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autodocs 2017-12-18 18:40:55 +00:00
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commit cab5326518
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/*
* The default CSS style for Documenter.jl generated sites
*
* Heavily inspired by the Julia Sphinx theme
* https://github.com/JuliaLang/JuliaDoc
* which extends the sphinx_rtd_theme
* https://github.com/snide/sphinx_rtd_theme
*
* Part of Documenter.jl
* https://github.com/JuliaDocs/Documenter.jl
*
* License: MIT
*/
/* fonts */
body, input {
font-family: 'Lato', 'Helvetica Neue', Arial, sans-serif;
font-size: 16px;
color: #222;
text-rendering: optimizeLegibility;
}
pre, code, kbd {
font-family: 'Roboto Mono', Monaco, courier, monospace;
font-size: 0.90em;
}
pre code {
font-size: 1em;
}
a {
color: #2980b9;
text-decoration: none;
}
a:hover {
color: #3091d1;
}
a:visited {
color: #9b59b6;
}
body {
line-height: 1.5;
}
h1 {
font-size: 1.75em;
}
/* Unless the <h1> the is very first thing on the page (i.e. the second element
* in the <article>, * after the <header>, we add some additional styling to it
* to make it stand out a bit more. This way we get a reasonable fallback if CSS3
* selectors are not supported in the browser.
*/
article > h1:not(:nth-child(2)) {
margin: 2.5em 0 0;
padding-bottom: 0.30em;
border-bottom: 1px solid #e5e5e5;
}
h2 {
font-size: 1.50em;
margin: 2.3em 0 0;
padding-bottom: 0.25em;
border-bottom: 1px solid #e5e5e5;
}
h3 {
font-size: 1.25em;
margin: 2.0em 0 0;
}
h4 { font-size: 1.15em; }
h5 { font-size: 1.10em; }
h6 { font-size: 1em; }
h4, h5, h6 {
margin-top: 1.5em;
margin-bottom: 1em;
}
img {
max-width: 100%;
}
table {
border-collapse: collapse;
margin: 1em 0;
}
th, td {
border: 1px solid #e1e4e5;
padding: 0.5em 1em;
}
th {
border-bottom-width: 2px;
}
tr:nth-child(even) {
background-color: #f3f6f6;
}
hr {
border: 0;
border-top: 1px solid #e5e5e5;
}
/* Inline code and code blocks */
code {
padding: 0.1em;
background-color: rgba(0,0,0,.04);
border-radius: 3px;
}
pre {
background-color: #f5f5f5;
border: 1px solid #dddddd;
border-radius: 3px;
padding: 0.5em;
overflow: auto;
}
pre code {
padding: 0;
background-color: initial;
}
kbd {
font-size: 0.70em;
display: inline-block;
padding: 0.1em 0.5em 0.4em 0.5em;
line-height: 1.0em;
color: #444d56;
vertical-align: middle;
background-color: #fafbfc;
border: solid 1px #c6cbd1;
border-bottom-color: #959da5;
border-radius: 3px;
box-shadow: inset 0 -1px 0 #959da5;
}
/* Headers in admonitions and docstrings */
.admonition h1,
article section.docstring h1 {
font-size: 1.25em;
}
.admonition h2,
article section.docstring h2 {
font-size: 1.10em;
}
.admonition h3,
.admonition h4,
.admonition h5,
.admonition h6,
article section.docstring h3,
article section.docstring h4,
article section.docstring h5,
article section.docstring h6 {
font-size: 1em;
}
/* Navigation */
nav.toc {
position: fixed;
top: 0;
left: 0;
bottom: 0;
width: 20em;
overflow-y: auto;
padding: 1em 0;
background-color: #fcfcfc;
box-shadow: inset -14px 0px 5px -12px rgb(210,210,210);
}
nav.toc .logo {
margin: 0 auto;
display: block;
max-height: 6em;
max-width: 18em;
}
nav.toc h1 {
text-align: center;
margin-top: .57em;
margin-bottom: 0;
}
nav.toc select {
display: block;
height: 2em;
padding: 0 1.6em 0 1em;
min-width: 7em;
max-width: 90%;
max-width: calc(100% - 5em);
margin: 0 auto;
font-size: .83em;
border: 1px solid #c9c9c9;
border-radius: 1em;
/* TODO: doesn't seem to be centered on Safari */
text-align: center;
text-align-last: center;
appearance: none;
-moz-appearance: none;
-webkit-appearance: none;
background: white url("arrow.svg");
background-size: 1.155em;
background-repeat: no-repeat;
background-position: right;
}
nav.toc select:hover {
border: 1px solid #a0a0a0;
}
nav.toc select option {
text-align: center;
}
nav.toc input {
display: block;
height: 2em;
width: 90%;
width: calc(100% - 5em);
margin: 1.2em auto;
padding: 0 1em;
border: 1px solid #c9c9c9;
border-radius: 1em;
font-size: .83em;
}
nav.toc > ul * {
margin: 0;
}
nav.toc ul {
color: #404040;
padding: 0;
list-style: none;
}
nav.toc ul .toctext {
color: inherit;
display: block;
}
nav.toc ul a:hover {
color: #fcfcfc;
background-color: #4e4a4a;
}
nav.toc ul.internal a {
color: inherit;
display: block;
}
nav.toc ul.internal a:hover {
background-color: #d6d6d6;
}
nav.toc ul.internal {
background-color: #e3e3e3;
box-shadow: inset -14px 0px 5px -12px rgb(210,210,210);
list-style: none;
}
nav.toc ul.internal li.toplevel {
border-top: 1px solid #c9c9c9;
font-weight: bold;
}
nav.toc ul.internal li.toplevel:first-child {
border-top: none;
}
nav.toc .toctext {
padding-top: 0.3em;
padding-bottom: 0.3em;
padding-right: 1em;
}
nav.toc ul .toctext {
padding-left: 1em;
}
nav.toc ul ul .toctext {
padding-left: 2em;
}
nav.toc ul ul ul .toctext {
padding-left: 3em;
}
nav.toc li.current > .toctext {
border-top: 1px solid #c9c9c9;
border-bottom: 1px solid #c9c9c9;
color: #404040;
font-weight: bold;
background-color: white;
}
article {
margin-left: 20em;
min-width: 20em;
max-width: 48em;
padding: 2em;
}
article > header {}
article > header div#topbar {
display: none;
}
article > header nav ul {
display: inline-block;
list-style: none;
margin: 0;
padding: 0;
}
article > header nav li {
display: inline-block;
padding-right: 0.2em;
}
article > header nav li:before {
content: "»";
padding-right: 0.2em;
}
article > header .edit-page {
float: right;
}
article > footer {}
article > footer a.prev {
float: left;
}
article > footer a.next {
float: right;
}
article > footer a .direction:after {
content: ": ";
}
article hr {
margin: 1em 0;
}
article section.docstring {
border: 1px solid #ddd;
margin: 0.5em 0;
padding: 0.5em;
border-radius: 3px;
}
article section.docstring .docstring-header {
margin-bottom: 1em;
}
article section.docstring .docstring-binding {
color: #333;
font-weight: bold;
}
article section.docstring .docstring-category {
font-style: italic;
}
article section.docstring a.source-link {
display: block;
font-weight: bold;
}
.nav-anchor,
.nav-anchor:hover,
.nav-anchor:visited {
color: #333;
}
/*
* Admonitions
*
* Colors (title, body)
* warning: #f0b37e #ffedcc (orange)
* note: #6ab0de #e7f2fa (blue)
* tip: #1abc9c #dbfaf4 (green)
*/
.admonition {
border-radius: 3px;
background-color: #eeeeee;
}
.admonition-title {
border-radius: 3px 3px 0 0;
background-color: #9b9b9b;
padding: 0.15em 0.5em;
}
.admonition-text {
padding: 0.5em;
}
.admonition-text > :first-child {
margin-top: 0;
}
.admonition-text > :last-child {
margin-bottom: 0;
}
.admonition > .admonition-title:before {
font-family: "FontAwesome";
margin-right: 5px;
content: "\f06a";
}
.admonition.warning > .admonition-title {
background-color: #f0b37e;
}
.admonition.warning {
background-color: #ffedcc;
}
.admonition.note > .admonition-title {
background-color: #6ab0de;
}
.admonition.note {
background-color: #e7f2fa;
}
.admonition.tip > .admonition-title {
background-color: #1abc9c;
}
.admonition.tip {
background-color: #dbfaf4;
}
/* footnotes */
.footnote {
padding-left: 0.8em;
border-left: 2px solid #ccc;
}
/* Search page */
#search-results .category {
font-size: smaller;
}
#search-results .category:before {
content: " ";
}
/* Overriding the <code> block style of highligh.js.
* We have to override the padding and the background-color, since we style this
* part ourselves. Specifically, we style the <pre> surrounding the <code>, while
* highlight.js applies the .hljs style directly to the <code> tag.
*/
.hljs {
background-color: transparent;
padding: 0;
}
@media only screen and (max-width: 768px) {
nav.toc {
position: fixed;
overflow-y: scroll;
width: 16em;
left: -16em;
-webkit-overflow-scrolling: touch;
-webkit-transition-property: left; /* Safari */
-webkit-transition-duration: 0.3s; /* Safari */
transition-property: left;
transition-duration: 0.3s;
-webkit-transition-timing-function: ease-out; /* Safari */
transition-timing-function: ease-out;
z-index: 2;
}
nav.toc.show {
left: 0;
}
article {
margin-left: 0;
padding: 3em 0.9em 0 0.9em; /* top right bottom left */
overflow-wrap: break-word;
}
article > header {
position: fixed;
left: 0;
z-index: 1;
}
article > header nav, hr {
display: none;
}
article > header div#topbar {
display: block; /* is mobile */
position: fixed;
width: 100%;
height: 1.5em;
padding-top: 1em;
padding-bottom: 1em;
background-color: #fcfcfc;
box-shadow: 0 1px 3px rgba(0,0,0,.26);
top: 0;
-webkit-transition-property: top; /* Safari */
-webkit-transition-duration: 0.3s; /* Safari */
transition-property: top;
transition-duration: 0.3s;
}
article > header div#topbar.headroom--unpinned.headroom--not-top.headroom--not-bottom {
top: -4em;
-webkit-transition-property: top; /* Safari */
-webkit-transition-duration: 0.7s; /* Safari */
transition-property: top;
transition-duration: 0.7s;
}
article > header div#topbar span {
position: fixed;
width: 80%;
height: 1.5em;
margin-top: -0.1em;
margin-left: 0.9em;
font-size: 1.2em;
overflow: hidden;
}
article > header div#topbar a.fa-bars {
float: right;
padding: 0.6em;
margin-top: -0.6em;
margin-right: 0.3em;
font-size: 1.5em;
}
article > header div#topbar a.fa-bars:visited {
color: #3091d1;
}
article table {
overflow-x: auto;
display: block;
}
article div.MathJax_Display {
overflow: scroll;
}
article span.MathJax {
overflow: hidden;
}
}
@media only screen and (max-width: 320px) {
body {
font-size: 15px;
}
}

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/*
* Part of Documenter.jl
* https://github.com/JuliaDocs/Documenter.jl
*
* License: MIT
*/
requirejs.config({
paths: {
'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.1.1/jquery.min',
'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.0/jquery-ui.min',
'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.9.3/headroom.min',
'mathjax': 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS_HTML',
'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/highlight.min',
'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/languages/julia.min',
'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/languages/julia-repl.min',
},
shim: {
'mathjax' : {
exports: "MathJax"
},
'highlight-julia': ['highlight'],
'highlight-julia-repl': ['highlight'],
}
});
// Load MathJax
require(['mathjax'], function(MathJax) {
MathJax.Hub.Config({
"tex2jax": {
inlineMath: [['$','$'], ['\\(','\\)']],
processEscapes: true
}
});
MathJax.Hub.Config({
config: ["MMLorHTML.js"],
jax: [
"input/TeX",
"output/HTML-CSS",
"output/NativeMML"
],
extensions: [
"MathMenu.js",
"MathZoom.js",
"TeX/AMSmath.js",
"TeX/AMSsymbols.js",
"TeX/autobold.js",
"TeX/autoload-all.js"
]
});
MathJax.Hub.Config({
TeX: { equationNumbers: { autoNumber: "AMS" } }
});
})
require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($, hljs) {
$(document).ready(function() {
hljs.initHighlighting();
})
})
// update the version selector with info from the siteinfo.js and ../versions.js files
require(['jquery'], function($) {
$(document).ready(function() {
var version_selector = $("#version-selector");
// add the current version to the selector based on siteinfo.js, but only if the selector is empty
if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) {
var option = $("<option value='#' selected='selected'>" + DOCUMENTER_CURRENT_VERSION + "</option>");
version_selector.append(option);
}
if (typeof DOC_VERSIONS !== 'undefined') {
var existing_versions = $('#version-selector > option');
var existing_versions_texts = existing_versions.map(function(i,x){return x.text});
DOC_VERSIONS.forEach(function(each) {
var version_url = documenterBaseURL + "/../" + each;
var existing_id = $.inArray(each, existing_versions_texts);
// if not already in the version selector, add it as a new option,
// otherwise update the old option with the URL and enable it
if (existing_id == -1) {
var option = $("<option value='" + version_url + "'>" + each + "</option>");
version_selector.append(option);
} else {
var option = existing_versions[existing_id];
option.value = version_url;
option.disabled = false;
}
});
}
// only show the version selector if the selector has been populated
if ($('#version-selector > option').length > 0) {
version_selector.css("visibility", "visible");
}
})
})
// mobile
require(['jquery', 'headroom'], function($, Headroom) {
$(document).ready(function() {
var navtoc = $("nav.toc");
$("nav.toc li.current a.toctext").click(function() {
navtoc.toggleClass('show');
});
$("article > header div#topbar a.fa-bars").click(function(ev) {
ev.preventDefault();
navtoc.toggleClass('show');
if (navtoc.hasClass('show')) {
var title = $("article > header div#topbar span").text();
$("nav.toc ul li a:contains('" + title + "')").focus();
}
});
$("article#docs").bind('click', function(ev) {
if ($(ev.target).is('div#topbar a.fa-bars')) {
return;
}
if (navtoc.hasClass('show')) {
navtoc.removeClass('show');
}
});
if ($("article > header div#topbar").css('display') == 'block') {
var headroom = new Headroom(document.querySelector("article > header div#topbar"), {"tolerance": {"up": 10, "down": 10}});
headroom.init();
}
})
})

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/*
* Part of Documenter.jl
* https://github.com/JuliaDocs/Documenter.jl
*
* License: MIT
*/
// parseUri 1.2.2
// (c) Steven Levithan <stevenlevithan.com>
// MIT License
function parseUri (str) {
var o = parseUri.options,
m = o.parser[o.strictMode ? "strict" : "loose"].exec(str),
uri = {},
i = 14;
while (i--) uri[o.key[i]] = m[i] || "";
uri[o.q.name] = {};
uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) {
if ($1) uri[o.q.name][$1] = $2;
});
return uri;
};
parseUri.options = {
strictMode: false,
key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"],
q: {
name: "queryKey",
parser: /(?:^|&)([^&=]*)=?([^&]*)/g
},
parser: {
strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/,
loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/
}
};
requirejs.config({
paths: {
'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.1.1/jquery.min',
'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.1.3/lunr.min',
'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.4/lodash.min',
}
});
var currentScript = document.currentScript;
require(["jquery", "lunr", "lodash"], function($, lunr, _) {
$("#search-form").submit(function(e) {
e.preventDefault()
})
// list below is the lunr 2.1.3 list minus the intersect with names(Base)
// (all, any, get, in, is, which) and (do, else, for, let, where, while, with)
// ideally we'd just filter the original list but it's not available as a variable
lunr.stopWordFilter = lunr.generateStopWordFilter([
'a',
'able',
'about',
'across',
'after',
'almost',
'also',
'am',
'among',
'an',
'and',
'are',
'as',
'at',
'be',
'because',
'been',
'but',
'by',
'can',
'cannot',
'could',
'dear',
'did',
'does',
'either',
'ever',
'every',
'from',
'got',
'had',
'has',
'have',
'he',
'her',
'hers',
'him',
'his',
'how',
'however',
'i',
'if',
'into',
'it',
'its',
'just',
'least',
'like',
'likely',
'may',
'me',
'might',
'most',
'must',
'my',
'neither',
'no',
'nor',
'not',
'of',
'off',
'often',
'on',
'only',
'or',
'other',
'our',
'own',
'rather',
'said',
'say',
'says',
'she',
'should',
'since',
'so',
'some',
'than',
'that',
'the',
'their',
'them',
'then',
'there',
'these',
'they',
'this',
'tis',
'to',
'too',
'twas',
'us',
'wants',
'was',
'we',
'were',
'what',
'when',
'who',
'whom',
'why',
'will',
'would',
'yet',
'you',
'your'
])
// add . as a separator, because otherwise "title": "Documenter.Anchors.add!"
// would not find anything if searching for "add!", only for the entire qualification
lunr.tokenizer.separator = /[\s\-\.]+/
// custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
lunr.trimmer = function (token) {
return token.update(function (s) {
return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '')
})
}
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julia&gt; onehot(:b, [:a, :b, :c])
3-element Flux.OneHotVector:
false
true
false
julia&gt; onehot(:c, [:a, :b, :c])
3-element Flux.OneHotVector:
false
false
true</code></pre><p>The inverse is <code>argmax</code> (which can take a general probability distribution, as well as just booleans).</p><pre><code class="language-julia">julia&gt; argmax(ans, [:a, :b, :c])
:c
julia&gt; argmax([true, false, false], [:a, :b, :c])
:a
julia&gt; argmax([0.3, 0.2, 0.5], [:a, :b, :c])
:c</code></pre><h2><a class="nav-anchor" id="Batches-1" href="#Batches-1">Batches</a></h2><p><code>onehotbatch</code> creates a batch (matrix) of one-hot vectors, and <code>argmax</code> treats matrices as batches.</p><pre><code class="language-julia">julia&gt; using Flux: onehotbatch
julia&gt; onehotbatch([:b, :a, :b], [:a, :b, :c])
3×3 Flux.OneHotMatrix:
false true false
true false true
false false false
julia&gt; onecold(ans, [:a, :b, :c])
3-element Array{Symbol,1}:
:b
:a
:b</code></pre><p>Note that these operations returned <code>OneHotVector</code> and <code>OneHotMatrix</code> rather than <code>Array</code>s. <code>OneHotVector</code>s behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.</p><footer><hr/><a class="previous" href="../training/training.html"><span class="direction">Previous</span><span class="title">Training</span></a><a class="next" href="../gpu.html"><span class="direction">Next</span><span class="title">GPU Support</span></a></footer></article></body></html>

