/*!
*
* IPython notebook
*
*/
/* CSS font colors for translated ANSI escape sequences */
/* The color values are a mix of
http://www.xcolors.net/dl/baskerville-ivorylight and
http://www.xcolors.net/dl/euphrasia */
.ansi-black-fg {
color: #3E424D;
}
.ansi-black-bg {
background-color: #3E424D;
}
.ansi-black-intense-fg {
color: #282C36;
}
.ansi-black-intense-bg {
background-color: #282C36;
}
.ansi-red-fg {
color: #E75C58;
}
.ansi-red-bg {
background-color: #E75C58;
}
.ansi-red-intense-fg {
color: #B22B31;
}
.ansi-red-intense-bg {
background-color: #B22B31;
}
.ansi-green-fg {
color: #00A250;
}
.ansi-green-bg {
background-color: #00A250;
}
.ansi-green-intense-fg {
color: #007427;
}
.ansi-green-intense-bg {
background-color: #007427;
}
.ansi-yellow-fg {
color: #DDB62B;
}
.ansi-yellow-bg {
background-color: #DDB62B;
}
.ansi-yellow-intense-fg {
color: #B27D12;
}
.ansi-yellow-intense-bg {
background-color: #B27D12;
}
.ansi-blue-fg {
color: #208FFB;
}
.ansi-blue-bg {
background-color: #208FFB;
}
.ansi-blue-intense-fg {
color: #0065CA;
}
.ansi-blue-intense-bg {
background-color: #0065CA;
}
.ansi-magenta-fg {
color: #D160C4;
}
.ansi-magenta-bg {
background-color: #D160C4;
}
.ansi-magenta-intense-fg {
color: #A03196;
}
.ansi-magenta-intense-bg {
background-color: #A03196;
}
.ansi-cyan-fg {
color: #60C6C8;
}
.ansi-cyan-bg {
background-color: #60C6C8;
}
.ansi-cyan-intense-fg {
color: #258F8F;
}
.ansi-cyan-intense-bg {
background-color: #258F8F;
}
.ansi-white-fg {
color: #C5C1B4;
}
.ansi-white-bg {
background-color: #C5C1B4;
}
.ansi-white-intense-fg {
color: #A1A6B2;
}
.ansi-white-intense-bg {
background-color: #A1A6B2;
}
.ansi-default-inverse-fg {
color: #FFFFFF;
}
.ansi-default-inverse-bg {
background-color: #000000;
}
.ansi-bold {
font-weight: bold;
}
.ansi-underline {
text-decoration: underline;
}
/* The following styles are deprecated an will be removed in a future version */
.ansibold {
font-weight: bold;
}
.ansi-inverse {
outline: 0.5px dotted;
}
/* use dark versions for foreground, to improve visibility */
.ansiblack {
color: black;
}
.ansired {
color: darkred;
}
.ansigreen {
color: darkgreen;
}
.ansiyellow {
color: #c4a000;
}
.ansiblue {
color: darkblue;
}
.ansipurple {
color: darkviolet;
}
.ansicyan {
color: steelblue;
}
.ansigray {
color: gray;
}
/* and light for background, for the same reason */
.ansibgblack {
background-color: black;
}
.ansibgred {
background-color: red;
}
.ansibggreen {
background-color: green;
}
.ansibgyellow {
background-color: yellow;
}
.ansibgblue {
background-color: blue;
}
.ansibgpurple {
background-color: magenta;
}
.ansibgcyan {
background-color: cyan;
}
.ansibggray {
background-color: gray;
}
div.cell {
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: vertical;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: vertical;
-moz-box-align: stretch;
display: box;
box-orient: vertical;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: column;
align-items: stretch;
border-radius: 2px;
box-sizing: border-box;
-moz-box-sizing: border-box;
-webkit-box-sizing: border-box;
border-width: 1px;
border-style: solid;
border-color: transparent;
width: 100%;
padding: 5px;
/* This acts as a spacer between cells, that is outside the border */
margin: 0px;
outline: none;
position: relative;
overflow: visible;
}
div.cell:before {
position: absolute;
display: block;
top: -1px;
left: -1px;
width: 5px;
height: calc(100% + 2px);
content: ”;
background: transparent;
}
div.cell.jupyter-soft-selected {
border-left-color: #E3F2FD;
border-left-width: 1px;
padding-left: 5px;
border-right-color: #E3F2FD;
border-right-width: 1px;
background: #E3F2FD;
}
@media print {
div.cell.jupyter-soft-selected {
border-color: transparent;
}
}
div.cell.selected,
div.cell.selected.jupyter-soft-selected {
border-color: #ababab;
}
div.cell.selected:before,
div.cell.selected.jupyter-soft-selected:before {
position: absolute;
display: block;
top: -1px;
left: -1px;
width: 5px;
height: calc(100% + 2px);
content: ”;
background: #42A5F5;
}
@media print {
div.cell.selected,
div.cell.selected.jupyter-soft-selected {
