torch.nn.functional.normalize参数说明

函数定义

torch.nn.functional.normalize(input, p=2.0, dim=1, eps=1e-12, out=None)
# type: (Tensor, float, int, float, Optional[Tensor]) -> Tensor

公式为
$$\frac{v}{\max (\Vert v{\Vert }_p,ϵ)}$$

参数及功能

F.normalize(data, p=2/1, dim=0/1/-1) 将某一个维度除以那个维度对应的范数(默认是2范数)
input:输入的数据（tensor）
p:L2/L1_norm运算，(默认是2范数)
dim:0表示按列操作，则每列都是除以该列下平方和的开方；1表示按行操作，则每行都是除以该行下所有元素平方和的开方，-1表示按行
eps：防止分母为0

功能：将某一个维度除以那个维度对应的范数(默认是2范数)，也称为标准化。

官方说明

先放两张图，如果能看明白就不需要看下面实例解释

二维数据实例解释

参数dim=0

import torch
import torch.nn.functional as F

a = torch.tensor([[0.0861, 0.1087, 0.0518, 0.3551],
                   [0.8067, 0.4128, 0.0592, 0.2884],
                   [0.1072, 0.4785, 0.8890, 0.3565]])
print(a.shape)
print("=============================================")
print(a)
print("=============================================")
c = F.normalize(a, dim=0)
print(c)

结果为

torch.Size([3, 4])
=============================================
tensor([[0.0861, 0.1087, 0.0518, 0.3551],
        [0.8067, 0.4128, 0.0592, 0.2884],
        [0.1072, 0.4785, 0.8890, 0.3565]])
=============================================
tensor([[0.1052, 0.1695, 0.0580, 0.6123],
        [0.9858, 0.6438, 0.0663, 0.4973],
        [0.1310, 0.7462, 0.9961, 0.6147]])

代码中针对维度0进行归一化，也就是对二维数据的列进行归一化，具体的计算细节为

$$0.1052=\frac{0.0861}{\sqrt{0.0861^2+0.8067^2+0.1072^2}}$$
$$0.1695=\frac{0.1087}{\sqrt{0.1087^2+0.4128^2+0.4785^2}}$$
$$0.0580=\frac{0.0518}{\sqrt{0.0518^2+0.0592^2+0.8890^2}}$$
$$0.6123=\frac{0.3551}{\sqrt{0.3551^2+0.2884^2+0.3565^2}}$$

参数dim=1

import torch
import torch.nn.functional as F

a = torch.tensor([[0.0861, 0.1087, 0.0518, 0.3551],
                   [0.8067, 0.4128, 0.0592, 0.2884],
                   [0.1072, 0.4785, 0.8890, 0.3565]])
print(a.shape)
print("=============================================")
print(a)
print("=============================================")
c = F.normalize(a, dim=1)
print(c)

结果为

torch.Size([3, 4])
=============================================
tensor([[0.0861, 0.1087, 0.0518, 0.3551],
        [0.8067, 0.4128, 0.0592, 0.2884],
        [0.1072, 0.4785, 0.8890, 0.3565]])
=============================================
tensor([[0.2237, 0.2825, 0.1347, 0.9230],
        [0.8467, 0.4332, 0.0621, 0.3027],
        [0.0996, 0.4447, 0.8262, 0.3313]])

代码中针对维度1进行归一化，也就是对二维数据的行进行归一化，具体的计算细节为

参数dim=-1

与dim=2结果一致，相当于看做逆序索引

三维数据实例解释

参数dim=0

import torch
import torch.nn.functional as F

a = torch.tensor([[[0.0861, 0.1087, 0.0518, 0.3551],
                   [0.8067, 0.4128, 0.0592, 0.2884],
                   [0.1072, 0.4785, 0.8890, 0.3565]]])
print(a.shape)
print("=============================================")
print(a)
print("=============================================")
c = F.normalize(a, dim=0)
print(c)

结果为

torch.Size([1, 3, 4])
=============================================
tensor([[[0.0861, 0.1087, 0.0518, 0.3551],
         [0.8067, 0.4128, 0.0592, 0.2884],
         [0.1072, 0.4785, 0.8890, 0.3565]]])
=============================================
tensor([[[1., 1., 1., 1.],
         [1., 1., 1., 1.],
         [1., 1., 1., 1.]]])

这里作用的是维度0；维度0上只有1个通道，因此归一化之后全为1，即

参数dim=1

a = torch.tensor([[[0.0861, 0.1087, 0.0518, 0.3551],
                   [0.8067, 0.4128, 0.0592, 0.2884],
                   [0.1072, 0.4785, 0.8890, 0.3565]]])
print(a.shape)
print("=============================================")
print(a)
print("=============================================")
c = F.normalize(a, dim=1)
print(c)

结果为

torch.Size([1, 3, 4])
=============================================
tensor([[[0.0861, 0.1087, 0.0518, 0.3551],
         [0.8067, 0.4128, 0.0592, 0.2884],
         [0.1072, 0.4785, 0.8890, 0.3565]]])
=============================================
tensor([[[0.1052, 0.1695, 0.0580, 0.6123],
         [0.9858, 0.6438, 0.0663, 0.4973],
         [0.1310, 0.7462, 0.9961, 0.6147]]])

代码中针对维度1进行归一化。维度1有3个通道，具体的计算细节为

$$0.1052=\frac{0.0861}{\sqrt{0.0861^2+0.8067^2+0.1072^2}}$$
$$0.1695=\frac{0.1087}{\sqrt{0.1087^2+0.4128^2+0.4785^2}}$$
$$0.0580=\frac{0.0518}{\sqrt{0.0518^2+0.0592^2+0.8890^2}}$$
$$0.6123=\frac{0.3551}{\sqrt{0.3551^2+0.2884^2+0.3565^2}}$$

参数dim=2

a = torch.tensor([[[0.0861, 0.1087, 0.0518, 0.3551],
                   [0.8067, 0.4128, 0.0592, 0.2884],
                   [0.1072, 0.4785, 0.8890, 0.3565]]])
print(a.shape)
print("=============================================")
print(a)
print("=============================================")
c = F.normalize(a, dim=2)
print(c)

结果为

torch.Size([1, 3, 4])
=============================================
tensor([[[0.0861, 0.1087, 0.0518, 0.3551],
         [0.8067, 0.4128, 0.0592, 0.2884],
         [0.1072, 0.4785, 0.8890, 0.3565]]])
=============================================
tensor([[[0.2237, 0.2825, 0.1347, 0.9230],
         [0.8467, 0.4332, 0.0621, 0.3027],
         [0.0996, 0.4447, 0.8262, 0.3313]]])

这里作用的是维度2，可以认为维度2有4个通道，计算细节为：

参数dim=-1

与dim=2结果一致，相当于看做逆序索引

参考博文及感谢

部分内容参考以下链接，这里表示感谢 Thanks♪(･ω･)ﾉ
参考博文1 官方文档
https://pytorch.org/docs/stable/generated/torch.nn.functional.normalize.html
参考博文2 Pytorch中关于F.normalize计算理解
https://www.jb51.net/article/274086.htm
参考博文3 【Pytorch】F.normalize计算理解
https://blog.youkuaiyun.com/lj2048/article/details/118115681