans are detected in the given paragraph, which cannot be considered by the traditional RC models. Take Figure 1 as an example, all text spans contain `fat' are treated as answer span, so we detect two answer spans in Paragraph1. Thirdly, they assume that the start position and end position of an answer span is independent. However, the end position is evidently related with the start position, especially when there are multiple answer spans in a paragraph. Therefore, it may introduce some problems when using such independence assumption. For example, the detected end position may correspond to another answer span, rather than the answer span located by the start position. In Figure 1 Paragraph1, `fat in their $\cdots $ insulating effect fat' has a high confidence to be an answer span under independence assumption. In this paper, we propose a Hierarchical Answer Span Model, named HAS-QA, based on a new three-level probabilistic formulation of OpenQA task, as shown in Figure 2 . At the question level, the conditional probability of the answer string given a question and a collection of paragraphs, named answer probability, is defined as the product of the paragraph probability and conditional answer probability, based on the law of total probability. At the paragraph level, paragraph probability is defined as the degree to which a paragraph can answer the question. This probability is used to measure the quality of a paragraph and targeted to tackle the first problem mentioned, i.e. identify the useless paragraphs. For calculation, we first apply bidirectional GRU and an attention mechanism on the question aware context embedding to obtain a score. Then, we normalize the scores across the multiple paragraphs. In the training phase, we adopt a negative sampling strategy for optimization. Conditional answer probability is the conditional probability that a text string is the answer given the paragraph. Considering multiple answer spans in a paragraph, the conditional answer probability can be further represented as the aggregation of several span probability, defined later. In this paper, four types of functions, i.e. HEAD, RAND, MAX and SUM, are used for aggregation. At the span level, span probability represents the probability that a text span in a paragraph is the answer span. Similarly to previous work BIBREF3 , span probability can be computed as the product of two location probability, i.e., location start probability and location end probability. Then a conditional pointer network is proposed to model the probabilistic dependences between the start and end positions, by making generation of end position depended on the start position directly, rather than internal representation of start position BIBREF10 . The contributions of this paper include: 1) a probabilistic formulation of the OpenQA task, based on the a three-level hierarchical structure, i.e. the question level, the paragraph level and the answer span level; 2) the proposal of an end-to-end HAS-QA model to implement the three-level probabilistic formulation of OpenQA task (Section "HAS-QA Model" ), which tackles the three problems of direct applying existing RC models to OpenQA; 3) extensive experiments on QuasarT, TriviaQA and SearchQA datasets, which show that HAS-QA outperforms traditional RC baselines and recent OpenQA baselines.

Question: What does "explicitly leverages their probabilistic correlation to guide the training process of both models" mean?
Answer: The framework jointly learns parametrized QA and QG models subject to the constraint in equation 2. In more detail, they minimize QA and QG loss functions, with a third dual loss for regularization.