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.

Example Input: We also perform a fine-grained syntactic analysis that shows how our method enables to control the morphological realization of first and second-person pronouns, together with verbs and adjectives related to them.
Example Output: What conclusions are drawn from the syntactic analysis?

Example Input: We first use state-of-the-art PDTB taggers for our baseline BIBREF13 , BIBREF12 for the evaluation of the causality prediction of our models ( BIBREF12 requires sentences extracted from the text as its input, so we used our parser to extract sentences from the message).
Example Output: What baselines did they consider?

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