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引言与启发

自从ViT之后，关于vision transformer的研究呈井喷式爆发，从思路上分主要沿着两大个方向，一是提升ViT在图像分类的效果；二就是将ViT应用在其它图像任务中，比如分割和检测任务上，这里介绍的PVT（Pyramid Vision Transformer） 就属于后者。PVT相比ViT引入了和CNN类似的金字塔结构，使得PVT像CNN那样作为backbone应用在dense prediction任务（分割和检测等）。

设计思路

PVT的设计思路是目前在CNN中特征要想获取多尺度特征可以通过FPN（特征金字塔网络），那么Transformer是否也可以这样做呢，由此提出了PVT（Pyramid Vision Transformer）这个模块可以很轻松的与DETR类模型相结合从而实现端到端检测。
其实PVT的思想很简单，就是将Transformer与FPN相结合，通过卷积来将特征图变小，进而减少计算。

结合上图，我们可以看到其主要创新点为：

1. 相较于ViT，其使用了细粒度的图像patch，可以学习高分辨率的特征表示
2. 借鉴于CNN，设计了金字塔结构，可以进行多尺度特征的学习
3. 引入了SRA模块，主要用于改进多头注意力模块来减少QKV的计算量

模型流程

模型的初始化参数，在后面会对其进行讲解

def pvt_small():
    model = PyramidVisionTransformer(
        patch_size=4, embed_dims=[64, 128, 320, 512], num_heads=[1, 2, 5, 8], mlp_ratios=[8, 8, 4, 4], qkv_bias=True,
        norm_layer=partial(nn.LayerNorm, eps=1e-6), depths=[3, 4, 6, 3], sr_ratios=[8, 4, 2, 1])

首先我们的输入图片为torch.Size([2, 3, 224, 224])，即batch-size=2，channel=3，W=H=224
随后送入stage1：

        x, (H, W) = self.patch_embed1(x)
        pos_embed1 = self._get_pos_embed(self.pos_embed1, self.patch_embed1, H, W)
        x = x + pos_embed1
        x = self.pos_drop1(x)
        for blk in self.block1:
            x = blk(x, H, W)
        x = x.reshape(B, H, W, -1).permute(0, 3, 1, 2).contiguous()
        outs.append(x)

Patch操作

首先对输入图片进行patch操作，其完成对图片的切分以及线性映射（维度转换）
stage1时的patchEmbed定义为：

PatchEmbed(
  (proj): Conv2d(3, 64, kernel_size=(4, 4), stride=(4, 4))
  (norm): LayerNorm((64,), eps=1e-05, elementwise_affine=True)
)

  def forward(self, x):
        B, C, H, W = x.shape
        x = self.proj(x).flatten(2).transpose(1, 2)
        x = self.norm(x)
        H, W = H // self.patch_size[0], W // self.patch_size[1]
        return x, (H, W)

可以看到，送入patch_embed模块的向量首先获取其各个参数（B，C，W，H)
随后调用self.proj操作

self.proj = nn.Conv2d(in_chans, embed_dim, kernel_size=patch_size, stride=patch_size)

其为一个二维卷积：Conv2d(3, 64, kernel_size=(4, 4), stride=(4, 4))

卷积层输出尺寸： o = ⌊(i + 2p - k) / s⌋ + 1

padding默认为0，则输出大小为【2，64，56，56】
随后经过flatten展平操作得到【2，64，56X56】
随后transpose进行维度转换为：【2，56X56，64】即torch.Size([2, 3136, 64])
随后便是归一化操作以及对W，H大小改变并返还，此时W=H=56

位置编码

位置编码方面其使用的是可学习位置编码方式。
pos_embed是由下列方式初始化得到的，此时大小为：torch.Size([1, 3136, 64])

self.pos_embed1 = nn.Parameter(torch.zeros(1, self.patch_embed1.num_patches, embed_dims[0]))

随后进行处理：

pos_embed1 = self._get_pos_embed(self.pos_embed1, self.patch_embed1, H, W)

处理过程为：

def _get_pos_embed(self, pos_embed, patch_embed, H, W):
    if H * W == self.patch_embed1.num_patches:
        return pos_embed
    else:
        return F.interpolate(
            pos_embed.reshape(1, patch_embed.H, patch_embed.W, -1).permute(0, 3, 1, 2),
            size=(H, W), mode="bilinear").reshape(1, -1, H * W).permute(0, 2, 1)

