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# KLDivLoss¶

class torch.nn.KLDivLoss(size_average=None, reduce=None, reduction='mean', log_target=False)[source]

The Kullback-Leibler divergence loss.

For tensors of the same shape $y_{\text{pred}},\ y_{\text{true}}$, where $y_{\text{pred}}$ is the input and $y_{\text{true}}$ is the target, we define the pointwise KL-divergence as

$L(y_{\text{pred}},\ y_{\text{true}}) = y_{\text{true}} \cdot \log \frac{y_{\text{true}}}{y_{\text{pred}}} = y_{\text{true}} \cdot (\log y_{\text{true}} - \log y_{\text{pred}})$

To avoid underflow issues when computing this quantity, this loss expects the argument input in the log-space. The argument target may also be provided in the log-space if log_target= True.

To summarise, this function is roughly equivalent to computing

if not log_target: # default
loss_pointwise = target * (target.log() - input)
else:
loss_pointwise = target.exp() * (target - input)

and then reducing this result depending on the argument reduction as

if reduction == "mean":  # default
loss = loss_pointwise.mean()
elif reduction == "batchmean":  # mathematically correct
loss = loss_pointwise.sum() / input.size(0)
elif reduction == "sum":
loss = loss_pointwise.sum()
else:  # reduction == "none"
loss = loss_pointwise

Note

As all the other losses in PyTorch, this function expects the first argument, input, to be the output of the model (e.g. the neural network) and the second, target, to be the observations in the dataset. This differs from the standard mathematical notation $KL(P\ ||\ Q)$ where $P$ denotes the distribution of the observations and $Q$ denotes the model.

Warning

reduction= “mean” doesn’t return the true KL divergence value, please use reduction= “batchmean” which aligns with the mathematical definition. In a future release, “mean” will be changed to be the same as “batchmean”.

Parameters:
• 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 are 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 (str, optional) – Specifies the reduction to apply to the output. Default: “mean”

• log_target (bool, optional) – Specifies whether target is the log space. Default: False

Shape:
• Input: $(*)$, where $*$ means any number of dimensions.

• Target: $(*)$, same shape as the input.

• Output: scalar by default. If reduction is ‘none’, then $(*)$, same shape as the input.

Examples:

>>> import torch.nn.functional as F
>>> kl_loss = nn.KLDivLoss(reduction="batchmean")
>>> # input should be a distribution in the log space
>>> input = F.log_softmax(torch.randn(3, 5, requires_grad=True), dim=1)
>>> # Sample a batch of distributions. Usually this would come from the dataset
>>> target = F.softmax(torch.rand(3, 5), dim=1)
>>> output = kl_loss(input, target)

>>> kl_loss = nn.KLDivLoss(reduction="batchmean", log_target=True)
>>> log_target = F.log_softmax(torch.rand(3, 5), dim=1)
>>> output = kl_loss(input, log_target)

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