# 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:

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

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

Another mathematical representation that may be found in other references:

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

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>