Add softmax_focal_loss() to allow multi-class focal loss

[dhruvbird]

In image segmentation tasks, focal loss is useful when trying to classify an image pixel as one of N classes. Unfortunately, sigmoid_focal_loss() isn't useful in such cases. I found that other have been asking for this as well here #3250 so I decided to submit a PR for the same.

I'm opening this PR to check if this is something the pytorch-vision team is interested in merging.

[pytorch-bot]

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[rehno-lindeque]

I don't see a conditional checking if alpha is -1 anywhere.

[rehno-lindeque]

I have my doubts that the alpha term used here is correct. In fact we want alpha_t.

Although the paper doesn't explicitly give the formula for alpha_t, it states in it's definition

For notational convenience, we define $α_t$ analogously to how we defined $p_t$

So given that

$ \begin{align*} p_t = \begin{cases} \alpha & \text{if } y = 1 \\ (1 - p) & \text{otherwise} \end{cases} \end{align*}$

Therefore I believe $\alpha_t$ should be analogously be interpreted as

$ \begin{align*} \alpha_t = \begin{cases} \alpha & \text{if } y = 1 \\ (1 - \alpha) & \text{otherwise} \end{cases} \end{align*}$

Torchvision's sigmoid_focal_loss does something like this in its implementation:

vision/torchvision/ops/focal_loss.py

Lines 43 to 45 in cc0f9d0

	if alpha >= 0:
	alpha_t = alpha * targets + (1 - alpha) * (1 - targets)
	loss = alpha_t * loss

However I've seen another implementation in the wild pass through alpha to the weights of nll_loss:

AdeelH/pytorch-multi-class-focal-loss/focal_loss.py

This strikes me as the correct approach since it allows one to weigh each class separately in a multi-class setting where there are no "negative" classes.

In other words, there's a subtle difference in the intent here versus the sigmoid BCE approach (sigmoid_focal_loss) where every class is effectively split into separate positive / negative predictions.

[dhruvbird]

I agree with your assessment above.

I have put up a revised PR at #7760 since I switched local branches.