jax.nn.sparse_sigmoid

jax.nn.sparse_sigmoid(x)

Sparse sigmoid activation function.

Computes the function:

\[\begin{split}\mathrm{sparse\_sigmoid}(x) = \begin{cases} 0, & x \leq -1\\ \frac{1}{2}(x+1), & -1 < x < 1 \\ 1, & 1 \leq x \end{cases}\end{split}\]

This is the twin function of the sigmoid activation ensuring a zero output for inputs less than -1, a 1 output for inputs greater than 1, and a linear output for inputs between -1 and 1. It is the derivative of sparse_plus.

For more information, see Learning with Fenchel-Young Losses (section 6.2).

Parameters:

x (ArrayLike) – input array

Returns:

An array.

Return type:

Array

See also

sigmoid()