The classifier head — FC + softmax

Background

After the conv stack, a CNN flattens the features and runs a fully-connected layer followed by softmax to produce class probabilities, then predicts the top class:

$$\mathbf{z} = \mathbf{f}^\top W + \mathbf{b}, \qquad \mathbf{p} = \text{softmax}(\mathbf{z}), \qquad \hat{y} = \arg\max_k p_k$$

Problem statement

Implement classify_head(features, W, b) returning (label, probs).

Input

• features — array-like of length D, the flattened feature vector.
• W — array-like of shape (D, K), the FC weight matrix (K classes).
• b — array-like of length K, the bias.

Output

Returns (label, probs): label is the int predicted class; probs is an np.ndarray of K probabilities summing to 1.

Examples

Example 1

Input:  features = [1, 0], W = [[2, 0], [0, 2]], b = [0, 0]
Output: label = 0, probs ≈ [0.8808, 0.1192]

Explanation: logits $= [2, 0]$; softmax $\approx [0.88, 0.12]$; argmax is class 0.

Constraints

• Compute logits features @ W + b, softmax (numerically stable), then argmax.
• Return (int label, np.ndarray probs) with probs summing to 1.

Notes

• Subtract the max logit before exponentiating to avoid overflow — the standard stable softmax.