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2017 年推出《Attention is All You Need》以来，transformers 曾经成为自然语言解决 (NLP) 的最新技术。2021 年，《An Image is Worth 16×16 Words》，胜利地将 transformers 用于计算机视觉工作。从那时起，许多基于 transformers 的计算机视觉体系结构被提出。
本文将深入探讨注意力层在计算机视觉环境中的工作原理。咱们将探讨单头注意力和多头注意力。它包含注意力层的代码，以及根底数学的概念解释。
在 NLP 利用中，注意力通常被形容为句子中单词 (标记) 之间的关系。而在计算机视觉应用程序中，注意力关注图像中 patches (标记)之间的关系。
有多种办法能够将图像合成为一系列标记。原始的 ViT²将图像宰割成小块，而后将小块平摊成标记。《token -to- token ViT》³开发了一种更简单的从图像创立标记的办法。
点积注意力
《Attention is All You Need》中定义的点积 (相当于乘法) 注意力是目前咱们最常见也是最简略的一种中注意力机制，他的代码实现非常简单：
classAttention(nn.Module):
def__init__(self,
dim: int,
chan: int,
num_heads: int=1,
qkv_bias: bool=False,
qk_scale: NoneFloat=None):
""" Attention Module
Args:
dim (int): input size of a single token
chan (int): resulting size of a single token (channels)
num_heads(int): number of attention heads in MSA
qkv_bias (bool): determines if the qkv layer learns an addative bias
qk_scale (NoneFloat): value to scale the queries and keys by;
if None, queries and keys are scaled by ``head_dim ** -0.5``
"""
super().__init__()
## Define Constants
self.num_heads=num_heads
self.chan=chan
self.head_dim=self.chan//self.num_heads
self.scale=qk_scaleorself.head_dim**-0.5
assertself.chan%self.num_heads==0, '"Chan" must be evenly divisible by "num_heads".'
## Define Layers
self.qkv=nn.Linear(dim, chan*3, bias=qkv_bias)
#### Each token gets projected from starting length (dim) to channel length (chan) 3 times (for each Q, K, V)
self.proj=nn.Linear(chan, chan)
defforward(self, x):
B, N, C=x.shape
## Dimensions: (batch, num_tokens, token_len)
## Calcuate QKVs
qkv=self.qkv(x).reshape(B, N, 3, self.num_heads, self.head_dim).permute(2, 0, 3, 1, 4)
#### Dimensions: (3, batch, heads, num_tokens, chan/num_heads = head_dim)
q, k, v=qkv[0], qkv[1], qkv[2]
## Calculate Attention
attn= (q*self.scale) @k.transpose(-2, -1)
attn=attn.softmax(dim=-1)
#### Dimensions: (batch, heads, num_tokens, num_tokens)
## Attention Layer
x= (attn@v).transpose(1, 2).reshape(B, N, self.chan)
#### Dimensions: (batch, heads, num_tokens, chan)
## Projection Layers
x=self.proj(x)
## Skip Connection Layer
v=v.transpose(1, 2).reshape(B, N, self.chan)
x=v+x
#### Because the original x has different size with current x, use v to do skip connection
returnx单头注意力
对于单个注意力头，让咱们逐渐理解向前传递每一个 patch，应用 7 * 7=49 作为起始 patch 大小（因为这是 T2T-ViT 模型中的起始标记大小）。通道数 64 这也是 T2T-ViT 的默认值。而后假如有 100 标记，并且应用批大小为 13 进行前向流传（抉择这两个数值是为了不会与任何其余参数混同）。
# Define an Input
token_len=7*7
channels=64
num_tokens=100
batch=13
x=torch.rand(batch, num_tokens, token_len)
B, N, C=x.shape
print('Input dimensions are\n\tbatchsize:', x.shape[0], '\n\tnumber of tokens:', x.shape[1], '\n\ttoken size:', x.shape[2])
# Define the Module
A=Attention(dim=token_len, chan=channels, num_heads=1, qkv_bias=False, qk_scale=None)
A.eval();输出的维度是这样的额：
Input dimensions are
batchsize: 13
number of tokens: 100
token size: 49依据查问、键和值矩阵定义的。第一步是通过一个可学习的线性层来计算这些。qkv_bias 项示意这些线性层是否有偏置项。这一步还将标记的长度从输出 49 更改为 chan 参数（64）。
qkv=A.qkv(x).reshape(B, N, 3, A.num_heads, A.head_dim).permute(2, 0, 3, 1, 4)
q, k, v=qkv[0], qkv[1], qkv[2]
print('Dimensions for Queries are\n\tbatchsize:', q.shape[0], '\n\tattention heads:', q.shape[1], '\n\tnumber of tokens:', q.shape[2], '\n\tnew length of tokens:', q.shape[3])
