分类： 人工智能

code：https://github.com/microsoft/Swin-Transformer

代码详解： https://zhuanlan.zhihu.com/p/367111046

预处理：

对于分类模型，输入图像尺寸为 224×224×3 ，即 H=W=224 。按照原文描述，模型先将图像分割成每块大小为 4×4 的patch，那么就会有 56×56 个patch，这就是初始resolution，也是后面每个stage会降采样的维度。后面每个stage都会降采样时长宽降到一半，特征数加倍。按照原文及原图描述，划分的每个patch具有 4×4×3=48 维特征。

• 实际在代码中，首先使用了PatchEmbed模块（这里的PatchEmbed包括上图中的Linear Embedding 和 patch partition层），定义如下：

class PatchEmbed(nn.Module):
    def __init__(self, img_size=224, patch_size=4, in_chans=3, embed_dim=96, norm_layer=None): # embed_dim就是上图中的C超参数
        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

        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]})."
        x = self.proj(x).flatten(2).transpose(1, 2)  # B Ph*Pw C
        if self.norm is not None:
            x = self.norm(x)
        return x

可以看到，实际操作使用了一个卷积层conv2d(3, 96, 4, 4)，直接就做了划分patch和编码初始特征的工作，对于输入 x:B×3×224×224 ，经过一层conv2d和LayerNorm得到 x:B×562×96 。然后作为对比，可以选择性地加上每个patch的绝对位置编码，原文实验表示这种做法不好，因此不会采用（ape=false）。最后经过一层dropout，至此，预处理完成。另外，要注意的是，代码和上面流程图并不符，其实在stage 1之前，即预处理完成后，维度已经是 H/4×W/4×C ，stage 1之后已经是 H/8×W/8×2C ，不过在stage 4后不再降采样，得到的还是 H/32×W/32×8C 。

stage处理

我们先梳理整个stage的大体过程，把简单的部分先说了，再深入到复杂得的细节。每个stage，即代码中的BasicLayer，由若干个block组成，而block的数目由depth列表中的元素决定。每个block就是W-MSA（window-multihead self attention）或者SW-MSA（shift window multihead self attention），一般有偶数个block，两种SA交替出现，比如6个block，0，2，4是W-MSA，1，3，5是SW-MSA。在经历完一个stage后，会进行下采样，定义的下采样比较有意思。比如还是 56×56 个patch，四个为一组，分别取每组中的左上，右上、左下、右下堆叠一起，经过一个layernorm，linear层，实现维度下采样、特征加倍的效果。实际上它可以看成一种加权池化的过程。代码如下：

class PatchMerging(nn.Module):
    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)

        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

在经历完4个stage后，得到的是 (H/32×W/32)×8C 的特征，将其转到 8C×(H/32×W/32) 后，接一个AdaptiveAvgPool1d(1)，全局平均池化，得到 8C 特征，最后接一个分类器。

Block处理

SwinTransformerBlock的结构，由LayerNorm层、windowAttention层（Window MultiHead self -attention， W-MSA）、MLP层以及shiftWindowAttention层（SW-MSA）组成。

上面说到有两种block，block的代码如下：

class SwinTransformerBlock(nn.Module):
    r""" Swin Transformer Block.

    Args:
        dim (int): Number of input channels.
        input_resolution (tuple[int]): Input resulotion.
        num_heads (int): Number of attention heads.
        window_size (int): Window size.
        shift_size (int): Shift size for SW-MSA.
        mlp_ratio (float): Ratio of mlp hidden dim to embedding dim.
        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.
        drop (float, optional): Dropout rate. Default: 0.0
        attn_drop (float, optional): Attention dropout rate. Default: 0.0
        drop_path (float, optional): Stochastic depth rate. Default: 0.0
        act_layer (nn.Module, optional): Activation layer. Default: nn.GELU
        norm_layer (nn.Module, optional): Normalization layer.  Default: nn.LayerNorm
    """

