Vision Transformer结构解析-编程知识

Vision Transformer结构解析

ViT简介
ViT参数量
ViT三大模块
- ViT图像预处理模块——PatchEmbed
- 多层Transformer Encoder模块
- MLP（FFN）模块
基本的Transformer模块
Vision Transformer类的实现
Transformer知识点
- 网络结构
- 计算复杂度对比
- Transformer的参数量和计算量
- - Transformer的参数量
  - Transformer的计算量

ViT简介

Vision Transformer。transformer于2017年的Attention is all your need提出，该模型最大的创新点就是将transformer应用于cv任务。

论文题目：An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale
论文链接：https://arxiv.org/pdf/2010.11929.pdf
代码地址：https://github.com/google-research/vision_transformer

ViT模型整体结构图如下：
在这里插入图片描述

ViT三种不同尺寸模型的参数对比：

ViT参数量

vit_base_patch16_224，num_classes=5, has_logits=False

Total params: 85,650,437
Trainable params: 85,650,437
Non-trainable params: 0
----------------------------------------------------------------
Input size (MB): 0.57
Forward/backward pass size (MB): 408.54
Params size (MB): 326.73
Estimated Total Size (MB): 735.84
----------------------------------------------------------------

vit_base_patch32_224，num_classes=5, has_logits=False

Total params: 87,419,909
Trainable params: 87,419,909
Non-trainable params: 0
----------------------------------------------------------------
Input size (MB): 0.57
Forward/backward pass size (MB): 95.61
Params size (MB): 333.48
Estimated Total Size (MB): 429.66
----------------------------------------------------------------

vit_large_patch32_224，num_classes=5, has_logits=False

Total params: 305,463,301
Trainable params: 305,463,301
Non-trainable params: 0
----------------------------------------------------------------
Input size (MB): 0.57
Forward/backward pass size (MB): 253.01
Params size (MB): 1165.25
Estimated Total Size (MB): 1418.84

vit_huge_patch14_224，num_classes=5, has_logits=False

Total params: 630,440,965
Trainable params: 630,440,965
Non-trainable params: 0
----------------------------------------------------------------
Input size (MB): 0.57
Forward/backward pass size (MB): 2358.66
Params size (MB): 2404.94
Estimated Total Size (MB): 4764.17
----------------------------------------------------------------