紧接着将处理的语义特征信息与位置编码信息直接相加，注意：
此时的pos_embed1为：torch.Size([1, 3136, 64]) x 为 torch.Size([2, 3136, 64])，也是可以相加的

x = x + pos_embed1

如下测试，利用广播机制扩充维度进行计算

import torch
data = torch.randn((2, 1, 2, 2))
data1 = torch.randn((1, 1, 2, 2))
print(data)
print(data1)
print(data+data1)

注意力计算

进入注意力计算模块，每个stage中的注意力层有多个

for blk in self.block1:
    x = blk(x, H, W)

随后开始注意力的计算：
Q构造：经过一个linear进行构造，并进行分头计算（多头注意力）

self.q = nn.Linear(dim, dim, bias=qkv_bias)
 q = self.q(x).reshape(B, N, self.num_heads, C // self.num_heads).permute(0, 2, 1, 3)

得到q为：torch.Size([2, 1, 3136, 64])
随后进入到其创新的模块了，其是对K，V进行下采样，减小其数量：self.sr_ratio是缩小规模
x为torch.Size([2, 3136, 64])，首先经过permute进行维度变换为torch.Size([2, 64,3136]),随后经过reshape为：torch.Size([2, 64, 56, 56])

x_ = x.permute(0, 2, 1).reshape(B, C, H, W)

然后通过卷积操作进行降维：

self.sr = nn.Conv2d(dim, dim, kernel_size=sr_ratio, stride=sr_ratio)
x_ = self.sr(x_).reshape(B, C, -1).permute(0, 2, 1)

self.sr为：Conv2d(64, 64, kernel_size=(8, 8), stride=(8, 8))
通过 卷积层输出尺寸： o = ⌊(i + 2p - k) / s⌋ + 1
可得输出尺寸为：7即49 对应的tensor为：torch.Size([2, 49, 64])

然后便是使用x_来获取kv

self.kv = nn.Linear(dim, dim * 2, bias=qkv_bias)
kv = self.kv(x_).reshape(B, -1, 2, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)

得到kv为torch.Size([2, 2, 1, 49, 64])，k,v皆为torch.Size([2, 1, 49, 64])，但数值上不同
完整代码如下：

  if self.sr_ratio > 1:
        x_ = x.permute(0, 2, 1).reshape(B, C, H, W)
        x_ = self.sr(x_).reshape(B, C, -1).permute(0, 2, 1)
        x_ = self.norm(x_)
        kv = self.kv(x_).reshape(B, -1, 2, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
    else:
        kv = self.kv(x).reshape(B, -1, 2, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)

然后便是进行一系列计算了：

x = (attn @ v).transpose(1, 2).reshape(B, N, C)
@实际为x@y=x.matmul(y)

最终计算得到注意力机制的结果x结果仍为torch.Size([2, 3136, 64])

注意力机制模块完整代码如下：

def forward(self, x, H, W):
    B, N, C = x.shape
    q = self.q(x).reshape(B, N, self.num_heads, C // self.num_heads).permute(0, 2, 1, 3)
    if self.sr_ratio > 1:
        x_ = x.permute(0, 2, 1).reshape(B, C, H, W)
        x_ = self.sr(x_).reshape(B, C, -1).permute(0, 2, 1)
        x_ = self.norm(x_)
        kv = self.kv(x_).reshape(B, -1, 2, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
    else:
        kv = self.kv(x).reshape(B, -1, 2, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
    k, v = kv[0], kv[1]
    attn = (q @ k.transpose(-2, -1)) * self.scale
    attn = attn.softmax(dim=-1)
    attn = self.attn_drop(attn)

    x = (attn @ v).transpose(1, 2).reshape(B, N, C)
    x = self.proj(x)
    x = self.proj_drop(x)

    return x

最终得到x经过reshape恢复为2维结果，再次进入下一个stage进行计算

x = x.reshape(B, H, W, -1).permute(0, 3, 1, 2).contiguous()

随后经过卷积缩小特征图大小，在空间上的损失由维度进行补偿，下一个阶段x为：

torch.Size([2, 784, 128])

通过依次该过程，便将其大小进行缩减，通过也将其获取了多尺度信息。值得注意的是，只有stage1上patch=4，在后面的三个stage上patch都为2，这样也就参考卷积，其是一个二倍大小的关系。

