Label Smoothing

Implement label smoothing from “Rethinking the Inception Architecture” (Szegedy et al., 2016).

Label smoothing replaces hard one-hot targets with soft targets to prevent overconfidence:

$$y_i' = (1 - \epsilon) \cdot y_i + \frac{\epsilon}{K}$$

Where:

• $y_i$ is the original one-hot label
• $\epsilon$ is the smoothing factor
• $K$ is the number of classes

Given:

• labels: shape (batch,) — integer class labels
• n_classes: integer K
• epsilon: float smoothing factor

Output: Tensor of shape (batch, n_classes) — smoothed label distribution.