Loss Functions

Custom fastai loss functions

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BaseLoss

 BaseLoss (loss_cls, *args, axis:int=-1, flatten:bool=True,
           floatify:bool=False, is_2d:bool=True, **kwargs)

Same as loss_cls, but flattens input and target.

	Type	Default	Details
loss_cls			Uninitialized PyTorch-compatible loss
args
axis	int	-1
flatten	bool	True
floatify	bool	False
is_2d	bool	True
kwargs

Wrapping a general loss function inside of BaseLoss provides extra functionalities to your loss functions:

• flattens the tensors before trying to take the losses since it’s more convenient (with a potential tranpose to put axis at the end)
• a potential activation method that tells the library if there is an activation fused in the loss (useful for inference and methods such as Learner.get_preds or Learner.predict)
• a potential decodes method that is used on predictions in inference (for instance, an argmax in classification)

The args and kwargs will be passed to loss_cls during the initialization to instantiate a loss function. axis is put at the end for losses like softmax that are often performed on the last axis. If floatify=True, the targs will be converted to floats (useful for losses that only accept float targets like BCEWithLogitsLoss), and is_2d determines if we flatten while keeping the first dimension (batch size) or completely flatten the input. We want the first for losses like Cross Entropy, and the second for pretty much anything else.

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CrossEntropyLossFlat

 CrossEntropyLossFlat (*args, axis:int=-1, weight=None, ignore_index=-100,
                       reduction='mean', flatten:bool=True,
                       floatify:bool=False, is_2d:bool=True)

Same as nn.CrossEntropyLoss, but flattens input and target.

tst = CrossEntropyLossFlat(reduction='none')
output = torch.randn(32, 5, 10)
target = torch.randint(0, 10, (32,5))
#nn.CrossEntropy would fail with those two tensors, but not our flattened version.
_ = tst(output, target)

test_fail(lambda x: nn.CrossEntropyLoss()(output,target))

#Associated activation is softmax
test_eq(tst.activation(output), F.softmax(output, dim=-1))
#This loss function has a decodes which is argmax
test_eq(tst.decodes(output), output.argmax(dim=-1))

#In a segmentation task, we want to take the softmax over the channel dimension
tst = CrossEntropyLossFlat(axis=1)
output = torch.randn(32, 5, 128, 128)
target = torch.randint(0, 5, (32, 128, 128))
_ = tst(output, target)

test_eq(tst.activation(output), F.softmax(output, dim=1))
test_eq(tst.decodes(output), output.argmax(dim=1))

Focal Loss is the same as cross entropy except easy-to-classify observations are down-weighted in the loss calculation. The strength of down-weighting is proportional to the size of the gamma parameter. Put another way, the larger gamma the less the easy-to-classify observations contribute to the loss.

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FocalLossFlat

 FocalLossFlat (*args, gamma:float=2.0, axis:int=-1, weight=None,
                reduction='mean', **kwargs)

Same as CrossEntropyLossFlat but with focal paramter, gamma. Focal loss is introduced by Lin et al.  https://arxiv.org/pdf/1708.02002.pdf. Note the class weighting factor in the paper, alpha, can be implemented through pytorch weight argument passed through to F.cross_entropy.

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FocalLoss

 FocalLoss (gamma:float=2.0, weight:Tensor=None, reduction:str='mean')

Same as nn.Module, but no need for subclasses to call super().__init__

	Type	Default	Details
gamma	float	2.0	Focusing parameter. Higher values down-weight easy examples’ contribution to loss
weight	Tensor	None	Manual rescaling weight given to each class
reduction	str	mean	PyTorch reduction to apply to the output

#Compare focal loss with gamma = 0 to cross entropy
fl = FocalLossFlat(gamma=0)
ce = CrossEntropyLossFlat()
output = torch.randn(32, 5, 10)
target = torch.randint(0, 10, (32,5))
test_close(fl(output, target), ce(output, target))
#Test focal loss with gamma > 0 is different than cross entropy
fl = FocalLossFlat(gamma=2)
test_ne(fl(output, target), ce(output, target))

#In a segmentation task, we want to take the softmax over the channel dimension
fl = FocalLossFlat(gamma=0, axis=1)
ce = CrossEntropyLossFlat(axis=1)
output = torch.randn(32, 5, 128, 128)
target = torch.randint(0, 5, (32, 128, 128))
test_close(fl(output, target), ce(output, target), eps=1e-4)
test_eq(fl.activation(output), F.softmax(output, dim=1))
test_eq(fl.decodes(output), output.argmax(dim=1))

