注：为了更加实例化的说明，本文假设输入图像大小为（224,224,3）

整体架构

        对于一张224*224的图像，首先，经过4*4的卷积，将图像维度化为 4,56,56,128的特征图，对特征图维度进行变换，得到4*3136*128的图像，即对图像进行了embeding，然后将图像输入transforer block，将特征图转变为8*8的窗口，进行注意力机制的计算，一个transformer block包含窗口自注意力W-MAS，计算8*8窗口内部的特征和滑动窗口自注意力SW-MSA，计算窗口间的特征，经过transformer的计算后，再进行patch mergeing将特征图大小减半,类似于卷积。

1.图像数据patch编码

        首先，对于输入的图像，假设为224*224，我们采用4*4的卷积，然后将图像进行flatten，形成一个个patch,最后输出维度为batch_size * HW * Channels,H=W=224/4

代码如下:

class PatchEmbed(nn.Module):
    r""" Image to Patch Embedding
    Args:
        img_size (int): Image size.  Default: 224.
        patch_size (int): Patch token size. Default: 4.
        in_chans (int): Number of input image channels. Default: 3.
        embed_dim (int): Number of linear projection output channels. Default: 96.
        norm_layer (nn.Module, optional): Normalization layer. Default: None
    """
    def __init__(self, img_size=224, patch_size=4, in_chans=3, embed_dim=96, norm_layer=None):
        super().__init__()
        img_size = to_2tuple(img_size)
        patch_size = to_2tuple(patch_size)
        patches_resolution = [img_size[0] // patch_size[0], img_size[1] // patch_size[1]]
        self.img_size = img_size
        self.patch_size = patch_size
        self.patches_resolution = patches_resolution
        self.num_patches = patches_resolution[0] * patches_resolution[1]
        self.in_chans = in_chans
        self.embed_dim = embed_dim
        # in_channels:3,out_channels:128
        self.proj = nn.Conv2d(in_chans, embed_dim, kernel_size=patch_size, stride=patch_size)
        if norm_layer is not None:
            self.norm = norm_layer(embed_dim)
        else:
            self.norm = None
    def forward(self, x):
        B, C, H, W = x.shape
        # FIXME look at relaxing size constraints
        assert H == self.img_size[0] and W == self.img_size[1], \
            f"Input image size ({H}*{W}) doesn't match model ({self.img_size[0]}*{self.img_size[1]})."
        # 卷积
        x = self.proj(x).flatten(2).transpose(1, 2)  # B Ph*Pw C
        # print(x.shape) #4 3136 96 其中3136就是 224/4 * 224/4 相当于有这么长的序列，其中每个元素是96维向量
        if self.norm is not None:
            x = self.norm(x)
        # print(x.shape)
        return x
    def flops(self):
        Ho, Wo = self.patches_resolution
        flops = Ho * Wo * self.embed_dim * self.in_chans * (self.patch_size[0] * self.patch_size[1])
        if self.norm is not None:
            flops += Ho * Wo * self.embed_dim
        return flops

3.transformer block

一个transformer block由w-MSA和SW-MSA组成 

W-MSA/SW-MSA

        输入维度为4,3136,128的序列x，首先将其维度变换为4,56,56,128，再经过维度变换，将维度变成 256, 49, 128，即表示，有256个特征图，每个特征图有49个tokens，每个token是128维的向量。

        首先做W-MSA，对于W-SMA，不对窗口进行偏移，经过多头注意力的计算，得到结果，对于SW-MSA，窗口进行偏移，加入mask后，做相同的多头注意力的计算。最后将窗口再偏移回去。

         多头注意力：首先构造维度为256, 4, 49, 32的q,k,v辅助向量，256表示有256个特征图，4表示有4个head,49表示有49个tokens，32表示，每个头32个向量，然后经过多头注意力的计算，其中，会加入相对位置编码

