critical information, we apply the same structure multi-hop self-attention on top of the encoding layer to aggregate the news weighted by an assigned attention value. Specifically:

[1.0]{} $$\begin{aligned}
    A = softmax(W_5tanh(W_4N^{t\intercal}))\end{aligned}$$ $$\begin{aligned}
   D_t = AN^t\end{aligned}$$ $$\begin{aligned}
    D_t = tanh(W_6D_t+b_2)\end{aligned}$$

Here, $N^t=(N_1^t,....,N_m^t)$ and $N^t\in R^{m*2u}$, in which $m$ refers to the number of news in date $t$. Note that the weights $[{W_4,W_5,W_6,b_2}]$ in the news level attention layer are different from the word level attention layer weight $[{W_1,W_2,W_3,b_1}]$. A vector $D_t$ represents the temporal sequence for all the news proposed in the date $t$. The merit of using multi-hop self-attention mechanism is that it learns and assign different groups of attention value to the news encoding. Formally, the first group of attention reward the news that contains positive sentiments to the stock market(“raise”, “growth” or “decrease”, “down” etc). Whereas the second group of attention assign there reward to the news that mentions the major companies in the S&P 500 (“Microsoft”,“Google” instead of a small company outside of the S&P 500).

Obviously, the attention layer can be trained end-to-end and thus gradually learn to assign more attention to the reliable and informative news based on its content.

### Day level Bi-LSTM and 