Softmax

Softmax function is defined as:

for j= 1, ..., p. Softmax function is also known as the normalized exponential (see [Bishop2006] for exact definitions).

Problem Statement

Given n feature vectors x 1 = (x 11 , … , x 1p ), ... , x n = (x n1 , … , x np ) of dimension p, the problem is to compute the (n x p)-dimensional matrix Y = (y i j ) n x p such that:

The library supports the numerically stable version of the softmax function:

For more complete information about compiler optimizations, see our Optimization Notice.
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