    def __init__(self, dim, input_resolution, num_heads, window_size=7, shift_size=0,
                 mlp_ratio=4., qkv_bias=True, qk_scale=None, drop=0., attn_drop=0., drop_path=0.,
                 act_layer=nn.GELU, norm_layer=nn.LayerNorm):
        super().__init__()
        self.dim = dim
        self.input_resolution = input_resolution
        self.num_heads = num_heads
        self.window_size = window_size
        self.shift_size = shift_size
        self.mlp_ratio = mlp_ratio
        if min(self.input_resolution) <= self.window_size:
            # if window size is larger than input resolution, we don't partition windows
            self.shift_size = 0
            self.window_size = min(self.input_resolution)
        assert 0 <= self.shift_size < self.window_size, "shift_size must in 0-window_size"

        # 左图中最下边的LN层layerNorm层
        self.norm1 = norm_layer(dim)
        # W_MSA层或者SW-MSA层，详细的介绍看WindowAttention部分的代码
        self.attn = WindowAttention(
            dim, window_size=to_2tuple(self.window_size), num_heads=num_heads,
            qkv_bias=qkv_bias, qk_scale=qk_scale, attn_drop=attn_drop, proj_drop=drop)

        self.drop_path = DropPath(drop_path) if drop_path > 0. else nn.Identity()
        # 左图中间部分的LN层
        self.norm2 = norm_layer(dim)
        mlp_hidden_dim = int(dim * mlp_ratio)
        # 左图最上边的MLP层
        self.mlp = Mlp(in_features=dim, hidden_features=mlp_hidden_dim, act_layer=act_layer, drop=drop)

        # 这里利用shift_size控制是否执行shift window操作
        # 当shift_size为0时，不执行shift操作，对应W-MSA，也就是在每个stage中,W-MSA与SW-MSA交替出现
        # 例如第一个stage中存在两个block，那么第一个shift_size=0就是W-MSA，第二个shift_size不为0
        # 就是SW-MSA
        if self.shift_size > 0:
            # calculate attention mask for SW-MSA
            H, W = self.input_resolution
            img_mask = torch.zeros((1, H, W, 1))  # 1 H W 1
#slice() 函数实现切片对象，主要用在切片操作函数里的参数传递。class slice(start, stop[, step])
            h_slices = (slice(0, -self.window_size),
                        slice(-self.window_size, -self.shift_size),
                        slice(-self.shift_size, None))
            w_slices = (slice(0, -self.window_size),
                        slice(-self.window_size, -self.shift_size),
                        slice(-self.shift_size, None))
            cnt = 0
            for h in h_slices:
                for w in w_slices:
                    img_mask[:, h, w, :] = cnt
                    cnt += 1
## 上述操作是为了给每个窗口给上索引

            mask_windows = window_partition(img_mask, self.window_size)  # nW, window_size, window_size, 1
            mask_windows = mask_windows.view(-1, self.window_size * self.window_size)
            attn_mask = mask_windows.unsqueeze(1) - mask_windows.unsqueeze(2)
            attn_mask = attn_mask.masked_fill(attn_mask != 0, float(-100.0)).masked_fill(attn_mask == 0, float(0.0))
        else:
            attn_mask = None

        self.register_buffer("attn_mask", attn_mask)

    def forward(self, x):
        H, W = self.input_resolution
        B, L, C = x.shape
        assert L == H * W, "input feature has wrong size"

        shortcut = x
        x = self.norm1(x)
        x = x.view(B, H, W, C)

        # cyclic shift
        # 如果需要计算 SW-MSA就需要进行循环移位。
        if self.shift_size > 0:
            shifted_x = torch.roll(x, shifts=(-self.shift_size, -self.shift_size), dims=(1, 2))
        else:
            shifted_x = x

        # partition windows
        x_windows = window_partition(shifted_x, self.window_size)  # nW*B, window_size, window_size, C
        x_windows = x_windows.view(-1, self.window_size * self.window_size, C)  # nW*B, window_size*window_size, C

