Problems

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Label Smoothing Loss

Loss Functions

Medium

Label smoothing is a regularization technique that prevents a model from becoming overconfident. Instead of using hard one-hot targets (1 for the correct class, 0 for all others), it softens the target distribution by redistributing a small fraction of probability mass to the incorrect classes.

Given a predicted probability distribution, a target class index, and a smoothing parameter epsilon, compute the cross-entropy loss with smoothed labels.

Algorithm

Build the smoothed target distribution. For K classes and smoothing factor epsilon:

q_i = (1 - \epsilon) + \frac{\epsilon}{K} \quad \text{if } i = \text{target}

q_i = \frac{\epsilon}{K} \quad \text{if } i \ne \text{target}

Compute the cross-entropy loss between the smoothed targets q and the predictions p:

L = -\sum_{i=0}^{K-1} q_i \cdot \ln(p_i)

Loading visualization...

Examples

Input: predictions = [0.9, 0.05, 0.05], target = 0, epsilon = 0.1

Output: 0.29805196618423724

Explanation: The correct class receives 0.933333 target mass and each other class receives 0.033333.

Input: predictions = [0.7, 0.3], target = 0, epsilon = 0.2

Output: 0.44140472997745284

Hint 1

Give every class epsilon divided by the class count.

Hint 2

Add one minus epsilon to the target class before accumulating cross-entropy.

Requirements

Build the smoothed target distribution using the formula above
Compute cross-entropy between smoothed targets and predictions
K (number of classes) is the length of the predictions list
Return a single float

Constraints

predictions contains positive probabilities that sum to approximately 1
0 <= epsilon <= 1
0 <= target < len(predictions)
Return a single float
Time limit: 300 ms

Try Similar Problems

Cross Entropy Loss Kl Divergence Softmax Function Focal Loss Log Loss Per Sample

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Label Smoothing Loss

Loss Functions

Medium

Given a predicted probability distribution, a target class index, and a smoothing parameter epsilon, compute the cross-entropy loss with smoothed labels.

Algorithm

Build the smoothed target distribution. For K classes and smoothing factor epsilon:

q_i = (1 - \epsilon) + \frac{\epsilon}{K} \quad \text{if } i = \text{target}

q_i = \frac{\epsilon}{K} \quad \text{if } i \ne \text{target}

Compute the cross-entropy loss between the smoothed targets q and the predictions p:

L = -\sum_{i=0}^{K-1} q_i \cdot \ln(p_i)

Loading visualization...

Examples

Input: predictions = [0.9, 0.05, 0.05], target = 0, epsilon = 0.1

Output: 0.29805196618423724

Explanation: The correct class receives 0.933333 target mass and each other class receives 0.033333.

Input: predictions = [0.7, 0.3], target = 0, epsilon = 0.2

Output: 0.44140472997745284

Hint 1

Give every class epsilon divided by the class count.

Hint 2

Add one minus epsilon to the target class before accumulating cross-entropy.

Requirements

Build the smoothed target distribution using the formula above
Compute cross-entropy between smoothed targets and predictions
K (number of classes) is the length of the predictions list
Return a single float

Constraints

predictions contains positive probabilities that sum to approximately 1
0 <= epsilon <= 1
0 <= target < len(predictions)
Return a single float
Time limit: 300 ms

Try Similar Problems

Cross Entropy Loss Kl Divergence Softmax Function Focal Loss Log Loss Per Sample

Case 1

Case 2

predictions =

Accepts: array

target =

Accepts: number

epsilon =

Accepts: number

Given a predicted probability distribution, a target class index, and a smoothing parameter epsilon, compute the cross-entropy loss with smoothed labels.

Algorithm

Build the smoothed target distribution. For K classes and smoothing factor epsilon:

q_i = (1 - \epsilon) + \frac{\epsilon}{K} \quad \text{if } i = \text{target}

q_i = \frac{\epsilon}{K} \quad \text{if } i \ne \text{target}

Compute the cross-entropy loss between the smoothed targets q and the predictions p:

L = -\sum_{i=0}^{K-1} q_i \cdot \ln(p_i)