How to calculate correlation in Figure 2?

[Redaimao]

Hi,
Thanks for your wonderful work.
I am unsure about how you've derived the correlation matrix as per figure 2 in terms of the variables used in the calculation as well as the derivation for the correlation matrix.

For instance, does the word-to-word correlation matrix uses the correlation of w_i W^{Q,1} and w_j W^{K,1}T as the variable for the calculation?
Also, how do you reduce the dimension for the correlation matrix as the standard correlation calculation only deals with scalar variables?

Thanks!

[guolinke]

Hi, @Redaimao

1. we use the first self-attention layer to calculate, as the later layers have residuals.
2. then, as there is Dropout(LayerNorm(x)) for word_emb+pos_emb before transformer. Since LayerNorm(a + b) != LayerNorm(a) + LayerNorm(b), you need to calculate word_emb and pos_emb correctly.
3. then, in the first self-attention layer, you can calculate four correlation items for word and pos.
4. for the final results, we randomly pick a batch (size=32), and average the correlation matrix along batch dimension. then, there are multiple heads, we pick one head for demonstration.
5. I think you misunderstand the term correlation in our paper, it actually is the attention scores (logits before softmax).