Question about Eq.1

[LeungWaiHo]

I noticed "compute their semantic correlation as the verification score" about Eq.1
My question:

1. Does it work as a similarity function?
2. Could it be replaced by other similarity functions, such as cosine ...?

[yangli18]

@LeungWaiHo
A1: Yes, it can be understood as a similarity function, which measures how relevant each visual feature is to the content described in the text.
A2: The output of this function, which measures the correlation/relevance between visual and text features, should range from 0 to 1, yet the cosine function has an output range of [-1, 1]. We use Eq.1 to adapt the cosine similarity outputs to [0, 1]. You can try other functions with similar effects.

[wildwolff]

I cannot understand why this S(x,y) in Eq.1 can be seen as the relevance score, and the code computes verify_score by element-wise multiplication without Transpose，which is a little different with Eq.1. Could you further explain it？Thanks a lot！

text_embed = self.text_proj(text_info)
img_embed = self.img_proj(img_feat)
verify_score = (F.normalize(img_embed, p=2, dim=-1) *
F.normalize(text_embed, p=2, dim=-1)).sum(dim=-1, keepdim=True)
verify_score = self.tf_scale *
torch.exp( - (1 - verify_score).pow(self.tf_pow)
/ (2 * self.tf_sigma**2))

[yangli18]

It's just a matter of implementation. The inside part of Eq. 1 essentially computes the inner product of two feature vectors. Actually, you can use bmm after transposing the matrix/vector ( [Bx1xC] * [BxCx1] = [Bx1x1]), which is equivalent to the way I implemented it.