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BCEWithLogitsLossFlat

 BCEWithLogitsLossFlat (*args, axis:int=-1, floatify:bool=True,
                        thresh:float=0.5, weight=None, reduction='mean',
                        pos_weight=None, flatten:bool=True,
                        is_2d:bool=True)

Same as nn.BCEWithLogitsLoss, but flattens input and target.

tst = BCEWithLogitsLossFlat()
output = torch.randn(32, 5, 10)
target = torch.randn(32, 5, 10)
#nn.BCEWithLogitsLoss would fail with those two tensors, but not our flattened version.
_ = tst(output, target)
test_fail(lambda x: nn.BCEWithLogitsLoss()(output,target))
output = torch.randn(32, 5)
target = torch.randint(0,2,(32, 5))
#nn.BCEWithLogitsLoss would fail with int targets but not our flattened version.
_ = tst(output, target)
test_fail(lambda x: nn.BCEWithLogitsLoss()(output,target))

tst = BCEWithLogitsLossFlat(pos_weight=torch.ones(10))
output = torch.randn(32, 5, 10)
target = torch.randn(32, 5, 10)
_ = tst(output, target)
test_fail(lambda x: nn.BCEWithLogitsLoss()(output,target))

#Associated activation is sigmoid
test_eq(tst.activation(output), torch.sigmoid(output))

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BCELossFlat

 BCELossFlat (*args, axis:int=-1, floatify:bool=True, weight=None,
              reduction='mean')

Same as nn.BCELoss, but flattens input and target.

tst = BCELossFlat()
output = torch.sigmoid(torch.randn(32, 5, 10))
target = torch.randint(0,2,(32, 5, 10))
_ = tst(output, target)
test_fail(lambda x: nn.BCELoss()(output,target))

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MSELossFlat

 MSELossFlat (*args, axis:int=-1, floatify:bool=True, reduction='mean')

Same as nn.MSELoss, but flattens input and target.

tst = MSELossFlat()
output = torch.sigmoid(torch.randn(32, 5, 10))
target = torch.randint(0,2,(32, 5, 10))
_ = tst(output, target)
test_fail(lambda x: nn.MSELoss()(output,target))

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L1LossFlat

 L1LossFlat (*args, axis=-1, floatify=True, reduction='mean')

Same as nn.L1Loss, but flattens input and target.

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LabelSmoothingCrossEntropy

 LabelSmoothingCrossEntropy (eps:float=0.1, weight:Tensor=None,
                             reduction:str='mean')

Same as nn.Module, but no need for subclasses to call super().__init__

	Type	Default	Details
eps	float	0.1	The weight for the interpolation formula
weight	Tensor	None	Manual rescaling weight given to each class passed to F.nll_loss
reduction	str	mean	PyTorch reduction to apply to the output

lmce = LabelSmoothingCrossEntropy()
output = torch.randn(32, 5, 10)
target = torch.randint(0, 10, (32,5))
test_close(lmce(output.flatten(0,1), target.flatten()), lmce(output.transpose(-1,-2), target))

On top of the formula we define:

• a reduction attribute, that will be used when we call Learner.get_preds
• weight attribute to pass to BCE.
• an activation function that represents the activation fused in the loss (since we use cross entropy behind the scenes). It will be applied to the output of the model when calling Learner.get_preds or Learner.predict
• a decodes function that converts the output of the model to a format similar to the target (here indices). This is used in Learner.predict and Learner.show_results to decode the predictions

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LabelSmoothingCrossEntropyFlat

 LabelSmoothingCrossEntropyFlat (*args, axis:int=-1, eps=0.1,
                                 reduction='mean', flatten:bool=True,
                                 floatify:bool=False, is_2d:bool=True)

Same as LabelSmoothingCrossEntropy, but flattens input and target.

#These two should always equal each other since the Flat version is just passing data through
lmce = LabelSmoothingCrossEntropy()
lmce_flat = LabelSmoothingCrossEntropyFlat()
output = torch.randn(32, 5, 10)
target = torch.randint(0, 10, (32,5))
test_close(lmce(output.transpose(-1,-2), target), lmce_flat(output,target))

We present a general Dice loss for segmentation tasks. It is commonly used together with CrossEntropyLoss or FocalLoss in kaggle competitions. This is very similar to the DiceMulti metric, but to be able to derivate through, we replace the argmax activation by a softmax and compare this with a one-hot encoded target mask. This function also adds a smooth parameter to help numerical stabilities in the intersection over union division. If your network has problem learning with this DiceLoss, try to set the square_in_union parameter in the DiceLoss constructor to True.