        # W-MSA/SW-MSA
        attn_windows = self.attn(x_windows, mask=self.attn_mask)  # nW*B, window_size*window_size, C

        # merge windows
        attn_windows = attn_windows.view(-1, self.window_size, self.window_size, C)
        shifted_x = window_reverse(attn_windows, self.window_size, H, W)  # B H' W' C

        # reverse cyclic shift
        if self.shift_size > 0:
#shifts (python:int 或 tuple of python:int) —— 张量元素移位的位数。如果该参数是一个元组（例如shifts=(x,y)），dims必须是一个相同大小的元组（例如dims=(a,b)），相当于在第a维度移x位，在b维度移y位
            x = torch.roll(shifted_x, shifts=(self.shift_size, self.shift_size), dims=(1, 2))
        else:
            x = shifted_x
        x = x.view(B, H * W, C)

        # FFN
        x = shortcut + self.drop_path(x)
        x = x + self.drop_path(self.mlp(self.norm2(x)))

        return x

    def extra_repr(self) -> str:
        return f"dim={self.dim}, input_resolution={self.input_resolution}, num_heads={self.num_heads}, " \
               f"window_size={self.window_size}, shift_size={self.shift_size}, mlp_ratio={self.mlp_ratio}"

    def flops(self):
        flops = 0
        H, W = self.input_resolution
        # norm1
        flops += self.dim * H * W
        # W-MSA/SW-MSA
        nW = H * W / self.window_size / self.window_size
        flops += nW * self.attn.flops(self.window_size * self.window_size)
        # mlp
        flops += 2 * H * W * self.dim * self.dim * self.mlp_ratio
        # norm2
        flops += self.dim * H * W
        return flops

W-MSA

W-MSA比较简单，只要其中shift_size设置为0就是W-MSA。下面跟着代码走一遍过程。

• 输入： x:B×562×96 ， H,W=56
• 经过一层layerNorm
• 变形： x:B×56×56×96
• 直接赋值给shifted_x
• 调用window_partition函数，输入shifted_x，window_size=7：
• 注意窗口大小以patch为单位，比如7就是7个patch，如果56的分辨率就会有8个窗口。
• 这个函数对shifted_x做一系列变形，最终变成 82B×7×7×96
• 返回赋值给x_windows，再变形成 82B×72×96 ，这表示所有图片，每个图片的64个window，每个window内有49个patch。
• 调用WindowAttention层，这里以它的num_head为3为例。输入参数为x_windows和self.attn_mask，对于W-MSA，attn_mask为None，可以不用管。

WindowAttention代码如下：

代码中使用7×7的windowsize，将feature map分割为不同的window，在每个window中计算自注意力。

Self-attention的计算公式（B为相对位置编码）

绝对位置编码是在进行self-attention计算之前为每一个token添加一个可学习的参数，相对位置编码如上式所示，是在进行self-attention计算时，在计算过程中添加一个可学习的相对位置参数。

假设window_size = 2*2即每个窗口有4个token (M=2) ，如图1所示，在计算self-attention时，每个token都要与所有的token计算QK值，如图6所示，当位置1的token计算self-attention时，要计算位置1与位置(1,2,3,4)的QK值，即以位置1的token为中心点，中心点位置坐标(0,0)，其他位置计算与当前位置坐标的偏移量。

最后生成的是相对位置索引,relative_position_index.shape = (M2，M2) ，在网络中注册成为一个不可学习的变量，relative_position_index的作用就是根据最终的索引值找到对应的可学习的相对位置编码。relative_position_index的数值范围(0~8)，即 (2M−1)∗(2M−1) ,所以相对位置编码（relative position bias table）可以由一个3*3的矩阵表示，如图7所示：这样就根据index对应位置的索引找到table对应位置的值作为相对位置编码。

图7中的0-8为索引值，每个索引值都对应了 M2 维可学习数据(每个token都要计算 M2 个QK值，每个QK值都要加上对应的相对位置编码)

继续以图6中 M=2 的窗口为例，当计算位置1对应的 M2 个QK值时，应用的relative_position_index = [ 4, 5, 7, 8] (M2)个 ，对应的数据就是图7中位置索引4,5,7,8位置对应的 M2 维数据，即relative_position.shape = (M2∗M2)