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W = cu(rand(2, 5)) # a 2×5 CuArray
b = cu(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = cu(rand(5)), cu(rand(2)) # Dummy data
loss(x, y) # ~ 3</code></pre><p>Note that we convert both the parameters (<code>W</code>, <code>b</code>) and the data set (<code>x</code>, <code>y</code>) to cuda arrays. Taking derivatives and training works exactly as before.</p><p>If you define a structured model, like a <code>Dense</code> layer or <code>Chain</code>, you just need to convert the internal parameters. Flux provides <code>mapleaves</code>, which allows you to alter all parameters of a model at once.</p><pre><code class="language-julia">d = Dense(10, 5, σ)
d = mapleaves(cu, d)
d.W # Tracked CuArray
d(cu(rand(10))) # CuArray output
m = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)
m = mapleaves(cu, m)
d(cu(rand(10)))</code></pre><p>The <a href="https://github.com/FluxML/model-zoo/blob/master/mnist/mnist.jl">mnist example</a> contains the code needed to run the model on the GPU; just uncomment the lines after <code>using CuArrays</code>.</p><footer><hr/><a class="previous" href="data/onehot.html"><span class="direction">Previous</span><span class="title">One-Hot Encoding</span></a><a class="next" href="community.html"><span class="direction">Next</span><span class="title">Community</span></a></footer></article></body></html>

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Pkg.test(&quot;Flux&quot;) # Check things installed correctly</code></pre><p>Start with the <a href="models/basics.html">basics</a>. The <a href="https://github.com/FluxML/model-zoo/">model zoo</a> is also a good starting point for many common kinds of models.</p><footer><hr/><a class="next" href="models/basics.html"><span class="direction">Next</span><span class="title">Basics</span></a></footer></article></body></html>

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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li class="current"><a class="toctext" href="basics.html">Basics</a><ul class="internal"><li><a class="toctext" href="#Taking-Gradients-1">Taking Gradients</a></li><li><a class="toctext" href="#Building-Layers-1">Building Layers</a></li><li><a class="toctext" href="#Stacking-It-Up-1">Stacking It Up</a></li><li><a class="toctext" href="#Layer-helpers-1">Layer helpers</a></li></ul></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="layers.html">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="basics.html">Basics</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/basics.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Basics</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Model-Building-Basics-1" href="#Model-Building-Basics-1">Model-Building Basics</a></h1><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>Consider a simple linear regression, which tries to predict an output array <code>y</code> from an input <code>x</code>. (It&#39;s a good idea to follow this example in the Julia repl.)</p><pre><code class="language-julia">W = rand(2, 5)
b = rand(2)
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = rand(5), rand(2) # Dummy data
loss(x, y) # ~ 3</code></pre><p>To improve the prediction we can take the gradients of <code>W</code> and <code>b</code> with respect to the loss function and perform gradient descent. We could calculate gradients by hand, but Flux will do it for us if we tell it that <code>W</code> and <code>b</code> are trainable <em>parameters</em>.</p><pre><code class="language-julia">using Flux.Tracker
W = param(W)
b = param(b)
l = loss(x, y)
back!(l)</code></pre><p><code>loss(x, y)</code> returns the same number, but it&#39;s now a <em>tracked</em> value that records gradients as it goes along. Calling <code>back!</code> then calculates the gradient of <code>W</code> and <code>b</code>. We can see what this gradient is, and modify <code>W</code> to train the model.</p><pre><code class="language-julia">W.grad
# Update the parameter
W.data .-= 0.1(W.grad)
loss(x, y) # ~ 2.5</code></pre><p>The loss has decreased a little, meaning that our prediction <code>x</code> is closer to the target <code>y</code>. If we have some data we can already try <a href="../training/training.html">training the model</a>.</p><p>All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, models can <em>look</em> very different – they might have millions of parameters or complex control flow, and there are ways to manage this complexity. Let&#39;s see what that looks like.</p><h2><a class="nav-anchor" id="Building-Layers-1" href="#Building-Layers-1">Building Layers</a></h2><p>It&#39;s common to create more complex models than the linear regression above. For example, we might want to have two linear layers with a nonlinearity like <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> (<code>σ</code>) in between them. In the above style we could write this as:</p><pre><code class="language-julia">W1 = param(rand(3, 5))
b1 = param(rand(3))
layer1(x) = W1 * x .+ b1
W2 = param(rand(2, 3))
b2 = param(rand(2))
layer2(x) = W2 * x .+ b2
model(x) = layer2(σ.(layer1(x)))
model(rand(5)) # =&gt; 2-element vector</code></pre><p>This works but is fairly unwieldy, with a lot of repetition – especially as we add more layers. One way to factor this out is to create a function that returns linear layers.</p><pre><code class="language-julia">function linear(in, out)
W = param(randn(out, in))
b = param(randn(out))
x -&gt; W * x .+ b
end
linear1 = linear(5, 3) # we can access linear1.W etc
linear2 = linear(3, 2)
model(x) = linear2(σ.(linear1(x)))
model(x) # =&gt; 2-element vector</code></pre><p>Another (equivalent) way is to create a struct that explicitly represents the affine layer.</p><pre><code class="language-julia">struct Affine
W
b
end
Affine(in::Integer, out::Integer) =
Affine(param(randn(out, in)), param(randn(out)))
# Overload call, so the object can be used as a function
(m::Affine)(x) = m.W * x .+ m.b
a = Affine(10, 5)
a(rand(10)) # =&gt; 5-element vector</code></pre><p>Congratulations! You just built the <code>Dense</code> layer that comes with Flux. Flux has many interesting layers available, but they&#39;re all things you could have built yourself very easily.</p><p>(There is one small difference with <code>Dense</code> – for convenience it also takes an activation function, like <code>Dense(10, 5, σ)</code>.)</p><h2><a class="nav-anchor" id="Stacking-It-Up-1" href="#Stacking-It-Up-1">Stacking It Up</a></h2><p>It&#39;s pretty common to write models that look something like:</p><pre><code class="language-julia">layer1 = Dense(10, 5, σ)
# ...
model(x) = layer3(layer2(layer1(x)))</code></pre><p>For long chains, it might be a bit more intuitive to have a list of layers, like this:</p><pre><code class="language-julia">using Flux
layers = [Dense(10, 5, σ), Dense(5, 2), softmax]
model(x) = foldl((x, m) -&gt; m(x), x, layers)
model(rand(10)) # =&gt; 2-element vector</code></pre><p>Handily, this is also provided for in Flux:</p><pre><code class="language-julia">model2 = Chain(
Dense(10, 5, σ),
Dense(5, 2),
softmax)
model2(rand(10)) # =&gt; 2-element vector</code></pre><p>This quickly starts to look like a high-level deep learning library; yet you can see how it falls out of simple abstractions, and we lose none of the power of Julia code.</p><p>A nice property of this approach is that because &quot;models&quot; are just functions (possibly with trainable parameters), you can also see this as simple function composition.</p><pre><code class="language-julia">m = Dense(5, 2) ∘ Dense(10, 5, σ)
m(rand(10))</code></pre><p>Likewise, <code>Chain</code> will happily work with any Julia function.</p><pre><code class="language-julia">m = Chain(x -&gt; x^2, x -&gt; x+1)
m(5) # =&gt; 26</code></pre><h2><a class="nav-anchor" id="Layer-helpers-1" href="#Layer-helpers-1">Layer helpers</a></h2><p>Flux provides a set of helpers for custom layers, which you can enable by calling</p><pre><code class="language-julia">Flux.treelike(Affine)</code></pre><p>This enables a useful extra set of functionality for our <code>Affine</code> layer, such as <a href="../training/optimisers.html">collecting its parameters</a> or <a href="../gpu.html">moving it to the GPU</a>.</p><footer><hr/><a class="previous" href="../index.html"><span class="direction">Previous</span><span class="title">Home</span></a><a class="next" href="recurrence.html"><span class="direction">Next</span><span class="title">Recurrence</span></a></footer></article></body></html>

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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Model Reference · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="basics.html">Basics</a></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li class="current"><a class="toctext" href="layers.html">Model Reference</a><ul class="internal"><li><a class="toctext" href="#Basic-Layers-1">Basic Layers</a></li><li><a class="toctext" href="#Recurrent-Layers-1">Recurrent Layers</a></li><li><a class="toctext" href="#Activation-Functions-1">Activation Functions</a></li><li><a class="toctext" href="#Normalisation-and-Regularisation-1">Normalisation &amp; Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="layers.html">Model Reference</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Model Reference</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Basic-Layers-1" href="#Basic-Layers-1">Basic Layers</a></h2><p>These core layers form the foundation of almost all neural networks.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Chain" href="#Flux.Chain"><code>Flux.Chain</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Chain(layers...)</code></pre><p>Chain multiple layers / functions together, so that they are called in sequence on a given input.</p><pre><code class="language-julia">m = Chain(x -&gt; x^2, x -&gt; x+1)
m(5) == 26
m = Chain(Dense(10, 5), Dense(5, 2))
x = rand(10)
m(x) == m[2](m[1](x))</code></pre><p><code>Chain</code> also supports indexing and slicing, e.g. <code>m[2]</code> or <code>m[1:end-1]</code>. <code>m[1:3](x)</code> will calculate the output of the first three layers.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/basic.jl#L1-L18">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dense" href="#Flux.Dense"><code>Flux.Dense</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Dense(in::Integer, out::Integer, σ = identity)</code></pre><p>Creates a traditional <code>Dense</code> layer with parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-none">y = σ.(W * x .+ b)</code></pre><p>The input <code>x</code> must be a vector of length <code>in</code>, or a batch of vectors represented as an <code>in × N</code> matrix. The out <code>y</code> will be a vector or batch of length <code>out</code>.</p><pre><code class="language-julia">julia&gt; d = Dense(5, 2)
Dense(5, 2)
julia&gt; d(rand(5))
Tracked 2-element Array{Float64,1}:
0.00257447
-0.00449443</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/basic.jl#L40-L59">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Conv2D" href="#Flux.Conv2D"><code>Flux.Conv2D</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Conv2D(size, in=&gt;out)
Conv2d(size, in=&gt;out, relu)</code></pre><p>Standard convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>out</code> specify the number of input and output channels respectively.</p><p>Data should be stored in HWCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/conv.jl#L1-L12">source</a></section><h2><a class="nav-anchor" id="Recurrent-Layers-1" href="#Recurrent-Layers-1">Recurrent Layers</a></h2><p>Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.RNN" href="#Flux.RNN"><code>Flux.RNN</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">RNN(in::Integer, out::Integer, σ = tanh)</code></pre><p>The most basic recurrent layer; essentially acts as a <code>Dense</code> layer, but with the output fed back into the input each time step.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/recurrent.jl#L98-L103">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LSTM" href="#Flux.LSTM"><code>Flux.LSTM</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">LSTM(in::Integer, out::Integer, σ = tanh)</code></pre><p>Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/recurrent.jl#L143-L151">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Recur" href="#Flux.Recur"><code>Flux.Recur</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here&#39;s a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
rnn = Flux.Recur(accum, 0)
rnn(2) # 2
rnn(3) # 3
rnn.state # 5
rnn.(1:10) # apply to a sequence
rnn.state # 60</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/recurrent.jl#L8-L27">source</a></section><h2><a class="nav-anchor" id="Activation-Functions-1" href="#Activation-Functions-1">Activation Functions</a></h2><p>Non-linearities that go between layers of your model. Most of these functions are defined in <a href="https://github.com/FluxML/NNlib.jl">NNlib</a> but are available by default in Flux.</p><p>Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call <code>σ.(xs)</code>, <code>relu.(xs)</code> and so on.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.σ" href="#NNlib.σ"><code>NNlib.σ</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">σ(x) = 1 / (1 + exp(-x))</code></pre><p>Classic <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> activation function.</p><pre><code class="language-none">1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀│
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│⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
0 │⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L1-L24">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.relu" href="#NNlib.relu"><code>NNlib.relu</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">relu(x) = max(0, x)</code></pre><p><a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function.</p><pre><code class="language-none">3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
0 │⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L39-L61">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.leakyrelu" href="#NNlib.leakyrelu"><code>NNlib.leakyrelu</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">leakyrelu(x) = max(0.01x, x)</code></pre><p>Leaky <a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function. You can also specify the coefficient explicitly, e.g. <code>leakyrelu(x, 0.01)</code>.</p><pre><code class="language-none"> 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│
-1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L65-L86">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.elu" href="#NNlib.elu"><code>NNlib.elu</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">elu(x, α = 1) =
x &gt; 0 ? x : α * (exp(x) - 1)</code></pre><p>Exponential Linear Unit activation function. See <a href="https://arxiv.org/abs/1511.07289">Fast and Accurate Deep Network Learning by Exponential Linear Units</a>. You can also specify the coefficient explicitly, e.g. <code>elu(x, 1)</code>.</p><pre><code class="language-none"> 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠖⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-1 │⣀⣀⠤⠤⠤⠤⠔⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L89-L113">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.swish" href="#NNlib.swish"><code>NNlib.swish</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">swish(x) = x * σ(x)</code></pre><p>Self-gated actvation function. See <a href="https://arxiv.org/pdf/1710.05941.pdf">Swish: a Self-Gated Activation Function</a>.</p><pre><code class="language-none"> 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
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-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L116-L138">source</a></section><h2><a class="nav-anchor" id="Normalisation-and-Regularisation-1" href="#Normalisation-and-Regularisation-1">Normalisation &amp; Regularisation</a></h2><p>These layers don&#39;t affect the structure of the network but may improve training times or reduce overfitting.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.testmode!" href="#Flux.testmode!"><code>Flux.testmode!</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">testmode!(m)
testmode!(m, false)</code></pre><p>Put layers like <a href="layers.html#Flux.Dropout"><code>Dropout</code></a> and <a href="layers.html#Flux.BatchNorm"><code>BatchNorm</code></a> into testing mode (or back to training mode with <code>false</code>).</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/normalisation.jl#L1-L7">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.BatchNorm" href="#Flux.BatchNorm"><code>Flux.BatchNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">BatchNorm(dims...; λ = identity,
initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1)</code></pre><p>Batch Normalization Layer for <a href="layers.html#Flux.Dense"><code>Dense</code></a> layer.</p><p>See <a href="https://arxiv.org/pdf/1502.03167.pdf">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a></p><p>In the example of MNIST, in order to normalize the input of other layer, put the <code>BatchNorm</code> layer before activation function.</p><pre><code class="language-julia">m = Chain(
Dense(28^2, 64),
BatchNorm(64, λ = relu),
Dense(64, 10),
BatchNorm(10),
softmax)</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/normalisation.jl#L70-L91">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dropout" href="#Flux.Dropout"><code>Flux.Dropout</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Dropout(p)</code></pre><p>A Dropout layer. For each input, either sets that input to <code>0</code> (with probability <code>p</code>) or scales it by <code>1/(1-p)</code>. This is used as a regularisation, i.e. it reduces overfitting during training.</p><p>Does nothing to the input once in <a href="layers.html#Flux.testmode!"><code>testmode!</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/normalisation.jl#L15-L23">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LayerNorm" href="#Flux.LayerNorm"><code>Flux.LayerNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">LayerNorm(h::Integer)</code></pre><p>A <a href="https://arxiv.org/pdf/1607.06450.pdf">normalisation layer</a> designed to be used with recurrent hidden states of size <code>h</code>. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/normalisation.jl#L47-L54">source</a></section><footer><hr/><a class="previous" href="recurrence.html"><span class="direction">Previous</span><span class="title">Recurrence</span></a><a class="next" href="../training/optimisers.html"><span class="direction">Next</span><span class="title">Optimisers</span></a></footer></article></body></html>

