GELU- Gaussian Error Linear Unit

Versioned name : Gelu-7

Category : Activation function

Short description : Gaussian error linear unit element-wise activation function.

Detailed description :

Gelu operation is introduced in this article. It performs element-wise activation function on a given input tensor, based on the following mathematical formula:

\[Gelu(x) = x\cdot\Phi(x)\]

where Φ(x) is the Cumulative Distribution Function for Gaussian Distribution.

The Gelu function may be approximated in two different ways based on approximation_mode attribute.

For erf approximation mode, Gelu function is represented as:

\[Gelu(x) = x\cdot\Phi(x) = x\cdot\frac{1}{2}\cdot\left[1 + erf\frac{x}{\sqrt{2}}\right]\]

For tanh approximation mode, Gelu function is represented as:

\[Gelu(x) \approx x\cdot\frac{1}{2}\cdot \left(1 + \tanh\left[\sqrt{\frac{2}{\pi}} \cdot (x + 0.044715 \cdot x^3)\right]\right)\]

Attributes

  • approximation_mode

    • Description : Specifies the formulae to calculate the Gelu function.

    • Range of values :

      • erf - calculate output using the Gauss error function

      • tanh - calculate output using tanh approximation

    • Type : string

    • Default value : erf

    • Required : no

Inputs :

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

Outputs :

  • 1 : The result of element-wise Gelu 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.

Examples

Example: tanh approximation mode

<layer ... type="Gelu">
    <data approximation_mode="tanh"/>
    <input>
        <port id="0">
            <dim>1</dim>
            <dim>128</dim>
        </port>
    </input>
    <output>
        <port id="1">
            <dim>1</dim>
            <dim>128</dim>
        </port>
    </output>
</layer>

Example: erf approximation mode

<layer ... type="Gelu">
    <data approximation_mode="erf"/>
    <input>
        <port id="0">
            <dim>3</dim>
            <dim>7</dim>
            <dim>9</dim>
        </port>
    </input>
    <output>
        <port id="1">
            <dim>3</dim>
            <dim>7</dim>
            <dim>9</dim>
        </port>
    </output>
</layer>