相对位置编码在源码WindowAttention中应用，了解原理之后就很容易能够读懂程序：

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 # 输入通道的数量
        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  初始化表

        # get pair-wise relative position index for each token inside the window
        coords_h = torch.arange(self.window_size[0]) # coords_h = tensor([0,1,2,...,self.window_size[0]-1])  维度=Wh
        coords_w = torch.arange(self.window_size[1]) # coords_w = tensor([0,1,2,...,self.window_size[1]-1])  维度=Ww

        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

        '''
        后面我们需要将其展开成一维偏移量。而对于(2,1)和(1,2)这两个坐标，在二维上是不同的，但是通过将x\y坐标相加转换为一维偏移的时候
        他们的偏移量是相等的，所以需要对其做乘法操作，进行区分
        '''

        relative_coords[:, :, 0] *= 2 * self.window_size[1] - 1
        # 计算得到相对位置索引
        # relative_position_index.shape = (M2, M2) 意思是一共有这么多个位置
        relative_position_index = relative_coords.sum(-1)  # Wh*Ww, Wh*Ww 

        '''
        relative_position_index注册为一个不参与网络学习的变量
        '''
        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)

        '''
        使用从截断正态分布中提取的值填充输入张量
        self.relative_position_bias_table 是全0张量，通过trunc_normal_ 进行数值填充
        '''
        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)
            N: number of all patches in the window
            C: 输入通过线性层转化得到的维度C
            mask: (0/-inf) mask with shape of (num_windows, Wh*Ww, Wh*Ww) or None
        """
        B_, N, C = x.shape
        '''
        x.shape = (num_windows*B, N, C)
        self.qkv(x).shape = (num_windows*B, N, 3C)
        self.qkv(x).reshape(B_, N, 3, self.num_heads, C // self.num_heads).shape = (num_windows*B, N, 3, num_heads, C//num_heads)
        self.qkv(x).reshape(B_, N, 3, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4).shape = (3, num_windows*B, num_heads, N, C//num_heads)
        '''
        qkv = self.qkv(x).reshape(B_, N, 3, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
        '''
        q.shape = k.shape = v.shape = (num_windows*B, num_heads, N, C//num_heads)
        N = M2 代表patches的数量
        C//num_heads代表Q,K,V的维数
        '''
        q, k, v = qkv[0], qkv[1], qkv[2]  # make torchscript happy (cannot use tensor as tuple)

        # q乘上一个放缩系数，对应公式中的sqrt(d)
        q = q * self.scale

        # attn.shape = (num_windows*B, num_heads, N, N)  N = M2 代表patches的数量
        attn = (q @ k.transpose(-2, -1))

        '''
        self.relative_position_bias_table.shape = (2*Wh-1 * 2*Ww-1, nH)
        self.relative_position_index.shape = (Wh*Ww, Wh*Ww)
        self.relative_position_index矩阵中的所有值都是从self.relative_position_bias_table中取的
        self.relative_position_index是计算出来不可学习的量
        '''
        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

        '''
        attn.shape = (num_windows*B, num_heads, M2, M2)  N = M2 代表patches的数量
        .unsqueeze(0)：扩张维度，在0对应的位置插入维度1
        relative_position_bias.unsqueeze(0).shape = (1, num_heads, M2, M2)
        num_windows*B 通过广播机制传播，relative_position_bias.unsqueeze(0).shape = (1, nH, M2, M2) 的维度1会broadcast到数量num_windows*B
        表示所有batch通用一个索引矩阵和相对位置矩阵
        '''
        attn = attn + relative_position_bias.unsqueeze(0)

