data-science/backprop_with_equations/Backprop_explained_with_mathjax.html at master · piyush-daga/data-science · GitHub

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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />

<title>Backprop_explained_with_mathjax</title>

<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>


<style type="text/css">
    /*!
*
* Twitter Bootstrap
*
*/
/*!
 * Bootstrap v3.3.7 (http://getbootstrap.com)
 * Copyright 2011-2016 Twitter, Inc.
 * Licensed under MIT (https://github.com/twbs/bootstrap/blob/master/LICENSE)
 */
/*! normalize.css v3.0.3 | MIT License | github.com/necolas/normalize.css */
html {
  font-family: sans-serif;
  -ms-text-size-adjust: 100%;
  -webkit-text-size-adjust: 100%;
}
body {
  margin: 0;
}
article,
aside,
details,
figcaption,
figure,
footer,
header,
hgroup,
main,
menu,
nav,
section,
summary {
  display: block;
}
audio,
canvas,
progress,
video {
  display: inline-block;
  vertical-align: baseline;
}
audio:not([controls]) {
  display: none;
  height: 0;
}
[hidden],
template {
  display: none;
}
a {
  background-color: transparent;
}
a:active,
a:hover {
  outline: 0;
}
abbr[title] {
  border-bottom: 1px dotted;
}
b,
strong {
  font-weight: bold;
}
dfn {
  font-style: italic;
}
h1 {
  font-size: 2em;
  margin: 0.67em 0;
}
mark {
  background: #ff0;
  color: #000;
}
small {
  font-size: 80%;
}
sub,
sup {
  font-size: 75%;
  line-height: 0;
  position: relative;
  vertical-align: baseline;
}
sup {
  top: -0.5em;
}
sub {
  bottom: -0.25em;
}
img {
  border: 0;
}
svg:not(:root) {
  overflow: hidden;
}
figure {
  margin: 1em 40px;
}
hr {
  box-sizing: content-box;
  height: 0;
}
pre {
  overflow: auto;
}
code,
kbd,
pre,
samp {
  font-family: monospace, monospace;
  font-size: 1em;
}
button,
input,
optgroup,
select,
textarea {
  color: inherit;
  font: inherit;
  margin: 0;
}
button {
  overflow: visible;
}
button,
select {
  text-transform: none;
}
button,
html input[type="button"],
input[type="reset"],
input[type="submit"] {
  -webkit-appearance: button;
  cursor: pointer;
}
button[disabled],
html input[disabled] {
  cursor: default;
}
button::-moz-focus-inner,
input::-moz-focus-inner {
  border: 0;
  padding: 0;
}
input {
  line-height: normal;
}
input[type="checkbox"],
input[type="radio"] {
  box-sizing: border-box;
  padding: 0;
}
input[type="number"]::-webkit-inner-spin-button,
input[type="number"]::-webkit-outer-spin-button {
  height: auto;
}
input[type="search"] {
  -webkit-appearance: textfield;
  box-sizing: content-box;
}
input[type="search"]::-webkit-search-cancel-button,
input[type="search"]::-webkit-search-decoration {
  -webkit-appearance: none;
}
fieldset {
  border: 1px solid #c0c0c0;
  margin: 0 2px;
  padding: 0.35em 0.625em 0.75em;
}
legend {
  border: 0;
  padding: 0;
}
textarea {
  overflow: auto;
}
optgroup {
  font-weight: bold;
}
table {
  border-collapse: collapse;
  border-spacing: 0;
}
td,
th {
  padding: 0;
}
/*! Source: https://github.com/h5bp/html5-boilerplate/blob/master/src/css/main.css */
@media print {
  *,
  *:before,
  *:after {
    background: transparent !important;
    box-shadow: none !important;
    text-shadow: none !important;
  }
  a,
  a:visited {
    text-decoration: underline;
  }
  a[href]:after {
    content: " (" attr(href) ")";
  }
  abbr[title]:after {
    content: " (" attr(title) ")";
  }
  a[href^="#"]:after,
  a[href^="javascript:"]:after {
    content: "";
  }
  pre,
  blockquote {
    border: 1px solid #999;
    page-break-inside: avoid;
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  thead {
    display: table-header-group;
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  tr,
  img {
    page-break-inside: avoid;
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  img {
    max-width: 100% !important;
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  h3 {
    orphans: 3;
    widows: 3;
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  h3 {
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  .navbar {
    display: none;
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  .btn > .caret,
  .dropup > .btn > .caret {
    border-top-color: #000 !important;
  }
  .label {
    border: 1px solid #000;
  }
  .table {