总体来看，Pyramid Version Transformer的设计还是较为容易理解的，下面博主从代码入手，来详细讲解PVT的构建过程。

完整代码如下：

import torch
import torch.nn as nn
import torch.nn.functional as F
from functools import partial

from timm.models.layers import DropPath, to_2tuple, trunc_normal_
from timm.models.registry import register_model
from timm.models.vision_transformer import _cfg


class Mlp(nn.Module):
    def __init__(self, in_features, hidden_features=None, out_features=None, act_layer=nn.GELU, drop=0.):
        super().__init__()
        out_features = out_features or in_features
        hidden_features = hidden_features or in_features
        self.fc1 = nn.Linear(in_features, hidden_features)
        self.act = act_layer()
        self.fc2 = nn.Linear(hidden_features, out_features)
        self.drop = nn.Dropout(drop)

    def forward(self, x):
        x = self.fc1(x)
        x = self.act(x)
        x = self.drop(x)
        x = self.fc2(x)
        x = self.drop(x)
        return x


class Attention(nn.Module):
    def __init__(self, dim, num_heads=8, qkv_bias=False, qk_scale=None, attn_drop=0., proj_drop=0., sr_ratio=1):
        super().__init__()
        assert dim % num_heads == 0, f"dim {dim} should be divided by num_heads {num_heads}."

        self.dim = dim
        self.num_heads = num_heads
        head_dim = dim // num_heads
        self.scale = qk_scale or head_dim ** -0.5

        self.q = nn.Linear(dim, dim, bias=qkv_bias)
        self.kv = nn.Linear(dim, dim * 2, bias=qkv_bias)
        self.attn_drop = nn.Dropout(attn_drop)
        self.proj = nn.Linear(dim, dim)
        self.proj_drop = nn.Dropout(proj_drop)

        self.sr_ratio = sr_ratio
        if sr_ratio > 1:
            self.sr = nn.Conv2d(dim, dim, kernel_size=sr_ratio, stride=sr_ratio)
            self.norm = nn.LayerNorm(dim)

    def forward(self, x, H, W):
        B, N, C = x.shape
        q = self.q(x).reshape(B, N, self.num_heads, C // self.num_heads).permute(0, 2, 1, 3)

        if self.sr_ratio > 1:
            x_ = x.permute(0, 2, 1).reshape(B, C, H, W)
            x_ = self.sr(x_).reshape(B, C, -1).permute(0, 2, 1)
            x_ = self.norm(x_)
            kv = self.kv(x_).reshape(B, -1, 2, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
        else:
            kv = self.kv(x).reshape(B, -1, 2, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
        k, v = kv[0], kv[1]

        attn = (q @ k.transpose(-2, -1)) * self.scale
        attn = attn.softmax(dim=-1)
        attn = self.attn_drop(attn)

        x = (attn @ v).transpose(1, 2).reshape(B, N, C)
        x = self.proj(x)
        x = self.proj_drop(x)

        return x


class Block(nn.Module):

    def __init__(self, dim, num_heads, mlp_ratio=4., qkv_bias=False, qk_scale=None, drop=0., attn_drop=0.,
                 drop_path=0., act_layer=nn.GELU, norm_layer=nn.LayerNorm, sr_ratio=1):
        super().__init__()
        self.norm1 = norm_layer(dim)
        self.attn = Attention(
            dim,
            num_heads=num_heads, qkv_bias=qkv_bias, qk_scale=qk_scale,
            attn_drop=attn_drop, proj_drop=drop, sr_ratio=sr_ratio)
        # NOTE: drop path for stochastic depth, we shall see if this is better than dropout here
        self.drop_path = DropPath(drop_path) if drop_path > 0. else nn.Identity()
        self.norm2 = norm_layer(dim)
        mlp_hidden_dim = int(dim * mlp_ratio)
        self.mlp = Mlp(in_features=dim, hidden_features=mlp_hidden_dim, act_layer=act_layer, drop=drop)

    def forward(self, x, H, W):
        x = x + self.drop_path(self.attn(self.norm1(x), H, W))
        x = x + self.drop_path(self.mlp(self.norm2(x)))

        return x


class PatchEmbed(nn.Module):
    """ Image to Patch Embedding
    """

    def __init__(self, img_size=224, patch_size=16, in_chans=3, embed_dim=768):
        super().__init__()
        img_size = to_2tuple(img_size)
        patch_size = to_2tuple(patch_size)

        self.img_size = img_size
        self.patch_size = patch_size
        assert img_size[0] % patch_size[0] == 0 and img_size[1] % patch_size[1] == 0, 
            f"img_size {img_size} should be divided by patch_size {patch_size}."
        self.H, self.W = img_size[0] // patch_size[0], img_size[1] // patch_size[1]
        self.num_patches = self.H * self.W
        self.proj = nn.Conv2d(in_chans, embed_dim, kernel_size=patch_size, stride=patch_size)
        self.norm = nn.LayerNorm(embed_dim)

