softmax function

Soft-Max function

Softmax for a vector x is defined as

softmax(x)

dsoftmax(x)

Arguments

• x: A numeric vector or matrix

Returns

softmax returns the softmax of x; rowwise if x is a matrix.

dsoftmax returns the Jacobi-matrix of softmax(x) at x. x must be a vector.

Details

$s_i = \exp(x_i) / \sum_k \exp(x_k)$

It satisfies sum(s) == 1.0 and can be used to smoothly enforce a sum constraint.

Examples

softmax(c(5, 5))
softmax(diag(nrow = 5, ncol = 6))