print('See that the dimensions for queries, keys, and values are all the same:')
print('\tShape of Q:', q.shape, '\n\tShape of K:', k.shape, '\n\tShape of V:', v.shape)能够看到 查问、键和值的维度是雷同的，13 代表批次，1 是咱们的注意力头数，100 是咱们输出的标记长度（序列长度），64 是咱们的通道数。
Dimensions for Queries are
batchsize: 13
attention heads: 1
number of tokens: 100
new length of tokens: 64
See that the dimensions for queries, keys, and values are all the same:
Shape of Q: torch.Size([13, 1, 100, 64])
Shape of K: torch.Size([13, 1, 100, 64])
Shape of V: torch.Size([13, 1, 100, 64])咱们看看可注意力是如何计算的，它被定义为:
Q、K、V 别离为查问、键和值;dₖ是键的维数，它等于键标记的长度，也等于键的长度。
第一步是计算:
而后是
最初
Q·K 的矩阵乘法看起来是这样的
这些就是咱们注意力的次要局部，代码是这样的
attn= (q*A.scale) @k.transpose(-2, -1)
print('Dimensions for Attn are\n\tbatchsize:', attn.shape[0], '\n\tattention heads:', attn.shape[1], '\n\tnumber of tokens:', attn.shape[2], '\n\tnumber of tokens:', attn.shape[3])后果如下：
Dimensions for Attn are
batchsize: 13
attention heads: 1
number of tokens: 100
number of tokens: 100下一步就是计算 A 的 softmax，这不会扭转它的形态。
attn=attn.softmax(dim=-1)最初，咱们计算出 A·V=x:
x=attn@v
print('Dimensions for x are\n\tbatchsize:', x.shape[0], '\n\tattention heads:', x.shape[1], '\n\tnumber of tokens:', x.shape[2], '\n\tlength of tokens:', x.shape[3])就失去了咱们最终的后果
Dimensions for x are
batchsize: 13
attention heads: 1
number of tokens: 100
length of tokens: 64因为只有一个头，所以咱们去掉头数 1
x = x.transpose(1, 2).reshape(B, N, A.chan)而后咱们将 x 输出一个可学习的线性层，这个线性层不会扭转它的形态。
x=A.proj(x)最初咱们实现的跳过连贯
orig_shape= (batch, num_tokens, token_len)
curr_shape= (x.shape[0], x.shape[1], x.shape[2])
v=v.transpose(1, 2).reshape(B, N, A.chan)
v_shape= (v.shape[0], v.shape[1], v.shape[2])
print('Original shape of input x:', orig_shape)
print('Current shape of x:', curr_shape)
print('Shape of V:', v_shape)
x=v+x
print('After skip connection, dimensions for x are\n\tbatchsize:', x.shape[0], '\n\tnumber of tokens:', x.shape[1], '\n\tlength of tokens:', x.shape[2])后果如下：
Original shape of input x: (13, 100, 49)
Current shape of x: (13, 100, 64)
Shape of V: (13, 100, 64)
After skip connection, dimensions for x are
batchsize: 13
number of tokens: 100
length of tokens: 64这是咱们单头注意力层!
多头注意力
咱们能够扩大到多头留神。在计算机视觉中，这通常被称为多头自注意力(MSA)。咱们不会具体介绍所有步骤，而是关注矩阵形态不同的中央。
对于多头的注意力，注意力头的数量必须能够整除以通道的数量，所以在这个例子中，咱们将应用 4 个留神头。
# Define an Input
token_len=7*7
channels=64
num_tokens=100
batch=13
num_heads=4
x=torch.rand(batch, num_tokens, token_len)
B, N, C=x.shape
print('Input dimensions are\n\tbatchsize:', x.shape[0], '\n\tnumber of tokens:', x.shape[1], '\n\ttoken size:', x.shape[2])
# Define the Module
MSA=Attention(dim=token_len, chan=channels, num_heads=num_heads, qkv_bias=False, qk_scale=None)
MSA.eval();后果如下：
Input dimensions are
batchsize: 13
number of tokens: 100
token size: 49计算查问、键和值的过程与单头的过程雷同。然而能够看到标记的新长度是 chan/num_heads。Q、K 和 V 矩阵的总大小没有扭转; 它们的内容只是散布在头部维度上。你能够把它看作是将单个矩阵宰割为多个:
咱们将子矩阵示意为 Qₕ对于查问头 i。
qkv=MSA.qkv(x).reshape(B, N, 3, MSA.num_heads, MSA.head_dim).permute(2, 0, 3, 1, 4)
q, k, v=qkv[0], qkv[1], qkv[2]
print('Head Dimension = chan / num_heads =', MSA.chan, '/', MSA.num_heads, '=', MSA.head_dim)
