Given the task definition and input, reply with output. In this task, you will be presented with a context from an academic paper and a question separated with a 
. You have to answer the question based on the context.

The input of our model are the words in the input text $x[1], ... , x[n]$ and query $q[1], ... , q[n]$ . We concatenate pre-trained word embeddings from GloVe BIBREF40 and character embeddings trained by CharCNN BIBREF41 to represent input words. The $2d$ -dimension embedding vectors of input text $x_1, ... , x_n$ and query $q_1, ... , q_n$ are then fed into a Highway Layer BIBREF42 to improve the capability of word embeddings and character embeddings as

$$\begin{split} g_t &= {\rm sigmoid}(W_gx_t+b_g) \\ s_t &= {\rm relu } (W_xx_t+b_x) \\ u_t &= g_t \odot s_t + (1 - g_t) \odot x_t~. \end{split}$$ (Eq. 18) The same Highway Layer is applied to $q_t$ and produces $v_t$ . Next, $u_t$ and $v_t$ are fed into a Bi-Directional Long Short-Term Memory Network (BiLSTM) BIBREF44 respectively in order to model the temporal interactions between sequence words: Then we feed $\mathbf {U}$ and $\mathbf {V}$ into the attention flow layer BIBREF27 to model the interactions between the input text and query. Therefore, we introduce Self-Matching Layer BIBREF29 in our model as

$$\begin{split} o_t &= {\rm BiLSTM}(o_{t-1}, [h_t, c_t]) \\ s_j^t &= w^T {\rm tanh}(W_hh_j+\tilde{W_h}h_t)\\ \alpha _i^t &= {\rm exp}(s_i^t)/\Sigma _{j=1}^n{\rm exp}(s_j^t)\\ c_t &= \Sigma _{i=1}^n\alpha _i^th_i ~. \end{split}$$ (Eq. 20) Finally we feed the embeddings $\mathbf {O} = [o_1, ... , o_n]$ into a Pointer Network BIBREF39 to decode the answer sequence as

$$\begin{split} p_t &= {\rm LSTM}(p_{t-1}, c_t) \\ s_j^t &= w^T {\rm tanh}(W_oo_j+W_pp_{t-1})\\ \beta _i^t &= {\rm exp}(s_i^t)/\Sigma _{j=1}^n{\rm exp}(s_j^t)\\ c_t &= \Sigma _{i=1}^n\beta _i^to_i~. \end{split}$$ (Eq. 21) Therefore, the probability of generating the answer sequence $\textbf {a}$ is as follows

$${\rm P}(\textbf {a}|\mathbf {O}) = \prod _t {\rm P}(a^t | a^1, ... , a^{t-1}, \mathbf {O})~.$$ (Eq. 23) 
 Question: What QA models were used?

A pointer network decodes the answer from a bidirectional LSTM with attention flow layer and self-matching layer, whose inputs come from word and character embeddings of the query and input text fed through a highway layer.