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DiceLoss

 DiceLoss (axis:int=1, smooth:float=1e-06, reduction:str='sum',
           square_in_union:bool=False)

Dice loss for segmentation

	Type	Default	Details
axis	int	1	Class axis
smooth	float	1e-06	Helps with numerical stabilities in the IoU division
reduction	str	sum	PyTorch reduction to apply to the output
square_in_union	bool	False	Squares predictions to increase slope of gradients

dl = DiceLoss()
_x         = tensor( [[[1, 0, 2],
                       [2, 2, 1]]])
_one_hot_x = tensor([[[[0, 1, 0],
                       [0, 0, 0]],
                      [[1, 0, 0],
                       [0, 0, 1]],
                      [[0, 0, 1],
                       [1, 1, 0]]]])
test_eq(dl._one_hot(_x, 3), _one_hot_x)

dl = DiceLoss()
model_output = tensor([[[[2., 1.],
                         [1., 5.]],
                        [[1,  2.],
                         [3., 1.]],
                        [[3., 0],
                         [4., 3.]]]])
target       =  tensor([[[2, 1],
                         [2, 0]]])
dl_out = dl(model_output, target)
test_eq(dl.decodes(model_output), target)

dl = DiceLoss(reduction="mean")
#identical masks
model_output = tensor([[[.1], [.1], [100.]]])
target = tensor([[2]])
test_close(dl(model_output, target), 0)

#50% intersection
model_output = tensor([[[.1, 100.], [.1, .1], [100., .1]]])
target = tensor([[2, 1]])
test_close(dl(model_output, target), .66, eps=0.01)

As a test case for the dice loss consider satellite image segmentation. Let us say we have three classes: Background (0), River (1) and Road (2). Let us look at a specific target

target = torch.zeros(100,100)
target[:,5] = 1
target[:,50] = 2
plt.imshow(target);

Nearly everything is background in this example, and we have a thin river at the left of the image as well as a thin road in the middle of the image. If all our data looks similar to this, we say that there is a class imbalance, meaning that some classes (like river and road) appear relatively infrequently. If our model just predicted “background” (i.e. the value 0) for all pixels, it would be correct for most pixels. But this would be a bad model and the diceloss should reflect that

model_output_all_background = torch.zeros(3, 100,100)
# assign probability 1 to class 0 everywhere
# to get probability 1, we just need a high model output before softmax gets applied
model_output_all_background[0,:,:] = 100

# add a batch dimension
model_output_all_background = torch.unsqueeze(model_output_all_background,0)
target = torch.unsqueeze(target,0)

Our dice score should be around 1/3 here, because the “background” class is predicted correctly (and that for nearly every pixel), but the other two clases are never predicted correctly. Dice score of 1/3 means dice loss of 1 - 1/3 = 2/3:

test_close(dl(model_output_all_background, target), 0.67, eps=0.01)

If the model would predict everything correctly, the dice loss should be zero:

correct_model_output = torch.zeros(3, 100,100)
correct_model_output[0,:,:] = 100
correct_model_output[0,:,5] = 0
correct_model_output[0,:,50] = 0
correct_model_output[1,:,5] = 100
correct_model_output[2,:,50] = 100
correct_model_output = torch.unsqueeze(correct_model_output, 0)

test_close(dl(correct_model_output, target), 0)

You could easily combine this loss with FocalLoss defining a CombinedLoss, to balance between global (Dice) and local (Focal) features on the target mask.

class CombinedLoss:
    "Dice and Focal combined"
    def __init__(self, axis=1, smooth=1., alpha=1.):
        store_attr()
        self.focal_loss = FocalLossFlat(axis=axis)
        self.dice_loss =  DiceLoss(axis, smooth)
        
    def __call__(self, pred, targ):
        return self.focal_loss(pred, targ) + self.alpha * self.dice_loss(pred, targ)
    
    def decodes(self, x):    return x.argmax(dim=self.axis)
    def activation(self, x): return F.softmax(x, dim=self.axis)

cl = CombinedLoss()
output = torch.randn(32, 4, 5, 10)
target = torch.randint(0,2,(32, 5, 10))
_ = cl(output, target)