Softmax of Vector

Problem

Compute the softmax of a vector:

softmax(v)[i] = exp(v[i] - m) / sum_j exp(v[j] - m)

with m = max(v) for numerical stability. The outputs are positive and sum to 1.

Hint

Softmax is invariant to adding a constant to every input, which is why max subtraction is safe.

case 1

in: [[0,0]]

expected: [0.5,0.5]

case 2

in: [[1,2,3]]

expected: [0.09003057317038046,0.24472847105479764,0.6652409557748218]

case 3

in: [[0,1]]

expected: [0.2689414213699951,0.7310585786300049]

case 4

in: [[1000,1000]]

expected: [0.5,0.5]

Starter codePython

def softmax(v):
    # Your code here
    pass

4 test cases · run your code against them in the editor