class WindowAttention(nn.Module):
    r""" Window based multi-head self attention (W-MSA) module with relative position bias.
    It supports both of shifted and non-shifted window.
    Args:
        dim (int): Number of input channels.
        window_size (tuple[int]): The height and width of the window.
        num_heads (int): Number of attention heads.
        qkv_bias (bool, optional):  If True, add a learnable bias to query, key, value. Default: True
        qk_scale (float | None, optional): Override default qk scale of head_dim ** -0.5 if set
        attn_drop (float, optional): Dropout ratio of attention weight. Default: 0.0
        proj_drop (float, optional): Dropout ratio of output. Default: 0.0
    """
    def __init__(self, dim, window_size, num_heads, qkv_bias=True, qk_scale=None, attn_drop=0., proj_drop=0.):
        super().__init__()
        self.dim = dim
        self.window_size = window_size  # Wh, Ww
        self.num_heads = num_heads
        head_dim = dim // num_heads
        self.scale = qk_scale or head_dim ** -0.5
        # define a parameter table of relative position bias
        self.relative_position_bias_table = nn.Parameter(
            torch.zeros((2 * window_size[0] - 1) * (2 * window_size[1] - 1), num_heads))  # 2*Wh-1 * 2*Ww-1, nH
        # get pair-wise relative position index for each token inside the window
        coords_h = torch.arange(self.window_size[0])
        coords_w = torch.arange(self.window_size[1])
        coords = torch.stack(torch.meshgrid([coords_h, coords_w]))  # 2, Wh, Ww
        coords_flatten = torch.flatten(coords, 1)  # 2, Wh*Ww
        relative_coords = coords_flatten[:, :, None] - coords_flatten[:, None, :]  # 2, Wh*Ww, Wh*Ww
        relative_coords = relative_coords.permute(1, 2, 0).contiguous()  # Wh*Ww, Wh*Ww, 2
        relative_coords[:, :, 0] += self.window_size[0] - 1  # shift to start from 0
        relative_coords[:, :, 1] += self.window_size[1] - 1
        relative_coords[:, :, 0] *= 2 * self.window_size[1] - 1
        relative_position_index = relative_coords.sum(-1)  # Wh*Ww, Wh*Ww
        self.register_buffer("relative_position_index", relative_position_index)
        self.qkv = nn.Linear(dim, dim * 3, bias=qkv_bias)
        self.attn_drop = nn.Dropout(attn_drop)
        self.proj = nn.Linear(dim, dim)
        self.proj_drop = nn.Dropout(proj_drop)
        trunc_normal_(self.relative_position_bias_table, std=.02)
        self.softmax = nn.Softmax(dim=-1)
    def forward(self, x, mask=None):
        """
        Args:
            x: input features with shape of (num_windows*B, N, C)
            mask: (0/-inf) mask with shape of (num_windows, Wh*Ww, Wh*Ww) or None
        """
        # num_windows, Wh*Ww, Wh*Ww
        B_, N, C = x.shape
        # 3, 256, 4, 49, 32
        qkv = self.qkv(x).reshape(B_, N, 3, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
        # print(qkv.shape)
        # 256, 4, 49, 32
        q, k, v = qkv[0], qkv[1], qkv[2]  # make torchscript happy (cannot use tensor as tuple)
        # print(q.shape)
        # print(k.shape)
        # print(v.shape)
        # 256, 4, 49, 49
        q = q * self.scale
        attn = (q @ k.transpose(-2, -1))
        # print(attn.shape)
        # 相对位置编码 49*49*4
        relative_position_bias = self.relative_position_bias_table[self.relative_position_index.view(-1)].view(
            self.window_size[0] * self.window_size[1], self.window_size[0] * self.window_size[1], -1)  # Wh*Ww,Wh*Ww,nH
        # print(relative_position_bias.shape)
        # 4, 49, 49
        relative_position_bias = relative_position_bias.permute(2, 0, 1).contiguous()  # nH, Wh*Ww, Wh*Ww
        # print(relative_position_bias.shape)
        # 加入位置编码  256, 4, 49, 49
        attn = attn + relative_position_bias.unsqueeze(0)
        # print(attn.shape)
        if mask is not None:
            nW = mask.shape[0]
            attn = attn.view(B_ // nW, nW, self.num_heads, N, N) + mask.unsqueeze(1).unsqueeze(0)
            attn = attn.view(-1, self.num_heads, N, N)
            attn = self.softmax(attn)
        else:
            attn = self.softmax(attn)
        # dropout层
        attn = self.attn_drop(attn)
        # print(attn.shape)
        # qkv
        x = (attn @ v).transpose(1, 2).reshape(B_, N, C)
        # print(x.shape)
        # 全连接层
        x = self.proj(x)
        # print(x.shape)
        # dropout层
        x = self.proj_drop(x)
        # print(x.shape)
        return x

