# SoftPlus¶

Versioned name : SoftPlus-4

Category : Activation function

Short description : SoftPlus is a rectified-based element-wise activation function.

Detailed description

SoftPlus operation is introduced in this article.

SoftPlus performs element-wise activation function on a given input tensor, based on the following mathematical formula:

$\begin{split}SoftPlus(x) = \left\{\begin{array}{r} x \qquad \mbox{if } x \geq threshold \\ log(e^{x} + 1.0) \qquad \mbox{if } x < threshold \end{array}\right.\end{split}$

Note : For numerical stability the operation reverts to the linear function when x > threshold where threshold depends on T and is chosen in such a way that the difference between the linear function and exact calculation is no more than 1e-6. The threshold can be calculated with the following formula where alpha is the number of digits after the decimal point, beta is maximum value of T data type:

$-log(e^{10^{-\alpha}} - 1.0) < threshold < log(\beta)$

For example, if T is fp32, threshold should be 20 or if T is fp16, threshold should be 11.

Attributes : SoftPlus operation has no attributes.

Inputs :

• 1 : A tensor of type T and arbitrary shape. Required.

Outputs :

• 1 : The result of element-wise SoftPlus function applied to the input tensor. A tensor of type T and the same shape as input tensor.

Types

• T : arbitrary supported floating-point type.

Example

<layer ... type="SoftPlus">
<input>
<port id="0">
<dim>256</dim>
<dim>56</dim>
</port>
</input>
<output>
<port id="1">
<dim>256</dim>
<dim>56</dim>
</port>
</output>
</layer>