openvino/docs/ops/activation/SoftPlus_4.md

SoftPlus

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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:

.. math::

\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*}

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:

.. math::

-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

.. code-block:: cpp

<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>

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