Some questions about 'Criss-Cross Attention'

[yiyi-today]

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I have some questions about 'Criss-Cross Attention'. Here should be C×W×H or C×H×W in the place marked by the red circle？

At the same time, I have some questions about Affinity. Which variables corresponds to the codes in the place marked by the blue line，proj_query_H and proj_key_H , or proj_query_W and proj_key_W? I don’t understand the definition of Qu and Ωu very well. Is it convenient for you to answer? Looking forward to your answer, thank you very much!

[Asthestarsfalll]

1. I think it's a typo, or maybe it doesn't matter.
2. Q_u is a pixel vector in spatial position u with shape [b, c', 1, 1], so the x_q contains h*w Q_u

x_q = self.q(x) #b, c', h, w

3.\gamma_u is a set which contains the key pixel vectors in the same row and column with position u, so its shape is [b, c', h+w-1].Actually, in code they split the key set to H and W，and calculate the attention scores for h and w respectively.

[yiyi-today]

1. I think it's a typo, or maybe it doesn't matter.
2. Q_u is a pixel vector in spatial position u with shape [b, c', 1, 1], so the x_q contains h*w Q_u

x_q = self.q(x) #b, c', h, w

3.\gamma_u is a set which contains the key pixel vectors in the same row and column with position u, so its shape is [b, c', h+w-1].Actually, in code they split the key set to H and W，and calculate the attention scores for h and w respectively.

Thank you very much for your answer.