        # mask.shape = (num_windows, M2, M2)
        # attn.shape = (num_windows*B, num_heads, M2, M2)
        if mask is not None:
            nW = mask.shape[0]
            # attn.view(B_ // nW, nW, self.num_heads, N, N).shape = (B, num_windows, num_heads, M2, M2) 第一个M2代表有M2个token，第二个M2代表每个token要计算M2次QKT的值
            # mask.unsqueeze(1).unsqueeze(0).shape =                (1, num_windows, 1,         M2, M2) 第一个M2代表有M2个token，第二个M2代表每个token要计算M2次QKT的值
            # broadcast相加
            attn = attn.view(B_ // nW, nW, self.num_heads, N, N) + mask.unsqueeze(1).unsqueeze(0)
            # attn.shape = (B, num_windows, num_heads, M2, M2)
            attn = attn.view(-1, self.num_heads, N, N)
            attn = self.softmax(attn)
        else:
            attn = self.softmax(attn)

        attn = self.attn_drop(attn)

        '''
        v.shape = (num_windows*B, num_heads, M2, C//num_heads)  N=M2 代表patches的数量, C//num_heads代表输入的维度
        attn.shape = (num_windows*B, num_heads, M2, M2)
        attn@v .shape = (num_windows*B, num_heads, M2, C//num_heads)
        '''
        x = (attn @ v).transpose(1, 2).reshape(B_, N, C)   # B_:num_windows*B  N:M2  C=num_heads*C//num_heads

        #   self.proj = nn.Linear(dim, dim)  dim = C
        #   self.proj_drop = nn.Dropout(proj_drop)
        x = self.proj(x)
        x = self.proj_drop(x)
        return x  # x.shape = (num_windows*B, N, C)  N:窗口中所有patches的数量

    def extra_repr(self) -> str:
        return f'dim={self.dim}, window_size={self.window_size}, num_heads={self.num_heads}'

    def flops(self, N):
        # calculate flops for 1 window with token length of N
        flops = 0
        # qkv = self.qkv(x)
        flops += N * self.dim * 3 * self.dim
        # attn = (q @ k.transpose(-2, -1))
        flops += self.num_heads * N * (self.dim // self.num_heads) * N
        #  x = (attn @ v)
        flops += self.num_heads * N * N * (self.dim // self.num_heads)
        # x = self.proj(x)
        flops += N * self.dim * self.dim
        return flops

在上述程序中有一段mask相关程序：

if mask is not None:
            nW = mask.shape[0]
            # attn.view(B_ // nW, nW, self.num_heads, N, N).shape = (B, num_windows, num_heads, M2, M2) 第一个M2代表有M2个token，第二个M2代表每个token要计算M2次QKT的值
            # mask.unsqueeze(1).unsqueeze(0).shape =                (1, num_windows, 1,         M2, M2) 第一个M2代表有M2个token，第二个M2代表每个token要计算M2次QKT的值
            # broadcast相加
            attn = attn.view(B_ // nW, nW, self.num_heads, N, N) + mask.unsqueeze(1).unsqueeze(0)
            # attn.shape = (B, num_windows, num_heads, M2, M2)
            attn = attn.view(-1, self.num_heads, N, N)
            attn = self.softmax(attn)
        else:
            attn = self.softmax(attn)

这个部分对应的是Swin Transformer Block 中的SW-MSA

• 输入 x:82B×72×96 。
• 产生 QKV ，调用线性层后，得到 82B×72×(96×3) ，拆分给不同的head，得到 82B×72×3×3×32 ，第一个3是 QKV 的3，第二个3是3个head。再permute成 3×82B×3×72×32 ，再拆解成 q,k,v ，每个都是 82B×3×72×32 。表示所有图片的每个图片64个window，每个window对应到3个不同的head，都有一套49个patch、32维的特征。
• q 归一化
• qk 矩阵相乘求特征内积，得到 attn:82B×3×72×72
• 得到相对位置的编码信息relative_position_bias：
  • 代码如下：

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)

