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Implement Cross-Entropy Loss

Loss Functions

Medium

Compute the mean multiclass cross-entropy loss from correct class labels and predicted class probabilities. For sample $i$ , select the probability assigned to its correct class:

L_i = -\log(p_{i,y_i})

Average the sample losses:

L = -\frac{1}{N} \sum_{i=1}^{N} \log(p_{i,y_i})

Here, $N$ is the number of samples, $y_i$ is the correct class index for sample $i$ , and $p_{i,y_i}$ is the predicted probability of that class. Use the natural logarithm and return the mean loss as a Python float.

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Examples

Input: y_true = [0, 1], y_pred = [[0.9, 0.1], [0.3, 0.7]]

Output: 0.231018

Explanation: The selected probabilities are 0.9 and 0.7, and the output is the mean of their negative logarithms.

Input: y_true = [2], y_pred = [[0.1, 0.1, 0.8]]

Output: 0.223144

Input: y_true = [1, 0, 1], y_pred = [[0.2, 0.8], [0.6, 0.4], [0.49, 0.51]]

Output: 0.469105

Hint 1

np.arange(len(y_true)) provides the row indices for advanced indexing.

Hint 2

y_pred[row_indices, y_true] selects one correct-class probability per sample.

Hint 3

Use np.log() followed by np.mean() for the final reduction.

Requirements

y_true contains one valid class index for each row of y_pred
y_pred contains probabilities rather than logits
Select all correct-class probabilities without a Python loop over samples
Return the mean loss as a Python float

Constraints

y_pred has shape $(N, K)$ and y_true has length $N$
$1 \leq N \leq 100{,}000$ and $2 \leq K \leq 100$
Every probability is positive and each probability row sums to 1
Use NumPy only

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