网络结构打印，以常用的【vit_base_patch32_224，num_classes=5】为例：

----------------------------------------------------------------Layer (type)               Output Shape         Param #
================================================================Conv2d-1            [-1, 768, 7, 7]       2,360,064Identity-2              [-1, 49, 768]               0PatchEmbed-3              [-1, 49, 768]               0Dropout-4              [-1, 50, 768]               0LayerNorm-5              [-1, 50, 768]           1,536Linear-6             [-1, 50, 2304]       1,771,776Dropout-7           [-1, 12, 50, 50]               0Linear-8              [-1, 50, 768]         590,592Dropout-9              [-1, 50, 768]               0Attention-10              [-1, 50, 768]               0Identity-11              [-1, 50, 768]               0LayerNorm-12              [-1, 50, 768]           1,536Linear-13             [-1, 50, 3072]       2,362,368GELU-14             [-1, 50, 3072]               0Dropout-15             [-1, 50, 3072]               0Linear-16              [-1, 50, 768]       2,360,064Dropout-17              [-1, 50, 768]               0Mlp-18              [-1, 50, 768]               0Identity-19              [-1, 50, 768]               0Block-20              [-1, 50, 768]               0LayerNorm-21              [-1, 50, 768]           1,536Linear-22             [-1, 50, 2304]       1,771,776Dropout-23           [-1, 12, 50, 50]               0Linear-24              [-1, 50, 768]         590,592Dropout-25              [-1, 50, 768]               0Attention-26              [-1, 50, 768]               0Identity-27              [-1, 50, 768]               0LayerNorm-28              [-1, 50, 768]           1,536Linear-29             [-1, 50, 3072]       2,362,368GELU-30             [-1, 50, 3072]               0Dropout-31             [-1, 50, 3072]               0Linear-32              [-1, 50, 768]       2,360,064Dropout-33              [-1, 50, 768]               0Mlp-34              [-1, 50, 768]               0Identity-35              [-1, 50, 768]               0Block-36              [-1, 50, 768]               0LayerNorm-37              [-1, 50, 768]           1,536Linear-38             [-1, 50, 2304]       1,771,776Dropout-39           [-1, 12, 50, 50]               0Linear-40              [-1, 50, 768]         590,592Dropout-41              [-1, 50, 768]               0Attention-42              [-1, 50, 768]               0Identity-43              [-1, 50, 768]               0LayerNorm-44              [-1, 50, 768]           1,536Linear-45             [-1, 50, 3072]       2,362,368GELU-46             [-1, 50, 3072]               0Dropout-47             [-1, 50, 3072]               0Linear-48              [-1, 50, 768]       2,360,064Dropout-49              [-1, 50, 768]               0Mlp-50              [-1, 50, 768]               0Identity-51              [-1, 50, 768]               0Block-52              [-1, 50, 768]               0LayerNorm-53              [-1, 50, 768]           1,536Linear-54             [-1, 50, 2304]       1,771,776Dropout-55           [-1, 12, 50, 50]               0Linear-56              [-1, 50, 768]         590,592Dropout-57              [-1, 50, 768]               0Attention-58              [-1, 50, 768]               0Identity-59              [-1, 50, 768]               0LayerNorm-60              [-1, 50, 768]           1,536Linear-61             [-1, 50, 3072]       2,362,368GELU-62             [-1, 50, 3072]               0Dropout-63             [-1, 50, 3072]               0Linear-64              [-1, 50, 768]       2,360,064Dropout-65              [-1, 50, 768]               0Mlp-66              [-1, 50, 768]               0Identity-67              [-1, 50, 768]               0Block-68              [-1, 50, 768]               0LayerNorm-69              [-1, 50, 768]           1,536Linear-70             [-1, 50, 2304]       1,771,776Dropout-71           [-1, 12, 50, 50]               0Linear-72              [-1, 50, 768]         590,592Dropout-73              [-1, 50, 768]               0Attention-74              [-1, 50, 768]               0Identity-75              [-1, 50, 768]               0LayerNorm-76              [-1, 50, 768]           1,536Linear-77             [-1, 50, 3072]       2,362,368GELU-78             [-1, 50, 3072]               0Dropout-79             [-1, 50, 3072]               0Linear-80              [-1, 50, 768]       2,360,064Dropout-81              [-1, 50, 768]               0Mlp-82              [-1, 50, 768]               0Identity-83              [-1, 50, 768]               0Block-84              [-1, 50, 768]               0LayerNorm-85              [-1, 50, 768]           1,536Linear-86             [-1, 50, 2304]       1,771,776Dropout-87           [-1, 12, 50, 50]               0Linear-88              [-1, 50, 768]         590,592Dropout-89              [-1, 50, 768]               0Attention-90              [-1, 50, 768]               0Identity-91              [-1, 50, 768]               0LayerNorm-92              [-1, 50, 768]           1,536Linear-93             [-1, 50, 3072]       2,362,368GELU-94             [-1, 50, 3072]               0Dropout-95             [-1, 50, 3072]               0Linear-96              [-1, 50, 768]       2,360,064Dropout-97              [-1, 50, 768]               0Mlp-98              [-1, 50, 768]               0Identity-99              [-1, 50, 768]               