• 这里以window_size=3为例，解释以下过程：首先生成 coords:2×3×3 ，就是在一个 3×3 的窗口内，每个位置的 y,x 坐标，而relative_coords为 2×9×9 ，就是9个点中，每个点的 y 或 x 与其他所有点的差值，比如 [0][3][1] 表示3号点（第二行第一个点）与1号点（第一行第二个点）的 y 坐标的差值。然后变形，并让两个坐标分别加上 3−1=2 ，是因为这些坐标值范围 [0,2] ，因此差值的最小值为-2，加上2后从0开始。最后让 y 坐标乘上 2×3−1=5 ，应该是一个trick，调整差值范围。最后将两个维度的差值相加，得到relative_position_index， 32×32 ，为9个点之间两两之间的相对位置编码值，最后用来到self.relative_position_bias_table中寻址，注意相对位置的最大值为 (2M−2)(2M−1) ，而这个table最多有 (2M−1)(2M−1) 行，因此保证可以寻址，得到了一组给多个head使用的相对位置编码信息，这个table是可训练的参数。
• 回到代码中，得到的relative_position_bias为 3×72×72
• 将其加到attn上，最后一个维度softmax，dropout
• 与 v 矩阵相乘，并转置，合并多个头的信息，得到 82B×72×96
• 经过一层线性层，dropout，返回
• 返回赋值给attn_windows，变形为 82B×7×7×96
• 调用window_reverse，打回原状： B×56×56×96
• 返回给 x ，经过FFN：先加上原来的输入 x 作为residue结构，注意这里用到timm的DropPath，并且drop的概率是整个网络结构线性增长的。然后再加上两层mlp的结果。
• 返回结果 x 。

这样，整个过程就完成了，剩下的就是SW-MSA的一些不同的操作。

1. 首先将windows进行半个窗口的循环移位，上图中的1， 2步骤，使用torch.roll实现。
2. 在相同的窗口中计算自注意力，计算结果如下右图所示，window0的结构保存，但是针对window2的计算，其中3与3、6与6的计算生成了attn mask 中window2中的黄色区域，针对windows2中3与6、6与3之间不应该计算自注意力（attn mask中window2的蓝色区域），将蓝色区域mask赋值为-100，经过softmax之后，起作用可以忽略不计。同理window1与window3的计算一致。
3. 最后再进行循环移位，恢复原来的位置。

原论文图中的Stage和程序中的一个Stage不同：

程序中的BasicLayer为一个Stage，在BasicLayer中调用了上面讲到的SwinTransformerBlock和PatchMerging模块:

class BasicLayer(nn.Module):  # 论文图中每个stage里对应的若干个SwinTransformerBlock
    """ A basic Swin Transformer layer for one stage.

    Args:
        dim (int): Number of input channels.
        input_resolution (tuple[int]): Input resolution.
        depth (int): Number of blocks.
        num_heads (int): Number of attention heads.
        window_size (int): Local window size.
        mlp_ratio (float): Ratio of mlp hidden dim to embedding dim.
        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.
        drop (float, optional): Dropout rate. Default: 0.0
        attn_drop (float, optional): Attention dropout rate. Default: 0.0
        drop_path (float | tuple[float], optional): Stochastic depth rate. Default: 0.0
        norm_layer (nn.Module, optional): Normalization layer. Default: nn.LayerNorm
        downsample (nn.Module | None, optional): Downsample layer at the end of the layer. Default: None
        use_checkpoint (bool): Whether to use checkpointing to save memory. Default: False.
    """

    def __init__(self, dim, input_resolution, depth, num_heads, window_size,
                 mlp_ratio=4., qkv_bias=True, qk_scale=None, drop=0., attn_drop=0.,
                 drop_path=0., norm_layer=nn.LayerNorm, downsample=None, use_checkpoint=False):

        super().__init__()
        self.dim = dim
        self.input_resolution = input_resolution
        self.depth = depth # swin_transformer blocks的个数
        self.use_checkpoint = use_checkpoint

        # build blocks  从0开始的偶数位置的SwinTransformerBlock计算的是W-MSA,奇数位置的Block计算的是SW-MSA，且shift_size = window_size//2
        self.blocks = nn.ModuleList([
            SwinTransformerBlock(dim=dim, input_resolution=input_resolution,
                                 num_heads=num_heads, window_size=window_size,
                                 shift_size=0 if (i % 2 == 0) else window_size // 2,
                                 mlp_ratio=mlp_ratio,
                                 qkv_bias=qkv_bias, qk_scale=qk_scale,
                                 drop=drop, attn_drop=attn_drop,
                                 drop_path=drop_path[i] if isinstance(drop_path, list) else drop_path,
                                 norm_layer=norm_layer)
            for i in range(depth)])

