LSTM
http://colah.github.io/posts/2015-08-Understanding-LSTMs/
Tree-Structured LSTMs
A generalization of the standard LSTM architecture to tree structure.
Input $x_i$ regards $x_{i-1}$ as its child, then generalize one child to more.
Child-Sum Tree-LSTMs
Usage
Since the Child-Sum Tree-LSTM unit conditions its components on the sum of child hidden states $h_k$ , it is well-suited for trees with high branching factor or whose children are unordered.
For example, it is a good choice for dependency trees, where the number of dependents of a head can be highly variable.
We refer to a Child-Sum Tree-LSTM applied to a dependency tree as a Dependency Tree-LSTM.
N-ary Tree-LSTMs
Usage
In Eq. 10, we define a parameterization of the kth child’s forget gate $f_{jk}$ that contains “off-diagonal” parameter matrices $U_{kl}^{(f)}$,$ k \not= l $. This parameterization allows for more flexible control of information propagation from child to parent.
We can naturally apply Binary Tree-LSTM units to binarized constituency trees since left and right child nodes are distinguished.
We refer to this application of Binary Tree-LSTMs as a Constituency Tree-LSTM.