    def forward(self, x):
        B, C, H, W = x.shape

        x = self.proj(x).flatten(2).transpose(1, 2)
        x = self.norm(x)
        H, W = H // self.patch_size[0], W // self.patch_size[1]

        return x, (H, W)


class PyramidVisionTransformer(nn.Module):
    def __init__(self, img_size=224, patch_size=16, in_chans=3, num_classes=1000, embed_dims=[64, 128, 256, 512],
                 num_heads=[1, 2, 4, 8], mlp_ratios=[4, 4, 4, 4], qkv_bias=False, qk_scale=None, drop_rate=0.,
                 attn_drop_rate=0., drop_path_rate=0., norm_layer=nn.LayerNorm,
                 depths=[3, 4, 6, 3], sr_ratios=[8, 4, 2, 1], F4=False):
        super().__init__()
        self.num_classes = num_classes
        self.depths = depths
        self.F4 = F4

        # patch_embed
        self.patch_embed1 = PatchEmbed(img_size=img_size, patch_size=patch_size, in_chans=in_chans,
                                       embed_dim=embed_dims[0])
        self.patch_embed2 = PatchEmbed(img_size=img_size // 4, patch_size=2, in_chans=embed_dims[0],
                                       embed_dim=embed_dims[1])
        self.patch_embed3 = PatchEmbed(img_size=img_size // 8, patch_size=2, in_chans=embed_dims[1],
                                       embed_dim=embed_dims[2])
        self.patch_embed4 = PatchEmbed(img_size=img_size // 16, patch_size=2, in_chans=embed_dims[2],
                                       embed_dim=embed_dims[3])

        # pos_embed
        self.pos_embed1 = nn.Parameter(torch.zeros(1, self.patch_embed1.num_patches, embed_dims[0]))
        self.pos_drop1 = nn.Dropout(p=drop_rate)
        self.pos_embed2 = nn.Parameter(torch.zeros(1, self.patch_embed2.num_patches, embed_dims[1]))
        self.pos_drop2 = nn.Dropout(p=drop_rate)
        self.pos_embed3 = nn.Parameter(torch.zeros(1, self.patch_embed3.num_patches, embed_dims[2]))
        self.pos_drop3 = nn.Dropout(p=drop_rate)
        self.pos_embed4 = nn.Parameter(torch.zeros(1, self.patch_embed4.num_patches + 1, embed_dims[3]))
        self.pos_drop4 = nn.Dropout(p=drop_rate)

        # transformer encoder
        dpr = [x.item() for x in torch.linspace(0, drop_path_rate, sum(depths))]  # stochastic depth decay rule
        cur = 0
        self.block1 = nn.ModuleList([Block(
            dim=embed_dims[0], num_heads=num_heads[0], mlp_ratio=mlp_ratios[0], qkv_bias=qkv_bias, qk_scale=qk_scale,
            drop=drop_rate, attn_drop=attn_drop_rate, drop_path=dpr[cur + i], norm_layer=norm_layer,
            sr_ratio=sr_ratios[0])
            for i in range(depths[0])])

        cur += depths[0]
        self.block2 = nn.ModuleList([Block(
            dim=embed_dims[1], num_heads=num_heads[1], mlp_ratio=mlp_ratios[1], qkv_bias=qkv_bias, qk_scale=qk_scale,
            drop=drop_rate, attn_drop=attn_drop_rate, drop_path=dpr[cur + i], norm_layer=norm_layer,
            sr_ratio=sr_ratios[1])
            for i in range(depths[1])])

        cur += depths[1]
        self.block3 = nn.ModuleList([Block(
            dim=embed_dims[2], num_heads=num_heads[2], mlp_ratio=mlp_ratios[2], qkv_bias=qkv_bias, qk_scale=qk_scale,
            drop=drop_rate, attn_drop=attn_drop_rate, drop_path=dpr[cur + i], norm_layer=norm_layer,
            sr_ratio=sr_ratios[2])
            for i in range(depths[2])])

        cur += depths[2]
        self.block4 = nn.ModuleList([Block(
            dim=embed_dims[3], num_heads=num_heads[3], mlp_ratio=mlp_ratios[3], qkv_bias=qkv_bias, qk_scale=qk_scale,
            drop=drop_rate, attn_drop=attn_drop_rate, drop_path=dpr[cur + i], norm_layer=norm_layer,
            sr_ratio=sr_ratios[3])
            for i in range(depths[3])])