0Block-100              [-1, 50, 768]               0LayerNorm-101              [-1, 50, 768]           1,536Linear-102             [-1, 50, 2304]       1,771,776Dropout-103           [-1, 12, 50, 50]               0Linear-104              [-1, 50, 768]         590,592Dropout-105              [-1, 50, 768]               0Attention-106              [-1, 50, 768]               0Identity-107              [-1, 50, 768]               0LayerNorm-108              [-1, 50, 768]           1,536Linear-109             [-1, 50, 3072]       2,362,368GELU-110             [-1, 50, 3072]               0Dropout-111             [-1, 50, 3072]               0Linear-112              [-1, 50, 768]       2,360,064Dropout-113              [-1, 50, 768]               0Mlp-114              [-1, 50, 768]               0Identity-115              [-1, 50, 768]               0Block-116              [-1, 50, 768]               0LayerNorm-117              [-1, 50, 768]           1,536Linear-118             [-1, 50, 2304]       1,771,776Dropout-119           [-1, 12, 50, 50]               0Linear-120              [-1, 50, 768]         590,592Dropout-121              [-1, 50, 768]               0Attention-122              [-1, 50, 768]               0Identity-123              [-1, 50, 768]               0LayerNorm-124              [-1, 50, 768]           1,536Linear-125             [-1, 50, 3072]       2,362,368GELU-126             [-1, 50, 3072]               0Dropout-127             [-1, 50, 3072]               0Linear-128              [-1, 50, 768]       2,360,064Dropout-129              [-1, 50, 768]               0Mlp-130              [-1, 50, 768]               0Identity-131              [-1, 50, 768]               0Block-132              [-1, 50, 768]               0LayerNorm-133              [-1, 50, 768]           1,536Linear-134             [-1, 50, 2304]       1,771,776Dropout-135           [-1, 12, 50, 50]               0Linear-136              [-1, 50, 768]         590,592Dropout-137              [-1, 50, 768]               0Attention-138              [-1, 50, 768]               0Identity-139              [-1, 50, 768]               0LayerNorm-140              [-1, 50, 768]           1,536Linear-141             [-1, 50, 3072]       2,362,368GELU-142             [-1, 50, 3072]               0Dropout-143             [-1, 50, 3072]               0Linear-144              [-1, 50, 768]       2,360,064Dropout-145              [-1, 50, 768]               0Mlp-146              [-1, 50, 768]               0Identity-147              [-1, 50, 768]               0Block-148              [-1, 50, 768]               0LayerNorm-149              [-1, 50, 768]           1,536Linear-150             [-1, 50, 2304]       1,771,776Dropout-151           [-1, 12, 50, 50]               0Linear-152              [-1, 50, 768]         590,592Dropout-153              [-1, 50, 768]               0Attention-154              [-1, 50, 768]               0Identity-155              [-1, 50, 768]               0LayerNorm-156              [-1, 50, 768]           1,536Linear-157             [-1, 50, 3072]       2,362,368GELU-158             [-1, 50, 3072]               0Dropout-159             [-1, 50, 3072]               0Linear-160              [-1, 50, 768]       2,360,064Dropout-161              [-1, 50, 768]               0Mlp-162              [-1, 50, 768]               0Identity-163              [-1, 50, 768]               0Block-164              [-1, 50, 768]               0LayerNorm-165              [-1, 50, 768]           1,536Linear-166             [-1, 50, 2304]       1,771,776Dropout-167           [-1, 12, 50, 50]               0Linear-168              [-1, 50, 768]         590,592Dropout-169              [-1, 50, 768]               0Attention-170              [-1, 50, 768]               0Identity-171              [-1, 50, 768]               0LayerNorm-172              [-1, 50, 768]           1,536Linear-173             [-1, 50, 3072]       2,362,368GELU-174             [-1, 50, 3072]               0Dropout-175             [-1, 50, 3072]               0Linear-176              [-1, 50, 768]       2,360,064Dropout-177              [-1, 50, 768]               0Mlp-178              [-1, 50, 768]               0Identity-179              [-1, 50, 768]               0Block-180              [-1, 50, 768]               0LayerNorm-181              [-1, 50, 768]           1,536Linear-182             [-1, 50, 2304]       1,771,776Dropout-183           [-1, 12, 50, 50]               0Linear-184              [-1, 50, 768]         590,592Dropout-185              [-1, 50, 768]               0Attention-186              [-1, 50, 768]               0Identity-187              [-1, 50, 768]               0LayerNorm-188              [-1, 50, 768]           1,536Linear-189             [-1, 50, 3072]       2,362,368GELU-190             [-1, 50, 3072]               0Dropout-191             [-1, 50, 3072]               0Linear-192              [-1, 50, 768]       2,360,064Dropout-193              [-1, 50, 768]               0Mlp-194              [-1, 50, 768]               0Identity-195              [-1, 50, 768]               0Block-196              [-1, 50, 768]               0LayerNorm-197              [-1, 50, 768]           1,536Identity-198                  [-1, 768]               0Linear-199                    [-1, 5]           3,845
================================================================

