the $ith$ news title after encoding in date $t$ and $m$ refers to the sequence number.

[1.0]{} $$\begin{aligned}
    \overrightarrow{h_n} = \overrightarrow{LSTM}(e^s)\end{aligned}$$ $$\begin{aligned}
    \overleftarrow{h_n} = \overleftarrow{LSTM}(e^s)\end{aligned}$$

***Word level Self-attention layer***: Instead of taking the average of the hidden vector after the sentence encoding, we leverage multi-hop self-attention mechanism [@lin2017structured] on top of the Bi-LSTM layer. The attention mechanism takes the whole LSTM hidden states $H^t_i$ as input, and outputs a vector of weights $A$:

$$\begin{aligned}
    A = softmax(W_2tanh(W_1H_i^{t\intercal}))\end{aligned}$$

Shown in figure \[fig:attention\], here $W_1$ is a weight matrix with a shape of $W_1\in R^{d_a*2u}$ which u refers to the hidden unit of the news level Bi-LSTM. and $W_2$ is a vector of parameters with size $W_2\in R^{r*d_a}$, $d_a$ and $r$ are hyper parameter that can be set arbitrarily. $H_i^t$ are sized $H_i^t\in R^{n*2u}$, and the annotation vector $A$ will have a size $A\in R^{r*n}$, the $softmax()$ ensures all the computed weights sum up to 1. Then we sum up the LSTM hidden states $H_i^t$ according to the weight provided by $A$ to get a vector representation $N_i^t$ for the input sentence. We can deem Equation (10) as a 2-layer MLP without bias, whose hidden units numbers are $d_a$ and parameters are 