# 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:

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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")
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)``````
``````# Tests to catch future changes to pickle which cause some loss functions to be 'unpicklable'.
# This causes problems with `Learner.export` as the model can't be pickled with these particular loss funcitons.

losses_picklable = [
(BCELossFlat(), True),
(BCEWithLogitsLossFlat(), True),
(CombinedLoss(), True),
(CrossEntropyLossFlat(), True),
(DiceLoss(), True),
(FocalLoss(), True),
(FocalLossFlat(), True),
(L1LossFlat(), True),
(LabelSmoothingCrossEntropyFlat(), True),
(LabelSmoothingCrossEntropy(), True),
(MSELossFlat(), True),
]

for loss, picklable in losses_picklable:
try:
pickle.dumps(loss, protocol=2)
except (pickle.PicklingError, TypeError) as e:
if picklable:
# Loss was previously picklable but isn't currently
raise e``````