ViT三大模块

ViT主要包含三大模块：PatchEmbed、多层Transformer Encoder、MLP（FFN），下面用结构图和代码解析这第三大模块。

ViT图像预处理模块——PatchEmbed

VIT划分patches的原理：
输入图像尺寸(224x224x3)，按16x16的大小进行划分，共(224x224) / (16x16) = 196个patches，每个patch的维度为(16x16x3)，为满足Transformer的需求，对每个patch进行投影，[16, 16, 3]->[768]，这样就将原始的[224, 224, 3]转化为[196, 768]。

代码实现如下：

class PatchEmbed(nn.Module):"""2D Image to Patch Embedding，二维图像patch Embedding"""def __init__(self, img_size=224, patch_size=16, in_c=3, embed_dim=768, norm_layer=None):super().__init__()img_size = (img_size, img_size)  # 图片尺寸224*224patch_size = (patch_size, patch_size)  #下采样倍数，一个grid cell包含了16*16的图片信息self.img_size = img_sizeself.patch_size = patch_size# grid_size是经过patchembed后的特征层的尺寸self.grid_size = (img_size[0] // patch_size[0], img_size[1] // patch_size[1])self.num_patches = self.grid_size[0] * self.grid_size[1] #path个数 14*14=196# 通过一个卷积，完成patchEmbedself.proj = nn.Conv2d(in_c, embed_dim, kernel_size=patch_size, stride=patch_size)# 如果使用了norm层，如BatchNorm2d，将通道数传入，以进行归一化，否则进行恒等映射self.norm = norm_layer(embed_dim) if norm_layer else nn.Identity()def forward(self, x):B, C, H, W = x.shape  #batch,channels,heigth,weigth# 输入图片的尺寸要满足既定的尺寸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]})."# proj: [B, C, H, W] -> [B, C, H,W] , [B,3,224,224]-> [B,768,14,14]# flatten: [B, C, H, W] -> [B, C, HW] , [B,768,14,14]-> [B,768,196]# transpose: [B, C, HW] -> [B, HW, C] , [B,768,196]-> [B,196,768]x = self.proj(x).flatten(2).transpose(1, 2)x = self.norm(x)return x

多层Transformer Encoder模块

该模块的主要结构是Muti-head Attention，也就是self-attention，它能够使得网络看到全局的信息，而不是CNN的局部感受野。

self-attention的结构示例如下：

class Attention(nn.Module):"""muti-head attention模块，也是transformer最主要的操作"""def __init__(self,dim,   # 输入token的dim,768num_heads=8, #muti-head的head个数，实例化时base尺寸的vit默认为12qkv_bias=False,qk_scale=None,attn_drop_ratio=0.,proj_drop_ratio=0.):super(Attention, self).__init__()self.num_heads = num_headshead_dim = dim // num_heads  #平均每个head的维度self.scale = qk_scale or head_dim ** -0.5  #进行query操作时，缩放因子# qkv矩阵相乘操作，dim * 3使得一次性进行qkv操作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] 如 [bactn,197,768]B, N, C = x.shape  # N:197 , C:768# qkv进行注意力操作，reshape进行muti-head的维度分配，permute维度调换以便后续操作# qkv(): -> [batch_size, num_patches + 1, 3 * total_embed_dim] 如 [b,197,2304]# reshape: -> [batch_size, num_patches + 1, 3, num_heads, embed_dim_per_head] 如 [b,197,3,12,64]# 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)# qkv的维度相同，[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  #矩阵相乘操作attn = attn.softmax(dim=-1) #每一path进行softmax操作attn = self.attn_drop(attn)# [b,12,197,197]@[b,12,197,64] -> [b,12,197,64]# @: multiply -> [batch_size, num_heads, num_patches + 1, embed_dim_per_head]# 维度交换 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)  #经过一层卷积x = self.proj_drop(x)  #Dropoutreturn x

MLP（FFN）模块

一个MLP模块的结构如下：

class Mlp(nn.Module):"""MLP as used in Vision Transformer, MLP-Mixer and related networks"""def __init__(self, in_features, hidden_features=None, out_features=None,act_layer=nn.GELU,  # GELU是更加平滑的reludrop=0.):super().__init__()out_features = out_features or in_features  #如果out_features不存在，则为in_featureshidden_features = hidden_features or in_features #如果hidden_features不存在，则为in_featuresself.fc1 = nn.Linear(in_features, hidden_features) # fc层1self.act = act_layer() #激活self.fc2 = nn.Linear(hidden_features, out_features)  # fc层2self.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

