VIT（Vision Transformer）笔记_viv transformer矩阵计算

1. Self Attention公式

先理解,一个矩阵乘以它自己的转置,是在计算第一个行向量与自己的内积,表征两个向量的夹角，表征一个向量在另一个向量上的投影

投影的值大，说明两个向量相关度高。

矩阵是一个方阵，我们以行向量的角度理解，里面保存了每个向量与自己和其他向量进行内积运算的结果。 

Softmax之后，这些数字的和为1了

之后再乘X矩阵

这个新的行向量就是"早"字词向量经过注意力机制加权求和之后的表示。 

对于QKV矩阵，其实都是X矩阵的线性表示，采用W矩阵，是为了提高矩阵的拟合能力。

对于，是为了使方差变为1，使得模型稳定。

2. Multi-Head Attention

首先和self-attention一样，将a分成QKV,之后根据头数，将QKV均分

接着将每个head得到的结果进行concat拼接

接着将拼接后的结果与W融合

 代码实现如下

class Attention(nn.Module):
    def __init__(self,
                 dim,   # 输入token的dim
                 num_heads=8,
                 qkv_bias=False,
                 qk_scale=None,
                 attn_drop_ratio=0.,
                 proj_drop_ratio=0.):
        super(Attention, self).__init__()
        self.num_heads = num_heads
        head_dim = dim // num_heads
        self.scale = qk_scale or head_dim ** -0.5
        self.qkv = nn.Linear(dim, dim * 3, bias=qkv_bias)
        self.attn_drop = nn.Dropout(attn_drop_ratio)
        self.proj = nn.Linear(dim, dim)
        self.proj_drop = nn.Dropout(proj_drop_ratio)
 
    def forward(self, x):
        # [batch_size, num_patches + 1, total_embed_dim]
        B, N, C = x.shape
 
        # qkv(): -> [batch_size, num_patches + 1, 3 * total_embed_dim]
        # reshape: -> [batch_size, num_patches + 1, 3, num_heads, embed_dim_per_head]
        # permute: -> [3, batch_size, num_heads, num_patches + 1, embed_dim_per_head]
        qkv = self.qkv(x).reshape(B, N, 3, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
        # [batch_size, num_heads, num_patches + 1, embed_dim_per_head]
        q, k, v = qkv[0], qkv[1], qkv[2]  # make torchscript happy (cannot use tensor as tuple)
 
        # transpose: -> [batch_size, num_heads, embed_dim_per_head, num_patches + 1]
        # @: multiply -> [batch_size, num_heads, num_patches + 1, num_patches + 1]
        attn = (q @ k.transpose(-2, -1)) * self.scale
        attn = attn.softmax(dim=-1)
        attn = self.attn_drop(attn)
 
        # @: multiply -> [batch_size, num_heads, num_patches + 1, embed_dim_per_head]
        # transpose: -> [batch_size, num_patches + 1, num_heads, embed_dim_per_head]
        # reshape: -> [batch_size, num_patches + 1, total_embed_dim]
        x = (attn @ v).transpose(1, 2).reshape(B, N, C)
        x = self.proj(x)
        x = self.proj_drop(x)
        return x

3. Embedding层

将图片划分成一堆Patches

将输入图片(224x224)按照16x16大小的Patch进行划分，划分后会得到（224/16）^2 = 196个patch，每个patch的shape的大小则为【16,16,3】，之后将其拉成16*16*3=768的向量（token）

 代码实现如下

class PatchEmbed(nn.Module):
    """
    2D Image to Patch Embedding
    """
    def __init__(self, img_size=224, patch_size=16, in_c=3, embed_dim=768):
        super().__init__()
        img_size = (img_size, img_size)
        patch_size = (patch_size, patch_size)
        self.img_size = img_size
        self.patch_size = patch_size
        #224/16=14,224/16=14
        self.grid_size = (img_size[0] // patch_size[0], img_size[1] // patch_size[1])
        #14*14=196
        self.num_patches = self.grid_size[0] * self.grid_size[1]
 
        self.proj = nn.Conv2d(in_c, embed_dim, kernel_size=patch_size, stride=patch_size)
 
    def forward(self, x):
        B, C, H, W = x.shap
        # flatten: [B, C, H, W] -> [B, C, HW]    B*768*196
        # transpose: [B, C, HW] -> [B, HW, C]    B*196*768
        x = self.proj(x).flatten(2).transpose(1, 2)
        x = self.norm(x)
        return x

在Embedding层后，需增加一个Positional Encoding【196,768】->【197,768】 

# 定义一个可学习的Class token
self.cls_token = nn.Parameter(torch.zeros(1, 1, embed_dim))  # 第一个1为batch_size   embed_dim=768 
cls_token = self.cls_token.expand(x.shape[0], -1, -1)        # 保证cls_token的batch维度和x一致
if self.dist_token is None:
    x = torch.cat((cls_token, x), dim=1)  # [B, 197, 768]    self.dist_token为None,会执行这句
else:
    x = torch.cat((cls_token, self.dist_token.expand(x.shape[0], -1, -1), x), dim=1)
 

之后再加上一个位置编码

 # 定义一个可学习的位置编码
self.pos_embed = nn.Parameter(torch.zeros(1, num_patches + self.num_tokens, embed_dim))   #这个维度为（1，197，768）
x = x + self.pos_embed

4. Transformer Encoder

其实就是重复堆叠Encoder Block L次

5. MLP Head 

从【197,768】中取出【1,768】，然后进行分类

6. 网络结构