softmax :: Functions (Neural Network Toolbox™)

softmax

Purpose

Soft max transfer function

Graph and Symbol

Syntax

A = softmax(N,FP)
dA_dN = softmax('dn',N,A,FP)
info = softmax(code)

Description

softmax is a neural transfer function. Transfer functions calculate a layer's output from its net input.

softmax(N,FP) takes N and optional function parameters,

N
S x Q matrix of net input (column) vectors

FP
Struct of function parameters (ignored)

`N`	`S` x `Q` matrix of net input (column) vectors
`FP`	Struct of function parameters (ignored)

and returns A, the S x Q matrix of the softmax competitive function applied to each column of N.

softmax('dn',N,A,FP) returns the S x S x Q derivative of A with respect to N. If A or FP are not supplied or are set to [], FP reverts to the default parameters, and A is calculated from N.

softmax('name') returns the name of this function.

softmax('output',FP) returns the [min max] output range.

softmax('active',FP) returns the [min max] active input range.

softmax('fullderiv') returns 1 or 0, depending on whether dA_dN is S x S x Q or S x Q.

softmax('fpnames') returns the names of the function parameters.

softmax('fpdefaults') returns the default function parameters.

Examples

Here you define a net input vector N, calculate the output, and plot both with bar graphs.

n = [0; 1; -0.5; 0.5];
a = softmax(n);
subplot(2,1,1), bar(n), ylabel('n')
subplot(2,1,2), bar(a), ylabel('a')

Assign this transfer function to layer i of a network.

```
net.layers{i}.transferFcn = 'softmax';
```

Algorithm

```
a = softmax(n) = exp(n)/sum(exp(n))
```