border-color: transparent;
}
}
.edit_mode div.cell.selected {
border-color: #66BB6A;
}
.edit_mode div.cell.selected:before {
position: absolute;
display: block;
top: -1px;
left: -1px;
width: 5px;
height: calc(100% + 2px);
content: ”;
background: #66BB6A;
}
@media print {
.edit_mode div.cell.selected {
border-color: transparent;
}
}
.prompt {
/* This needs to be wide enough for 3 digit prompt numbers: In[100]: */
min-width: 14ex;
/* This padding is tuned to match the padding on the CodeMirror editor. */
padding: 0.4em;
margin: 0px;
font-family: monospace;
text-align: right;
/* This has to match that of the the CodeMirror class line-height below */
line-height: 1.21429em;
/* Don’t highlight prompt number selection */
-webkit-touch-callout: none;
-webkit-user-select: none;
-khtml-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
/* Use default cursor */
cursor: default;
}
@media (max-width: 540px) {
.prompt {
text-align: left;
}
}
div.inner_cell {
min-width: 0;
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: vertical;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: vertical;
-moz-box-align: stretch;
display: box;
box-orient: vertical;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: column;
align-items: stretch;
/* Old browsers */
-webkit-box-flex: 1;
-moz-box-flex: 1;
box-flex: 1;
/* Modern browsers */
flex: 1;
}
/* input_area and input_prompt must match in top border and margin for alignment */
div.input_area {
border: 1px solid #cfcfcf;
border-radius: 2px;
background: #f7f7f7;
line-height: 1.21429em;
}
/* This is needed so that empty prompt areas can collapse to zero height when there
is no content in the output_subarea and the prompt. The main purpose of this is
to make sure that empty JavaScript output_subareas have no height. */
div.prompt:empty {
padding-top: 0;
padding-bottom: 0;
}
div.unrecognized_cell {
padding: 5px 5px 5px 0px;
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: horizontal;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: horizontal;
-moz-box-align: stretch;
display: box;
box-orient: horizontal;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: row;
align-items: stretch;
}
div.unrecognized_cell .inner_cell {
border-radius: 2px;
padding: 5px;
font-weight: bold;
color: red;
border: 1px solid #cfcfcf;
background: #eaeaea;
}
div.unrecognized_cell .inner_cell a {
color: inherit;
text-decoration: none;
}
div.unrecognized_cell .inner_cell a:hover {
color: inherit;
text-decoration: none;
}
@media (max-width: 540px) {
div.unrecognized_cell > div.prompt {
display: none;
}
}
div.code_cell {
/* avoid page breaking on code cells when printing */
}
@media print {
div.code_cell {
page-break-inside: avoid;
}
}
/* any special styling for code cells that are currently running goes here */
div.input {
page-break-inside: avoid;
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: horizontal;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: horizontal;
-moz-box-align: stretch;
display: box;
box-orient: horizontal;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: row;
align-items: stretch;
}
@media (max-width: 540px) {
div.input {
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: vertical;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: vertical;
-moz-box-align: stretch;
display: box;
box-orient: vertical;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: column;
align-items: stretch;
}
}
/* input_area and input_prompt must match in top border and margin for alignment */
div.input_prompt {
color: #303F9F;
border-top: 1px solid transparent;
}
div.input_area > div.highlight {
margin: 0.4em;
border: none;
padding: 0px;
background-color: transparent;
}
div.input_area > div.highlight > pre {
margin: 0px;
border: none;
padding: 0px;
background-color: transparent;
}
/* The following gets added to the if it is detected that the user has a
* monospace font with inconsistent normal/bold/italic height. See
* notebookmain.js. Such fonts will have keywords vertically offset with
* respect to the rest of the text. The user should select a better font.