        # patch merging layer
        if downsample is not None:
            self.downsample = downsample(input_resolution, dim=dim, norm_layer=norm_layer)
        else:
            self.downsample = None

    def forward(self, x):
        for blk in self.blocks:
            if self.use_checkpoint:
                x = checkpoint.checkpoint(blk, x)
            else:
                x = blk(x)  # blk = SwinTransformerBlock
        if self.downsample is not None:
            x = self.downsample(x)
        return x

    def extra_repr(self) -> str:
        return f"dim={self.dim}, input_resolution={self.input_resolution}, depth={self.depth}"

    def flops(self):
        flops = 0
        for blk in self.blocks:
            flops += blk.flops()
        if self.downsample is not None:
            flops += self.downsample.flops()
        return flops

Part 3 : 不同视觉任务输出

程序中对应的是图片分类任务，经过Part 2 之后的数据通过 norm/avgpool/flatten:

 x = self.norm(x)  # B L C
 x = self.avgpool(x.transpose(1, 2))  # B C 1
 x = torch.flatten(x, 1) # B C

之后通过nn.Linear将特征转化为对应的类别：

self.head = nn.Linear(self.num_features, num_classes) if num_classes > 0 else nn.Identity()

应用于其他不同的视觉任务时，只需要将输出进行特定的修改即可。

完整的SwinTransformer程序如下：

class SwinTransformer(nn.Module):
    r""" Swin Transformer
        A PyTorch impl of : `Swin Transformer: Hierarchical Vision Transformer using Shifted Windows`  -
          https://arxiv.org/pdf/2103.14030

    Args:
        img_size (int | tuple(int)): Input image size. Default 224
        patch_size (int | tuple(int)): Patch size. Default: 4
        in_chans (int): Number of input image channels. Default: 3
        num_classes (int): Number of classes for classification head. Default: 1000
        embed_dim (int): Patch embedding dimension. Default: 96
        depths (tuple(int)): Depth of each Swin Transformer layer.
        num_heads (tuple(int)): Number of attention heads in different layers.
        window_size (int): Window size. Default: 7
        mlp_ratio (float): Ratio of mlp hidden dim to embedding dim. Default: 4
        qkv_bias (bool): If True, add a learnable bias to query, key, value. Default: True
        qk_scale (float): Override default qk scale of head_dim ** -0.5 if set. Default: None
        drop_rate (float): Dropout rate. Default: 0
        attn_drop_rate (float): Attention dropout rate. Default: 0
        drop_path_rate (float): Stochastic depth rate. Default: 0.1
        norm_layer (nn.Module): Normalization layer. Default: nn.LayerNorm.
        ape (bool): If True, add absolute position embedding to the patch embedding. Default: False
        patch_norm (bool): If True, add normalization after patch embedding. Default: True
        use_checkpoint (bool): Whether to use checkpointing to save memory. Default: False
    """

    def __init__(self, img_size=224, patch_size=4, in_chans=3, num_classes=1000,
                 embed_dim=96, depths=[2, 2, 6, 2], num_heads=[3, 6, 12, 24],
                 window_size=7, mlp_ratio=4., qkv_bias=True, qk_scale=None,
                 drop_rate=0., attn_drop_rate=0., drop_path_rate=0.1,
                 norm_layer=nn.LayerNorm, ape=False, patch_norm=True,
                 use_checkpoint=False, **kwargs):
        super().__init__()

        self.num_classes = num_classes # 1000
        self.num_layers = len(depths) # [2, 2, 6, 2]  Swin_T 的配置
        self.embed_dim = embed_dim # 96
        self.ape = ape # False
        self.patch_norm = patch_norm # True
        self.num_features = int(embed_dim * 2 ** (self.num_layers - 1))  # 96*2^3
        self.mlp_ratio = mlp_ratio # 4