    border-collapse: collapse !important;
  }
  .table td,
  .table th {
    background-color: #fff !important;
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  .table-bordered th,
  .table-bordered td {
    border: 1px solid #ddd !important;
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}
@font-face {
  font-family: 'Glyphicons Halflings';
  src: url('../components/bootstrap/fonts/glyphicons-halflings-regular.eot');
  src: url('../components/bootstrap/fonts/glyphicons-halflings-regular.eot?#iefix') format('embedded-opentype'), url('../components/bootstrap/fonts/glyphicons-halflings-regular.woff2') format('woff2'), url('../components/bootstrap/fonts/glyphicons-halflings-regular.woff') format('woff'), url('../components/bootstrap/fonts/glyphicons-halflings-regular.ttf') format('truetype'), url('../components/bootstrap/fonts/glyphicons-halflings-regular.svg#glyphicons_halflingsregular') format('svg');
}
.glyphicon {
  position: relative;
  top: 1px;
  display: inline-block;
  font-family: 'Glyphicons Halflings';
  font-style: normal;
  font-weight: normal;
  line-height: 1;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
}
.glyphicon-asterisk:before {
  content: "\002a";
}
.glyphicon-plus:before {
  content: "\002b";
}
.glyphicon-euro:before,
.glyphicon-eur:before {
  content: "\20ac";
}
.glyphicon-minus:before {
  content: "\2212";
}
.glyphicon-cloud:before {
  content: "\2601";
}
.glyphicon-envelope:before {
  content: "\2709";
}
.glyphicon-pencil:before {
  content: "\270f";
}
.glyphicon-glass:before {
  content: "\e001";
}
.glyphicon-music:before {
  content: "\e002";
}
.glyphicon-search:before {
  content: "\e003";
}
.glyphicon-heart:before {
  content: "\e005";
}
.glyphicon-star:before {
  content: "\e006";
}
.glyphicon-star-empty:before {
  content: "\e007";
}
.glyphicon-user:before {
  content: "\e008";
}
.glyphicon-film:before {
  content: "\e009";
}
.glyphicon-th-large:before {
  content: "\e010";
}
.glyphicon-th:before {
  content: "\e011";
}
.glyphicon-th-list:before {
  content: "\e012";
}
.glyphicon-ok:before {
  content: "\e013";
}
.glyphicon-remove:before {
  content: "\e014";
}
.glyphicon-zoom-in:before {
  content: "\e015";
}
.glyphicon-zoom-out:before {
  content: "\e016";
}
.glyphicon-off:before {
  content: "\e017";
}
.glyphicon-signal:before {
  content: "\e018";
}
.glyphicon-cog:before {
  content: "\e019";
}
.glyphicon-trash:before {
  content: "\e020";
}
.glyphicon-home:before {
  content: "\e021";
}
.glyphicon-file:before {
  content: "\e022";
}
.glyphicon-time:before {
  content: "\e023";
}
.glyphicon-road:before {
  content: "\e024";
}
.glyphicon-download-alt:before {
  content: "\e025";
}
.glyphicon-download:before {
  content: "\e026";
}
.glyphicon-upload:before {
  content: "\e027";
}
.glyphicon-inbox:before {
  content: "\e028";
}
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  content: "\e029";
}
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  content: "\e030";
}
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}
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  content: "\e032";
}
.glyphicon-lock:before {
  content: "\e033";
}
.glyphicon-flag:before {
  content: "\e034";
}
.glyphicon-headphones:before {
  content: "\e035";
}
.glyphicon-volume-off:before {
  content: "\e036";
}
.glyphicon-volume-down:before {
  content: "\e037";
}
.glyphicon-volume-up:before {
  content: "\e038";
}
.glyphicon-qrcode:before {
  content: "\e039";
}
.glyphicon-barcode:before {
  content: "\e040";
}
.glyphicon-tag:before {
  content: "\e041";
}
.glyphicon-tags:before {
  content: "\e042";
}
.glyphicon-book:before {
  content: "\e043";
}
.glyphicon-bookmark:before {
  content: "\e044";
}
.glyphicon-print:before {
  content: "\e045";
}
.glyphicon-camera:before {
  content: "\e046";
}
.glyphicon-font:before {
  content: "\e047";
}
.glyphicon-bold:before {
  content: "\e048";
}
.glyphicon-italic:before {
  content: "\e049";
}
.glyphicon-text-height:before {
  content: "\e050";
}
.glyphicon-text-width:before {
  content: "\e051";
}
.glyphicon-align-left:before {
  content: "\e052";
}
.glyphicon-align-center:before {
  content: "\e053";
}
.glyphicon-align-right:before {
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}
.glyphicon-align-justify:before {
