What is max aggregation on a set of word embeddings? In a paper I see:




$\mathcal{Q}$ is a set of words.

$\psi_{G^w}$ are word embeddings.

so, $\{\psi_{G^w}(w_t), \forall w_t \in \mathcal{Q}\}$ gives me a set of embeddings for all words in $\mathcal{Q}$.

For example, if I have: 

Q = {'a', 'b', 'c'}
embedding_gw.shape = (1000, 8) # 1000 words in vocab, embedding size is 8


I will get:

{
  [1,2,3,4,5,6,7,8], #embedding of 'a'
  [8,7,6,5,4,3,2,1], #embedding of 'b'
  [4,5,3,6,7,8,1,2]  #embedding of 'c'
}


The result of $\max\{\psi_{G^w}(w_t), \forall w_t \in \mathcal{Q}\}$ is supposed to be a single vector.

My question is, how do I get this single $\max$ vector?


Do I sum all values in each embedding and pick the largest one?
Do I pick the $\max$ value of each $i^{th}$ position, creating a completely new vector?
Do I do something else?
The second option is the right one. From the paper:


  In this case, we perform a component-wise max over the start
  embeddings of all instances of w to obtain the best features across
  all occurrences of w.


The previous quote can be found a few paragraphs before equation 17, second column, top of the page.