基本的Transformer模块

由Self-attention和MLP可以组合成Transformer的基本模块。Transformer的基本模块还使用了残差连接结构。
一个Transformer Block的结构如下：

class Block(nn.Module):"""基本的Transformer模块"""def __init__(self,dim,num_heads,mlp_ratio=4.,qkv_bias=False,qk_scale=None,drop_ratio=0.,attn_drop_ratio=0.,drop_path_ratio=0.,act_layer=nn.GELU,norm_layer=nn.LayerNorm):super(Block, self).__init__()self.norm1 = norm_layer(dim)  #norm层self.attn = Attention(dim, num_heads=num_heads, qkv_bias=qkv_bias, qk_scale=qk_scale,attn_drop_ratio=attn_drop_ratio, proj_drop_ratio=drop_ratio)# NOTE: drop path for stochastic depth, we shall see if this is better than dropout here# 代码使用了DropPath，而不是原版的dropoutself.drop_path = DropPath(drop_path_ratio) if drop_path_ratio > 0. else nn.Identity()self.norm2 = norm_layer(dim) #norm层mlp_hidden_dim = int(dim * mlp_ratio)  #隐藏层维度扩张后的通道数# 多层感知机self.mlp = Mlp(in_features=dim, hidden_features=mlp_hidden_dim, act_layer=act_layer, drop=drop_ratio)def forward(self, x):x = x + self.drop_path(self.attn(self.norm1(x)))  # attention后残差连接x = x + self.drop_path(self.mlp(self.norm2(x)))   # mlp后残差连接return x