* See: https://github.com/ipython/ipython/issues/1503
*
* .CodeMirror span {
* vertical-align: bottom;
* }
*/
.CodeMirror {
line-height: 1.21429em;
/* Changed from 1em to our global default */
font-size: 14px;
height: auto;
/* Changed to auto to autogrow */
background: none;
/* Changed from white to allow our bg to show through */
}
.CodeMirror-scroll {
/* The CodeMirror docs are a bit fuzzy on if overflow-y should be hidden or visible.*/
/* We have found that if it is visible, vertical scrollbars appear with font size changes.*/
overflow-y: hidden;
overflow-x: auto;
}
.CodeMirror-lines {
/* In CM2, this used to be 0.4em, but in CM3 it went to 4px. We need the em value because */
/* we have set a different line-height and want this to scale with that. */
/* Note that this should set vertical padding only, since CodeMirror assumes
that horizontal padding will be set on CodeMirror pre */
padding: 0.4em 0;
}
.CodeMirror-linenumber {
padding: 0 8px 0 4px;
}
.CodeMirror-gutters {
border-bottom-left-radius: 2px;
border-top-left-radius: 2px;
}
.CodeMirror pre {
/* In CM3 this went to 4px from 0 in CM2. This sets horizontal padding only,
use .CodeMirror-lines for vertical */
padding: 0 0.4em;
border: 0;
border-radius: 0;
}
.CodeMirror-cursor {
border-left: 1.4px solid black;
}
@media screen and (min-width: 2138px) and (max-width: 4319px) {
.CodeMirror-cursor {
border-left: 2px solid black;
}
}
@media screen and (min-width: 4320px) {
.CodeMirror-cursor {
border-left: 4px solid black;
}
}
/*
Original style from softwaremaniacs.org (c) Ivan Sagalaev
Adapted from GitHub theme
*/
.highlight-base {
color: #000;
}
.highlight-variable {
color: #000;
}
.highlight-variable-2 {
color: #1a1a1a;
}
.highlight-variable-3 {
color: #333333;
}
.highlight-string {
color: #BA2121;
}
.highlight-comment {
color: #408080;
font-style: italic;
}
.highlight-number {
color: #080;
}
.highlight-atom {
color: #88F;
}
.highlight-keyword {
color: #008000;
font-weight: bold;
}
.highlight-builtin {
color: #008000;
}
.highlight-error {
color: #f00;
}
.highlight-operator {
color: #AA22FF;
font-weight: bold;
}
.highlight-meta {
color: #AA22FF;
}
/* previously not defined, copying from default codemirror */
.highlight-def {
color: #00f;
}
.highlight-string-2 {
color: #f50;
}
.highlight-qualifier {
color: #555;
}
.highlight-bracket {
color: #997;
}
.highlight-tag {
color: #170;
}
.highlight-attribute {
color: #00c;
}
.highlight-header {
color: blue;
}
.highlight-quote {
color: #090;
}
.highlight-link {
color: #00c;
}
/* apply the same style to codemirror */
.cm-s-ipython span.cm-keyword {
color: #008000;
font-weight: bold;
}
.cm-s-ipython span.cm-atom {
color: #88F;
}
.cm-s-ipython span.cm-number {
color: #080;
}
.cm-s-ipython span.cm-def {
color: #00f;
}
.cm-s-ipython span.cm-variable {
color: #000;
}
.cm-s-ipython span.cm-operator {
color: #AA22FF;
font-weight: bold;
}
.cm-s-ipython span.cm-variable-2 {
color: #1a1a1a;
}
.cm-s-ipython span.cm-variable-3 {
color: #333333;
}
.cm-s-ipython span.cm-comment {
color: #408080;
font-style: italic;
}
.cm-s-ipython span.cm-string {
color: #BA2121;
}
.cm-s-ipython span.cm-string-2 {
color: #f50;
}
.cm-s-ipython span.cm-meta {
color: #AA22FF;
}
.cm-s-ipython span.cm-qualifier {
color: #555;
}
.cm-s-ipython span.cm-builtin {
color: #008000;
}
.cm-s-ipython span.cm-bracket {
color: #997;
}
.cm-s-ipython span.cm-tag {
color: #170;
}
.cm-s-ipython span.cm-attribute {
color: #00c;
}
.cm-s-ipython span.cm-header {
color: blue;
}
.cm-s-ipython span.cm-quote {
color: #090;
}
.cm-s-ipython span.cm-link {
color: #00c;
}
