stable-softmax-logits — Netflix case

The team needs a reliable implementation for score-to-probability conversion in a production-oriented ML workflow. A small implementation error can change the model input or metric enough to make a downstream result misleading.

Given a vector of model logits, convert them into probabilities without overflowing when logits are large.

Use the maximum-subtraction form of softmax so that logits in the thousands do not overflow.

Implement solve(logits).

Returns. Return a NumPy vector of probabilities with the same length as logits; the entries are positive and sum to 1.

Examples

Example 1

Input:

solve([1000.0, 1001.0])

Output:

[0.268941, 0.731059]

Example 2

Input:

solve([0.0, 0.0, 0.0])

Output:

[0.333333, 0.333333, 0.333333]

Example 3

Input:

solve([-1000.0, 0.0])

Output:

[0.0, 1.0]