What is: Channel-wise Cross Attention?

Channel-wise Cross Attention is a module for semantic segmentation used in the UCTransNet architecture. It is used to fuse features of inconsistent semantics between the Channel Transformer and U-Net decoder. It guides the channel and information filtration of the Transformer features and eliminates the ambiguity with the decoder features.

Mathematically, we take the $i$-th level Transformer output $\mathbf{O\_{i}} \in \mathbb{R}^{C×H×W}$ and i-th level decoder feature map $\mathbf{D\_{i}} \in \mathbb{R}^{C×H×W}$ as the inputs of Channel-wise Cross Attention. Spatial squeeze is performed by a global average pooling (GAP) layer, producing vector $\mathcal{G}\left(\mathbf{X}\right) \in \mathbb{R}^{C×1×1}$ with its $k$th channel $\mathcal{G}\left(\mathbf{X}\right) = \frac{1}{H×W}\sum^{H}\_{i=1}\sum^{W}\_{j=1}\mathbf{X}^{k}\left(i, j\right)$. We use this operation to embed the global spatial information and then generate the attention mask:

$\mathbf{M}\_{i} = \mathbf{L}\_{1} \cdot \mathcal{G}\left(\mathbf{O\_{i}}\right) + \mathbf{L}\_{2} \cdot \mathcal{G}\left(\mathbf{D}\_{i}\right)$

where $\mathbf{L}\_{1} \in \mathbb{R}^{C×C}$ and $\mathbf{L}\_{2} \in \mathbb{R}^{C×C}$ and being weights of two Linear layers and the ReLU operator $\delta\left(\cdot\right)$. This operation in the equation above encodes the channel-wise dependencies. Following ECA-Net which empirically showed avoiding dimensionality reduction is important for learning channel attention, the authors use a single Linear layer and sigmoid function to build the channel attention map. The resultant vector is used to recalibrate or excite $\mathbf{O\_{i}}$ to $\mathbf{\bar{O}\_{i}} = \sigma\left(\mathbf{M\_{i}}\right) \cdot \mathbf{O\_{i}}$, where the activation $\sigma\left(\mathbf{M\_{i}}\right)$ indicates the importance of each channel. Finally, the masked $\mathbf{\bar{O}}\_{i}$ is concatenated with the up-sampled features of the $i$-th level decoder.