Stretch: Softmax + Categorical Cross-Entropy

The problem, from first principles

Binary sigmoid chooses between two outcomes. Multiclass classification needs every candidate class to compete for one shared unit of confidence, then needs a loss that scores only the probability assigned to each example's true class.

From theory to code

Implement row-wise softmax(Z) and cce_loss(P, y_indices). Theory maps the stable normalization and the one-correct-class lookup to the exact NumPy operations.

Constraints

• Z and P have shape (n_samples, n_classes); each softmax row sums to one.
• y_indices has one integer class index per sample.
• Subtract every row's maximum before exponentiating.
• Select one correct-class probability per row, clip it to [1e-12, 1.0], and return a Python float.
• Use P[np.arange(n), y_indices], not an all-rows column selection.

Hints

Open one at a time. Each gives away a little more than the last.