.cm-s-ipython span.cm-error {
color: #f00;
}
.cm-s-ipython span.cm-tab {
background: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAMCAYAAAAkuj5RAAAAAXNSR0IArs4c6QAAAGFJREFUSMft1LsRQFAQheHPowAKoACx3IgEKtaEHujDjORSgWTH/ZOdnZOcM/sgk/kFFWY0qV8foQwS4MKBCS3qR6ixBJvElOobYAtivseIE120FaowJPN75GMu8j/LfMwNjh4HUpwg4LUAAAAASUVORK5CYII=);
background-position: right;
background-repeat: no-repeat;
}
div.output_wrapper {
/* this position must be relative to enable descendents to be absolute within it */
position: relative;
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: vertical;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: vertical;
-moz-box-align: stretch;
display: box;
box-orient: vertical;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: column;
align-items: stretch;
z-index: 1;
}
/* class for the output area when it should be height-limited */
div.output_scroll {
/* ideally, this would be max-height, but FF barfs all over that */
height: 24em;
/* FF needs this *and the wrapper* to specify full width, or it will shrinkwrap */
width: 100%;
overflow: auto;
border-radius: 2px;
-webkit-box-shadow: inset 0 2px 8px rgba(0, 0, 0, 0.8);
box-shadow: inset 0 2px 8px rgba(0, 0, 0, 0.8);
display: block;
}
/* output div while it is collapsed */
div.output_collapsed {
margin: 0px;
padding: 0px;
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: vertical;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: vertical;
-moz-box-align: stretch;
display: box;
box-orient: vertical;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: column;
align-items: stretch;
}
div.out_prompt_overlay {
height: 100%;
padding: 0px 0.4em;
position: absolute;
border-radius: 2px;
}
div.out_prompt_overlay:hover {
/* use inner shadow to get border that is computed the same on WebKit/FF */
-webkit-box-shadow: inset 0 0 1px #000;
box-shadow: inset 0 0 1px #000;
background: rgba(240, 240, 240, 0.5);
}
div.output_prompt {
color: #D84315;
}
/* This class is the outer container of all output sections. */
div.output_area {
padding: 0px;
page-break-inside: avoid;
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: horizontal;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: horizontal;
-moz-box-align: stretch;
display: box;
box-orient: horizontal;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: row;
align-items: stretch;
}
div.output_area .MathJax_Display {
text-align: left !important;
}
div.output_area
div.output_area
div.output_area img,
div.output_area svg {
max-width: 100%;
height: auto;
}
div.output_area img.unconfined,
div.output_area svg.unconfined {
max-width: none;
}
div.output_area .mglyph > img {
max-width: none;
}
/* This is needed to protect the pre formating from global settings such
as that of bootstrap */
.output {
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: vertical;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: vertical;
-moz-box-align: stretch;
display: box;
box-orient: vertical;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: column;
align-items: stretch;
}
@media (max-width: 540px) {
div.output_area {
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: vertical;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: vertical;
-moz-box-align: stretch;
display: box;
box-orient: vertical;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: column;
align-items: stretch;
}
}
div.output_area pre {
margin: 0;
padding: 1px 0 1px 0;
border: 0;
vertical-align: baseline;
color: black;
background-color: transparent;
border-radius: 0;
}
/* This class is for the output subarea inside the output_area and after