  content: "\e055";
}
.glyphicon-list:before {
  content: "\e056";
}
.glyphicon-indent-left:before {
  content: "\e057";
}
.glyphicon-indent-right:before {
  content: "\e058";
}
.glyphicon-facetime-video:before {
  content: "\e059";
}
.glyphicon-picture:before {
  content: "\e060";
}
.glyphicon-map-marker:before {
  content: "\e062";
}
.glyphicon-adjust:before {
  content: "\e063";
}
.glyphicon-tint:before {
  content: "\e064";
}
.glyphicon-edit:before {
  content: "\e065";
}
.glyphicon-share:before {
  content: "\e066";
}
.glyphicon-check:before {
  content: "\e067";
}
.glyphicon-move:before {
  content: "\e068";
}
.glyphicon-step-backward:before {
  content: "\e069";
}
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}
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}
.glyphicon-play:before {
  content: "\e072";
}
.glyphicon-pause:before {
  content: "\e073";
}
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  content: "\e074";
}
.glyphicon-forward:before {
  content: "\e075";
}
.glyphicon-fast-forward:before {
  content: "\e076";
}
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  content: "\e077";
}
.glyphicon-eject:before {
  content: "\e078";
}
.glyphicon-chevron-left:before {
  content: "\e079";
}
.glyphicon-chevron-right:before {
  content: "\e080";
}
.glyphicon-plus-sign:before {
  content: "\e081";
}
.glyphicon-minus-sign:before {
  content: "\e082";
}
.glyphicon-remove-sign:before {
  content: "\e083";
}
.glyphicon-ok-sign:before {
  content: "\e084";
}
.glyphicon-question-sign:before {
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}
.glyphicon-info-sign:before {
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}
.glyphicon-screenshot:before {
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}
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}
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}
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}
.glyphicon-arrow-left:before {
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}
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}
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}
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}
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}
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}
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}
.glyphicon-exclamation-sign:before {
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
.glyphicon-resize-horizontal:before {
  content: "\e120";
}
.glyphicon-hdd:before {
  content: "\e121";
}
.glyphicon-bullhorn:before {
  content: "\e122";
}
.glyphicon-bell:before {
  content: "\e123";
}
.glyphicon-certificate:before {
  content: "\e124";
}
.glyphicon-thumbs-up:before {
  content: "\e125";
}
.glyphicon-thumbs-down:before {
  content: "\e126";
}
.glyphicon-hand-right:before {
  content: "\e127";
}
.glyphicon-hand-left:before {
  content: "\e128";
}
.glyphicon-hand-up:before {
  content: "\e129";
}
.glyphicon-hand-down:before {
  content: "\e130";
}
.glyphicon-circle-arrow-right:before {
  content: "\e131";
}
.glyphicon-circle-arrow-left:before {
  content: "\e132";
}
.glyphicon-circle-arrow-up:before {
  content: "\e133";
}
.glyphicon-circle-arrow-down:before {
  content: "\e134";
}
.glyphicon-globe:before {
  content: "\e135";
}
.glyphicon-wrench:before {
  content: "\e136";
}
.glyphicon-tasks:before {
  content: "\e137";
}
.glyphicon-filter:before {
  content: "\e138";
}
.glyphicon-briefcase:before {
  content: "\e139";
}
.glyphicon-fullscreen:before {
  content: "\e140";
}
.glyphicon-dashboard:before {
  content: "\e141";
}
.glyphicon-paperclip:before {
  content: "\e142";
}
.glyphicon-heart-empty:before {
  content: "\e143";
}
.glyphicon-link:before {
  content: "\e144";
}
.glyphicon-phone:before {
  content: "\e145";
}
.glyphicon-pushpin:before {
  content: "\e146";
}
.glyphicon-usd:before {
  content: "\e148";
}
.glyphicon-gbp:before {
  content: "\e149";
}
.glyphicon-sort:before {
  content: "\e150";
}
.glyphicon-sort-by-alphabet:before {
  content: "\e151";
}
.glyphicon-sort-by-alphabet-alt:before {
  content: "\e152";
}
.glyphicon-sort-by-order:before {
  content: "\e153";
}
.glyphicon-sort-by-order-alt:before {
  content: "\e154";
}
