Now, we can compute the error message for the two children of p 2 : where we define The children of p 2 , will then each take half of this vector and add their own softmax error message for the complete δ.
we have where δ p 2 ,down [d + 1 : 2d] indicates that p 1 is the right child of p 2 and hence takes the 2nd half of the error, for the final word vector derivative for a, it will be δ p 2 ,down The full derivative for slice V [k] for this trigram tree then is the sum at each node: and similarly for W .