Softmax Temperature

Apply softmax with a temperature to a vector of logits: divide the logits by temperature, then take a numerically stable softmax. The temperature must be positive.

Implement solve(logits,temperature).

Returns. Return a NumPy vector of probabilities that sums to 1.

Examples

Example 1

Input:

solve([1.0, 2.0, 3.0], 1.0)

Output:

[0.090031, 0.244728, 0.665241]

Example 2

Input:

solve([1.0, 2.0, 3.0], 0.5)

Output:

[0.015876, 0.11731, 0.866813]

Example 3

Input:

solve([1.0, 2.0, 3.0], 100.0)

Output:

[0.330006, 0.333322, 0.336672]