Medium

Categorical Cross-Entropy

Medium

~15 min

code completion

Categorical Cross-Entropy Loss

For multi-class classification with one-hot labels, the categorical cross-entropy loss is:

L = - \frac{1}{m} i = 1 \sum m k = 1 \sum K y_{ik} lo g (\overset{p}{^}_{ik})

Since labels are one-hot ( $y_{ik} \in {0, 1}$ , exactly one 1 per row), this simplifies to:

L = - \frac{1}{m} i = 1 \sum m lo g (\overset{p}{^}_{i, c_{i}})

where $c_{i}$ is the true class for sample $i$ — we only penalize the predicted probability for the correct class.

Your task:

Implement categorical_cross_entropy(y_true, y_pred) where y_true is one-hot encoded and y_pred contains probabilities (rows sum to 1). Assume all y_pred > 0.

Example Tests

Perfect predictions: loss ≈ 0

Input: {"y_pred":[[0.99,0.005,0.005],[0.005,0.99,0.005]],"y_true":[[1,0,0],[0,1,0]]}

Expected: 0.01005

Uniform predictions: loss = log(K)

Input: {"y_pred":[[0.33333,0.33333,0.33334],[0.33333,0.33333,0.33334],[0.33333,0.33333,0.33334]],"y_true":[[1,0,0],[0,1,0],[0,0,1]]}

Expected: 1.09861

Single sample, true class 0 with p=0.7

Input: {"y_pred":[[0.7,0.2,0.1]],"y_true":[[1,0,0]]}

Expected: 0.35667

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