Problems

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Binary Focal Loss

Loss Functions

Medium

Binary focal loss addresses the class imbalance problem in binary classification by down-weighting the loss contribution from easy (well-classified) examples. This allows the model to focus training on hard, misclassified examples. It was introduced in the RetinaNet paper for object detection.

Given predicted probabilities, binary targets, a balancing factor alpha, and a focusing parameter gamma, compute the mean binary focal loss.

Algorithm

For each sample, let p be the predicted probability and y be the target (0 or 1):

Compute the probability assigned to the true class:

p_t = p \quad \text{if } y = 1

p_t = 1 - p \quad \text{if } y = 0

Compute the focal loss for this sample:

FL = -\alpha \cdot (1 - p_t)^{\gamma} \cdot \ln(p_t)

Return the mean focal loss across all samples.

Return the mean focal loss as a float.

Loading visualization...

Examples

Input: predictions = [0.9], targets = [1], alpha = 1, gamma = 2

Output: 0.001054

Explanation: The factor (1 - 0.9)² strongly reduces the loss of this confident correct prediction.

Input: predictions = [0.1], targets = [1], alpha = 1, gamma = 2

Output: 1.865094

Hint 1

Select p when the target is 1 and one minus p when the target is 0.

Hint 2

Accumulate the focal term with math.log, then divide by the sample count.

Requirements

Compute p_t based on whether the target is 1 or 0
Apply the focal modulating factor (1 - p_t)^gamma
Scale by the alpha parameter
Return the mean loss across all samples

Constraints

predictions contains values strictly between 0 and 1
targets contains only 0s and 1s
predictions and targets have the same length (at least 1)
alpha > 0, gamma >= 0
Return a single float (mean loss)
Time limit: 300 ms

Try Similar Problems

Focal Loss Cross Entropy Loss Hinge Loss Log Loss Per Sample Dice Loss

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Binary Focal Loss

Loss Functions

Medium

Given predicted probabilities, binary targets, a balancing factor alpha, and a focusing parameter gamma, compute the mean binary focal loss.

Algorithm

For each sample, let p be the predicted probability and y be the target (0 or 1):

Compute the probability assigned to the true class:

p_t = p \quad \text{if } y = 1

p_t = 1 - p \quad \text{if } y = 0

Compute the focal loss for this sample:

FL = -\alpha \cdot (1 - p_t)^{\gamma} \cdot \ln(p_t)

Return the mean focal loss across all samples.

Return the mean focal loss as a float.

Loading visualization...

Examples

Input: predictions = [0.9], targets = [1], alpha = 1, gamma = 2

Output: 0.001054

Explanation: The factor (1 - 0.9)² strongly reduces the loss of this confident correct prediction.

Input: predictions = [0.1], targets = [1], alpha = 1, gamma = 2

Output: 1.865094

Hint 1

Select p when the target is 1 and one minus p when the target is 0.

Hint 2

Accumulate the focal term with math.log, then divide by the sample count.

Requirements

Compute p_t based on whether the target is 1 or 0
Apply the focal modulating factor (1 - p_t)^gamma
Scale by the alpha parameter
Return the mean loss across all samples

Constraints

predictions contains values strictly between 0 and 1
targets contains only 0s and 1s
predictions and targets have the same length (at least 1)
alpha > 0, gamma >= 0
Return a single float (mean loss)
Time limit: 300 ms

Try Similar Problems

Focal Loss Cross Entropy Loss Hinge Loss Log Loss Per Sample Dice Loss

Case 1

Case 2

predictions =

Accepts: array

targets =

Accepts: array

alpha =

Accepts: number

gamma =

Accepts: number

Given predicted probabilities, binary targets, a balancing factor alpha, and a focusing parameter gamma, compute the mean binary focal loss.

Algorithm

For each sample, let p be the predicted probability and y be the target (0 or 1):

Compute the probability assigned to the true class:

p_t = p \quad \text{if } y = 1

p_t = 1 - p \quad \text{if } y = 0

Compute the focal loss for this sample:

FL = -\alpha \cdot (1 - p_t)^{\gamma} \cdot \ln(p_t)

Return the mean focal loss across all samples.

Return the mean focal loss as a float.