pytorch 计算 kl散度 F.kl_div()

先附上官方文档说明：torch.nn.functional — PyTorch 1.13 documentation

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：第一个参数传入的是一个对数概率矩阵，第二个参数传入的是概率矩阵。这里很重要，不然求出来的kl散度可能是个负值。

比如现在我有两个矩阵X, Y。因为kl散度具有不对称性，存在一个指导和被指导的关系，因此这连个矩阵输入的顺序需要确定一下。

举个例子：如果现在想用Y指导X，第一个参数要传X，第二个要传Y。就是被指导的放在前面，然后求相应的概率和对数概率就可以了。

import torch
import torch.nn.functional as F

# 定义两个矩阵
x = torch.randn((4, 5))
y = torch.randn((4, 5))

# 因为要用y指导x,所以求x的对数概率，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)

贴一下下面的评论解释一下reduction参数，比如mean是对所有元素求平均，那么最后kl_sum就是kl_mean的4*5=20倍，即3.41是0.17的20倍。