        # split image into non-overlapping patches
        self.patch_embed = PatchEmbed(
            img_size=img_size, patch_size=patch_size, in_chans=in_chans, embed_dim=embed_dim,
            norm_layer=norm_layer if self.patch_norm else None)
        num_patches = self.patch_embed.num_patches
        patches_resolution = self.patch_embed.patches_resolution
        self.patches_resolution = patches_resolution

        # absolute position embedding
        if self.ape:
            self.absolute_pos_embed = nn.Parameter(torch.zeros(1, num_patches, embed_dim))
            trunc_normal_(self.absolute_pos_embed, std=.02)

        self.pos_drop = nn.Dropout(p=drop_rate)

        # stochastic depth
        dpr = [x.item() for x in torch.linspace(0, drop_path_rate, sum(depths))]  # stochastic depth decay rule

        # build layers
        self.layers = nn.ModuleList()
        for i_layer in range(self.num_layers):
            layer = BasicLayer(dim=int(embed_dim * 2 ** i_layer),
                               input_resolution=(patches_resolution[0] // (2 ** i_layer),
                                                 patches_resolution[1] // (2 ** i_layer)),
                               depth=depths[i_layer],
                               num_heads=num_heads[i_layer],
                               window_size=window_size,
                               mlp_ratio=self.mlp_ratio,
                               qkv_bias=qkv_bias, qk_scale=qk_scale,
                               drop=drop_rate, attn_drop=attn_drop_rate,
                               drop_path=dpr[sum(depths[:i_layer]):sum(depths[:i_layer + 1])],
                               norm_layer=norm_layer,
                               downsample=PatchMerging if (i_layer < self.num_layers - 1) else None,
                               use_checkpoint=use_checkpoint)
            self.layers.append(layer)

        self.norm = norm_layer(self.num_features) # norm_layer = nn.LayerNorm
        self.avgpool = nn.AdaptiveAvgPool1d(1)
        self.head = nn.Linear(self.num_features, num_classes) if num_classes > 0 else nn.Identity()

        self.apply(self._init_weights)  # 使用self.apply 初始化参数

    def _init_weights(self, m):
        # is_instance 判断对象是否为已知类型
        if isinstance(m, nn.Linear):
            trunc_normal_(m.weight, std=.02)
            if isinstance(m, nn.Linear) and m.bias is not None:
                nn.init.constant_(m.bias, 0)
        elif isinstance(m, nn.LayerNorm):
            nn.init.constant_(m.bias, 0)
            nn.init.constant_(m.weight, 1.0)

    @torch.jit.ignore
    def no_weight_decay(self):
        return {'absolute_pos_embed'}

    @torch.jit.ignore
    def no_weight_decay_keywords(self):
        return {'relative_position_bias_table'}

    def forward_features(self, x):
        x = self.patch_embed(x)  # x.shape = (H//4, W//4, C)
        if self.ape:
            x = x + self.absolute_pos_embed
        x = self.pos_drop(x)  # self.pos_drop = nn.Dropout(p=drop_rate)

        for layer in self.layers:
            x = layer(x)

        x = self.norm(x)  # B L C
        x = self.avgpool(x.transpose(1, 2))  # B C 1
        x = torch.flatten(x, 1) # B C
        return x

    def forward(self, x):
        x = self.forward_features(x)  # x是论文图中Figure 3 a图中最后的输出
        #  self.head = nn.Linear(self.num_features, num_classes) if num_classes > 0 else nn.Identity()
        x = self.head(x) # x.shape = (B, num_classes)
        return x

    def flops(self):
        flops = 0
        flops += self.patch_embed.flops()
        for i, layer in enumerate(self.layers):
            flops += layer.flops()
        flops += self.num_features * self.patches_resolution[0] * self.patches_resolution[1] // (2 ** self.num_layers)
        flops += self.num_features * self.num_classes
        return flops

补充：有关swin transformer相对位置编码：