4.下采样 

         下采样操作，但是不同于池化，这个相当于间接的 （对H和W维度进行间隔采样后拼接在一起，得到H/2,W/2,C*4）

代码如下：

class PatchMerging(nn.Module):
    r""" Patch Merging Layer.
    Args:
        input_resolution (tuple[int]): Resolution of input feature.
        dim (int): Number of input channels.
        norm_layer (nn.Module, optional): Normalization layer.  Default: nn.LayerNorm
    """
    def __init__(self, input_resolution, dim, norm_layer=nn.LayerNorm):
        super().__init__()
        self.input_resolution = input_resolution
        self.dim = dim
        self.reduction = nn.Linear(4 * dim, 2 * dim, bias=False)
        self.norm = norm_layer(4 * dim)
    def forward(self, x):
        """
        x: B, H*W, C
        """
        H, W = self.input_resolution
        B, L, C = x.shape
        assert L == H * W, "input feature has wrong size"
        assert H % 2 == 0 and W % 2 == 0, f"x size ({H}*{W}) are not even."
        x = x.view(B, H, W, C)
        # 间隔采样
        x0 = x[:, 0::2, 0::2, :]  # B H/2 W/2 C
        x1 = x[:, 1::2, 0::2, :]  # B H/2 W/2 C
        x2 = x[:, 0::2, 1::2, :]  # B H/2 W/2 C
        x3 = x[:, 1::2, 1::2, :]  # B H/2 W/2 C
        x = torch.cat([x0, x1, x2, x3], -1)  # B H/2 W/2 4*C
        x = x.view(B, -1, 4 * C)  # B H/2*W/2 4*C
        x = self.norm(x)
        x = self.reduction(x)
        return x
    def extra_repr(self) -> str:
        return f"input_resolution={self.input_resolution}, dim={self.dim}"
    def flops(self):
        H, W = self.input_resolution
        flops = H * W * self.dim
        flops += (H // 2) * (W // 2) * 4 * self.dim * 2 * self.dim
        return flops

5.相对位置编码

有关swin transformer相对位置编码的理解：

假设window_size是7*7

那么窗口中共有49个patch，共有49*49个相对位置，每个相对位置有两个索引对应x和y两个方向，每个索引值的取值范围是[-6,6]。（第0行相对第6行，x索引相对值为-6；第6行相对第0行，x索引相对值为6；所以索引取值范围是[-6,6]）

    # get pair-wise relative position index for each token inside the window
    coords_h = torch.arange(self.window_size[0])
    coords_w = torch.arange(self.window_size[1])
    coords = torch.stack(torch.meshgrid([coords_h, coords_w]))  # 2, Wh, Ww
    coords_flatten = torch.flatten(coords, 1)  # 2, Wh*Ww
    # 2, Wh*Ww, Wh*Ww, https://www.cnblogs.com/sgdd123/p/7603004.html
    relative_coords = coords_flatten[:, :, None] - coords_flatten[:, None, :]  
    # Wh*Ww, Wh*Ww, 2, [i,j,:]表示窗口内第i个patch相对于第j个patch的坐标
    relative_coords = relative_coords.permute(1, 2, 0).contiguous()

此时，构建出来的relative_coords的shape是[49, 49, 2]，[i, j, :]表示窗口内第i个patch相对于第j个patch的坐标。

由于此时索引取值范围中包含负值，可分别在每个方向上加上6，使得索引取值从0开始。此时，索引取值范围为[0,12]

    relative_coords[:, :, 0] += self.window_size[0] - 1  # shift to start from 0
    relative_coords[:, :, 1] += self.window_size[1] - 1

有了这些相对位置坐标之后，就可以根据这些坐标获取对应的position bias，即论文中公式（4）中的B：

这个时候可以构建一个shape为[13,13]的table，则当相对位置为(i，j)时，B=table[i, j]。（i，j的取值范围都是[0, 12]） 

由于论文中使用的时multi-head-self-attention，所以table[i, j]的值应该是一个维度为num_heads的一维向量。

在代码中，实现如下：(注意，此时的table将二维的位置关系，合并为了一维的位置关系）

    # define a parameter table of relative position bias  # shape : 2*Wh-1 * 2*Ww-1, nH
    self.relative_position_bias_table = nn.Parameter(
        torch.zeros((2 * window_size[0] - 1) * (2 * window_size[1] - 1), num_heads))

为了与table对应，根据相对位置坐标取值时，也需要将二维相对坐标(i, j)映射为一维相对坐标(i*13+j)， 在代码中体现为：

     relative_coords[:, :, 0] *= 2 * self.window_size[1] - 1
    relative_position_index = relative_coords.sum(-1)  # Wh*Ww, Wh*Ww

最后，就可以根据映射后的坐标来对B进行取值了：

    relative_position_bias = self.relative_position_bias_table[self.relative_position_index.view(-1)].view(
        self.window_size[0] * self.window_size[1], self.window_size[0] * self.window_size[1], -1)  # Wh*Ww,Wh*Ww,nH
    relative_position_bias = relative_position_bias.permute(2, 0, 1).contiguous()  # nH, Wh*Ww, Wh*Ww

附注：

将二维相对坐标(i, j)映射为一维相对坐标时，最简单的映射方式是将i和j相加，但这样无法区分(0, 2)和(2, 0)，因为相加的结果都是2；所以作者采用了i*13+j这种方式，其中13 = 2*window_size - 1, 即j取值的最大值。类似于将一个二维数组打平后，每个元素的位置。

参考信息：

https://blog.csdn.net/weixin_42364196/article/details/119954379