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A.1 Tree-Based Stick-Breaking Construction
Figure 6 describes the process of the tree-based stick-breaking construction (Wang and Blei, 2009). At the first level, the stick length is  $\pi_1 = 1$ . Then, the stick-breaking construction is applied to the first level stick to obtain the path distribution over the second level. For instance, if the second level contains  $K = 3$  topics, the probability of each path is obtained as  $\pi_{11} = \pi_1\nu_{11}$ ,  $\pi_{12} = \pi_1\nu_{12}(1 - \nu_{11})$  and the remaining stick  $\pi_{13} = \pi_1(1 - \nu_{12})(1 - \nu_{11})$ . Generally, for any values of  $K$ , it satisfies  $\sum_{k=1}^{K} \pi_{1k} = \pi_1$ . The same process is applied to each stick proportion of the second level and continues until it reaches to the bottom level.
Figure 6: Tree-based stick-breaking construction.
Figure 7: Doubly-recurrent neural networks.
A.2 Doubly-Recurrent Neural Networks
Figure 7 shows the architecture of doubly-recurrent neural networks (Alvarez-Melis and Jaakkola, 2017). It consists of two recurrent neural networks over respectively the ancestors and siblings that are combined in each cell as described in (9).