        # init weights
        trunc_normal_(self.pos_embed1, std=.02)
        trunc_normal_(self.pos_embed2, std=.02)
        trunc_normal_(self.pos_embed3, std=.02)
        trunc_normal_(self.pos_embed4, std=.02)
        self.apply(self._init_weights)

    def init_weights(self, pretrained=True):
        import torch

        # if isinstance(pretrained, str):
        #     logger = get_root_logger()
        #     load_checkpoint(self, pretrained, map_location='cpu', strict=False, logger=logger)

    def reset_drop_path(self, drop_path_rate):
        dpr = [x.item() for x in torch.linspace(0, drop_path_rate, sum(self.depths))]
        cur = 0
        for i in range(self.depths[0]):
            self.block1[i].drop_path.drop_prob = dpr[cur + i]

        cur += self.depths[0]
        for i in range(self.depths[1]):
            self.block2[i].drop_path.drop_prob = dpr[cur + i]

        cur += self.depths[1]
        for i in range(self.depths[2]):
            self.block3[i].drop_path.drop_prob = dpr[cur + i]

        cur += self.depths[2]
        for i in range(self.depths[3]):
            self.block4[i].drop_path.drop_prob = dpr[cur + i]

    def _init_weights(self, m):
        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)

    def _get_pos_embed(self, pos_embed, patch_embed, H, W):
        if H * W == self.patch_embed1.num_patches:
            return pos_embed
        else:
            return F.interpolate(
                pos_embed.reshape(1, patch_embed.H, patch_embed.W, -1).permute(0, 3, 1, 2),
                size=(H, W), mode="bilinear").reshape(1, -1, H * W).permute(0, 2, 1)

    def forward_features(self, x):
        outs = []

        B = x.shape[0]

        # stage 1
        x, (H, W) = self.patch_embed1(x)
        pos_embed1 = self._get_pos_embed(self.pos_embed1, self.patch_embed1, H, W)
        x = x + pos_embed1
        x = self.pos_drop1(x)
        for blk in self.block1:
            x = blk(x, H, W)
        x = x.reshape(B, H, W, -1).permute(0, 3, 1, 2).contiguous()
        outs.append(x)

        # stage 2
        x, (H, W) = self.patch_embed2(x)
        pos_embed2 = self._get_pos_embed(self.pos_embed2, self.patch_embed2, H, W)
        x = x + pos_embed2
        x = self.pos_drop2(x)
        for blk in self.block2:
            x = blk(x, H, W)
        x = x.reshape(B, H, W, -1).permute(0, 3, 1, 2).contiguous()
        outs.append(x)

        # stage 3
        x, (H, W) = self.patch_embed3(x)
        pos_embed3 = self._get_pos_embed(self.pos_embed3, self.patch_embed3, H, W)
        x = x + pos_embed3
        x = self.pos_drop3(x)
        for blk in self.block3:
            x = blk(x, H, W)
        x = x.reshape(B, H, W, -1).permute(0, 3, 1, 2).contiguous()
        outs.append(x)

        # stage 4
        x, (H, W) = self.patch_embed4(x)
        pos_embed4 = self._get_pos_embed(self.pos_embed4[:, 1:], self.patch_embed4, H, W)
        x = x + pos_embed4
        x = self.pos_drop4(x)
        for blk in self.block4:
            x = blk(x, H, W)
        x = x.reshape(B, H, W, -1).permute(0, 3, 1, 2).contiguous()
        outs.append(x)

        return outs

    def forward(self, x):
        x = self.forward_features(x)

        if self.F4:
            x = x[3:4]

        return x


def _conv_filter(state_dict, patch_size=16):
    """ convert patch embedding weight from manual patchify + linear proj to conv"""
    out_dict = {}
    for k, v in state_dict.items():
        if 'patch_embed.proj.weight' in k:
            v = v.reshape((v.shape[0], 3, patch_size, patch_size))
        out_dict[k] = v

    return out_dict

def pvt_small():
    model = PyramidVisionTransformer(
        patch_size=4, embed_dims=[64, 128, 320, 512], num_heads=[1, 2, 5, 8], mlp_ratios=[8, 8, 4, 4], qkv_bias=True,
        norm_layer=partial(nn.LayerNorm, eps=1e-6), depths=[3, 4, 6, 3], sr_ratios=[8, 4, 2, 1])

    return model

model = pvt_small()
data = torch.randn((2, 3, 224, 224))
feature = model(data)
print(model)
for out in feature:
    print(out.shape)