Selu

Versioned name: Selu-1

Category: Activation function

Short description: Selu is a scaled exponential linear unit element-wise activation function.

Detailed Description

Selu operation is introduced in this article, as activation function for self-normalizing neural networks (SNNs).

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

\f[ Selu(x) = \lambda \left{\begin{array}{r} x \quad \mbox{if } x > 0 \ \alpha(e^{x} - 1) \quad \mbox{if } x \le 0 \end{array}\right. \f]

where α and λ correspond to inputs alpha and lambda respectively.

Another mathematical representation that may be found in other references:

\f[ Selu(x) = \lambda\cdot\big(\max(0, x) + \min(0, \alpha(e^{x}-1))\big) \f]

Attributes: Selu operation has no attributes.

Inputs

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

• 2: alpha. 1D tensor with one element of type T. Required.

• 3: lambda. 1D tensor with one element of type T. Required.

Outputs

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

Types

• T: arbitrary supported floating-point type.

Example

<layer ... type="Selu">
    <input>
        <port id="0">
            <dim>256</dim>
            <dim>56</dim>
        </port>
        <port id="1">
            <dim>1</dim>
        </port>
        <port id="2">
            <dim>1</dim>
        </port>
    </input>
    <output>
        <port id="3">
            <dim>256</dim>
            <dim>56</dim>
        </port>
    </output>
</layer>