Definition: In this task, you will be presented with a context from an academic paper and you have to write an answerable question based on the context. Your questions can be extractive, abstractive, or yes-no questions.

Positive Example 1 -
Input: Questions are gathered from anonymized, aggregated queries to the Google search engine. Queries that are likely to be yes/no questions are heuristically identified: we found selecting queries where the first word is in a manually constructed set of indicator words and are of sufficient length, to be effective.

Questions are only kept if a Wikipedia page is returned as one of the first five results, in which case the question and Wikipedia page are given to a human annotator for further processing.

Annotators label question/article pairs in a three-step process. First, they decide if the question is good, meaning it is comprehensible, unambiguous, and requesting factual information. This judgment is made before the annotator sees the Wikipedia page. Next, for good questions, annotators find a passage within the document that contains enough information to answer the question. Annotators can mark questions as “not answerable" if the Wikipedia article does not contain the requested information. Finally, annotators mark whether the question's answer is “yes" or “no". Annotating data in this manner is quite expensive since annotators need to search entire Wikipedia documents for relevant evidence and read the text carefully.
Output: how was the dataset built?

Positive Example 2 -
Input: Using this annotation model, we create a new large publicly available dataset of English tweets.
Output: In what language are the tweets?

Negative Example 1 -
Input: Using this annotation model, we create a new large publicly available dataset of English tweets.
Output: In what language is tweets?

Negative Example 2 -
Input: Questions are gathered from anonymized, aggregated queries to the Google search engine. Queries that are likely to be yes/no questions are heuristically identified: we found selecting queries where the first word is in a manually constructed set of indicator words and are of sufficient length, to be effective.

Questions are only kept if a Wikipedia page is returned as one of the first five results, in which case the question and Wikipedia page are given to a human annotator for further processing.

Annotators label question/article pairs in a three-step process. First, they decide if the question is good, meaning it is comprehensible, unambiguous, and requesting factual information. This judgment is made before the annotator sees the Wikipedia page. Next, for good questions, annotators find a passage within the document that contains enough information to answer the question. Annotators can mark questions as “not answerable" if the Wikipedia article does not contain the requested information. Finally, annotators mark whether the question's answer is “yes" or “no". Annotating data in this manner is quite expensive since annotators need to search entire Wikipedia documents for relevant evidence and read the text carefully.
Output: What is the size of the dataset?

Now complete the following example -
Input: Moreover, QA and QG have probabilistic correlation as both tasks relate to the joint probability between $q$ and $a$ . Given a question-answer pair $\langle q, a \rangle $ , the joint probability $P(q, a)$ can be computed in two equivalent ways.

$$P(q, a) = P(a) P(q|a) = P(q)P(a|q)$$ (Eq. 1)

The conditional distribution $P(q|a)$ is exactly the QG model, and the conditional distribution $P(a|q)$ is closely related to the QA model. Existing studies typically learn the QA model and the QG model separately by minimizing their own loss functions, while ignoring the probabilistic correlation between them.

Based on these considerations, we introduce a training framework that exploits the duality of QA and QG to improve both tasks. There might be different ways of exploiting the duality of QA and QG. In this work, we leverage the probabilistic correlation between QA and QG as the regularization term to influence the training process of both tasks. Specifically, the training objective of our framework is to jointly learn the QA model parameterized by $\theta _{qa}$ and the QG model parameterized by $\theta _{qg}$ by minimizing their loss functions subject to the following constraint.

$$P_a(a) P(q|a;\theta _{qg}) = P_q(q)P(a|q;\theta _{qa})$$ (Eq. 3)

$P_a(a)$ and $P_q(q)$ are the language models for answer sentences and question sentences, respectively. Overall, the framework includes three components, namely a QA model, a QG model and a regularization term that reflects the duality of QA and QG. The QA specific objective aims to minimize the loss function $l_{qa}(f_{qa}(a,q;\theta _{qa}), label)$ , where $label$ is 0 or 1 that indicates whether $a$ is the correct answer of $q$ or not. For each correct question-answer pair, the QG specific objective is to minimize the following loss function,

$$l_{qg}(q, a) = -log P_{qg}(q|a;\theta _{qg})$$ (Eq. 6)

where $a$ is the correct answer of $q$ . The third objective is the regularization term which satisfies the probabilistic duality constrains as given in Equation 3 . Specifically, given a correct $\langle q, a \rangle $ pair, we would like to minimize the following loss function,

$$ \nonumber l_{dual}(a,q;\theta _{qa}, \theta _{qg}) &= [logP_a(a) + log P(q|a;\theta _{qg}) \\ & - logP_q(q) - logP(a|q;\theta _{qa})]^2$$ (Eq. 9)

where $P_a(a)$ and $P_q(q)$ are marginal distributions, which could be easily obtained through language model.
Output: 



Output: What does "explicitly leverages their probabilistic correlation to guide the training process of both models" mean?