print('Dimensions for Queries are\n\tbatchsize:', q.shape[0], '\n\tattention heads:', q.shape[1], '\n\tnumber of tokens:', q.shape[2], '\n\tnew length of tokens:', q.shape[3])
print('See that the dimensions for queries, keys, and values are all the same:')
print('\tShape of Q:', q.shape, '\n\tShape of K:', k.shape, '\n\tShape of V:', v.shape)输入如下：
Head Dimension = chan / num_heads = 64 / 4 = 16
Dimensions for Queries are
batchsize: 13
attention heads: 4
number of tokens: 100
new length of tokens: 16
See that the dimensions for queries, keys, and values are all the same:
Shape of Q: torch.Size([13, 4, 100, 16])
Shape of K: torch.Size([13, 4, 100, 16])
Shape of V: torch.Size([13, 4, 100, 16])这里须要留神的是
咱们须要除以头数。num_heads = 4 个不同的 Attn 矩阵，看起来像:
attn= (q*MSA.scale) @k.transpose(-2, -1)
print('Dimensions for Attn are\n\tbatchsize:', attn.shape[0], '\n\tattention heads:', attn.shape[1], '\n\tnumber of tokens:', attn.shape[2], '\n\tnumber of tokens:', attn.shape[3]维度：
Dimensions for Attn are
batchsize: 13
attention heads: 4
number of tokens: 100
number of tokens: 100softmax 不会扭转维度，咱们略过，而后计算每一个头
这在多个留神头中是这样的:
attn = attn.softmax(dim=-1)
x = attn @ v
print('Dimensions for x are\n\tbatchsize:', x.shape[0], '\n\tattention heads:', x.shape[1], '\n\tnumber of tokens:', x.shape[2], '\n\tlength of tokens:', x.shape[3]维度如下：
Dimensions for x are
batchsize: 13
attention heads: 4
number of tokens: 100
length of tokens: 16最初须要维度重塑并把把所有的 xₕ` s 连贯在一起。这是第一步的逆操作:
x=x.transpose(1, 2).reshape(B, N, MSA.chan)
print('Dimensions for x are\n\tbatchsize:', x.shape[0], '\n\tnumber of tokens:', x.shape[1], '\n\tlength of tokens:', x.shape[2])后果如下：
Dimensions for x are
batchsize: 13
number of tokens: 100
length of tokens: 64咱们曾经将所有头的输入连贯在一起，注意力模块的其余部分放弃不变。
x = MSA.proj(x)
print('Dimensions for x are\n\tbatchsize:', x.shape[0], '\n\tnumber of tokens:', x.shape[1], '\n\tlength of tokens:', x.shape[2])
orig_shape = (batch, num_tokens, token_len)
curr_shape = (x.shape[0], x.shape[1], x.shape[2])
v = v.transpose(1, 2).reshape(B, N, A.chan)
v_shape = (v.shape[0], v.shape[1], v.shape[2])
print('Original shape of input x:', orig_shape)
print('Current shape of x:', curr_shape)
print('Shape of V:', v_shape)
x = v + x
print('After skip connection, dimensions for x are\n\tbatchsize:', x.shape[0], '\n\tnumber of tokens:', x.shape[1], '\n\tlength of tokens:', x.shape[2])后果如下：
Dimensions for x are
batchsize: 13
number of tokens: 100
length of tokens: 64
Original shape of input x: (13, 100, 49)
Current shape of x: (13, 100, 64)
Shape of V: (13, 100, 64)
After skip connection, dimensions for x are
batchsize: 13
number of tokens: 100
length of tokens: 64这就是多头注意力!
总结
在这篇文章中咱们实现了 ViT 中注意力层。为了更具体的阐明咱们进行了手动的代码编写，如果要理论的利用，能够应用 PyTorch 中的 torch.nn. multiheadeattention()，因为他的实现要快的多。
最初参考文章：
[1] Vaswani et al (2017). Attention Is All You Need.https://doi.org/10.48550/arXiv.1706.03762
[2] Dosovitskiy et al (2020). An Image is Worth 16×16 Words: Transformers for Image Recognition at Scale.https://doi.org/10.48550/arXiv.2010.11929
[3] Yuan et al (2021). Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet. https://doi.org/10.48550/arXiv.2101.11986GitHub code: https://github.com/yitu-opensource/T2T-ViT
https://avoid.overfit.cn/post/0d526cd56c8842c599b4fe1c9adcfd9f
作者：Skylar Jean Callis
