JMSLTM Numerical Library 7.2.0
com.imsl.datamining.neural

## Interface Activation

• 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).

Feed Forward Class Example 1, `Perceptron`
• ### 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, .
`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, `static Activation` `TANH`
The hyperbolic tangent activation function, .
• ### Method Summary

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, .
• #### 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.

• #### SOFTMAX

`static final Activation SOFTMAX`
The softmax activation function. .
• #### SQUASH

`static final Activation SQUASH`
The squash activation function, • #### TANH

`static final Activation TANH`
The hyperbolic tangent activation function, .
• ### Method Detail

• #### 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`.
• #### 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`.
JMSLTM Numerical Library 7.2.0
{"ft_lang_label":"__label__en","ft_lang_prob":0.7214872,"math_prob":0.8845517,"size":2119,"snap":"2021-31-2021-39","text_gpt3_token_len":467,"char_repetition_ratio":0.2496454,"word_repetition_ratio":0.12111801,"special_character_ratio":0.2005663,"punctuation_ratio":0.09798271,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99662876,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,2,null,2,null,2,null,2,null,1,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-01T04:13:59Z\",\"WARC-Record-ID\":\"<urn:uuid:13143545-7d73-4a5b-89af-0f1db4519673>\",\"Content-Length\":\"16139\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c696ae3d-80d5-4a60-b7a9-d3f88ea64482>\",\"WARC-Concurrent-To\":\"<urn:uuid:52a05c4d-b3d8-4dfa-a1ab-a9b3d00f3437>\",\"WARC-IP-Address\":\"13.91.82.80\",\"WARC-Target-URI\":\"https://help.imsl.com/java/7.2/manual/api/com/imsl/datamining/neural/Activation.html\",\"WARC-Payload-Digest\":\"sha1:EZQRSUHS6OLOT5B4K2X6IWTR7BN6DR34\",\"WARC-Block-Digest\":\"sha1:AEZVACO6QSH22WUIPQ46TSDQCSPCTK4E\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046154158.4_warc_CC-MAIN-20210801030158-20210801060158-00675.warc.gz\"}"}