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y₂ = f(x₂)
y₃ = f(x₃)
# ...</code></pre><p>Recurrent networks introduce a <em>hidden state</em> that gets carried over each time we run the model. The model now takes the old <code>h</code> as an input, and produces a new <code>h</code> as output, each time we run it.</p><pre><code class="language-julia">h = # ... initial state ...
h, y₁ = f(h, x₁)
h, y₂ = f(h, x₂)
h, y₃ = f(h, x₃)
# ...</code></pre><p>Information stored in <code>h</code> is preserved for the next prediction, allowing it to function as a kind of memory. This also means that the prediction made for a given <code>x</code> depends on all the inputs previously fed into the model.</p><p>(This might be important if, for example, each <code>x</code> represents one word of a sentence; the model&#39;s interpretation of the word &quot;bank&quot; should change if the previous input was &quot;river&quot; rather than &quot;investment&quot;.)</p><p>Flux&#39;s RNN support closely follows this mathematical perspective. The most basic RNN is as close as possible to a standard <code>Dense</code> layer, and the output is also the hidden state.</p><pre><code class="language-julia">Wxh = randn(5, 10)
Whh = randn(5, 5)
b = randn(5)
function rnn(h, x)
h = tanh.(Wxh * x .+ Whh * h .+ b)
return h, h
end
x = rand(10) # dummy data
h = rand(5) # initial hidden state
h, y = rnn(h, x)</code></pre><p>If you run the last line a few times, you&#39;ll notice the output <code>y</code> changing slightly even though the input <code>x</code> is the same.</p><p>We sometimes refer to functions like <code>rnn</code> above, which explicitly manage state, as recurrent <em>cells</em>. There are various recurrent cells available, which are documented in the <a href="layers.html">layer reference</a>. The hand-written example above can be replaced with:</p><pre><code class="language-julia">using Flux
rnn2 = Flux.RNNCell(10, 5)
x = rand(10) # dummy data
h = rand(5) # initial hidden state
h, y = rnn2(h, x)</code></pre><h2><a class="nav-anchor" id="Stateful-Models-1" href="#Stateful-Models-1">Stateful Models</a></h2><p>For the most part, we don&#39;t want to manage hidden states ourselves, but to treat our models as being stateful. Flux provides the <code>Recur</code> wrapper to do this.</p><pre><code class="language-julia">x = rand(10)
h = rand(5)
m = Flux.Recur(rnn, h)
y = m(x)</code></pre><p>The <code>Recur</code> wrapper stores the state between runs in the <code>m.state</code> field.</p><p>If you use the <code>RNN(10, 5)</code> constructor – as opposed to <code>RNNCell</code> – you&#39;ll see that it&#39;s simply a wrapped cell.</p><pre><code class="language-julia">julia&gt; RNN(10, 5)
Recur(RNNCell(Dense(15, 5)))</code></pre><h2><a class="nav-anchor" id="Sequences-1" href="#Sequences-1">Sequences</a></h2><p>Often we want to work with sequences of inputs, rather than individual <code>x</code>s.</p><pre><code class="language-julia">seq = [rand(10) for i = 1:10]</code></pre><p>With <code>Recur</code>, applying our model to each element of a sequence is trivial:</p><pre><code class="language-julia">m.(seq) # returns a list of 5-element vectors</code></pre><p>This works even when we&#39;ve chain recurrent layers into a larger model.</p><pre><code class="language-julia">m = Chain(LSTM(10, 15), Dense(15, 5))
m.(seq)</code></pre><h2><a class="nav-anchor" id="Truncating-Gradients-1" href="#Truncating-Gradients-1">Truncating Gradients</a></h2><p>By default, calculating the gradients in a recurrent layer involves the entire history. For example, if we call the model on 100 inputs, calling <code>back!</code> will calculate the gradient for those 100 calls. If we then calculate another 10 inputs we have to calculate 110 gradients – this accumulates and quickly becomes expensive.</p><p>To avoid this we can <em>truncate</em> the gradient calculation, forgetting the history.</p><pre><code class="language-julia">truncate!(m)</code></pre><p>Calling <code>truncate!</code> wipes the slate clean, so we can call the model with more inputs without building up an expensive gradient computation.</p><p><code>truncate!</code> makes sense when you are working with multiple chunks of a large sequence, but we may also want to work with a set of independent sequences. In this case the hidden state should be completely reset to its original value, throwing away any accumulated information. <code>reset!</code> does this for you.</p><footer><hr/><a class="previous" href="basics.html"><span class="direction">Previous</span><span class="title">Basics</span></a><a class="next" href="layers.html"><span class="direction">Next</span><span class="title">Model Reference</span></a></footer></article></body></html>

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"text": "In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.y₁ = f(x₁)\ny₂ = f(x₂)\ny₃ = f(x₃)\n# ...Recurrent networks introduce a hidden state that gets carried over each time we run the model. The model now takes the old h as an input, and produces a new h as output, each time we run it.h = # ... initial state ...\nh, y₁ = f(h, x₁)\nh, y₂ = f(h, x₂)\nh, y₃ = f(h, x₃)\n# ...Information stored in h is preserved for the next prediction, allowing it to function as a kind of memory. This also means that the prediction made for a given x depends on all the inputs previously fed into the model.(This might be important if, for example, each x represents one word of a sentence; the model's interpretation of the word \"bank\" should change if the previous input was \"river\" rather than \"investment\".)Flux's RNN support closely follows this mathematical perspective. The most basic RNN is as close as possible to a standard Dense layer, and the output is also the hidden state.Wxh = randn(5, 10)\nWhh = randn(5, 5)\nb = randn(5)\n\nfunction rnn(h, x)\n h = tanh.(Wxh * x .+ Whh * h .+ b)\n return h, h\nend\n\nx = rand(10) # dummy data\nh = rand(5) # initial hidden state\n\nh, y = rnn(h, x)If you run the last line a few times, you'll notice the output y changing slightly even though the input x is the same.We sometimes refer to functions like rnn above, which explicitly manage state, as recurrent cells. There are various recurrent cells available, which are documented in the layer reference. The hand-written example above can be replaced with:using Flux\n\nrnn2 = Flux.RNNCell(10, 5)\n\nx = rand(10) # dummy data\nh = rand(5) # initial hidden state\n\nh, y = rnn2(h, x)"
},
{
"location": "models/recurrence.html#Stateful-Models-1",
"page": "Recurrence",
"title": "Stateful Models",
"category": "section",
"text": "For the most part, we don't want to manage hidden states ourselves, but to treat our models as being stateful. Flux provides the Recur wrapper to do this.x = rand(10)\nh = rand(5)\n\nm = Flux.Recur(rnn, h)\n\ny = m(x)The Recur wrapper stores the state between runs in the m.state field.If you use the RNN(10, 5) constructor – as opposed to RNNCell – you'll see that it's simply a wrapped cell.julia> RNN(10, 5)\nRecur(RNNCell(Dense(15, 5)))"
},
{
"location": "models/recurrence.html#Sequences-1",
"page": "Recurrence",
"title": "Sequences",
"category": "section",
"text": "Often we want to work with sequences of inputs, rather than individual xs.seq = [rand(10) for i = 1:10]With Recur, applying our model to each element of a sequence is trivial:m.(seq) # returns a list of 5-element vectorsThis works even when we've chain recurrent layers into a larger model.m = Chain(LSTM(10, 15), Dense(15, 5))\nm.(seq)"
},
{
"location": "models/recurrence.html#Truncating-Gradients-1",
"page": "Recurrence",
"title": "Truncating Gradients",
"category": "section",
"text": "By default, calculating the gradients in a recurrent layer involves the entire history. For example, if we call the model on 100 inputs, calling back! will calculate the gradient for those 100 calls. If we then calculate another 10 inputs we have to calculate 110 gradients – this accumulates and quickly becomes expensive.To avoid this we can truncate the gradient calculation, forgetting the history.truncate!(m)Calling truncate! wipes the slate clean, so we can call the model with more inputs without building up an expensive gradient computation.truncate! makes sense when you are working with multiple chunks of a large sequence, but we may also want to work with a set of independent sequences. In this case the hidden state should be completely reset to its original value, throwing away any accumulated information. reset! does this for you."
},
{
"location": "models/layers.html#",
"page": "Model Reference",
"title": "Model Reference",
"category": "page",
"text": ""
},
{
"location": "models/layers.html#Flux.Chain",
"page": "Model Reference",
"title": "Flux.Chain",
"category": "Type",
"text": "Chain(layers...)\n\nChain multiple layers / functions together, so that they are called in sequence on a given input.\n\nm = Chain(x -> x^2, x -> x+1)\nm(5) == 26\n\nm = Chain(Dense(10, 5), Dense(5, 2))\nx = rand(10)\nm(x) == m[2](m[1](x))\n\nChain also supports indexing and slicing, e.g. m[2] or m[1:end-1]. m[1:3](x) will calculate the output of the first three layers.\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Dense",
"page": "Model Reference",
"title": "Flux.Dense",
"category": "Type",
"text": "Dense(in::Integer, out::Integer, σ = identity)\n\nCreates a traditional Dense layer with parameters W and b.\n\ny = σ.(W * x .+ b)\n\nThe input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length out.\n\njulia> d = Dense(5, 2)\nDense(5, 2)\n\njulia> d(rand(5))\nTracked 2-element Array{Float64,1}:\n 0.00257447\n -0.00449443\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Conv2D",
"page": "Model Reference",
"title": "Flux.Conv2D",
"category": "Type",
"text": "Conv2D(size, in=>out)\nConv2d(size, in=>out, relu)\n\nStandard convolutional layer. size should be a tuple like (2, 2). in and out specify the number of input and output channels respectively.\n\nData should be stored in HWCN order. In other words, a 100×100 RGB image would be a 100×100×3 array, and a batch of 50 would be a 100×100×3×50 array.\n\nTakes the keyword arguments pad and stride.\n\n\n\n"
},
{
"location": "models/layers.html#Basic-Layers-1",
"page": "Model Reference",
"title": "Basic Layers",
"category": "section",
"text": "These core layers form the foundation of almost all neural networks.Chain\nDense\nConv2D"
},
{
"location": "models/layers.html#Flux.RNN",
"page": "Model Reference",
"title": "Flux.RNN",
"category": "Function",
"text": "RNN(in::Integer, out::Integer, σ = tanh)\n\nThe most basic recurrent layer; essentially acts as a Dense layer, but with the output fed back into the input each time step.\n\n\n\n"
},
{
"location": "models/layers.html#Flux.LSTM",
"page": "Model Reference",
"title": "Flux.LSTM",
"category": "Function",
"text": "LSTM(in::Integer, out::Integer, σ = tanh)\n\nLong Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.\n\nSee this article for a good overview of the internals.\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Recur",
"page": "Model Reference",
"title": "Flux.Recur",
"category": "Type",
"text": "Recur(cell)\n\nRecur takes a recurrent cell and makes it stateful, managing the hidden state in the background. cell should be a model of the form:\n\nh, y = cell(h, x...)\n\nFor example, here's a recurrent network that keeps a running total of its inputs.\n\naccum(h, x) = (h+x, x)\nrnn = Flux.Recur(accum, 0)\nrnn(2) # 2\nrnn(3) # 3\nrnn.state # 5\nrnn.(1:10) # apply to a sequence\nrnn.state # 60\n\n\n\n"
},
{
"location": "models/layers.html#Recurrent-Layers-1",
"page": "Model Reference",
"title": "Recurrent Layers",
"category": "section",
"text": "Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).RNN\nLSTM\nFlux.Recur"
},
{
"location": "models/layers.html#NNlib.σ",
"page": "Model Reference",
"title": "NNlib.σ",
"category": "Function",
"text": "σ(x) = 1 / (1 + exp(-x))\n\nClassic sigmoid activation function.\n\n1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n0 │⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.relu",
"page": "Model Reference",
"title": "NNlib.relu",
"category": "Function",
"text": "relu(x) = max(0, x)\n\nRectified Linear Unit activation function.\n\n3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n0 │⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.leakyrelu",
"page": "Model Reference",
"title": "NNlib.leakyrelu",
"category": "Function",
"text": "leakyrelu(x) = max(0.01x, x)\n\nLeaky Rectified Linear Unit activation function. You can also specify the coefficient explicitly, e.g. leakyrelu(x, 0.01).\n\n 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│\n-1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.elu",
"page": "Model Reference",
"title": "NNlib.elu",
"category": "Function",
"text": "elu(x, α = 1) =\n x > 0 ? x : α * (exp(x) - 1)\n\nExponential Linear Unit activation function. See Fast and Accurate Deep Network Learning by Exponential Linear Units. You can also specify the coefficient explicitly, e.g. elu(x, 1).\n\n 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠖⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n-1 │⣀⣀⠤⠤⠤⠤⠔⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.swish",
"page": "Model Reference",
"title": "NNlib.swish",
"category": "Function",
"text": "swish(x) = x * σ(x)\n\nSelf-gated actvation function. See Swish: a Self-Gated Activation Function.\n\n 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⣒⣒⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣒⠶⠒⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│\n │⠀⠀⠀⠀⠉⠉⠉⠉⠉⠒⠒⠒⠒⠊⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n-1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#Activation-Functions-1",
"page": "Model Reference",
"title": "Activation Functions",
"category": "section",
"text": "Non-linearities that go between layers of your model. Most of these functions are defined in NNlib but are available by default in Flux.Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call σ.(xs), relu.(xs) and so on.σ\nrelu\nleakyrelu\nelu\nswish"
},
{
"location": "models/layers.html#Flux.testmode!",
"page": "Model Reference",
"title": "Flux.testmode!",
"category": "Function",
"text": "testmode!(m)\ntestmode!(m, false)\n\nPut layers like Dropout and BatchNorm into testing mode (or back to training mode with false).\n\n\n\n"
},
{
"location": "models/layers.html#Flux.BatchNorm",
"page": "Model Reference",
"title": "Flux.BatchNorm",
"category": "Type",
"text": "BatchNorm(dims...; λ = identity,\n initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1)\n\nBatch Normalization Layer for Dense layer.\n\nSee Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift\n\nIn the example of MNIST, in order to normalize the input of other layer, put the BatchNorm layer before activation function.\n\nm = Chain(\n Dense(28^2, 64),\n BatchNorm(64, λ = relu),\n Dense(64, 10),\n BatchNorm(10),\n softmax)\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Dropout",
"page": "Model Reference",
"title": "Flux.Dropout",
"category": "Type",
"text": "Dropout(p)\n\nA Dropout layer. For each input, either sets that input to 0 (with probability p) or scales it by 1/(1-p). This is used as a regularisation, i.e. it reduces overfitting during training.\n\nDoes nothing to the input once in testmode!.\n\n\n\n"
},
{
"location": "models/layers.html#Flux.LayerNorm",
"page": "Model Reference",
"title": "Flux.LayerNorm",
"category": "Type",
"text": "LayerNorm(h::Integer)\n\nA normalisation layer designed to be used with recurrent hidden states of size h. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.\n\n\n\n"
},
{
"location": "models/layers.html#Normalisation-and-Regularisation-1",
"page": "Model Reference",
"title": "Normalisation & Regularisation",
"category": "section",
"text": "These layers don't affect the structure of the network but may improve training times or reduce overfitting.Flux.testmode!\nBatchNorm\nDropout\nLayerNorm"
},
{
"location": "training/optimisers.html#",
"page": "Optimisers",
"title": "Optimisers",
"category": "page",
"text": ""
},
{
"location": "training/optimisers.html#Optimisers-1",
"page": "Optimisers",
"title": "Optimisers",
"category": "section",
"text": "Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.W = param(rand(2, 5))\nb = param(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = rand(5), rand(2) # Dummy data\nl = loss(x, y) # ~ 3\nback!(l)We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here's one way to do that:function update()\n η = 0.1 # Learning Rate\n for p in (W, b)\n p.data .-= η .* p.grad # Apply the update\n p.grad .= 0 # Clear the gradient\n end\nendIf we call update, the parameters W and b will change and our loss should go down.There are two pieces here: one is that we need a list of trainable parameters for the model ([W, b] in this case), and the other is the update step. In this case the update is simply gradient descent (x .-= η .* Δ), but we might choose to do something more advanced, like adding momentum.In this case, getting the variables is trivial, but you can imagine it'd be more of a pain with some complex stack of layers.m = Chain(\n Dense(10, 5, σ),\n Dense(5, 2), softmax)Instead of having to write [m[1].W, m[1].b, ...], Flux provides a params function params(m) that returns a list of all parameters in the model for you.For the update step, there's nothing whatsoever wrong with writing the loop above – it'll work just fine – but Flux provides various optimisers that make it more convenient.opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1\n\nopt() # Carry out the update, modifying `W` and `b`.An optimiser takes a parameter list and returns a function that does the same thing as update above. We can pass either opt or update to our training loop, which will then run the optimiser after every mini-batch of data."
},
{
"location": "training/optimisers.html#Flux.Optimise.SGD",
"page": "Optimisers",
"title": "Flux.Optimise.SGD",
"category": "Function",
"text": "SGD(params, η = 0.1; decay = 0)\n\nClassic gradient descent optimiser with learning rate η. For each parameter p and its gradient δp, this runs p -= η*δp.\n\nSupports inverse decaying learning rate if the decay argument is provided.\n\n\n\n"
},
{
"location": "training/optimisers.html#Flux.Optimise.Momentum",
"page": "Optimisers",
"title": "Flux.Optimise.Momentum",
"category": "Function",
"text": "Momentum(params, η = 0.01; ρ = 0.9, decay = 0)\n\nSGD with learning rate η, momentum ρ and optional learning rate inverse decay.\n\n\n\n"
},
{
"location": "training/optimisers.html#Flux.Optimise.Nesterov",
"page": "Optimisers",
"title": "Flux.Optimise.Nesterov",
"category": "Function",
"text": "Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)\n\nSGD with learning rate η, Nesterov momentum ρ and optional learning rate inverse decay.\n\n\n\n"
},
{
"location": "training/optimisers.html#Flux.Optimise.ADAM",
"page": "Optimisers",
"title": "Flux.Optimise.ADAM",
"category": "Function",
"text": "ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)\n\nADAM optimiser.\n\n\n\n"
},
{
"location": "training/optimisers.html#Optimiser-Reference-1",
"page": "Optimisers",
"title": "Optimiser Reference",
"category": "section",
"text": "All optimisers return a function that, when called, will update the parameters passed to it.SGD\nMomentum\nNesterov\nADAM"
},
{
"location": "training/training.html#",
"page": "Training",
"title": "Training",
"category": "page",
"text": ""
},
{
"location": "training/training.html#Training-1",
"page": "Training",
"title": "Training",
"category": "section",
"text": "To actually train a model we need three things:A model loss function, that evaluates how well a model is doing given some input data.\nA collection of data points that will be provided to the loss function.\nAn optimiser that will update the model parameters appropriately.With these we can call Flux.train!:Flux.train!(modelLoss, data, opt)There are plenty of examples in the model zoo."
},
{
"location": "training/training.html#Loss-Functions-1",
"page": "Training",
"title": "Loss Functions",
"category": "section",
"text": "The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:m = Chain(\n Dense(784, 32, σ),\n Dense(32, 10), softmax)\n\n# Model loss function\nloss(x, y) = Flux.mse(m(x), y)\n\n# later\nFlux.train!(loss, data, opt)The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or crossentropy for cross entropy loss, but you can calculate it however you want."
},
{
"location": "training/training.html#Datasets-1",
"page": "Training",
"title": "Datasets",
"category": "section",
"text": "The data argument provides a collection of data to train with (usually a set of inputs x and target outputs y). For example, here's a dummy data set with only one data point:x = rand(784)\ny = rand(10)\ndata = [(x, y)]Flux.train! will call loss(x, y), calculate gradients, update the weights and then move on to the next data point if there is one. We can train the model on the same data three times:data = [(x, y), (x, y), (x, y)]\n# Or equivalently\ndata = Iterators.repeated((x, y), 3)It's common to load the xs and ys separately. In this case you can use zip:xs = [rand(784), rand(784), rand(784)]\nys = [rand( 10), rand( 10), rand( 10)]\ndata = zip(xs, ys)"
},
{
"location": "training/training.html#Callbacks-1",
"page": "Training",
"title": "Callbacks",
"category": "section",
"text": "train! takes an additional argument, cb, that's used for callbacks so that you can observe the training process. For example:train!(loss, data, opt, cb = () -> println(\"training\"))Callbacks are called for every batch of training data. You can slow this down using Flux.throttle(f, timeout) which prevents f from being called more than once every timeout seconds.A more typical callback might look like this:test_x, test_y = # ... create single batch of test data ...\nevalcb() = @show(loss(test_x, test_y))\n\nFlux.train!(loss, data, opt,\n cb = throttle(evalcb, 5))"
},
{
"location": "data/onehot.html#",
"page": "One-Hot Encoding",
"title": "One-Hot Encoding",
"category": "page",
"text": ""
},
{
"location": "data/onehot.html#One-Hot-Encoding-1",
"page": "One-Hot Encoding",
"title": "One-Hot Encoding",
"category": "section",
"text": "It's common to encode categorical variables (like true, false or cat, dog) in \"one-of-k\" or \"one-hot\" form. Flux provides the onehot function to make this easy.julia> using Flux: onehot\n\njulia> onehot(:b, [:a, :b, :c])\n3-element Flux.OneHotVector:\n false\n true\n false\n\njulia> onehot(:c, [:a, :b, :c])\n3-element Flux.OneHotVector:\n false\n false\n trueThe inverse is argmax (which can take a general probability distribution, as well as just booleans).julia> argmax(ans, [:a, :b, :c])\n:c\n\njulia> argmax([true, false, false], [:a, :b, :c])\n:a\n\njulia> argmax([0.3, 0.2, 0.5], [:a, :b, :c])\n:c"
},
{
"location": "data/onehot.html#Batches-1",
"page": "One-Hot Encoding",
"title": "Batches",
"category": "section",
"text": "onehotbatch creates a batch (matrix) of one-hot vectors, and argmax treats matrices as batches.julia> using Flux: onehotbatch\n\njulia> onehotbatch([:b, :a, :b], [:a, :b, :c])\n3×3 Flux.OneHotMatrix:\n false true false\n true false true\n false false false\n\njulia> onecold(ans, [:a, :b, :c])\n3-element Array{Symbol,1}:\n :b\n :a\n :bNote that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood."
},
{
"location": "gpu.html#",
"page": "GPU Support",
"title": "GPU Support",
"category": "page",
"text": ""
},
{
"location": "gpu.html#GPU-Support-1",
"page": "GPU Support",
"title": "GPU Support",
"category": "section",
"text": "Support for array operations on other hardware backends, like GPUs, is provided by external packages like CuArrays and CLArrays. Flux doesn't care what array type you use, so we can just plug these in without any other changes.For example, we can use CuArrays (with the cu converter) to run our basic example on an NVIDIA GPU.using CuArrays\n\nW = cu(rand(2, 5)) # a 2×5 CuArray\nb = cu(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = cu(rand(5)), cu(rand(2)) # Dummy data\nloss(x, y) # ~ 3Note that we convert both the parameters (W, b) and the data set (x, y) to cuda arrays. Taking derivatives and training works exactly as before.If you define a structured model, like a Dense layer or Chain, you just need to convert the internal parameters. Flux provides mapleaves, which allows you to alter all parameters of a model at once.d = Dense(10, 5, σ)\nd = mapleaves(cu, d)\nd.W # Tracked CuArray\nd(cu(rand(10))) # CuArray output\n\nm = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)\nm = mapleaves(cu, m)\nd(cu(rand(10)))The mnist example contains the code needed to run the model on the GPU; just uncomment the lines after using CuArrays."
},
{
"location": "community.html#",
"page": "Community",
"title": "Community",
"category": "page",
"text": ""
},
{
"location": "community.html#Community-1",
"page": "Community",
"title": "Community",
"category": "section",
"text": "All Flux users are welcome to join our community on the Julia forum, the slack (channel #machine-learning), or Flux's Gitter. If you have questions or issues we'll try to help you out.If you're interested in hacking on Flux, the source code is open and easy to understand – it's all just the same Julia code you work with normally. You might be interested in our intro issues to get started."
},
]}