Vision Transformer类的实现

class VisionTransformer(nn.Module):def __init__(self, img_size=224, patch_size=16, in_c=3, num_classes=1000,embed_dim=768, depth=12, num_heads=12, mlp_ratio=4.0, qkv_bias=True,qk_scale=None, representation_size=None, distilled=False, drop_ratio=0.,attn_drop_ratio=0., drop_path_ratio=0., embed_layer=PatchEmbed, norm_layer=None,act_layer=None):"""Args:img_size (int, tuple): input image sizepatch_size (int, tuple): patch sizein_c (int): number of input channelsnum_classes (int): number of classes for classification headembed_dim (int): embedding dimensiondepth (int): depth of transformernum_heads (int): number of attention headsmlp_ratio (int): ratio of mlp hidden dim to embedding dimqkv_bias (bool): enable bias for qkv if Trueqk_scale (float): override default qk scale of head_dim ** -0.5 if setrepresentation_size (Optional[int]): enable and set representation layer (pre-logits) to this value if setdistilled (bool): model includes a distillation token and head as in DeiT modelsdrop_ratio (float): dropout rateattn_drop_ratio (float): attention dropout ratedrop_path_ratio (float): stochastic depth rateembed_layer (nn.Module): patch embedding layernorm_layer: (nn.Module): normalization layer"""super(VisionTransformer, self).__init__()self.num_classes = num_classes  #分类类别数量self.num_features = self.embed_dim = embed_dim  # num_features for consistency with other modelsself.num_tokens = 2 if distilled else 1  #distilled在vit中没有使用到norm_layer = norm_layer or partial(nn.LayerNorm, eps=1e-6) #层归一化act_layer = act_layer or nn.GELU  #激活函数self.patch_embed = embed_layer(img_size=img_size, patch_size=patch_size, in_c=in_c, embed_dim=embed_dim)num_patches = self.patch_embed.num_patchesself.cls_token = nn.Parameter(torch.zeros(1, 1, embed_dim))  #[1,1,768],以0填充self.dist_token = nn.Parameter(torch.zeros(1, 1, embed_dim)) if distilled else Noneself.pos_embed = nn.Parameter(torch.zeros(1, num_patches + self.num_tokens, embed_dim))self.pos_drop = nn.Dropout(p=drop_ratio)# 按照block数量等间距设置drop率dpr = [x.item() for x in torch.linspace(0, drop_path_ratio, depth)]  # stochastic depth decay ruleself.blocks = nn.Sequential(*[Block(dim=embed_dim, num_heads=num_heads, mlp_ratio=mlp_ratio, qkv_bias=qkv_bias, qk_scale=qk_scale,drop_ratio=drop_ratio, attn_drop_ratio=attn_drop_ratio, drop_path_ratio=dpr[i],norm_layer=norm_layer, act_layer=act_layer)for i in range(depth)])self.norm = norm_layer(embed_dim)  # layer_norm# Representation layerif representation_size and not distilled:self.has_logits = Trueself.num_features = representation_sizeself.pre_logits = nn.Sequential(OrderedDict([("fc", nn.Linear(embed_dim, representation_size)),("act", nn.Tanh())]))else:self.has_logits = Falseself.pre_logits = nn.Identity()# Classifier head(s)，分类头,self.num_features=768self.head = nn.Linear(self.num_features, num_classes) if num_classes > 0 else nn.Identity()self.head_dist = Noneif distilled:self.head_dist = nn.Linear(self.embed_dim, self.num_classes) if num_classes > 0 else nn.Identity()# Weight init，权重初始化nn.init.trunc_normal_(self.pos_embed, std=0.02)if self.dist_token is not None:nn.init.trunc_normal_(self.dist_token, std=0.02)nn.init.trunc_normal_(self.cls_token, std=0.02)self.apply(_init_vit_weights)def forward_features(self, x):# [B, C, H, W] -> [B, num_patches, embed_dim]x = self.patch_embed(x)  # [B, 196, 768]# cls_token类别token [1, 1, 768] -> [B, 1, 768]，扩张为batch个cls_tokencls_token = self.cls_token.expand(x.shape[0], -1, -1)if self.dist_token is None:x = torch.cat((cls_token, x), dim=1)  # [B, 196, 768]-> [B, 197, 768]，维度1上的catelse:x = torch.cat((cls_token, self.dist_token.expand(x.shape[0], -1, -1), x), dim=1)x = self.pos_drop(x + self.pos_embed)  #添加位置嵌入信息x = self.blocks(x)  #通过attention堆叠模块（12个）x = self.norm(x)  #layer_normif self.dist_token is None:return self.pre_logits(x[:, 0])  #返回第一层特征，即为分类值else:return x[:, 0], x[:, 1]def forward(self, x):# 分类头x = self.forward_features(x) # 经过att操作，但是没有进行分类头的前传if self.head_dist is not None:x, x_dist = self.head(x[0]), self.head_dist(x[1])if self.training and not torch.jit.is_scripting():# during inference, return the average of both classifier predictionsreturn x, x_distelse:return (x + x_dist) / 2else:x = self.head(x)return x

Transformer知识点

论文：Attention Is All You Need
论文地址：https://arxiv.org/pdf/1706.03762.pdf

Transformer由Attention和Feed Forward Neural Network(也称FFN)组成，其中Attention包含self Attention与Mutil-Head Attention。

网络结构

attention和multi-head-attention结构：

计算过程：

计算复杂度对比

Transformer的参数量和计算量

transformer模型由L个相同的层组成，每个层分为两部分：self-attention块和MLP块。

为表示方便，下面统一记transformer模型的层数为 $l$ ，隐藏层维度为 $h$ ，注意力头数为 $a$ 。词表大小为 $V$ ，训练数据的批次大小为 $b$ ，序列长度为 $s$ 。

Transformer的参数量

self-attention块的模型参数有Q、K、V的权重矩阵Wq、Wk、Wv和偏置，输出权重矩阵Wo和偏置，4个权重矩阵的形状为 $[h, h]$ ，4个偏置的形状为 $[h]$ 。所以self- attention块的参数量为 $4h^{2}+4h$ 。

MLP块由2个线性层组成，一般地，第一个线性层是先将维度从 $h$ 映射到 $4 h$ ，第二个线性层再将维度从 $4 h$ 映射到 $h$ 。第一个线性层的权重矩阵W1的形状为 $[h, 4 h]$ ，偏置的形状为 $[4 h]$ 。第二个线性层权重矩阵W2的形状为 $[4 h, h]$ ，偏置形状为 $[h]$ 。MLP块的参数量为 $8h^{2}+5h$ 。