.glyphicon-sort-by-attributes:before {
  content: "\e155";
}
.glyphicon-sort-by-attributes-alt:before {
  content: "\e156";
}
.glyphicon-unchecked:before {
  content: "\e157";
}
.glyphicon-expand:before {
  content: "\e158";
}
.glyphicon-collapse-down:before {
  content: "\e159";
}
.glyphicon-collapse-up:before {
  content: "\e160";
}
.glyphicon-log-in:before {
  content: "\e161";
}
.glyphicon-flash:before {
  content: "\e162";
}
.glyphicon-log-out:before {
  content: "\e163";
}
.glyphicon-new-window:before {
  content: "\e164";
}
.glyphicon-record:before {
  content: "\e165";
}
.glyphicon-save:before {
  content: "\e166";
}
.glyphicon-open:before {
  content: "\e167";
}
.glyphicon-saved:before {
  content: "\e168";
}
.glyphicon-import:before {
  content: "\e169";
}
.glyphicon-export:before {
  content: "\e170";
}
.glyphicon-send:before {
  content: "\e171";
}
.glyphicon-floppy-disk:before {
  content: "\e172";
}
.glyphicon-floppy-saved:before {
  content: "\e173";
}
.glyphicon-floppy-remove:before {
  content: "\e174";
}
.glyphicon-floppy-save:before {
  content: "\e175";
}
.glyphicon-floppy-open:before {
  content: "\e176";
}
.glyphicon-credit-card:before {
  content: "\e177";
}
.glyphicon-transfer:before {
  content: "\e178";
}
.glyphicon-cutlery:before {
  content: "\e179";
}
.glyphicon-header:before {
  content: "\e180";
}
.glyphicon-compressed:before {
  content: "\e181";
}
.glyphicon-earphone:before {
  content: "\e182";
}
.glyphicon-phone-alt:before {
  content: "\e183";
}
.glyphicon-tower:before {
  content: "\e184";
}
.glyphicon-stats:before {
  content: "\e185";
}
.glyphicon-sd-video:before {
  content: "\e186";
}
.glyphicon-hd-video:before {
  content: "\e187";
}
.glyphicon-subtitles:before {
  content: "\e188";
}
.glyphicon-sound-stereo:before {
  content: "\e189";
}
.glyphicon-sound-dolby:before {
  content: "\e190";
}
.glyphicon-sound-5-1:before {
  content: "\e191";
}
.glyphicon-sound-6-1:before {
  content: "\e192";
}
.glyphicon-sound-7-1:before {
  content: "\e193";
}
.glyphicon-copyright-mark:before {
  content: "\e194";
}
.glyphicon-registration-mark:before {
  content: "\e195";
}
.glyphicon-cloud-download:before {
  content: "\e197";
}
.glyphicon-cloud-upload:before {
  content: "\e198";
}
.glyphicon-tree-conifer:before {
  content: "\e199";
}
.glyphicon-tree-deciduous:before {
  content: "\e200";
}
.glyphicon-cd:before {
  content: "\e201";
}
.glyphicon-save-file:before {
  content: "\e202";
}
.glyphicon-open-file:before {
  content: "\e203";
}
.glyphicon-level-up:before {
  content: "\e204";
}
.glyphicon-copy:before {
  content: "\e205";
}
.glyphicon-paste:before {
  content: "\e206";
}
.glyphicon-alert:before {
  content: "\e209";
}
.glyphicon-equalizer:before {
  content: "\e210";
}
.glyphicon-king:before {
  content: "\e211";
}
.glyphicon-queen:before {
  content: "\e212";
}
.glyphicon-pawn:before {
  content: "\e213";
}
.glyphicon-bishop:before {
  content: "\e214";
}
.glyphicon-knight:before {
  content: "\e215";
}
.glyphicon-baby-formula:before {
  content: "\e216";
}
.glyphicon-tent:before {
  content: "\26fa";
}
.glyphicon-blackboard:before {
  content: "\e218";
}
.glyphicon-bed:before {
  content: "\e219";
}
.glyphicon-apple:before {
  content: "\f8ff";
}
.glyphicon-erase:before {
  content: "\e221";
}
.glyphicon-hourglass:before {
  content: "\231b";
}
.glyphicon-lamp:before {
  content: "\e223";
}
.glyphicon-duplicate:before {
  content: "\e224";
}
.glyphicon-piggy-bank:before {
  content: "\e225";
}
.glyphicon-scissors:before {
  content: "\e226";
}
.glyphicon-bitcoin:before {
  content: "\e227";
}
.glyphicon-btc:before {
  content: "\e227";
}
.glyphicon-xbt:before {
  content: "\e227";
}
.glyphicon-yen:before {
  content: "\00a5";
}
.glyphicon-jpy:before {
  content: "\00a5";
}
.glyphicon-ruble:before {
  content: "\20bd";
}
.glyphicon-rub:before {
  content: "\20bd";
}
.glyphicon-scale:before {
  content: "\e230";
}
.glyphicon-ice-lolly:before {
  content: "\e231";
}
.glyphicon-ice-lolly-tasted:before {
  content: "\e232";
}
.glyphicon-education:before {
  content: "\e233";
}
.glyphicon-option-horizontal:before {
  content: "\e234";
}
.glyphicon-option-vertical:before {
  content: "\e235";
}
.glyphicon-menu-hamburger:before {
  content: "\e236";