pytorch 實(shí)現(xiàn)計(jì)算 kl散度 F.kl_div()

先附上官方文檔說(shuō)明：https://pytorch.org/docs/stable/nn.functional.html

torch.nn.functional.kl_div(input, target, size_average=None, reduce=None, reduction='mean')

Parameters

input – Tensor of arbitrary shape

target – Tensor of the same shape as input

size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True

reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

reduction (string, optional) – Specifies the reduction to apply to the output: 'none' | 'batchmean' | 'sum' | 'mean'. 'none': no reduction will be applied 'batchmean': the sum of the output will be divided by the batchsize 'sum': the output will be summed 'mean': the output will be divided by the number of elements in the output Default: 'mean'

然后看看怎么用：

第一個(gè)參數(shù)傳入的是一個(gè)對(duì)數(shù)概率矩陣，第二個(gè)參數(shù)傳入的是概率矩陣。這里很重要，不然求出來(lái)的kl散度可能是個(gè)負(fù)值。

比如現(xiàn)在我有兩個(gè)矩陣X, Y。因?yàn)閗l散度具有不對(duì)稱性，存在一個(gè)指導(dǎo)和被指導(dǎo)的關(guān)系，因此這連個(gè)矩陣輸入的順序需要確定一下。

舉個(gè)例子：

如果現(xiàn)在想用Y指導(dǎo)X，第一個(gè)參數(shù)要傳X，第二個(gè)要傳Y。就是被指導(dǎo)的放在前面，然后求相應(yīng)的概率和對(duì)數(shù)概率就可以了。

import torch
import torch.nn.functional as F
# 定義兩個(gè)矩陣
x = torch.randn((4, 5))
y = torch.randn((4, 5))
# 因?yàn)橐脃指導(dǎo)x,所以求x的對(duì)數(shù)概率，y的概率
logp_x = F.log_softmax(x, dim=-1)
p_y = F.softmax(y, dim=-1)
 
 
kl_sum = F.kl_div(logp_x, p_y, reduction='sum')
kl_mean = F.kl_div(logp_x, p_y, reduction='mean')
 
print(kl_sum, kl_mean)
 
 
>>> tensor(3.4165) tensor(0.1708)

補(bǔ)充：pytorch中的kl散度，為什么kl散度是負(fù)數(shù)？

F.kl_div()或者nn.KLDivLoss()是pytroch中計(jì)算kl散度的函數(shù)，它的用法有很多需要注意的細(xì)節(jié)。

輸入

第一個(gè)參數(shù)傳入的是一個(gè)對(duì)數(shù)概率矩陣，第二個(gè)參數(shù)傳入的是概率矩陣。并且因?yàn)閗l散度具有不對(duì)稱性，存在一個(gè)指導(dǎo)和被指導(dǎo)的關(guān)系，因此這連個(gè)矩陣輸入的順序需要確定一下。如果現(xiàn)在想用Y指導(dǎo)X，第一個(gè)參數(shù)要傳X，第二個(gè)要傳Y。就是被指導(dǎo)的放在前面，然后求相應(yīng)的概率和對(duì)數(shù)概率就可以了。

所以，一隨機(jī)初始化一個(gè)tensor為例，對(duì)于第一個(gè)輸入，我們需要先對(duì)這個(gè)tensor進(jìn)行softmax（確保各維度和為1），然后再取log；對(duì)于第二個(gè)輸入，我們需要對(duì)這個(gè)tensor進(jìn)行softmax。

import torch
import torch.nn.functional as F

a = torch.tensor([[0,0,1.1,2,0,10,0],[0,0,1,2,0,10,0]])
log_a =F.log_softmax(a)

b = torch.tensor([[0,0,1.1,2,0,7,0],[0,0,1,2,0,10,0]])
softmax_b =F.softmax(b,dim=-1)

kl_mean = F.kl_div(log_a, softmax_b, reduction='mean')
print(kl_mean)

為什么KL散度計(jì)算出來(lái)為負(fù)數(shù)

先確保對(duì)第一個(gè)輸入進(jìn)行了softmax+log操作，對(duì)第二個(gè)參數(shù)進(jìn)行了softmax操作。不進(jìn)行softmax操作就可能為負(fù)。

然后查看自己的輸入是否是小數(shù)點(diǎn)后有很多位，當(dāng)小數(shù)點(diǎn)后很多位的時(shí)候，pytorch下的softmax會(huì)產(chǎn)生各維度和不為1的現(xiàn)象，導(dǎo)致kl散度為負(fù)，如下所示：

a = torch.tensor([[0.,0,0.000001,0.0000002,0,0.0000007,0]])
log_a =F.log_softmax(a,dim=-1)
print("log_a:",log_a)

b = torch.tensor([[0.,0,0.000001,0.0000002,0,0.0000007,0]])
softmax_b =F.softmax(b,dim=-1)
print("softmax_b:",softmax_b)

kl_mean = F.kl_div(log_a, softmax_b,reduction='mean')
print("kl_mean:",kl_mean)

輸出如下，我們可以看到softmax_b的各維度和不為1：

以上為個(gè)人經(jīng)驗(yàn)，希望能給大家一個(gè)參考，也希望大家多多支持腳本之家。