amino acid proposals and the ground truth sequential order, our next task is to select the same number of proposals as in the sequence and thread them over to form the complete protein chain. With $N_B$ predicted proposal set $B$ from the $A^2$-Net, and a sequence $S^*$ of length $T$ ($N_B > T$), our next task is to select $T$ boxes in sequence to form the complete protein chain. The categories and sequential orders of $S$ are given by $S^*$, and the proposals are selected from $B$. Each proposal is $S_t = (x_t, y_t, z_t, w_t, h_t, l_t, P_t)$, $P_t$ is the probability of different categories predicted by $A^2$-Net.

### Monte Carlo Tree Search

MCTS is a tree search algorithm in which a node is evaluated by performing random actions from the decision space until an outcome can be determined [@alphago; @ReinforceWalk]. Searching by MCTS is done by iteratively building a search tree where the nodes denotes different states, and the edges are the actions leading to one state from another. A node is recursively added to the tree during each iteration. Based on the reward of the new node, the reward values of all parent nodes are updated. A 