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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Optimisers · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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b = param(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = rand(5), rand(2) # Dummy data
l = loss(x, y) # ~ 3
back!(l)</code></pre><p>We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here&#39;s one way to do that:</p><pre><code class="language-julia">function update()
η = 0.1 # Learning Rate
for p in (W, b)
p.data .-= η .* p.grad # Apply the update
p.grad .= 0 # Clear the gradient
end
end</code></pre><p>If we call <code>update</code>, the parameters <code>W</code> and <code>b</code> will change and our loss should go down.</p><p>There are two pieces here: one is that we need a list of trainable parameters for the model (<code>[W, b]</code> in this case), and the other is the update step. In this case the update is simply gradient descent (<code>x .-= η .* Δ</code>), but we might choose to do something more advanced, like adding momentum.</p><p>In this case, getting the variables is trivial, but you can imagine it&#39;d be more of a pain with some complex stack of layers.</p><pre><code class="language-julia">m = Chain(
Dense(10, 5, σ),
Dense(5, 2), softmax)</code></pre><p>Instead of having to write <code>[m[1].W, m[1].b, ...]</code>, Flux provides a params function <code>params(m)</code> that returns a list of all parameters in the model for you.</p><p>For the update step, there&#39;s nothing whatsoever wrong with writing the loop above – it&#39;ll work just fine – but Flux provides various <em>optimisers</em> that make it more convenient.</p><pre><code class="language-julia">opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1
opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.SGD" href="#Flux.Optimise.SGD"><code>Flux.Optimise.SGD</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">SGD(params, η = 0.1; decay = 0)</code></pre><p>Classic gradient descent optimiser with learning rate <code>η</code>. For each parameter <code>p</code> and its gradient <code>δp</code>, this runs <code>p -= η*δp</code>.</p><p>Supports inverse decaying learning rate if the <code>decay</code> argument is provided.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L14-L21">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.Momentum" href="#Flux.Optimise.Momentum"><code>Flux.Optimise.Momentum</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">Momentum(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, momentum <code>ρ</code> and optional learning rate inverse decay.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L25-L29">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.Nesterov" href="#Flux.Optimise.Nesterov"><code>Flux.Optimise.Nesterov</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, Nesterov momentum <code>ρ</code> and optional learning rate inverse decay.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L33-L37">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.ADAM" href="#Flux.Optimise.ADAM"><code>Flux.Optimise.ADAM</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)</code></pre><p><a href="https://arxiv.org/abs/1412.6980v8">ADAM</a> optimiser.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L51-L55">source</a></section><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>

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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../models/basics.html">Basics</a></li><li><a class="toctext" href="../models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="../models/layers.html">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="optimisers.html">Optimisers</a></li><li class="current"><a class="toctext" href="training.html">Training</a><ul class="internal"><li><a class="toctext" href="#Loss-Functions-1">Loss Functions</a></li><li><a class="toctext" href="#Datasets-1">Datasets</a></li><li><a class="toctext" href="#Callbacks-1">Callbacks</a></li></ul></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Training Models</li><li><a href="training.html">Training</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/training/training.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Training</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Training-1" href="#Training-1">Training</a></h1><p>To actually train a model we need three things:</p><ul><li><p>A <em>model loss function</em>, that evaluates how well a model is doing given some input data.</p></li><li><p>A collection of data points that will be provided to the loss function.</p></li><li><p>An <a href="optimisers.html">optimiser</a> that will update the model parameters appropriately.</p></li></ul><p>With these we can call <code>Flux.train!</code>:</p><pre><code class="language-julia">Flux.train!(modelLoss, data, opt)</code></pre><p>There are plenty of examples in the <a href="https://github.com/FluxML/model-zoo">model zoo</a>.</p><h2><a class="nav-anchor" id="Loss-Functions-1" href="#Loss-Functions-1">Loss Functions</a></h2><p>The <code>loss</code> that we defined in <a href="../models/basics.html">basics</a> is completely valid for training. We can also define a loss in terms of some model:</p><pre><code class="language-julia">m = Chain(
Dense(784, 32, σ),
Dense(32, 10), softmax)
# Model loss function
loss(x, y) = Flux.mse(m(x), y)
# later
Flux.train!(loss, data, opt)</code></pre><p>The loss will almost always be defined in terms of some <em>cost function</em> that measures the distance of the prediction <code>m(x)</code> from the target <code>y</code>. Flux has several of these built in, like <code>mse</code> for mean squared error or <code>crossentropy</code> for cross entropy loss, but you can calculate it however you want.</p><h2><a class="nav-anchor" id="Datasets-1" href="#Datasets-1">Datasets</a></h2><p>The <code>data</code> argument provides a collection of data to train with (usually a set of inputs <code>x</code> and target outputs <code>y</code>). For example, here&#39;s a dummy data set with only one data point:</p><pre><code class="language-julia">x = rand(784)
y = rand(10)
data = [(x, y)]</code></pre><p><code>Flux.train!</code> will call <code>loss(x, y)</code>, calculate gradients, update the weights and then move on to the next data point if there is one. We can train the model on the same data three times:</p><pre><code class="language-julia">data = [(x, y), (x, y), (x, y)]
# Or equivalently
data = Iterators.repeated((x, y), 3)</code></pre><p>It&#39;s common to load the <code>x</code>s and <code>y</code>s separately. In this case you can use <code>zip</code>:</p><pre><code class="language-julia">xs = [rand(784), rand(784), rand(784)]
ys = [rand( 10), rand( 10), rand( 10)]
data = zip(xs, ys)</code></pre><h2><a class="nav-anchor" id="Callbacks-1" href="#Callbacks-1">Callbacks</a></h2><p><code>train!</code> takes an additional argument, <code>cb</code>, that&#39;s used for callbacks so that you can observe the training process. For example:</p><pre><code class="language-julia">train!(loss, data, opt, cb = () -&gt; println(&quot;training&quot;))</code></pre><p>Callbacks are called for every batch of training data. You can slow this down using <code>Flux.throttle(f, timeout)</code> which prevents <code>f</code> from being called more than once every <code>timeout</code> seconds.</p><p>A more typical callback might look like this:</p><pre><code class="language-julia">test_x, test_y = # ... create single batch of test data ...
evalcb() = @show(loss(test_x, test_y))
Flux.train!(loss, data, opt,
cb = throttle(evalcb, 5))</code></pre><footer><hr/><a class="previous" href="optimisers.html"><span class="direction">Previous</span><span class="title">Optimisers</span></a><a class="next" href="../data/onehot.html"><span class="direction">Next</span><span class="title">One-Hot Encoding</span></a></footer></article></body></html>

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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li class="current"><a class="toctext" href="basics.html">Basics</a><ul class="internal"><li><a class="toctext" href="#Taking-Gradients-1">Taking Gradients</a></li><li><a class="toctext" href="#Building-Layers-1">Building Layers</a></li><li><a class="toctext" href="#Stacking-It-Up-1">Stacking It Up</a></li></ul></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="layers.html">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="basics.html">Basics</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/basics.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Basics</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Model-Building-Basics-1" href="#Model-Building-Basics-1">Model-Building Basics</a></h1><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>Consider a simple linear regression, which tries to predict an output array <code>y</code> from an input <code>x</code>. (It&#39;s a good idea to follow this example in the Julia repl.)</p><pre><code class="language-julia">W = rand(2, 5)
</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li class="current"><a class="toctext" href="basics.html">Basics</a><ul class="internal"><li><a class="toctext" href="#Taking-Gradients-1">Taking Gradients</a></li><li><a class="toctext" href="#Building-Layers-1">Building Layers</a></li><li><a class="toctext" href="#Stacking-It-Up-1">Stacking It Up</a></li><li><a class="toctext" href="#Layer-helpers-1">Layer helpers</a></li></ul></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="layers.html">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="basics.html">Basics</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/basics.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Basics</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Model-Building-Basics-1" href="#Model-Building-Basics-1">Model-Building Basics</a></h1><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>Consider a simple linear regression, which tries to predict an output array <code>y</code> from an input <code>x</code>. (It&#39;s a good idea to follow this example in the Julia repl.)</p><pre><code class="language-julia">W = rand(2, 5)
b = rand(2)
predict(x) = W*x .+ b
@ -76,4 +76,4 @@ model2(rand(10)) # =&gt; 2-element vector</code></pre><p>This quickly starts to
m(rand(10))</code></pre><p>Likewise, <code>Chain</code> will happily work with any Julia function.</p><pre><code class="language-julia">m = Chain(x -&gt; x^2, x -&gt; x+1)
m(5) # =&gt; 26</code></pre><footer><hr/><a class="previous" href="../index.html"><span class="direction">Previous</span><span class="title">Home</span></a><a class="next" href="recurrence.html"><span class="direction">Next</span><span class="title">Recurrence</span></a></footer></article></body></html>
m(5) # =&gt; 26</code></pre><h2><a class="nav-anchor" id="Layer-helpers-1" href="#Layer-helpers-1">Layer helpers</a></h2><p>Flux provides a set of helpers for custom layers, which you can enable by calling</p><pre><code class="language-julia">Flux.treelike(Affine)</code></pre><p>This enables a useful extra set of functionality for our <code>Affine</code> layer, such as <a href="../training/optimisers.html">collecting its parameters</a> or <a href="../gpu.html">moving it to the GPU</a>.</p><footer><hr/><a class="previous" href="../index.html"><span class="direction">Previous</span><span class="title">Home</span></a><a class="next" href="recurrence.html"><span class="direction">Next</span><span class="title">Recurrence</span></a></footer></article></body></html>

