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:

0.3984

K = 3. Smoothed targets: q = [0.9333, 0.0333, 0.0333]. Loss = -0.9333 * ln(0.9) - 0.0333 * ln(0.05) - 0.0333 * ln(0.05).

Input:

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

Output:

0.4413

K = 2. Smoothed targets: q = [0.9, 0.1]. Loss = -0.9 * ln(0.7) - 0.1 * ln(0.3).

Hint 1

First compute K = len(predictions). For the target class, the smoothed label is (1 - epsilon + epsilon/K). For all other classes it is epsilon/K.

Hint 2

Use math.log() for the natural logarithm. Loop over all classes, multiply the smoothed label by log(prediction), and sum the negated values.

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:

0.3984

K = 3. Smoothed targets: q = [0.9333, 0.0333, 0.0333]. Loss = -0.9333 * ln(0.9) - 0.0333 * ln(0.05) - 0.0333 * ln(0.05).

Input:

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

Output:

0.4413

K = 2. Smoothed targets: q = [0.9, 0.1]. Loss = -0.9 * ln(0.7) - 0.1 * ln(0.3).

Hint 1

First compute K = len(predictions). For the target class, the smoothed label is (1 - epsilon + epsilon/K). For all other classes it is epsilon/K.

Hint 2

Use math.log() for the natural logarithm. Loop over all classes, multiply the smoothed label by log(prediction), and sum the negated values.

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)