SoftPlus¶

Versioned name: SoftPlus-4

Category: Activation function

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

Detailed description

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

\[\begin{split}\begin{equation*} \mathrm{SoftPlus}(x) = \begin{cases} x & \text{if } x \geq \mathrm{threshold} \\ \log(e^{x} + 1.0) & \text{if } x < \mathrm{threshold} \end{cases} \end{equation*}\end{split}\]

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>