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@ -64,6 +64,14 @@ var documenterSearchIndex = {"docs": [
"text": "It's pretty common to write models that look something like:layer1 = Dense(10, 5, σ)\n# ...\nmodel(x) = layer3(layer2(layer1(x)))For long chains, it might be a bit more intuitive to have a list of layers, like this:using Flux\n\nlayers = [Dense(10, 5, σ), Dense(5, 2), softmax]\n\nmodel(x) = foldl((x, m) -> m(x), x, layers)\n\nmodel(rand(10)) # => 2-element vectorHandily, this is also provided for in Flux:model2 = Chain(\n Dense(10, 5, σ),\n Dense(5, 2),\n softmax)\n\nmodel2(rand(10)) # => 2-element vectorThis quickly starts to look like a high-level deep learning library; yet you can see how it falls out of simple abstractions, and we lose none of the power of Julia code.A nice property of this approach is that because \"models\" are just functions (possibly with trainable parameters), you can also see this as simple function composition.m = Dense(5, 2) ∘ Dense(10, 5, σ)\n\nm(rand(10))Likewise, Chain will happily work with any Julia function.m = Chain(x -> x^2, x -> x+1)\n\nm(5) # => 26"
},
{
"location": "models/basics.html#Layer-helpers-1",
"page": "Basics",
"title": "Layer helpers",
"category": "section",
"text": "Flux provides a set of helpers for custom layers, which you can enable by callingFlux.treelike(Affine)This enables a useful extra set of functionality for our Affine layer, such as collecting its parameters or moving it to the GPU."
},
{
"location": "models/recurrence.html#",
"page": "Recurrence",
@ -136,12 +144,20 @@ var documenterSearchIndex = {"docs": [
"text": "Dense(in::Integer, out::Integer, σ = identity)\n\nCreates a traditional Dense layer with parameters W and b.\n\ny = σ.(W * x .+ b)\n\nThe input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length out.\n\njulia> d = Dense(5, 2)\nDense(5, 2)\n\njulia> d(rand(5))\nTracked 2-element Array{Float64,1}:\n 0.00257447\n -0.00449443\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Conv2D",
"page": "Model Reference",
"title": "Flux.Conv2D",
"category": "Type",
"text": "Conv2D(size, in=>out)\nConv2d(size, in=>out, relu)\n\nStandard convolutional layer. size should be a tuple like (2, 2). in and out specify the number of input and output channels respectively.\n\nData should be stored in HWCN order. In other words, a 100×100 RGB image would be a 100×100×3 array, and a batch of 50 would be a 100×100×3×50 array.\n\nTakes the keyword arguments pad and stride.\n\n\n\n"
},
{
"location": "models/layers.html#Basic-Layers-1",
"page": "Model Reference",
"title": "Basic Layers",
"category": "section",
"text": "These core layers form the foundation of almost all neural networks.Chain\nDense"
"text": "These core layers form the foundation of almost all neural networks.Chain\nDense\nConv2D"
},
{
@ -181,7 +197,7 @@ var documenterSearchIndex = {"docs": [
"page": "Model Reference",
"title": "NNlib.σ",
"category": "Function",
"text": "σ(x) = 1 / (1 + exp(-x))\n\nClassic sigmoid activation function.\n\n\n\n"
"text": "σ(x) = 1 / (1 + exp(-x))\n\nClassic sigmoid activation function.\n\n1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n0 │⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
@ -189,7 +205,7 @@ var documenterSearchIndex = {"docs": [
"page": "Model Reference",
"title": "NNlib.relu",
"category": "Function",
"text": "relu(x) = max(0, x)\n\nRectified Linear Unit activation function.\n\n\n\n"
"text": "relu(x) = max(0, x)\n\nRectified Linear Unit activation function.\n\n3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n0 │⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
@ -197,7 +213,7 @@ var documenterSearchIndex = {"docs": [
"page": "Model Reference",
"title": "NNlib.leakyrelu",
"category": "Function",
"text": "leakyrelu(x) = max(0.01x, x)\n\nLeaky Rectified Linear Unit activation function.\n\nYou can also specify the coefficient explicitly, e.g. leakyrelu(x, 0.01).\n\n\n\n"
"text": "leakyrelu(x) = max(0.01x, x)\n\nLeaky Rectified Linear Unit activation function. You can also specify the coefficient explicitly, e.g. leakyrelu(x, 0.01).\n\n 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│\n-1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
@ -205,7 +221,7 @@ var documenterSearchIndex = {"docs": [
"page": "Model Reference",
"title": "NNlib.elu",
"category": "Function",
"text": "elu(x; α = 1) = x > 0 ? x : α * (exp(x) - one(x)\n\nExponential Linear Unit activation function. See Fast and Accurate Deep Network Learning by Exponential Linear Units\n\n\n\n"
"text": "elu(x, α = 1) =\n x > 0 ? x : α * (exp(x) - 1)\n\nExponential Linear Unit activation function. See Fast and Accurate Deep Network Learning by Exponential Linear Units. You can also specify the coefficient explicitly, e.g. elu(x, 1).\n\n 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠖⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n-1 │⣀⣀⠤⠤⠤⠤⠔⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
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"text": "swish(x) = x * σ(x)\n\nSelf-gated actvation function.\n\nSee Swish: a Self-Gated Activation Function.\n\n\n\n"
"text": "swish(x) = x * σ(x)\n\nSelf-gated actvation function. See Swish: a Self-Gated Activation Function.\n\n 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⣒⣒⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣒⠶⠒⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│\n │⠀⠀⠀⠀⠉⠉⠉⠉⠉⠒⠒⠒⠒⠊⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n-1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
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@ -224,6 +240,22 @@ var documenterSearchIndex = {"docs": [
"text": "Non-linearities that go between layers of your model. Most of these functions are defined in NNlib but are available by default in Flux.Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call σ.(xs), relu.(xs) and so on.σ\nrelu\nleakyrelu\nelu\nswish"
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"location": "models/layers.html#Flux.testmode!",
"page": "Model Reference",
"title": "Flux.testmode!",
"category": "Function",
"text": "testmode!(m)\ntestmode!(m, false)\n\nPut layers like Dropout and BatchNorm into testing mode (or back to training mode with false).\n\n\n\n"
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"location": "models/layers.html#Flux.BatchNorm",
"page": "Model Reference",
"title": "Flux.BatchNorm",
"category": "Type",
"text": "BatchNorm(dims...; λ = identity,\n initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1)\n\nBatch Normalization Layer for Dense layer.\n\nSee Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift\n\nIn the example of MNIST, in order to normalize the input of other layer, put the BatchNorm layer before activation function.\n\nm = Chain(\n Dense(28^2, 64),\n BatchNorm(64, λ = relu),\n Dense(64, 10),\n BatchNorm(10),\n softmax)\n\n\n\n"
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"location": "models/layers.html#Flux.Dropout",
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@ -232,12 +264,20 @@ var documenterSearchIndex = {"docs": [
"text": "Dropout(p)\n\nA Dropout layer. For each input, either sets that input to 0 (with probability p) or scales it by 1/(1-p). This is used as a regularisation, i.e. it reduces overfitting during training.\n\nDoes nothing to the input once in testmode!.\n\n\n\n"
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"location": "models/layers.html#Flux.LayerNorm",
"page": "Model Reference",
"title": "Flux.LayerNorm",
"category": "Type",
"text": "LayerNorm(h::Integer)\n\nA normalisation layer designed to be used with recurrent hidden states of size h. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.\n\n\n\n"
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"location": "models/layers.html#Normalisation-and-Regularisation-1",
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"title": "Normalisation & Regularisation",
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"text": "These layers don't affect the structure of the network but may improve training times or reduce overfitting.Dropout"
"text": "These layers don't affect the structure of the network but may improve training times or reduce overfitting.Flux.testmode!\nBatchNorm\nDropout\nLayerNorm"
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@ -256,12 +296,44 @@ var documenterSearchIndex = {"docs": [
"text": "Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.W = param(rand(2, 5))\nb = param(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = rand(5), rand(2) # Dummy data\nl = loss(x, y) # ~ 3\nback!(l)We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here's one way to do that:function update()\n η = 0.1 # Learning Rate\n for p in (W, b)\n p.data .-= η .* p.grad # Apply the update\n p.grad .= 0 # Clear the gradient\n end\nendIf we call update, the parameters W and b will change and our loss should go down.There are two pieces here: one is that we need a list of trainable parameters for the model ([W, b] in this case), and the other is the update step. In this case the update is simply gradient descent (x .-= η .* Δ), but we might choose to do something more advanced, like adding momentum.In this case, getting the variables is trivial, but you can imagine it'd be more of a pain with some complex stack of layers.m = Chain(\n Dense(10, 5, σ),\n Dense(5, 2), softmax)Instead of having to write [m[1].W, m[1].b, ...], Flux provides a params function params(m) that returns a list of all parameters in the model for you.For the update step, there's nothing whatsoever wrong with writing the loop above – it'll work just fine – but Flux provides various optimisers that make it more convenient.opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1\n\nopt() # Carry out the update, modifying `W` and `b`.An optimiser takes a parameter list and returns a function that does the same thing as update above. We can pass either opt or update to our training loop, which will then run the optimiser after every mini-batch of data."
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"text": "SGD(params, η = 0.1; decay = 0)\n\nClassic gradient descent optimiser with learning rate η. For each parameter p and its gradient δp, this runs p -= η*δp.\n\nSupports inverse decaying learning rate if the decay argument is provided.\n\n\n\n"
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"page": "Optimisers",
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"text": "Momentum(params, η = 0.01; ρ = 0.9, decay = 0)\n\nSGD with learning rate η, momentum ρ and optional learning rate inverse decay.\n\n\n\n"
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"title": "Flux.Optimise.Nesterov",
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"text": "Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)\n\nSGD with learning rate η, Nesterov momentum ρ and optional learning rate inverse decay.\n\n\n\n"
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"text": "ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)\n\nADAM optimiser.\n\n\n\n"
},
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"page": "Optimisers",
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"text": "All optimisers return a function that, when called, will update the parameters passed to it.SGD\nMomentum\nNesterov\nADAM"
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8
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@ -24,10 +24,4 @@ end</code></pre><p>If we call <code>update</code>, the parameters <code>W</code>
Dense(10, 5, σ),
Dense(5, 2), softmax)</code></pre><p>Instead of having to write <code>[m[1].W, m[1].b, ...]</code>, Flux provides a params function <code>params(m)</code> that returns a list of all parameters in the model for you.</p><p>For the update step, there&#39;s nothing whatsoever wrong with writing the loop above – it&#39;ll work just fine – but Flux provides various <em>optimisers</em> that make it more convenient.</p><pre><code class="language-julia">opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1
opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><pre><code class="language-none">SGD
Momentum
Nesterov
RMSProp
ADAM
ADAGrad
ADADelta</code></pre><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>
opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.SGD" href="#Flux.Optimise.SGD"><code>Flux.Optimise.SGD</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">SGD(params, η = 0.1; decay = 0)</code></pre><p>Classic gradient descent optimiser with learning rate <code>η</code>. For each parameter <code>p</code> and its gradient <code>δp</code>, this runs <code>p -= η*δp</code>.</p><p>Supports inverse decaying learning rate if the <code>decay</code> argument is provided.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L14-L21">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.Momentum" href="#Flux.Optimise.Momentum"><code>Flux.Optimise.Momentum</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">Momentum(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, momentum <code>ρ</code> and optional learning rate inverse decay.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L25-L29">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.Nesterov" href="#Flux.Optimise.Nesterov"><code>Flux.Optimise.Nesterov</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, Nesterov momentum <code>ρ</code> and optional learning rate inverse decay.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L33-L37">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.ADAM" href="#Flux.Optimise.ADAM"><code>Flux.Optimise.ADAM</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)</code></pre><p><a href="https://arxiv.org/abs/1412.6980v8">ADAM</a> optimiser.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L51-L55">source</a></section><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>

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/*
* The default CSS style for Documenter.jl generated sites
*
* Heavily inspired by the Julia Sphinx theme
* https://github.com/JuliaLang/JuliaDoc
* which extends the sphinx_rtd_theme
* https://github.com/snide/sphinx_rtd_theme
*
* Part of Documenter.jl
* https://github.com/JuliaDocs/Documenter.jl
*
* License: MIT
*/
/* fonts */
body, input {
font-family: 'Lato', 'Helvetica Neue', Arial, sans-serif;
font-size: 16px;
color: #222;
text-rendering: optimizeLegibility;
}
pre, code, kbd {
font-family: 'Roboto Mono', Monaco, courier, monospace;
font-size: 0.90em;
}
pre code {
font-size: 1em;
}
a {
color: #2980b9;
text-decoration: none;
}
a:hover {
color: #3091d1;
}
a:visited {
color: #9b59b6;
}
body {
line-height: 1.5;
}
h1 {
font-size: 1.75em;
}
/* Unless the <h1> the is very first thing on the page (i.e. the second element
* in the <article>, * after the <header>, we add some additional styling to it
* to make it stand out a bit more. This way we get a reasonable fallback if CSS3
* selectors are not supported in the browser.
*/
article > h1:not(:nth-child(2)) {
margin: 2.5em 0 0;
padding-bottom: 0.30em;
border-bottom: 1px solid #e5e5e5;
}
h2 {
font-size: 1.50em;
margin: 2.3em 0 0;
padding-bottom: 0.25em;
border-bottom: 1px solid #e5e5e5;
}
h3 {
font-size: 1.25em;
margin: 2.0em 0 0;
}
h4 { font-size: 1.15em; }
h5 { font-size: 1.10em; }
h6 { font-size: 1em; }
h4, h5, h6 {
margin-top: 1.5em;
margin-bottom: 1em;
}
img {
max-width: 100%;
}
table {
border-collapse: collapse;
margin: 1em 0;
}
th, td {
border: 1px solid #e1e4e5;
padding: 0.5em 1em;
}
th {
border-bottom-width: 2px;
}
tr:nth-child(even) {
background-color: #f3f6f6;
}
hr {
border: 0;
border-top: 1px solid #e5e5e5;
}
/* Inline code and code blocks */
code {
padding: 0.1em;
background-color: rgba(0,0,0,.04);
border-radius: 3px;
}
pre {
background-color: #f5f5f5;
border: 1px solid #dddddd;
border-radius: 3px;
padding: 0.5em;
overflow: auto;
}
pre code {
padding: 0;
background-color: initial;
}
kbd {
font-size: 0.70em;
display: inline-block;
padding: 0.1em 0.5em 0.4em 0.5em;
line-height: 1.0em;
color: #444d56;
vertical-align: middle;
background-color: #fafbfc;
border: solid 1px #c6cbd1;
border-bottom-color: #959da5;
border-radius: 3px;
box-shadow: inset 0 -1px 0 #959da5;
}
/* Headers in admonitions and docstrings */
.admonition h1,
article section.docstring h1 {
font-size: 1.25em;
}
.admonition h2,
article section.docstring h2 {
font-size: 1.10em;
}
.admonition h3,
.admonition h4,
.admonition h5,
.admonition h6,
article section.docstring h3,
article section.docstring h4,
article section.docstring h5,
article section.docstring h6 {
font-size: 1em;
}
/* Navigation */
nav.toc {
position: fixed;
top: 0;
left: 0;
bottom: 0;
width: 20em;
overflow-y: auto;
padding: 1em 0;
background-color: #fcfcfc;
box-shadow: inset -14px 0px 5px -12px rgb(210,210,210);
}
nav.toc .logo {
margin: 0 auto;
display: block;
max-height: 6em;
max-width: 18em;
}
nav.toc h1 {
text-align: center;
margin-top: .57em;
margin-bottom: 0;
}
nav.toc select {
display: block;
height: 2em;
padding: 0 1.6em 0 1em;
min-width: 7em;
max-width: 90%;
max-width: calc(100% - 5em);
margin: 0 auto;
font-size: .83em;
border: 1px solid #c9c9c9;
border-radius: 1em;
/* TODO: doesn't seem to be centered on Safari */
text-align: center;
text-align-last: center;
appearance: none;
-moz-appearance: none;
-webkit-appearance: none;
background: white url("arrow.svg");
background-size: 1.155em;
background-repeat: no-repeat;
background-position: right;
}
nav.toc select:hover {
border: 1px solid #a0a0a0;
}
nav.toc select option {
text-align: center;
}
nav.toc input {
display: block;
height: 2em;
width: 90%;
width: calc(100% - 5em);
margin: 1.2em auto;
padding: 0 1em;
border: 1px solid #c9c9c9;
border-radius: 1em;
font-size: .83em;
}
nav.toc > ul * {
margin: 0;
}
nav.toc ul {
color: #404040;
padding: 0;
list-style: none;
}
nav.toc ul .toctext {
color: inherit;
display: block;
}
nav.toc ul a:hover {
color: #fcfcfc;
background-color: #4e4a4a;
}
nav.toc ul.internal a {
color: inherit;
display: block;
}
nav.toc ul.internal a:hover {
background-color: #d6d6d6;
}
nav.toc ul.internal {
background-color: #e3e3e3;
box-shadow: inset -14px 0px 5px -12px rgb(210,210,210);
list-style: none;
}
nav.toc ul.internal li.toplevel {
border-top: 1px solid #c9c9c9;
font-weight: bold;
}
nav.toc ul.internal li.toplevel:first-child {
border-top: none;
}
nav.toc .toctext {
padding-top: 0.3em;
padding-bottom: 0.3em;
padding-right: 1em;
}
nav.toc ul .toctext {
padding-left: 1em;
}
nav.toc ul ul .toctext {
padding-left: 2em;
}
nav.toc ul ul ul .toctext {
padding-left: 3em;
}
nav.toc li.current > .toctext {
border-top: 1px solid #c9c9c9;
border-bottom: 1px solid #c9c9c9;
color: #404040;
font-weight: bold;
background-color: white;
}
article {
margin-left: 20em;
min-width: 20em;
max-width: 48em;
padding: 2em;
}
article > header {}
article > header div#topbar {
display: none;
}
article > header nav ul {
display: inline-block;
list-style: none;
margin: 0;
padding: 0;
}
article > header nav li {
display: inline-block;
padding-right: 0.2em;
}
article > header nav li:before {
content: "»";
padding-right: 0.2em;
}
article > header .edit-page {
float: right;
}
article > footer {}
article > footer a.prev {
float: left;
}
article > footer a.next {
float: right;
}
article > footer a .direction:after {
content: ": ";
}
article hr {
margin: 1em 0;
}
article section.docstring {
border: 1px solid #ddd;
margin: 0.5em 0;
padding: 0.5em;
border-radius: 3px;
}
article section.docstring .docstring-header {
margin-bottom: 1em;
}
article section.docstring .docstring-binding {
color: #333;
font-weight: bold;
}
article section.docstring .docstring-category {
font-style: italic;
}
article section.docstring a.source-link {
display: block;
font-weight: bold;
}
.nav-anchor,
.nav-anchor:hover,
.nav-anchor:visited {
color: #333;
}
/*
* Admonitions
*
* Colors (title, body)
* warning: #f0b37e #ffedcc (orange)
* note: #6ab0de #e7f2fa (blue)
* tip: #1abc9c #dbfaf4 (green)
*/
.admonition {
border-radius: 3px;
background-color: #eeeeee;
}
.admonition-title {
border-radius: 3px 3px 0 0;
background-color: #9b9b9b;
padding: 0.15em 0.5em;
}
.admonition-text {
padding: 0.5em;
}
.admonition-text > :first-child {
margin-top: 0;
}
.admonition-text > :last-child {
margin-bottom: 0;
}
.admonition > .admonition-title:before {
font-family: "FontAwesome";
margin-right: 5px;
content: "\f06a";
}
.admonition.warning > .admonition-title {
background-color: #f0b37e;
}
.admonition.warning {
background-color: #ffedcc;
}
.admonition.note > .admonition-title {
background-color: #6ab0de;
}
.admonition.note {
background-color: #e7f2fa;
}
.admonition.tip > .admonition-title {
background-color: #1abc9c;
}
.admonition.tip {
background-color: #dbfaf4;
}
/* footnotes */
.footnote {
padding-left: 0.8em;
border-left: 2px solid #ccc;
}
/* Search page */
#search-results .category {
font-size: smaller;
}
#search-results .category:before {
content: " ";
}
/* Overriding the <code> block style of highligh.js.
* We have to override the padding and the background-color, since we style this
* part ourselves. Specifically, we style the <pre> surrounding the <code>, while
* highlight.js applies the .hljs style directly to the <code> tag.
*/
.hljs {
background-color: transparent;
padding: 0;
}
@media only screen and (max-width: 768px) {
nav.toc {
position: fixed;
overflow-y: scroll;
width: 16em;
left: -16em;
-webkit-overflow-scrolling: touch;
-webkit-transition-property: left; /* Safari */
-webkit-transition-duration: 0.3s; /* Safari */
transition-property: left;
transition-duration: 0.3s;
-webkit-transition-timing-function: ease-out; /* Safari */
transition-timing-function: ease-out;
z-index: 2;
}
nav.toc.show {
left: 0;
}
article {
margin-left: 0;
padding: 3em 0.9em 0 0.9em; /* top right bottom left */
overflow-wrap: break-word;
}
article > header {
position: fixed;
left: 0;
z-index: 1;
}
article > header nav, hr {
display: none;
}
article > header div#topbar {
display: block; /* is mobile */
position: fixed;
width: 100%;
height: 1.5em;
padding-top: 1em;
padding-bottom: 1em;
background-color: #fcfcfc;
box-shadow: 0 1px 3px rgba(0,0,0,.26);
top: 0;
-webkit-transition-property: top; /* Safari */
-webkit-transition-duration: 0.3s; /* Safari */
transition-property: top;
transition-duration: 0.3s;
}
article > header div#topbar.headroom--unpinned.headroom--not-top.headroom--not-bottom {
top: -4em;
-webkit-transition-property: top; /* Safari */
-webkit-transition-duration: 0.7s; /* Safari */
transition-property: top;
transition-duration: 0.7s;
}
article > header div#topbar span {
position: fixed;
width: 80%;
height: 1.5em;
margin-top: -0.1em;
margin-left: 0.9em;
font-size: 1.2em;
overflow: hidden;
}
article > header div#topbar a.fa-bars {
float: right;
padding: 0.6em;
margin-top: -0.6em;
margin-right: 0.3em;
font-size: 1.5em;
}
article > header div#topbar a.fa-bars:visited {
color: #3091d1;
}
article table {
overflow-x: auto;
display: block;
}
article div.MathJax_Display {
overflow: scroll;
}
article span.MathJax {
overflow: hidden;
}
}
@media only screen and (max-width: 320px) {
body {
font-size: 15px;
}
}

