ViT论文阅读

Vision Transformer

ViT

ViT首次将Transformer应用到图像处理领域，属于Transformer的Encoder-only类型。相比同参数量的CNN，经过大规模数据集训练后有着更好的效果。

ViT中使用到的方法

分块(Patch)

将Transformer应用到图像上，首先面临的问题就是token的规模过大，将占用大量内存。ViT中先将图像进行分块展平，再使用线性层映射到低维输入到Transformer中，有效地减少了token的长度。

对于2D图片$\mathbf x\in \mathbb{R}^{H\times W\times C}$，将其分割成$P\times P$的patch，展平得到$\mathbf x_p\in \mathbb{R}^{N\times (P^2\cdot C)},N=\frac{HW}{P^2}$。$N$对应Transformer输入序列的有效长度，而Transformer使用的向量长度为$D$，则需要使用可学习的线性映射将图像patch映射到$D$维上，即$\mathbf x_p\mathbf E\in \mathbb{R}^{N\times D}$。

将图像转为embedding的方式：

• 将图像分块，每一块展平作为一个token。

• 使用二维卷积预处理，将得到特征图flatten。

位置编码

使用可学习的一维位置编码，让模型自行学习图片像素的位置关系。

CNN的结构有以下特性：

• 相邻区域具有相似特征
• 平移不变性

ViT相比CNN，消除了这些归纳偏置。Encoder中只有MLP具有局部、平移不变的特性，而自注意力层则会关注全局特性。

Class Token

Class token的机制源于BERT，ViT希望也能将其用于图像分类任务中，提出在输入的token中加入一个class token作为第0个向量，与由图像得到的token一同输入到Transformer中。最后取Transformer输出中的第0个向量作为分类预测的依据。另一种处理方式为对输出的图像token进行平均池化，作为分类判断的特征。

ViT为了验证Transformer在图像处理中也能有优秀的处理能力，使用了前者。

Transformer Encoder

ViT的编码器设计与Transformer的编码器结构相同，由多个包含多头自注意力和MLP的块连接而成。每个块中包含两个残差结构，在残差结构的头部使用LayerNorm。MLP包含两层，使用GELU作为激活函数。

$$\begin{aligned} \mathbf{z_0}&=[\mathbf x_{\text{class}};\mathbf x_{p}^{1}\mathbf{E};\mathbf{x}_{p}^2\mathbf{E};\dots \mathbf{x}_{p}^N\mathbf{E}]+\mathbf{E}_{pos}, & \mathbf{E} \in \mathbb{R}^{(P^2 \cdot C)\times D}, \mathbf{E}_{\text{pos}}\in\mathbb{R}^{(N+1)\times D}\newline \mathbf{z}_l'&= \text{MSA}(\text{LN}(\mathbf {z}_{l-1}))+\mathbf{z}_{l-1}, & l=1\dots L\newline \mathbf{z}_l &= \text{MLP}(\text{LN}(\mathbf{z}'_l))+\mathbf{z}'_l, & l=1\dots L\newline \mathbf{y} &= \text{LN}(\mathbf{z}_L^0) \end{aligned}$$

多头注意力机制：

• 标准自注意力机制：

  通过MLP将序列$\mathbf z\in \mathbb R ^{N\times D}$映射到$q,k,v\in\mathbb R^{N\times D_h}$。注意力的权重$A_{ij}$由$q,k$的相似程度决定，并以加权的方式作用到$v$上：

  $$\begin{aligned} \left[\mathbf q, \mathbf k, \mathbf v\right]&=\mathbf z \mathbf U_{qkv}, &\mathbf U_{qkv}\in \mathbb R^{D\times 3D_h} \newline A&=\text{softmax}(\mathbf q\mathbf k^\top/\sqrt{D_h}), &A\in \mathbb R^{N\times N}\newline \text{SA}(\mathbf z)&=A\mathbf v \end{aligned}$$

• 多头自注意力机制：将输入序列$\mathbf z\in \mathbb R ^{N\times D}$拆分为$k$个等长的序列$\mathbf z_i\in\mathbb R^{N\times \frac Dk}$，并行运行$k$个自注意力操作，最后将多头的输出拼接为一个输出。

代码实现

vit-pytorch/vit_pytorch/vit.py

FeedForward对应Transformer Encoder内的MLP前馈部分：

class FeedForward(nn.Module):
    def __init__(self, dim, hidden_dim, dropout = 0.):
        super().__init__()
        self.net = nn.Sequential(
            nn.LayerNorm(dim),
            nn.Linear(dim, hidden_dim),
            nn.GELU(),
            nn.Dropout(dropout),
            nn.Linear(hidden_dim, dim),
            nn.Dropout(dropout)
        )

    def forward(self, x):
        return self.net(x)

