Activation (JMSL Numerical Library (jmsl) 2022.1.0 API)

All Superinterfaces:

Serializable
```
public interface Activation
extends Serializable
```
Interface implemented by perceptron activation functions.
Standard activation functions are defined as static members of this interface. New activation functions can be defined by implementing a method, g(double x), returning the value and a method, derivative(double x, double y), returning the derivative of g evaluated at x where y = g(x).

See Also:

Example

Field Summary

Fields
Modifier and Type	Field and Description
`static Activation`	`LINEAR` The identity activation function, g(x) = x.
`static Activation`	`LOGISTIC` The logistic activation function, $g(x)=\frac{1}{1+e^{-x}} $.
`static Activation`	`LOGISTIC_TABLE` The logistic activation function computed using a table.
`static Activation`	`SOFTMAX` The softmax activation function.
`static Activation`	`SQUASH` The squash activation function, $g(x) = \frac{x}{1+\|x\|}$
`static Activation`	`TANH` The hyperbolic tangent activation function, $g(x)=\tanh{x}= \frac{e^x-e^{-x}}{e^x+e^{-x}}$.

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method and Description
`double`	`derivative(double x, double y)` Returns the value of the derivative of the activation function.
`double`	`g(double x)` Returns the value of the activation function.

- Field Detail
  - LINEAR
```
static final Activation LINEAR
```
    The identity activation function, g(x) = x.
  - LOGISTIC
```
static final Activation LOGISTIC
```
    The logistic activation function, $g(x)=\frac{1}{1+e^{-x}} $.
  - LOGISTIC_TABLE
```
static final Activation LOGISTIC_TABLE
```
    The logistic activation function computed using a table. This is an approximation to the logistic function that is faster to compute.
    This version of the logistic function differs from the exact version by at most 4.0e-9.
    
    Networks trained using this activation should not use Activation.LOGISTIC for forecasting. Forecasting should be done using the specific function supplied during training.
  - TANH
```
static final Activation TANH
```
    The hyperbolic tangent activation function, $g(x)=\tanh{x}= \frac{e^x-e^{-x}}{e^x+e^{-x}}$.
  - SQUASH
```
static final Activation SQUASH
```
    The squash activation function, $g(x) = \frac{x}{1+|x|}$
  - SOFTMAX
```
static final Activation SOFTMAX
```
    The softmax activation function. $$ {\rm{softmax}}_{\rm{i}}=\frac{{{\mathop{\rm e}\nolimits} ^{Z_i } }} {{\sum\limits_{j = 1}^C {e^{Z_j } } }}$$.
- Method Detail
  - g
```
double g(double x)
```
    Returns the value of the activation function.
    
    Parameters:
    
    x - A double is the point at which the activation function is to be evaluated.
    
    Returns:
    
    A double containing the value of the activation function at x.
  - derivative
```
double derivative(double x,
                  double y)
```
    Returns the value of the derivative of the activation function.
    
    Parameters:
    
    x - A double which specifies the point at which the activation function is to be evaluated.
    
    y - A double which specifies y = g(x), the value of the activation function at x. This parameter is not mathematically required, but can sometimes be used to more quickly compute the derivative.
    
    Returns:
    
    A double containing the value of the derivative of the activation function at x.

Interface Activation

Field Summary

Method Summary

Field Detail

LINEAR

LOGISTIC

LOGISTIC_TABLE

TANH

SQUASH

SOFTMAX

Method Detail

g

derivative