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/*
* Part of Documenter.jl
* https://github.com/JuliaDocs/Documenter.jl
*
* License: MIT
*/
requirejs.config({
paths: {
'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.1.1/jquery.min',
'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.0/jquery-ui.min',
'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.9.3/headroom.min',
'mathjax': 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS_HTML',
'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/highlight.min',
'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/languages/julia.min',
'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/languages/julia-repl.min',
},
shim: {
'mathjax' : {
exports: "MathJax"
},
'highlight-julia': ['highlight'],
'highlight-julia-repl': ['highlight'],
}
});
// Load MathJax
require(['mathjax'], function(MathJax) {
MathJax.Hub.Config({
"tex2jax": {
inlineMath: [['$','$'], ['\\(','\\)']],
processEscapes: true
}
});
MathJax.Hub.Config({
config: ["MMLorHTML.js"],
jax: [
"input/TeX",
"output/HTML-CSS",
"output/NativeMML"
],
extensions: [
"MathMenu.js",
"MathZoom.js",
"TeX/AMSmath.js",
"TeX/AMSsymbols.js",
"TeX/autobold.js",
"TeX/autoload-all.js"
]
});
MathJax.Hub.Config({
TeX: { equationNumbers: { autoNumber: "AMS" } }
});
})
require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($, hljs) {
$(document).ready(function() {
hljs.initHighlighting();
})
})
// update the version selector with info from the siteinfo.js and ../versions.js files
require(['jquery'], function($) {
$(document).ready(function() {
var version_selector = $("#version-selector");
// add the current version to the selector based on siteinfo.js, but only if the selector is empty
if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) {
var option = $("<option value='#' selected='selected'>" + DOCUMENTER_CURRENT_VERSION + "</option>");
version_selector.append(option);
}
if (typeof DOC_VERSIONS !== 'undefined') {
var existing_versions = $('#version-selector > option');
var existing_versions_texts = existing_versions.map(function(i,x){return x.text});
DOC_VERSIONS.forEach(function(each) {
var version_url = documenterBaseURL + "/../" + each;
var existing_id = $.inArray(each, existing_versions_texts);
// if not already in the version selector, add it as a new option,
// otherwise update the old option with the URL and enable it
if (existing_id == -1) {
var option = $("<option value='" + version_url + "'>" + each + "</option>");
version_selector.append(option);
} else {
var option = existing_versions[existing_id];
option.value = version_url;
option.disabled = false;
}
});
}
// only show the version selector if the selector has been populated
if ($('#version-selector > option').length > 0) {
version_selector.css("visibility", "visible");
}
})
})
// mobile
require(['jquery', 'headroom'], function($, Headroom) {
$(document).ready(function() {
var navtoc = $("nav.toc");
$("nav.toc li.current a.toctext").click(function() {
navtoc.toggleClass('show');
});
$("article > header div#topbar a.fa-bars").click(function(ev) {
ev.preventDefault();
navtoc.toggleClass('show');
if (navtoc.hasClass('show')) {
var title = $("article > header div#topbar span").text();
$("nav.toc ul li a:contains('" + title + "')").focus();
}
});
$("article#docs").bind('click', function(ev) {
if ($(ev.target).is('div#topbar a.fa-bars')) {
return;
}
if (navtoc.hasClass('show')) {
navtoc.removeClass('show');
}
});
if ($("article > header div#topbar").css('display') == 'block') {
var headroom = new Headroom(document.querySelector("article > header div#topbar"), {"tolerance": {"up": 10, "down": 10}});
headroom.init();
}
})
})

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/*
* Part of Documenter.jl
* https://github.com/JuliaDocs/Documenter.jl
*
* License: MIT
*/
// parseUri 1.2.2
// (c) Steven Levithan <stevenlevithan.com>
// MIT License
function parseUri (str) {
var o = parseUri.options,
m = o.parser[o.strictMode ? "strict" : "loose"].exec(str),
uri = {},
i = 14;
while (i--) uri[o.key[i]] = m[i] || "";
uri[o.q.name] = {};
uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) {
if ($1) uri[o.q.name][$1] = $2;
});
return uri;
};
parseUri.options = {
strictMode: false,
key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"],
q: {
name: "queryKey",
parser: /(?:^|&)([^&=]*)=?([^&]*)/g
},
parser: {
strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/,
loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/
}
};
requirejs.config({
paths: {
'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.1.1/jquery.min',
'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.1.3/lunr.min',
'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.4/lodash.min',
}
});
var currentScript = document.currentScript;
require(["jquery", "lunr", "lodash"], function($, lunr, _) {
$("#search-form").submit(function(e) {
e.preventDefault()
})
// list below is the lunr 2.1.3 list minus the intersect with names(Base)
// (all, any, get, in, is, which) and (do, else, for, let, where, while, with)
// ideally we'd just filter the original list but it's not available as a variable
lunr.stopWordFilter = lunr.generateStopWordFilter([
'a',
'able',
'about',
'across',
'after',
'almost',
'also',
'am',
'among',
'an',
'and',
'are',
'as',
'at',
'be',
'because',
'been',
'but',
'by',
'can',
'cannot',
'could',
'dear',
'did',
'does',
'either',
'ever',
'every',
'from',
'got',
'had',
'has',
'have',
'he',
'her',
'hers',
'him',
'his',
'how',
'however',
'i',
'if',
'into',
'it',
'its',
'just',
'least',
'like',
'likely',
'may',
'me',
'might',
'most',
'must',
'my',
'neither',
'no',
'nor',
'not',
'of',
'off',
'often',
'on',
'only',
'or',
'other',
'our',
'own',
'rather',
'said',
'say',
'says',
'she',
'should',
'since',
'so',
'some',
'than',
'that',
'the',
'their',
'them',
'then',
'there',
'these',
'they',
'this',
'tis',
'to',
'too',
'twas',
'us',
'wants',
'was',
'we',
'were',
'what',
'when',
'who',
'whom',
'why',
'will',
'would',
'yet',
'you',
'your'
])
// add . as a separator, because otherwise "title": "Documenter.Anchors.add!"
// would not find anything if searching for "add!", only for the entire qualification
lunr.tokenizer.separator = /[\s\-\.]+/
// custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
lunr.trimmer = function (token) {
return token.update(function (s) {
return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '')
})
}
lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter')
lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer')
var index = lunr(function () {
this.ref('location')
this.field('title')
this.field('text')
documenterSearchIndex['docs'].forEach(function(e) {
this.add(e)
}, this)
})
var store = {}
documenterSearchIndex['docs'].forEach(function(e) {
store[e.location] = {title: e.title, category: e.category}
})
$(function(){
function update_search(querystring) {
tokens = lunr.tokenizer(querystring)
results = index.query(function (q) {
tokens.forEach(function (t) {
q.term(t.toString(), {
fields: ["title"],
boost: 10,
usePipeline: false,
editDistance: 2,
wildcard: lunr.Query.wildcard.NONE
})
q.term(t.toString(), {
fields: ["text"],
boost: 1,
usePipeline: true,
editDistance: 2,
wildcard: lunr.Query.wildcard.NONE
})
})
})
$('#search-info').text("Number of results: " + results.length)
$('#search-results').empty()
results.forEach(function(result) {
data = store[result.ref]
link = $('<a>')
link.text(data.title)
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julia&gt; onehot(:b, [:a, :b, :c])
3-element Flux.OneHotVector:
false
true
false
julia&gt; onehot(:c, [:a, :b, :c])
3-element Flux.OneHotVector:
false
false
true</code></pre><p>The inverse is <code>argmax</code> (which can take a general probability distribution, as well as just booleans).</p><pre><code class="language-julia">julia&gt; argmax(ans, [:a, :b, :c])
:c
julia&gt; argmax([true, false, false], [:a, :b, :c])
:a
julia&gt; argmax([0.3, 0.2, 0.5], [:a, :b, :c])
:c</code></pre><h2><a class="nav-anchor" id="Batches-1" href="#Batches-1">Batches</a></h2><p><code>onehotbatch</code> creates a batch (matrix) of one-hot vectors, and <code>argmax</code> treats matrices as batches.</p><pre><code class="language-julia">julia&gt; using Flux: onehotbatch
julia&gt; onehotbatch([:b, :a, :b], [:a, :b, :c])
3×3 Flux.OneHotMatrix:
false true false
true false true
false false false
julia&gt; onecold(ans, [:a, :b, :c])
3-element Array{Symbol,1}:
:b
:a
:b</code></pre><p>Note that these operations returned <code>OneHotVector</code> and <code>OneHotMatrix</code> rather than <code>Array</code>s. <code>OneHotVector</code>s behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.</p><footer><hr/><a class="previous" href="../training/training.html"><span class="direction">Previous</span><span class="title">Training</span></a><a class="next" href="../gpu.html"><span class="direction">Next</span><span class="title">GPU Support</span></a></footer></article></body></html>

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W = cu(rand(2, 5)) # a 2×5 CuArray
b = cu(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = cu(rand(5)), cu(rand(2)) # Dummy data
loss(x, y) # ~ 3</code></pre><p>Note that we convert both the parameters (<code>W</code>, <code>b</code>) and the data set (<code>x</code>, <code>y</code>) to cuda arrays. Taking derivatives and training works exactly as before.</p><p>If you define a structured model, like a <code>Dense</code> layer or <code>Chain</code>, you just need to convert the internal parameters. Flux provides <code>mapleaves</code>, which allows you to alter all parameters of a model at once.</p><pre><code class="language-julia">d = Dense(10, 5, σ)
d = mapleaves(cu, d)
d.W # Tracked CuArray
d(cu(rand(10))) # CuArray output
m = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)
m = mapleaves(cu, m)
d(cu(rand(10)))</code></pre><p>The <a href="https://github.com/FluxML/model-zoo/blob/master/mnist/mnist.jl">mnist example</a> contains the code needed to run the model on the GPU; just uncomment the lines after <code>using CuArrays</code>.</p><footer><hr/><a class="previous" href="data/onehot.html"><span class="direction">Previous</span><span class="title">One-Hot Encoding</span></a><a class="next" href="community.html"><span class="direction">Next</span><span class="title">Community</span></a></footer></article></body></html>

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Pkg.test(&quot;Flux&quot;) # Check things installed correctly</code></pre><p>Start with the <a href="models/basics.html">basics</a>. The <a href="https://github.com/FluxML/model-zoo/">model zoo</a> is also a good starting point for many common kinds of models.</p><footer><hr/><a class="next" href="models/basics.html"><span class="direction">Next</span><span class="title">Basics</span></a></footer></article></body></html>

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b = rand(2)
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = rand(5), rand(2) # Dummy data
loss(x, y) # ~ 3</code></pre><p>To improve the prediction we can take the gradients of <code>W</code> and <code>b</code> with respect to the loss function and perform gradient descent. We could calculate gradients by hand, but Flux will do it for us if we tell it that <code>W</code> and <code>b</code> are trainable <em>parameters</em>.</p><pre><code class="language-julia">using Flux.Tracker
W = param(W)
b = param(b)
l = loss(x, y)
back!(l)</code></pre><p><code>loss(x, y)</code> returns the same number, but it&#39;s now a <em>tracked</em> value that records gradients as it goes along. Calling <code>back!</code> then calculates the gradient of <code>W</code> and <code>b</code>. We can see what this gradient is, and modify <code>W</code> to train the model.</p><pre><code class="language-julia">W.grad
# Update the parameter
W.data .-= 0.1(W.grad)
loss(x, y) # ~ 2.5</code></pre><p>The loss has decreased a little, meaning that our prediction <code>x</code> is closer to the target <code>y</code>. If we have some data we can already try <a href="../training/training.html">training the model</a>.</p><p>All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, models can <em>look</em> very different – they might have millions of parameters or complex control flow, and there are ways to manage this complexity. Let&#39;s see what that looks like.</p><h2><a class="nav-anchor" id="Building-Layers-1" href="#Building-Layers-1">Building Layers</a></h2><p>It&#39;s common to create more complex models than the linear regression above. For example, we might want to have two linear layers with a nonlinearity like <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> (<code>σ</code>) in between them. In the above style we could write this as:</p><pre><code class="language-julia">W1 = param(rand(3, 5))
b1 = param(rand(3))
layer1(x) = W1 * x .+ b1
W2 = param(rand(2, 3))
b2 = param(rand(2))
layer2(x) = W2 * x .+ b2
model(x) = layer2(σ.(layer1(x)))
model(rand(5)) # =&gt; 2-element vector</code></pre><p>This works but is fairly unwieldy, with a lot of repetition – especially as we add more layers. One way to factor this out is to create a function that returns linear layers.</p><pre><code class="language-julia">function linear(in, out)
W = param(randn(out, in))
b = param(randn(out))
x -&gt; W * x .+ b
end
linear1 = linear(5, 3) # we can access linear1.W etc
linear2 = linear(3, 2)
model(x) = linear2(σ.(linear1(x)))
model(x) # =&gt; 2-element vector</code></pre><p>Another (equivalent) way is to create a struct that explicitly represents the affine layer.</p><pre><code class="language-julia">struct Affine
W
b
end
Affine(in::Integer, out::Integer) =
Affine(param(randn(out, in)), param(randn(out)))
# Overload call, so the object can be used as a function
(m::Affine)(x) = m.W * x .+ m.b
a = Affine(10, 5)
a(rand(10)) # =&gt; 5-element vector</code></pre><p>Congratulations! You just built the <code>Dense</code> layer that comes with Flux. Flux has many interesting layers available, but they&#39;re all things you could have built yourself very easily.</p><p>(There is one small difference with <code>Dense</code> – for convenience it also takes an activation function, like <code>Dense(10, 5, σ)</code>.)</p><h2><a class="nav-anchor" id="Stacking-It-Up-1" href="#Stacking-It-Up-1">Stacking It Up</a></h2><p>It&#39;s pretty common to write models that look something like:</p><pre><code class="language-julia">layer1 = Dense(10, 5, σ)
# ...
model(x) = layer3(layer2(layer1(x)))</code></pre><p>For long chains, it might be a bit more intuitive to have a list of layers, like this:</p><pre><code class="language-julia">using Flux
layers = [Dense(10, 5, σ), Dense(5, 2), softmax]
model(x) = foldl((x, m) -&gt; m(x), x, layers)
model(rand(10)) # =&gt; 2-element vector</code></pre><p>Handily, this is also provided for in Flux:</p><pre><code class="language-julia">model2 = Chain(
Dense(10, 5, σ),
Dense(5, 2),
softmax)
model2(rand(10)) # =&gt; 2-element vector</code></pre><p>This quickly starts to look like a high-level deep learning library; yet you can see how it falls out of simple abstractions, and we lose none of the power of Julia code.</p><p>A nice property of this approach is that because &quot;models&quot; are just functions (possibly with trainable parameters), you can also see this as simple function composition.</p><pre><code class="language-julia">m = Dense(5, 2) ∘ Dense(10, 5, σ)
m(rand(10))</code></pre><p>Likewise, <code>Chain</code> will happily work with any Julia function.</p><pre><code class="language-julia">m = Chain(x -&gt; x^2, x -&gt; x+1)
m(5) # =&gt; 26</code></pre><h2><a class="nav-anchor" id="Layer-helpers-1" href="#Layer-helpers-1">Layer helpers</a></h2><p>Flux provides a set of helpers for custom layers, which you can enable by calling</p><pre><code class="language-julia">Flux.treelike(Affine)</code></pre><p>This enables a useful extra set of functionality for our <code>Affine</code> layer, such as <a href="../training/optimisers.html">collecting its parameters</a> or <a href="../gpu.html">moving it to the GPU</a>.</p><footer><hr/><a class="previous" href="../index.html"><span class="direction">Previous</span><span class="title">Home</span></a><a class="next" href="recurrence.html"><span class="direction">Next</span><span class="title">Recurrence</span></a></footer></article></body></html>

