Categorical Cross Entropy Loss

题面

实现批量分类交叉熵（基于 logits 的稳定公式），对 N×C 的 logits 与 N 个真实标签，计算平均损失：
L_j = log( Σ_k e^{z_{j,k}} ) - z_{j,y_j}，L = (1/N) Σ_j L_j。

Implementation Requirements

• External libraries are not permitted
• The solve function signature must remain unchanged
• The final result (average loss) must be stored in loss

Examples

Example 1: N=2,C=3 → loss ≈ 0.3548926
Example 2: N=3,C=4 → loss ≈ 0.98820376

Constraints

• 1 ≤ N ≤ 10,000
• 2 ≤ C ≤ 1,000
• -10.0 ≤ logits[i,j] ≤ 10.0
• 0 ≤ true_labels[i] ≤ C
• Performance is measured with N = 10,000