# LogSoftMax#

Versioned name: LogSoftmax-5

Category: Activation function

Short description: LogSoftmax computes the natural logarithm of softmax values for the given input.

Note

This is recommended to not compute LogSoftmax directly as Log(Softmax(x, axis)), more numeric stable is to compute LogSoftmax as:

$\begin{split}t = (x - ReduceMax(x,\ axis)) \\ LogSoftmax(x, axis) = t - Log(ReduceSum(Exp(t),\ axis))\end{split}$

Attributes

• axis

• Description: axis represents the axis of which the LogSoftmax is calculated. Negative value means counting dimensions from the back.

• Range of values: any integer value

• Type: int

• Default value: 1

• Required: no

Inputs:

• 1: Input tensor x of type T with enough number of dimension to be compatible with axis attribute. Required.

Outputs:

• 1: The resulting tensor of the same shape and of type T.

Types

• T: any floating-point type.

Mathematical Formulation

$y_{c} = ln\left(\frac{e^{Z_{c}}}{\sum_{d=1}^{C}e^{Z_{d}}}\right)$

where $$C$$ is a size of tensor along axis dimension.

Example

<layer ... type="LogSoftmax" ... >
<data axis="1" />
<input>
<port id="0">
<dim>256</dim>
<dim>56</dim>
</port>
</input>
<output>
<port id="3">
<dim>256</dim>
<dim>56</dim>
</port>
</output>
</layer>