softmax()

Apply the softmax function to a list of logits.

Usage

softmax(logits)

Converts a vector of raw scores (logits) into a probability distribution where each element is in (0, 1) and all elements sum to 1.

Parameters

logits: list

A list of numeric values (raw scores).

Returns

list

A list of probabilities summing to 1.0.

Notes

Applies the softmax function:

\[ \sigma(z)_i = \frac{e^{z_i}}{\sum_{j=1}^{K} e^{z_j}} \]

For numerical stability, the implementation subtracts the maximum logit value before exponentiation:

\[ \sigma(z)_i = \frac{e^{z_i - \max(z)}}{\sum_{j=1}^{K} e^{z_j - \max(z)}} \]

This prevents overflow when logit values are large.

Examples

>>> result = softmax([1.0, 2.0, 3.0])
>>> round(sum(result), 5)
1.0

>>> softmax([0.0, 0.0])
[0.5, 0.5]