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According to Lin et al., 2018, it helps to apply a focal factor to down-weight easy examples and focus more on hard examples. By default, the focal tensor is computed as follows:

focal_factor = (1 - output)^gamma for class 1 focal_factor = output^gamma for class 0 where gamma is a focusing parameter. When gamma = 0, there is no focal effect on the binary crossentropy loss.

If apply_class_balancing == TRUE, this function also takes into account a weight balancing factor for the binary classes 0 and 1 as follows:

weight = alpha for class 1 (target == 1) weight = 1 - alpha for class 0 where alpha is a float in the range of [0, 1].

Binary cross-entropy loss is often used for binary (0 or 1) classification tasks. The loss function requires the following inputs:

  • y_true (true label): This is either 0 or 1.

  • y_pred (predicted value): This is the model's prediction, i.e, a single floating-point value which either represents a logit, (i.e, value in [-inf, inf] when from_logits=TRUE) or a probability (i.e, value in [0., 1.] when from_logits=FALSE).

According to Lin et al., 2018, it helps to apply a "focal factor" to down-weight easy examples and focus more on hard examples. By default, the focal tensor is computed as follows:

focal_factor = (1 - output) ** gamma for class 1 focal_factor = output ** gamma for class 0 where gamma is a focusing parameter. When gamma=0, this function is equivalent to the binary crossentropy loss.

Usage

loss_binary_focal_crossentropy(
  y_true,
  y_pred,
  apply_class_balancing = FALSE,
  alpha = 0.25,
  gamma = 2,
  from_logits = FALSE,
  label_smoothing = 0,
  axis = -1L,
  ...,
  reduction = "sum_over_batch_size",
  name = "binary_focal_crossentropy",
  dtype = NULL
)

Arguments

y_true

Ground truth values, of shape (batch_size, d0, .. dN).

y_pred

The predicted values, of shape (batch_size, d0, .. dN).

apply_class_balancing

A bool, whether to apply weight balancing on the binary classes 0 and 1.

alpha

A weight balancing factor for class 1, default is 0.25 as mentioned in reference Lin et al., 2018. The weight for class 0 is 1.0 - alpha.

gamma

A focusing parameter used to compute the focal factor, default is 2.0 as mentioned in the reference Lin et al., 2018.

from_logits

Whether to interpret y_pred as a tensor of logit values. By default, we assume that y_pred are probabilities (i.e., values in [0, 1]).

label_smoothing

Float in [0, 1]. When 0, no smoothing occurs. When > 0, we compute the loss between the predicted labels and a smoothed version of the true labels, where the smoothing squeezes the labels towards 0.5. Larger values of label_smoothing correspond to heavier smoothing.

axis

The axis along which to compute crossentropy (the features axis). Defaults to -1.

...

For forward/backward compatability.

reduction

Type of reduction to apply to the loss. In almost all cases this should be "sum_over_batch_size". Supported options are "sum", "sum_over_batch_size" or NULL.

name

Optional name for the loss instance.

dtype

The dtype of the loss's computations. Defaults to NULL, which means using config_floatx(). config_floatx() is a "float32" unless set to different value (via config_set_floatx()).

Value

Binary focal crossentropy loss value with shape = [batch_size, d0, .. dN-1].

Examples

y_true <- rbind(c(0, 1), c(0, 0))
y_pred <- rbind(c(0.6, 0.4), c(0.4, 0.6))
loss <- loss_binary_focal_crossentropy(y_true, y_pred, gamma = 2)
loss

## tf.Tensor([0.32986466 0.20579838], shape=(2), dtype=float64)

With the compile() API:

model %>% compile(
    loss = loss_binary_focal_crossentropy(
        gamma = 2.0, from_logits = TRUE),
    ...
)

As a standalone function:

# Example 1: (batch_size = 1, number of samples = 4)
y_true <- op_array(c(0, 1, 0, 0))
y_pred <- op_array(c(-18.6, 0.51, 2.94, -12.8))
loss <- loss_binary_focal_crossentropy(gamma = 2, from_logits = TRUE)
loss(y_true, y_pred)

## tf.Tensor(0.6912122, shape=(), dtype=float32)

# Apply class weight
loss <- loss_binary_focal_crossentropy(
  apply_class_balancing = TRUE, gamma = 2, from_logits = TRUE)
loss(y_true, y_pred)

## tf.Tensor(0.5101333, shape=(), dtype=float32)

# Example 2: (batch_size = 2, number of samples = 4)
y_true <- rbind(c(0, 1), c(0, 0))
y_pred <- rbind(c(-18.6, 0.51), c(2.94, -12.8))
# Using default 'auto'/'sum_over_batch_size' reduction type.
loss <- loss_binary_focal_crossentropy(
    gamma = 3, from_logits = TRUE)
loss(y_true, y_pred)

## tf.Tensor(0.6469951, shape=(), dtype=float32)

# Apply class weight
loss <- loss_binary_focal_crossentropy(
     apply_class_balancing = TRUE, gamma = 3, from_logits = TRUE)
loss(y_true, y_pred)

## tf.Tensor(0.48214132, shape=(), dtype=float32)

# Using 'sample_weight' attribute with focal effect
loss <- loss_binary_focal_crossentropy(
    gamma = 3, from_logits = TRUE)
loss(y_true, y_pred, sample_weight = c(0.8, 0.2))

## tf.Tensor(0.13312504, shape=(), dtype=float32)

# Apply class weight
loss <- loss_binary_focal_crossentropy(
     apply_class_balancing = TRUE, gamma = 3, from_logits = TRUE)
loss(y_true, y_pred, sample_weight = c(0.8, 0.2))

## tf.Tensor(0.09735977, shape=(), dtype=float32)

# Using 'sum' reduction` type.
loss <- loss_binary_focal_crossentropy(
    gamma = 4, from_logits = TRUE,
    reduction = "sum")
loss(y_true, y_pred)

## tf.Tensor(1.2218808, shape=(), dtype=float32)

# Apply class weight
loss <- loss_binary_focal_crossentropy(
    apply_class_balancing = TRUE, gamma = 4, from_logits = TRUE,
    reduction = "sum")
loss(y_true, y_pred)

## tf.Tensor(0.9140807, shape=(), dtype=float32)

# Using 'none' reduction type.
loss <- loss_binary_focal_crossentropy(
    gamma = 5, from_logits = TRUE,
    reduction = NULL)
loss(y_true, y_pred)

## tf.Tensor([0.00174837 1.1561027 ], shape=(2), dtype=float32)

# Apply class weight
loss <- loss_binary_focal_crossentropy(
    apply_class_balancing = TRUE, gamma = 5, from_logits = TRUE,
    reduction = NULL)
loss(y_true, y_pred)

## tf.Tensor([4.3709317e-04 8.6707699e-01], shape=(2), dtype=float32)