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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Model Reference · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="basics.html">Basics</a></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li class="current"><a class="toctext" href="layers.html">Model Reference</a><ul class="internal"><li><a class="toctext" href="#Basic-Layers-1">Basic Layers</a></li><li><a class="toctext" href="#Recurrent-Layers-1">Recurrent Layers</a></li><li><a class="toctext" href="#Activation-Functions-1">Activation Functions</a></li><li><a class="toctext" href="#Normalisation-and-Regularisation-1">Normalisation &amp; Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="layers.html">Model Reference</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Model Reference</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Basic-Layers-1" href="#Basic-Layers-1">Basic Layers</a></h2><p>These core layers form the foundation of almost all neural networks.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Chain" href="#Flux.Chain"><code>Flux.Chain</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Chain(layers...)</code></pre><p>Chain multiple layers / functions together, so that they are called in sequence on a given input.</p><pre><code class="language-julia">m = Chain(x -&gt; x^2, x -&gt; x+1)
m(5) == 26
m = Chain(Dense(10, 5), Dense(5, 2))
x = rand(10)
m(x) == m[2](m[1](x))</code></pre><p><code>Chain</code> also supports indexing and slicing, e.g. <code>m[2]</code> or <code>m[1:end-1]</code>. <code>m[1:3](x)</code> will calculate the output of the first three layers.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/basic.jl#L1-L18">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dense" href="#Flux.Dense"><code>Flux.Dense</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Dense(in::Integer, out::Integer, σ = identity)</code></pre><p>Creates a traditional <code>Dense</code> layer with parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-none">y = σ.(W * x .+ b)</code></pre><p>The input <code>x</code> must be a vector of length <code>in</code>, or a batch of vectors represented as an <code>in × N</code> matrix. The out <code>y</code> will be a vector or batch of length <code>out</code>.</p><pre><code class="language-julia">julia&gt; d = Dense(5, 2)
Dense(5, 2)
julia&gt; d(rand(5))
Tracked 2-element Array{Float64,1}:
0.00257447
-0.00449443</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/basic.jl#L40-L59">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Conv2D" href="#Flux.Conv2D"><code>Flux.Conv2D</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Conv2D(size, in=&gt;out)
Conv2d(size, in=&gt;out, relu)</code></pre><p>Standard convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>out</code> specify the number of input and output channels respectively.</p><p>Data should be stored in HWCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/conv.jl#L1-L12">source</a></section><h2><a class="nav-anchor" id="Recurrent-Layers-1" href="#Recurrent-Layers-1">Recurrent Layers</a></h2><p>Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.RNN" href="#Flux.RNN"><code>Flux.RNN</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">RNN(in::Integer, out::Integer, σ = tanh)</code></pre><p>The most basic recurrent layer; essentially acts as a <code>Dense</code> layer, but with the output fed back into the input each time step.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/recurrent.jl#L98-L103">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LSTM" href="#Flux.LSTM"><code>Flux.LSTM</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">LSTM(in::Integer, out::Integer, σ = tanh)</code></pre><p>Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/recurrent.jl#L143-L151">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Recur" href="#Flux.Recur"><code>Flux.Recur</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here&#39;s a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
rnn = Flux.Recur(accum, 0)
rnn(2) # 2
rnn(3) # 3
rnn.state # 5
rnn.(1:10) # apply to a sequence
rnn.state # 60</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/recurrent.jl#L8-L27">source</a></section><h2><a class="nav-anchor" id="Activation-Functions-1" href="#Activation-Functions-1">Activation Functions</a></h2><p>Non-linearities that go between layers of your model. Most of these functions are defined in <a href="https://github.com/FluxML/NNlib.jl">NNlib</a> but are available by default in Flux.</p><p>Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call <code>σ.(xs)</code>, <code>relu.(xs)</code> and so on.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.σ" href="#NNlib.σ"><code>NNlib.σ</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">σ(x) = 1 / (1 + exp(-x))</code></pre><p>Classic <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> activation function.</p><pre><code class="language-none">1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
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│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
0 │⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L1-L24">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.relu" href="#NNlib.relu"><code>NNlib.relu</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">relu(x) = max(0, x)</code></pre><p><a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function.</p><pre><code class="language-none">3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀│
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│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
0 │⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L39-L61">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.leakyrelu" href="#NNlib.leakyrelu"><code>NNlib.leakyrelu</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">leakyrelu(x) = max(0.01x, x)</code></pre><p>Leaky <a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function. You can also specify the coefficient explicitly, e.g. <code>leakyrelu(x, 0.01)</code>.</p><pre><code class="language-none"> 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│
-1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L65-L86">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.elu" href="#NNlib.elu"><code>NNlib.elu</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">elu(x, α = 1) =
x &gt; 0 ? x : α * (exp(x) - 1)</code></pre><p>Exponential Linear Unit activation function. See <a href="https://arxiv.org/abs/1511.07289">Fast and Accurate Deep Network Learning by Exponential Linear Units</a>. You can also specify the coefficient explicitly, e.g. <code>elu(x, 1)</code>.</p><pre><code class="language-none"> 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠖⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-1 │⣀⣀⠤⠤⠤⠤⠔⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L89-L113">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.swish" href="#NNlib.swish"><code>NNlib.swish</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">swish(x) = x * σ(x)</code></pre><p>Self-gated actvation function. See <a href="https://arxiv.org/pdf/1710.05941.pdf">Swish: a Self-Gated Activation Function</a>.</p><pre><code class="language-none"> 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⣒⣒⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣒⠶⠒⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│
│⠀⠀⠀⠀⠉⠉⠉⠉⠉⠒⠒⠒⠒⠊⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-3 0 3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/980c76824455003c4d179336cf65180a2ed925f8/src/activation.jl#L116-L138">source</a></section><h2><a class="nav-anchor" id="Normalisation-and-Regularisation-1" href="#Normalisation-and-Regularisation-1">Normalisation &amp; Regularisation</a></h2><p>These layers don&#39;t affect the structure of the network but may improve training times or reduce overfitting.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.testmode!" href="#Flux.testmode!"><code>Flux.testmode!</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">testmode!(m)
testmode!(m, false)</code></pre><p>Put layers like <a href="layers.html#Flux.Dropout"><code>Dropout</code></a> and <a href="layers.html#Flux.BatchNorm"><code>BatchNorm</code></a> into testing mode (or back to training mode with <code>false</code>).</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/normalisation.jl#L1-L7">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.BatchNorm" href="#Flux.BatchNorm"><code>Flux.BatchNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">BatchNorm(dims...; λ = identity,
initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1)</code></pre><p>Batch Normalization Layer for <a href="layers.html#Flux.Dense"><code>Dense</code></a> layer.</p><p>See <a href="https://arxiv.org/pdf/1502.03167.pdf">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a></p><p>In the example of MNIST, in order to normalize the input of other layer, put the <code>BatchNorm</code> layer before activation function.</p><pre><code class="language-julia">m = Chain(
Dense(28^2, 64),
BatchNorm(64, λ = relu),
Dense(64, 10),
BatchNorm(10),
softmax)</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/normalisation.jl#L70-L91">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dropout" href="#Flux.Dropout"><code>Flux.Dropout</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Dropout(p)</code></pre><p>A Dropout layer. For each input, either sets that input to <code>0</code> (with probability <code>p</code>) or scales it by <code>1/(1-p)</code>. This is used as a regularisation, i.e. it reduces overfitting during training.</p><p>Does nothing to the input once in <a href="layers.html#Flux.testmode!"><code>testmode!</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/normalisation.jl#L15-L23">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LayerNorm" href="#Flux.LayerNorm"><code>Flux.LayerNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">LayerNorm(h::Integer)</code></pre><p>A <a href="https://arxiv.org/pdf/1607.06450.pdf">normalisation layer</a> designed to be used with recurrent hidden states of size <code>h</code>. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/layers/normalisation.jl#L47-L54">source</a></section><footer><hr/><a class="previous" href="recurrence.html"><span class="direction">Previous</span><span class="title">Recurrence</span></a><a class="next" href="../training/optimisers.html"><span class="direction">Next</span><span class="title">Optimisers</span></a></footer></article></body></html>

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y₂ = f(x₂)
y₃ = f(x₃)
# ...</code></pre><p>Recurrent networks introduce a <em>hidden state</em> that gets carried over each time we run the model. The model now takes the old <code>h</code> as an input, and produces a new <code>h</code> as output, each time we run it.</p><pre><code class="language-julia">h = # ... initial state ...
h, y₁ = f(h, x₁)
h, y₂ = f(h, x₂)
h, y₃ = f(h, x₃)
# ...</code></pre><p>Information stored in <code>h</code> is preserved for the next prediction, allowing it to function as a kind of memory. This also means that the prediction made for a given <code>x</code> depends on all the inputs previously fed into the model.</p><p>(This might be important if, for example, each <code>x</code> represents one word of a sentence; the model&#39;s interpretation of the word &quot;bank&quot; should change if the previous input was &quot;river&quot; rather than &quot;investment&quot;.)</p><p>Flux&#39;s RNN support closely follows this mathematical perspective. The most basic RNN is as close as possible to a standard <code>Dense</code> layer, and the output is also the hidden state.</p><pre><code class="language-julia">Wxh = randn(5, 10)
Whh = randn(5, 5)
b = randn(5)
function rnn(h, x)
h = tanh.(Wxh * x .+ Whh * h .+ b)
return h, h
end
x = rand(10) # dummy data
h = rand(5) # initial hidden state
h, y = rnn(h, x)</code></pre><p>If you run the last line a few times, you&#39;ll notice the output <code>y</code> changing slightly even though the input <code>x</code> is the same.</p><p>We sometimes refer to functions like <code>rnn</code> above, which explicitly manage state, as recurrent <em>cells</em>. There are various recurrent cells available, which are documented in the <a href="layers.html">layer reference</a>. The hand-written example above can be replaced with:</p><pre><code class="language-julia">using Flux
rnn2 = Flux.RNNCell(10, 5)
x = rand(10) # dummy data
h = rand(5) # initial hidden state
h, y = rnn2(h, x)</code></pre><h2><a class="nav-anchor" id="Stateful-Models-1" href="#Stateful-Models-1">Stateful Models</a></h2><p>For the most part, we don&#39;t want to manage hidden states ourselves, but to treat our models as being stateful. Flux provides the <code>Recur</code> wrapper to do this.</p><pre><code class="language-julia">x = rand(10)
h = rand(5)
m = Flux.Recur(rnn, h)
y = m(x)</code></pre><p>The <code>Recur</code> wrapper stores the state between runs in the <code>m.state</code> field.</p><p>If you use the <code>RNN(10, 5)</code> constructor – as opposed to <code>RNNCell</code> – you&#39;ll see that it&#39;s simply a wrapped cell.</p><pre><code class="language-julia">julia&gt; RNN(10, 5)
Recur(RNNCell(Dense(15, 5)))</code></pre><h2><a class="nav-anchor" id="Sequences-1" href="#Sequences-1">Sequences</a></h2><p>Often we want to work with sequences of inputs, rather than individual <code>x</code>s.</p><pre><code class="language-julia">seq = [rand(10) for i = 1:10]</code></pre><p>With <code>Recur</code>, applying our model to each element of a sequence is trivial:</p><pre><code class="language-julia">m.(seq) # returns a list of 5-element vectors</code></pre><p>This works even when we&#39;ve chain recurrent layers into a larger model.</p><pre><code class="language-julia">m = Chain(LSTM(10, 15), Dense(15, 5))
m.(seq)</code></pre><h2><a class="nav-anchor" id="Truncating-Gradients-1" href="#Truncating-Gradients-1">Truncating Gradients</a></h2><p>By default, calculating the gradients in a recurrent layer involves the entire history. For example, if we call the model on 100 inputs, calling <code>back!</code> will calculate the gradient for those 100 calls. If we then calculate another 10 inputs we have to calculate 110 gradients – this accumulates and quickly becomes expensive.</p><p>To avoid this we can <em>truncate</em> the gradient calculation, forgetting the history.</p><pre><code class="language-julia">truncate!(m)</code></pre><p>Calling <code>truncate!</code> wipes the slate clean, so we can call the model with more inputs without building up an expensive gradient computation.</p><p><code>truncate!</code> makes sense when you are working with multiple chunks of a large sequence, but we may also want to work with a set of independent sequences. In this case the hidden state should be completely reset to its original value, throwing away any accumulated information. <code>reset!</code> does this for you.</p><footer><hr/><a class="previous" href="basics.html"><span class="direction">Previous</span><span class="title">Basics</span></a><a class="next" href="layers.html"><span class="direction">Next</span><span class="title">Model Reference</span></a></footer></article></body></html>