the prompt div. */
div.output_subarea {
overflow-x: auto;
padding: 0.4em;
/* Old browsers */
-webkit-box-flex: 1;
-moz-box-flex: 1;
box-flex: 1;
/* Modern browsers */
flex: 1;
max-width: calc(100% – 14ex);
}
div.output_scroll div.output_subarea {
overflow-x: visible;
}
/* The rest of the output_* classes are for special styling of the different
output types */
/* all text output has this class: */
div.output_text {
text-align: left;
color: #000;
/* This has to match that of the the CodeMirror class line-height below */
line-height: 1.21429em;
}
/* stdout/stderr are ‘text’ as well as ‘stream’, but execute_result/error are *not* streams */
div.output_stderr {
background: #fdd;
/* very light red background for stderr */
}
div.output_latex {
text-align: left;
}
/* Empty output_javascript divs should have no height */
div.output_javascript:empty {
padding: 0;
}
.js-error {
color: darkred;
}
/* raw_input styles */
div.raw_input_container {
line-height: 1.21429em;
padding-top: 5px;
}
pre.raw_input_prompt {
/* nothing needed here. */
}
input.raw_input {
font-family: monospace;
font-size: inherit;
color: inherit;
width: auto;
/* make sure input baseline aligns with prompt */
vertical-align: baseline;
/* padding + margin = 0.5em between prompt and cursor */
padding: 0em 0.25em;
margin: 0em 0.25em;
}
input.raw_input:focus {
box-shadow: none;
}
p.p-space {
margin-bottom: 10px;
}
div.output_unrecognized {
padding: 5px;
font-weight: bold;
color: red;
}
div.output_unrecognized a {
color: inherit;
text-decoration: none;
}
div.output_unrecognized a:hover {
color: inherit;
text-decoration: none;
}
.rendered_html {
color: #000;
/* any extras will just be numbers: */
}
.rendered_html :link {
text-decoration: underline;
}
.rendered_html :visited {
text-decoration: underline;
}
.rendered_html h1:first-child {
margin-top: 0.538em;
}
.rendered_html h2:first-child {
margin-top: 0.636em;
}
.rendered_html h3:first-child {
margin-top: 0.777em;
}
.rendered_html h4:first-child {
margin-top: 1em;
}
.rendered_html h5:first-child {
margin-top: 1em;
}
.rendered_html h6:first-child {
margin-top: 1em;
}
.rendered_html ul:not(.list-inline),
.rendered_html ol:not(.list-inline) {
padding-left: 2em;
}
.rendered_html * + ul {
margin-top: 1em;
}
.rendered_html * + ol {
margin-top: 1em;
}
.rendered_html pre,
.rendered_html tr,
.rendered_html th,
.rendered_html tbody tr:nth-child(odd) {
background: #f5f5f5;
}
.rendered_html tbody tr:hover {
background: rgba(66, 165, 245, 0.2);
}
.rendered_html * + table {
margin-top: 1em;
}
.rendered_html * + p {
margin-top: 1em;
}
.rendered_html * + img {
margin-top: 1em;
}
.rendered_html img,
.rendered_html img.unconfined,
.rendered_html * + .alert {
margin-top: 1em;
}
[dir=”rtl”]
div.text_cell {
/* Old browsers */
display: -webkit-box;
-webkit-box-orient: horizontal;
-webkit-box-align: stretch;
display: -moz-box;
-moz-box-orient: horizontal;
-moz-box-align: stretch;
display: box;
box-orient: horizontal;
box-align: stretch;
/* Modern browsers */
display: flex;
flex-direction: row;
align-items: stretch;
}
@media (max-width: 540px) {
div.text_cell > div.prompt {
display: none;
}
}
div.text_cell_render {
/*font-family: “Helvetica Neue”, Arial, Helvetica, Geneva, sans-serif;*/
outline: none;
resize: none;
width: inherit;
border-style: none;
padding: 0.5em 0.5em 0.5em 0.4em;
color: #000;
box-sizing: border-box;
-moz-box-sizing: border-box;
-webkit-box-sizing: border-box;
}
a.anchor-link:link {
text-decoration: none;
padding: 0px 20px;
visibility: hidden;
}
h1:hover .anchor-link,
h2:hover .anchor-link,
