MDTA模块（Restormer）

From a layer normalized tensor $\mathbf{Y}\in {\mathbb{R}}^{\hat{H}\times \hat{W}\times \hat{C}}$, our MDTA first generates query $(\mathbf{Q})$, key $(\mathbf{K})$ and value $(\mathbf{V})$ projections, enriched with local context. It is achieved by applying $1\times 1$ convolutions to aggregate pixel-wise cross-channel context followed by $3\times 3$ depth-wise convolutions to encode channel-wise spatial context, yielding $\mathbf{Q}=W_d^Q{W}_p^Q\mathbf{Y},\mathbf{K}=W_d^K{W}_p^K\mathbf{Y}$ and $\mathbf{V}=W_d^V{W}_p^V\mathbf{Y}$. Where $W_p^{(\cdot )}$ is the $1\times 1$ point-wise convolution and $W_d^{(\cdot )}$ is the $3\times 3$ depth-wise convolution. We use bias-free convolutional layers in the network. Next, we reshape query and key projections such that their dot-product interaction generates a transposed-attention map $\mathbf{A}$ of size ${\mathbb{R}}^{\hat{C}\times \hat{C}}$, instead of the huge regular attention map of size ${\mathbb{R}}^{\hat{H}\hat{W}\times \hat{H}\hat{W}}$. Overall, the MDTA process is defined as:
$$\begin{gathered} \hat{\mathbf{X}}=W_p\mathrm{Attention}(\hat{\mathbf{Q}},\hat{\mathbf{K}},\hat{\mathbf{V}})+\mathbf{X} \\ \mathrm{Attention}(\hat{\mathbf{Q}},\hat{\mathbf{K}},\hat{\mathbf{V}})=\hat{\mathbf{V}}\cdot \mathrm{Softmax}(\hat{\mathbf{K}}\cdot \hat{\mathbf{Q}}/\alpha ) \end{gathered}$$
where $\mathbf{X}$ and $\hat{\mathbf{X}}$ are the input and output feature maps; $\hat{\mathbf{Q}}\in {\mathbb{R}}^{\hat{H}\hat{W}\times \hat{C}};\hat{\mathbf{K}}\in {\mathbb{R}}^{\hat{C}\times \hat{H}\hat{W}};$ and $\hat{\mathbf{V}}\in {\mathbb{R}}^{\hat{H}\hat{W}\times \hat{C}}$ matrices are obtained after reshaping tensors from the original size ${\mathbb{R}}^{\hat{H}\times \hat{W}\times \hat{C}}$. Here, $\alpha$ is a learnable scaling parameter to control the magnitude of the dot product of $\hat{\mathbf{K}}$ and $\hat{\mathbf{Q}}$ before applying the softmax function. Similar to the conventional multi-head SA , we divide the number of channels into ‘heads’ and learn separate attention maps in parallel.

## Multi-DConv Head Transposed Self-Attention (MDTA)
class Attention(nn.Module):def __init__(self, dim, num_heads, bias):super(Attention, self).__init__()self.num_heads = num_headsself.temperature = nn.Parameter(torch.ones(num_heads, 1, 1))self.qkv = nn.Conv2d(dim, dim*3, kernel_size=1, bias=bias)self.qkv_dwconv = nn.Conv2d(dim*3, dim*3, kernel_size=3, stride=1, padding=1, groups=dim*3, bias=bias)self.project_out = nn.Conv2d(dim, dim, kernel_size=1, bias=bias)def forward(self, x):b, c, h, w = x.shapeqkv = self.qkv_dwconv(self.qkv(x))q, k, v = qkv.chunk(3, dim=1)q = rearrange(q, 'b (head c) h w -> b head c (h w)',head=self.num_heads)k = rearrange(k, 'b (head c) h w -> b head c (h w)',head=self.num_heads)v = rearrange(v, 'b (head c) h w -> b head c (h w)',head=self.num_heads)q = torch.nn.functional.normalize(q, dim=-1)k = torch.nn.functional.normalize(k, dim=-1)attn = (q @ k.transpose(-2, -1)) * self.temperatureattn = attn.softmax(dim=-1)out = (attn @ v)out = rearrange(out, 'b head c (h w) -> b (head c) h w',head=self.num_heads, h=h, w=w)out = self.project_out(out)return out

这段代码并没有实现图中的Norm模块，该模块的实现可以参考Layer Normalization（层规范化）。我们看一下Transformer Block是如何包装的：

class TransformerBlock(nn.Module):def __init__(self, dim, num_heads, ffn_expansion_factor, bias, LayerNorm_type):super(TransformerBlock, self).__init__()self.norm1 = LayerNorm(dim, LayerNorm_type)self.attn = Attention(dim, num_heads, bias)self.norm2 = LayerNorm(dim, LayerNorm_type)self.ffn = FeedForward(dim, ffn_expansion_factor, bias)def forward(self, x):x = x + self.attn(self.norm1(x))#MDTAx = x + self.ffn(self.norm2(x))return x

可以看到实现的时候是先Norm，然后通过Attention，最后再残差连接，这整个流程才是上图所示