# Tree-Paths as sequence input into a neural network

I'm currently trying to understand this paper but I struggle with the input into the NN. What I don't understand is what the input vectors should look like for the network described in b) in the image below.

As described in the paper the inputs are two sub-paths of a tree which are connected at a single node. Each node represents a feature vector, for example the word embedding of the word. My Question now is do I concatenate the vectors for two nodes that are at the same level in the tree? And if this is the case what do I do with vectors of sub-paths of unequal length?

To give an example lets say we have the following paths and the corresponding subtree of my dependency tree:

  v_root --> v_l1 --> v_l2 --> v_l3  --> v_l4
v_root --> v_r1 --> v_r2 --> v_r3

v_root
|--v_l1
|--v_l2
|--v_l3
|--v_l4
|--v_r1
|--v_r2
|--v_r3


The input-sequence is bottom up so I would assume, that the input for the tree looks like the table below. But if this is the case what about v_l4, there is no v_r4 or do I simply use a zero-vector where all values are 0 for v_r4?

Timestep | Input-Vectors (concatenated)
---------------------------------------
0 | v_l4:??
1 | v_l3:v_r3
2 | v_l3:v_r2
3 | v_l3:v_r1
4 | v_root:v_root