Attention对应Transformer Encoder内的Attention部分：

class Attention(nn.Module):
    def __init__(self, dim, heads = 8, dim_head = 64, dropout = 0.):
        super().__init__()
        inner_dim = dim_head *  heads	# 将输入的维度按照多头注意力机制划分
        project_out = not (heads == 1 and dim_head == dim) # 判断是否为多头自注意力

        self.heads = heads
        self.scale = dim_head ** -0.5

        self.norm = nn.LayerNorm(dim)

        self.attend = nn.Softmax(dim = -1)
        self.dropout = nn.Dropout(dropout)

        self.to_qkv = nn.Linear(dim, inner_dim * 3, bias = False)

        self.to_out = nn.Sequential(
            nn.Linear(inner_dim, dim),
            nn.Dropout(dropout)
        ) if project_out else nn.Identity()

    def forward(self, x):
        """
        Args:
        	x: torch.Tensor, token with dimension: [B, N, D]
        """
        x = self.norm(x)

        qkv = self.to_qkv(x).chunk(3, dim = -1)
        # qkv: List[torch.Tensor]
        q, k, v = map(lambda t: rearrange(t, 'b n (h d) -> b h n d', h = self.heads), qkv)
		# q, k, v: [N, D, heads, dim_head]
        dots = torch.matmul(q, k.transpose(-1, -2)) * self.scale
		# dots: [N, D, heads, heads]
        attn = self.attend(dots)
        attn = self.dropout(attn)

        out = torch.matmul(attn, v)
        out = rearrange(out, 'b h n d -> b n (h d)')
        return self.to_out(out)

ViT的Transformer部分（只需要Encoder）：

class Transformer(nn.Module):
    def __init__(self, dim, depth, heads, dim_head, mlp_dim, dropout = 0.):
        super().__init__()
        self.norm = nn.LayerNorm(dim)
        self.layers = nn.ModuleList([])
        for _ in range(depth):
            self.layers.append(nn.ModuleList([
                Attention(dim, heads = heads, dim_head = dim_head, dropout = dropout),
                FeedForward(dim, mlp_dim, dropout = dropout)
            ]))

    def forward(self, x):
        for attn, ff in self.layers:
            x = attn(x) + x
            x = ff(x) + x

        return self.norm(x)

class ViT(nn.Module):
    def __init__(self, *, image_size, patch_size, num_classes, dim, depth, heads, mlp_dim, pool = 'cls', channels = 3, dim_head = 64, dropout = 0., emb_dropout = 0.):
        super().__init__()
        image_height, image_width = pair(image_size)
        patch_height, patch_width = pair(patch_size)

        assert image_height % patch_height == 0 and image_width % patch_width == 0, 'Image dimensions must be divisible by the patch size.'

        num_patches = (image_height // patch_height) * (image_width // patch_width)
        patch_dim = channels * patch_height * patch_width
        assert pool in {'cls', 'mean'}, 'pool type must be either cls (cls token) or mean (mean pooling)'

        # 将patch的维度映射到Transformer能处理的token的长度
        self.to_patch_embedding = nn.Sequential(
            Rearrange('b c (h p1) (w p2) -> b (h w) (p1 p2 c)', p1 = patch_height, p2 = patch_width),
            nn.LayerNorm(patch_dim),
            nn.Linear(patch_dim, dim),
            nn.LayerNorm(dim),
        )

        self.pos_embedding = nn.Parameter(torch.randn(1, num_patches + 1, dim))
        self.cls_token = nn.Parameter(torch.randn(1, 1, dim))
        self.dropout = nn.Dropout(emb_dropout)

        self.transformer = Transformer(dim, depth, heads, dim_head, mlp_dim, dropout)

        self.pool = pool
        self.to_latent = nn.Identity()

        self.mlp_head = nn.Linear(dim, num_classes)

    def forward(self, img):
        """
        Args:
        	img: torch.Tensor, [B, C, H, W]
        """
        x = self.to_patch_embedding(img)
        # x: [B, N, D]
        b, n, _ = x.shape

        cls_tokens = repeat(self.cls_token, '1 1 d -> b 1 d', b = b)
        x = torch.cat((cls_tokens, x), dim=1)
        x += self.pos_embedding[:, :(n + 1)]
        x = self.dropout(x)

        x = self.transformer(x)

        x = x.mean(dim = 1) if self.pool == 'mean' else x[:, 0]

        x = self.to_latent(x)
        return self.mlp_head(x)