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"text": "Consider a simple linear regression, which tries to predict an output array y from an input x. (It's a good idea to follow this example in the Julia repl.)W = rand(2, 5)\nb = rand(2)\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = rand(5), rand(2) # Dummy data\nloss(x, y) # ~ 3To improve the prediction we can take the gradients of W and b with respect to the loss function and perform gradient descent. We could calculate gradients by hand, but Flux will do it for us if we tell it that W and b are trainable parameters.using Flux.Tracker\n\nW = param(W)\nb = param(b)\n\nl = loss(x, y)\n\nback!(l)loss(x, y) returns the same number, but it's now a tracked value that records gradients as it goes along. Calling back! then calculates the gradient of W and b. We can see what this gradient is, and modify W to train the model.W.grad\n\n# Update the parameter\nW.data .-= 0.1(W.grad)\n\nloss(x, y) # ~ 2.5The loss has decreased a little, meaning that our prediction x is closer to the target y. If we have some data we can already try training the model.All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, models can look very different – they might have millions of parameters or complex control flow, and there are ways to manage this complexity. Let's see what that looks like."
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"text": "It's pretty common to write models that look something like:layer1 = Dense(10, 5, σ)\n# ...\nmodel(x) = layer3(layer2(layer1(x)))For long chains, it might be a bit more intuitive to have a list of layers, like this:using Flux\n\nlayers = [Dense(10, 5, σ), Dense(5, 2), softmax]\n\nmodel(x) = foldl((x, m) -> m(x), x, layers)\n\nmodel(rand(10)) # => 2-element vectorHandily, this is also provided for in Flux:model2 = Chain(\n Dense(10, 5, σ),\n Dense(5, 2),\n softmax)\n\nmodel2(rand(10)) # => 2-element vectorThis quickly starts to look like a high-level deep learning library; yet you can see how it falls out of simple abstractions, and we lose none of the power of Julia code.A nice property of this approach is that because \"models\" are just functions (possibly with trainable parameters), you can also see this as simple function composition.m = Dense(5, 2) ∘ Dense(10, 5, σ)\n\nm(rand(10))Likewise, Chain will happily work with any Julia function.m = Chain(x -> x^2, x -> x+1)\n\nm(5) # => 26"
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"text": "In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.y₁ = f(x₁)\ny₂ = f(x₂)\ny₃ = f(x₃)\n# ...Recurrent networks introduce a hidden state that gets carried over each time we run the model. The model now takes the old h as an input, and produces a new h as output, each time we run it.h = # ... initial state ...\nh, y₁ = f(h, x₁)\nh, y₂ = f(h, x₂)\nh, y₃ = f(h, x₃)\n# ...Information stored in h is preserved for the next prediction, allowing it to function as a kind of memory. This also means that the prediction made for a given x depends on all the inputs previously fed into the model.(This might be important if, for example, each x represents one word of a sentence; the model's interpretation of the word \"bank\" should change if the previous input was \"river\" rather than \"investment\".)Flux's RNN support closely follows this mathematical perspective. The most basic RNN is as close as possible to a standard Dense layer, and the output is also the hidden state.Wxh = randn(5, 10)\nWhh = randn(5, 5)\nb = randn(5)\n\nfunction rnn(h, x)\n h = tanh.(Wxh * x .+ Whh * h .+ b)\n return h, h\nend\n\nx = rand(10) # dummy data\nh = rand(5) # initial hidden state\n\nh, y = rnn(h, x)If you run the last line a few times, you'll notice the output y changing slightly even though the input x is the same.We sometimes refer to functions like rnn above, which explicitly manage state, as recurrent cells. There are various recurrent cells available, which are documented in the layer reference. The hand-written example above can be replaced with:using Flux\n\nrnn2 = Flux.RNNCell(10, 5)\n\nx = rand(10) # dummy data\nh = rand(5) # initial hidden state\n\nh, y = rnn2(h, x)"
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"title": "Flux.Dense",
"category": "Type",
"text": "Dense(in::Integer, out::Integer, σ = identity)\n\nCreates a traditional Dense layer with parameters W and b.\n\ny = σ.(W * x .+ b)\n\nThe input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length out.\n\njulia> d = Dense(5, 2)\nDense(5, 2)\n\njulia> d(rand(5))\nTracked 2-element Array{Float64,1}:\n 0.00257447\n -0.00449443\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Conv2D",
"page": "Model Reference",
"title": "Flux.Conv2D",
"category": "Type",
"text": "Conv2D(size, in=>out)\nConv2d(size, in=>out, relu)\n\nStandard convolutional layer. size should be a tuple like (2, 2). in and out specify the number of input and output channels respectively.\n\nData should be stored in HWCN order. In other words, a 100×100 RGB image would be a 100×100×3 array, and a batch of 50 would be a 100×100×3×50 array.\n\nTakes the keyword arguments pad and stride.\n\n\n\n"
},
{
"location": "models/layers.html#Basic-Layers-1",
"page": "Model Reference",
"title": "Basic Layers",
"category": "section",
"text": "These core layers form the foundation of almost all neural networks.Chain\nDense\nConv2D"
},
{
"location": "models/layers.html#Flux.RNN",
"page": "Model Reference",
"title": "Flux.RNN",
"category": "Function",
"text": "RNN(in::Integer, out::Integer, σ = tanh)\n\nThe most basic recurrent layer; essentially acts as a Dense layer, but with the output fed back into the input each time step.\n\n\n\n"
},
{
"location": "models/layers.html#Flux.LSTM",
"page": "Model Reference",
"title": "Flux.LSTM",
"category": "Function",
"text": "LSTM(in::Integer, out::Integer, σ = tanh)\n\nLong Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.\n\nSee this article for a good overview of the internals.\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Recur",
"page": "Model Reference",
"title": "Flux.Recur",
"category": "Type",
"text": "Recur(cell)\n\nRecur takes a recurrent cell and makes it stateful, managing the hidden state in the background. cell should be a model of the form:\n\nh, y = cell(h, x...)\n\nFor example, here's a recurrent network that keeps a running total of its inputs.\n\naccum(h, x) = (h+x, x)\nrnn = Flux.Recur(accum, 0)\nrnn(2) # 2\nrnn(3) # 3\nrnn.state # 5\nrnn.(1:10) # apply to a sequence\nrnn.state # 60\n\n\n\n"
},
{
"location": "models/layers.html#Recurrent-Layers-1",
"page": "Model Reference",
"title": "Recurrent Layers",
"category": "section",
"text": "Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).RNN\nLSTM\nFlux.Recur"
},
{
"location": "models/layers.html#NNlib.σ",
"page": "Model Reference",
"title": "NNlib.σ",
"category": "Function",
"text": "σ(x) = 1 / (1 + exp(-x))\n\nClassic sigmoid activation function.\n\n1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n0 │⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.relu",
"page": "Model Reference",
"title": "NNlib.relu",
"category": "Function",
"text": "relu(x) = max(0, x)\n\nRectified Linear Unit activation function.\n\n3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n0 │⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.leakyrelu",
"page": "Model Reference",
"title": "NNlib.leakyrelu",
"category": "Function",
"text": "leakyrelu(x) = max(0.01x, x)\n\nLeaky Rectified Linear Unit activation function. You can also specify the coefficient explicitly, e.g. leakyrelu(x, 0.01).\n\n 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│\n-1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.elu",
"page": "Model Reference",
"title": "NNlib.elu",
"category": "Function",
"text": "elu(x, α = 1) =\n x > 0 ? x : α * (exp(x) - 1)\n\nExponential Linear Unit activation function. See Fast and Accurate Deep Network Learning by Exponential Linear Units. You can also specify the coefficient explicitly, e.g. elu(x, 1).\n\n 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠖⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n-1 │⣀⣀⠤⠤⠤⠤⠔⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.swish",
"page": "Model Reference",
"title": "NNlib.swish",
"category": "Function",
"text": "swish(x) = x * σ(x)\n\nSelf-gated actvation function. See Swish: a Self-Gated Activation Function.\n\n 3 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⣒⣒⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣒⠶⠒⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂│\n │⠀⠀⠀⠀⠉⠉⠉⠉⠉⠒⠒⠒⠒⠊⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n-1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│\n -3 0 3\n\n\n\n"
},
{
"location": "models/layers.html#Activation-Functions-1",
"page": "Model Reference",
"title": "Activation Functions",
"category": "section",
"text": "Non-linearities that go between layers of your model. Most of these functions are defined in NNlib but are available by default in Flux.Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call σ.(xs), relu.(xs) and so on.σ\nrelu\nleakyrelu\nelu\nswish"
},
{
"location": "models/layers.html#Flux.testmode!",
"page": "Model Reference",
"title": "Flux.testmode!",
"category": "Function",
"text": "testmode!(m)\ntestmode!(m, false)\n\nPut layers like Dropout and BatchNorm into testing mode (or back to training mode with false).\n\n\n\n"
},
{
"location": "models/layers.html#Flux.BatchNorm",
"page": "Model Reference",
"title": "Flux.BatchNorm",
"category": "Type",
"text": "BatchNorm(dims...; λ = identity,\n initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1)\n\nBatch Normalization Layer for Dense layer.\n\nSee Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift\n\nIn the example of MNIST, in order to normalize the input of other layer, put the BatchNorm layer before activation function.\n\nm = Chain(\n Dense(28^2, 64),\n BatchNorm(64, λ = relu),\n Dense(64, 10),\n BatchNorm(10),\n softmax)\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Dropout",
"page": "Model Reference",
"title": "Flux.Dropout",
"category": "Type",
"text": "Dropout(p)\n\nA Dropout layer. For each input, either sets that input to 0 (with probability p) or scales it by 1/(1-p). This is used as a regularisation, i.e. it reduces overfitting during training.\n\nDoes nothing to the input once in testmode!.\n\n\n\n"
},
{
"location": "models/layers.html#Flux.LayerNorm",
"page": "Model Reference",
"title": "Flux.LayerNorm",
"category": "Type",
"text": "LayerNorm(h::Integer)\n\nA normalisation layer designed to be used with recurrent hidden states of size h. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.\n\n\n\n"
},
{
"location": "models/layers.html#Normalisation-and-Regularisation-1",
"page": "Model Reference",
"title": "Normalisation & Regularisation",
"category": "section",
"text": "These layers don't affect the structure of the network but may improve training times or reduce overfitting.Flux.testmode!\nBatchNorm\nDropout\nLayerNorm"
},
{
"location": "training/optimisers.html#",
"page": "Optimisers",
"title": "Optimisers",
"category": "page",
"text": ""
},
{
"location": "training/optimisers.html#Optimisers-1",
"page": "Optimisers",
"title": "Optimisers",
"category": "section",
"text": "Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.W = param(rand(2, 5))\nb = param(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = rand(5), rand(2) # Dummy data\nl = loss(x, y) # ~ 3\nback!(l)We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here's one way to do that:function update()\n η = 0.1 # Learning Rate\n for p in (W, b)\n p.data .-= η .* p.grad # Apply the update\n p.grad .= 0 # Clear the gradient\n end\nendIf we call update, the parameters W and b will change and our loss should go down.There are two pieces here: one is that we need a list of trainable parameters for the model ([W, b] in this case), and the other is the update step. In this case the update is simply gradient descent (x .-= η .* Δ), but we might choose to do something more advanced, like adding momentum.In this case, getting the variables is trivial, but you can imagine it'd be more of a pain with some complex stack of layers.m = Chain(\n Dense(10, 5, σ),\n Dense(5, 2), softmax)Instead of having to write [m[1].W, m[1].b, ...], Flux provides a params function params(m) that returns a list of all parameters in the model for you.For the update step, there's nothing whatsoever wrong with writing the loop above – it'll work just fine – but Flux provides various optimisers that make it more convenient.opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1\n\nopt() # Carry out the update, modifying `W` and `b`.An optimiser takes a parameter list and returns a function that does the same thing as update above. We can pass either opt or update to our training loop, which will then run the optimiser after every mini-batch of data."
},
{
"location": "training/optimisers.html#Flux.Optimise.SGD",
"page": "Optimisers",
"title": "Flux.Optimise.SGD",
"category": "Function",
"text": "SGD(params, η = 0.1; decay = 0)\n\nClassic gradient descent optimiser with learning rate η. For each parameter p and its gradient δp, this runs p -= η*δp.\n\nSupports inverse decaying learning rate if the decay argument is provided.\n\n\n\n"
},
{
"location": "training/optimisers.html#Flux.Optimise.Momentum",
"page": "Optimisers",
"title": "Flux.Optimise.Momentum",
"category": "Function",
"text": "Momentum(params, η = 0.01; ρ = 0.9, decay = 0)\n\nSGD with learning rate η, momentum ρ and optional learning rate inverse decay.\n\n\n\n"
},
{
"location": "training/optimisers.html#Flux.Optimise.Nesterov",
"page": "Optimisers",
"title": "Flux.Optimise.Nesterov",
"category": "Function",
"text": "Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)\n\nSGD with learning rate η, Nesterov momentum ρ and optional learning rate inverse decay.\n\n\n\n"
},
{
"location": "training/optimisers.html#Flux.Optimise.ADAM",
"page": "Optimisers",
"title": "Flux.Optimise.ADAM",
"category": "Function",
"text": "ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)\n\nADAM optimiser.\n\n\n\n"
},
{
"location": "training/optimisers.html#Optimiser-Reference-1",
"page": "Optimisers",
"title": "Optimiser Reference",
"category": "section",
"text": "All optimisers return a function that, when called, will update the parameters passed to it.SGD\nMomentum\nNesterov\nADAM"
},
{
"location": "training/training.html#",
"page": "Training",
"title": "Training",
"category": "page",
"text": ""
},
{
"location": "training/training.html#Training-1",
"page": "Training",
"title": "Training",
"category": "section",
"text": "To actually train a model we need three things:A model loss function, that evaluates how well a model is doing given some input data.\nA collection of data points that will be provided to the loss function.\nAn optimiser that will update the model parameters appropriately.With these we can call Flux.train!:Flux.train!(modelLoss, data, opt)There are plenty of examples in the model zoo."
},
{
"location": "training/training.html#Loss-Functions-1",
"page": "Training",
"title": "Loss Functions",
"category": "section",
"text": "The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:m = Chain(\n Dense(784, 32, σ),\n Dense(32, 10), softmax)\n\n# Model loss function\nloss(x, y) = Flux.mse(m(x), y)\n\n# later\nFlux.train!(loss, data, opt)The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or crossentropy for cross entropy loss, but you can calculate it however you want."
},
{
"location": "training/training.html#Datasets-1",
"page": "Training",
"title": "Datasets",
"category": "section",
"text": "The data argument provides a collection of data to train with (usually a set of inputs x and target outputs y). For example, here's a dummy data set with only one data point:x = rand(784)\ny = rand(10)\ndata = [(x, y)]Flux.train! will call loss(x, y), calculate gradients, update the weights and then move on to the next data point if there is one. We can train the model on the same data three times:data = [(x, y), (x, y), (x, y)]\n# Or equivalently\ndata = Iterators.repeated((x, y), 3)It's common to load the xs and ys separately. In this case you can use zip:xs = [rand(784), rand(784), rand(784)]\nys = [rand( 10), rand( 10), rand( 10)]\ndata = zip(xs, ys)"
},
{
"location": "training/training.html#Callbacks-1",
"page": "Training",
"title": "Callbacks",
"category": "section",
"text": "train! takes an additional argument, cb, that's used for callbacks so that you can observe the training process. For example:train!(loss, data, opt, cb = () -> println(\"training\"))Callbacks are called for every batch of training data. You can slow this down using Flux.throttle(f, timeout) which prevents f from being called more than once every timeout seconds.A more typical callback might look like this:test_x, test_y = # ... create single batch of test data ...\nevalcb() = @show(loss(test_x, test_y))\n\nFlux.train!(loss, data, opt,\n cb = throttle(evalcb, 5))"
},
{
"location": "data/onehot.html#",
"page": "One-Hot Encoding",
"title": "One-Hot Encoding",
"category": "page",
"text": ""
},
{
"location": "data/onehot.html#One-Hot-Encoding-1",
"page": "One-Hot Encoding",
"title": "One-Hot Encoding",
"category": "section",
"text": "It's common to encode categorical variables (like true, false or cat, dog) in \"one-of-k\" or \"one-hot\" form. Flux provides the onehot function to make this easy.julia> using Flux: onehot\n\njulia> onehot(:b, [:a, :b, :c])\n3-element Flux.OneHotVector:\n false\n true\n false\n\njulia> onehot(:c, [:a, :b, :c])\n3-element Flux.OneHotVector:\n false\n false\n trueThe inverse is argmax (which can take a general probability distribution, as well as just booleans).julia> argmax(ans, [:a, :b, :c])\n:c\n\njulia> argmax([true, false, false], [:a, :b, :c])\n:a\n\njulia> argmax([0.3, 0.2, 0.5], [:a, :b, :c])\n:c"
},
{
"location": "data/onehot.html#Batches-1",
"page": "One-Hot Encoding",
"title": "Batches",
"category": "section",
"text": "onehotbatch creates a batch (matrix) of one-hot vectors, and argmax treats matrices as batches.julia> using Flux: onehotbatch\n\njulia> onehotbatch([:b, :a, :b], [:a, :b, :c])\n3×3 Flux.OneHotMatrix:\n false true false\n true false true\n false false false\n\njulia> onecold(ans, [:a, :b, :c])\n3-element Array{Symbol,1}:\n :b\n :a\n :bNote that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood."
},
{
"location": "gpu.html#",
"page": "GPU Support",
"title": "GPU Support",
"category": "page",
"text": ""
},
{
"location": "gpu.html#GPU-Support-1",
"page": "GPU Support",
"title": "GPU Support",
"category": "section",
"text": "Support for array operations on other hardware backends, like GPUs, is provided by external packages like CuArrays and CLArrays. Flux doesn't care what array type you use, so we can just plug these in without any other changes.For example, we can use CuArrays (with the cu converter) to run our basic example on an NVIDIA GPU.using CuArrays\n\nW = cu(rand(2, 5)) # a 2×5 CuArray\nb = cu(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = cu(rand(5)), cu(rand(2)) # Dummy data\nloss(x, y) # ~ 3Note that we convert both the parameters (W, b) and the data set (x, y) to cuda arrays. Taking derivatives and training works exactly as before.If you define a structured model, like a Dense layer or Chain, you just need to convert the internal parameters. Flux provides mapleaves, which allows you to alter all parameters of a model at once.d = Dense(10, 5, σ)\nd = mapleaves(cu, d)\nd.W # Tracked CuArray\nd(cu(rand(10))) # CuArray output\n\nm = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)\nm = mapleaves(cu, m)\nd(cu(rand(10)))The mnist example contains the code needed to run the model on the GPU; just uncomment the lines after using CuArrays."
},
{
"location": "community.html#",
"page": "Community",
"title": "Community",
"category": "page",
"text": ""
},
{
"location": "community.html#Community-1",
"page": "Community",
"title": "Community",
"category": "section",
"text": "All Flux users are welcome to join our community on the Julia forum, the slack (channel #machine-learning), or Flux's Gitter. If you have questions or issues we'll try to help you out.If you're interested in hacking on Flux, the source code is open and easy to understand – it's all just the same Julia code you work with normally. You might be interested in our intro issues to get started."
},
]}

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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Optimisers · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../models/basics.html">Basics</a></li><li><a class="toctext" href="../models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="../models/layers.html">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li class="current"><a class="toctext" href="optimisers.html">Optimisers</a><ul class="internal"><li><a class="toctext" href="#Optimiser-Reference-1">Optimiser Reference</a></li></ul></li><li><a class="toctext" href="training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Training Models</li><li><a href="optimisers.html">Optimisers</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/training/optimisers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Optimisers</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Optimisers-1" href="#Optimisers-1">Optimisers</a></h1><p>Consider a <a href="../models/basics.html">simple linear regression</a>. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-julia">W = param(rand(2, 5))
b = param(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = rand(5), rand(2) # Dummy data
l = loss(x, y) # ~ 3
back!(l)</code></pre><p>We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here&#39;s one way to do that:</p><pre><code class="language-julia">function update()
η = 0.1 # Learning Rate
for p in (W, b)
p.data .-= η .* p.grad # Apply the update
p.grad .= 0 # Clear the gradient
end
end</code></pre><p>If we call <code>update</code>, the parameters <code>W</code> and <code>b</code> will change and our loss should go down.</p><p>There are two pieces here: one is that we need a list of trainable parameters for the model (<code>[W, b]</code> in this case), and the other is the update step. In this case the update is simply gradient descent (<code>x .-= η .* Δ</code>), but we might choose to do something more advanced, like adding momentum.</p><p>In this case, getting the variables is trivial, but you can imagine it&#39;d be more of a pain with some complex stack of layers.</p><pre><code class="language-julia">m = Chain(
Dense(10, 5, σ),
Dense(5, 2), softmax)</code></pre><p>Instead of having to write <code>[m[1].W, m[1].b, ...]</code>, Flux provides a params function <code>params(m)</code> that returns a list of all parameters in the model for you.</p><p>For the update step, there&#39;s nothing whatsoever wrong with writing the loop above – it&#39;ll work just fine – but Flux provides various <em>optimisers</em> that make it more convenient.</p><pre><code class="language-julia">opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1
opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.SGD" href="#Flux.Optimise.SGD"><code>Flux.Optimise.SGD</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">SGD(params, η = 0.1; decay = 0)</code></pre><p>Classic gradient descent optimiser with learning rate <code>η</code>. For each parameter <code>p</code> and its gradient <code>δp</code>, this runs <code>p -= η*δp</code>.</p><p>Supports inverse decaying learning rate if the <code>decay</code> argument is provided.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L14-L21">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.Momentum" href="#Flux.Optimise.Momentum"><code>Flux.Optimise.Momentum</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">Momentum(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, momentum <code>ρ</code> and optional learning rate inverse decay.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L25-L29">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.Nesterov" href="#Flux.Optimise.Nesterov"><code>Flux.Optimise.Nesterov</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, Nesterov momentum <code>ρ</code> and optional learning rate inverse decay.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L33-L37">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.ADAM" href="#Flux.Optimise.ADAM"><code>Flux.Optimise.ADAM</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)</code></pre><p><a href="https://arxiv.org/abs/1412.6980v8">ADAM</a> optimiser.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/98b362729dd39c70d327f6f03c82fe949b4a2396/src/optimise/interface.jl#L51-L55">source</a></section><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>

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Dense(784, 32, σ),
Dense(32, 10), softmax)
# Model loss function
loss(x, y) = Flux.mse(m(x), y)
# later
Flux.train!(loss, data, opt)</code></pre><p>The loss will almost always be defined in terms of some <em>cost function</em> that measures the distance of the prediction <code>m(x)</code> from the target <code>y</code>. Flux has several of these built in, like <code>mse</code> for mean squared error or <code>crossentropy</code> for cross entropy loss, but you can calculate it however you want.</p><h2><a class="nav-anchor" id="Datasets-1" href="#Datasets-1">Datasets</a></h2><p>The <code>data</code> argument provides a collection of data to train with (usually a set of inputs <code>x</code> and target outputs <code>y</code>). For example, here&#39;s a dummy data set with only one data point:</p><pre><code class="language-julia">x = rand(784)
y = rand(10)
data = [(x, y)]</code></pre><p><code>Flux.train!</code> will call <code>loss(x, y)</code>, calculate gradients, update the weights and then move on to the next data point if there is one. We can train the model on the same data three times:</p><pre><code class="language-julia">data = [(x, y), (x, y), (x, y)]
# Or equivalently
data = Iterators.repeated((x, y), 3)</code></pre><p>It&#39;s common to load the <code>x</code>s and <code>y</code>s separately. In this case you can use <code>zip</code>:</p><pre><code class="language-julia">xs = [rand(784), rand(784), rand(784)]
ys = [rand( 10), rand( 10), rand( 10)]
data = zip(xs, ys)</code></pre><h2><a class="nav-anchor" id="Callbacks-1" href="#Callbacks-1">Callbacks</a></h2><p><code>train!</code> takes an additional argument, <code>cb</code>, that&#39;s used for callbacks so that you can observe the training process. For example:</p><pre><code class="language-julia">train!(loss, data, opt, cb = () -&gt; println(&quot;training&quot;))</code></pre><p>Callbacks are called for every batch of training data. You can slow this down using <code>Flux.throttle(f, timeout)</code> which prevents <code>f</code> from being called more than once every <code>timeout</code> seconds.</p><p>A more typical callback might look like this:</p><pre><code class="language-julia">test_x, test_y = # ... create single batch of test data ...
evalcb() = @show(loss(test_x, test_y))
Flux.train!(loss, data, opt,
cb = throttle(evalcb, 5))</code></pre><footer><hr/><a class="previous" href="optimisers.html"><span class="direction">Previous</span><span class="title">Optimisers</span></a><a class="next" href="../data/onehot.html"><span class="direction">Next</span><span class="title">One-Hot Encoding</span></a></footer></article></body></html>

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