h3:hover .anchor-link,
h4:hover .anchor-link,
h5:hover .anchor-link,
h6:hover .anchor-link {
visibility: visible;
}
.text_cell.rendered .input_area {
display: none;
}
.text_cell.rendered
.text_cell.rendered .rendered_html tr,
.text_cell.rendered .rendered_html th,
.text_cell.rendered
.text_cell.unrendered .text_cell_render {
display: none;
}
.text_cell .dropzone .input_area {
border: 2px dashed #bababa;
margin: -1px;
}
.cm-header-1,
.cm-header-2,
.cm-header-3,
.cm-header-4,
.cm-header-5,
.cm-header-6 {
font-weight: bold;
font-family: “Helvetica Neue”, Helvetica, Arial, sans-serif;
}
.cm-header-1 {
font-size: 185.7%;
}
.cm-header-2 {
font-size: 157.1%;
}
.cm-header-3 {
font-size: 128.6%;
}
.cm-header-4 {
font-size: 110%;
}
.cm-header-5 {
font-size: 100%;
font-style: italic;
}
.cm-header-6 {
font-size: 100%;
font-style: italic;
}
.highlight pre .hll { background-color: #ffffcc }
.highlight pre { background: #f8f8f8; }
.highlight pre .c { color: #408080; font-style: italic } /* Comment */
.highlight pre .err { border: 1px solid #FF0000 } /* Error */
.highlight pre .k { color: #008000; font-weight: bold } /* Keyword */
.highlight pre .o { color: #666666 } /* Operator */
.highlight pre .ch { color: #408080; font-style: italic } /* Comment.Hashbang */
.highlight pre .cm { color: #408080; font-style: italic } /* Comment.Multiline */
.highlight pre .cp { color: #BC7A00 } /* Comment.Preproc */
.highlight pre .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */
.highlight pre .c1 { color: #408080; font-style: italic } /* Comment.Single */
.highlight pre .cs { color: #408080; font-style: italic } /* Comment.Special */
.highlight pre .gd { color: #A00000 } /* Generic.Deleted */
.highlight pre .ge { font-style: italic } /* Generic.Emph */
.highlight pre .gr { color: #FF0000 } /* Generic.Error */
.highlight pre .gh { color: #000080; font-weight: bold } /* Generic.Heading */
.highlight pre .gi { color: #00A000 } /* Generic.Inserted */
.highlight pre .go { color: #888888 } /* Generic.Output */
.highlight pre .gp { color: #000080; font-weight: bold } /* Generic.Prompt */
.highlight pre .gs { font-weight: bold } /* Generic.Strong */
.highlight pre .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
.highlight pre .gt { color: #0044DD } /* Generic.Traceback */
.highlight pre .kc { color: #008000; font-weight: bold } /* Keyword.Constant */
.highlight pre .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */
.highlight pre .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */
.highlight pre .kp { color: #008000 } /* Keyword.Pseudo */
.highlight pre .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */
.highlight pre .kt { color: #B00040 } /* Keyword.Type */
.highlight pre .m { color: #666666 } /* Literal.Number */
.highlight pre .s { color: #BA2121 } /* Literal.String */
.highlight pre .na { color: #7D9029 } /* Name.Attribute */
.highlight pre .nb { color: #008000 } /* Name.Builtin */
.highlight pre .nc { color: #0000FF; font-weight: bold } /* Name.Class */
.highlight pre .no { color: #880000 } /* Name.Constant */
.highlight pre .nd { color: #AA22FF } /* Name.Decorator */
.highlight pre .ni { color: #999999; font-weight: bold } /* Name.Entity */
.highlight pre .ne { color: #D2413A; font-weight: bold } /* Name.Exception */
.highlight pre .nf { color: #0000FF } /* Name.Function */
.highlight pre .nl { color: #A0A000 } /* Name.Label */
.highlight pre .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */
.highlight pre .nt { color: #008000; font-weight: bold } /* Name.Tag */
.highlight pre .nv { color: #19177C } /* Name.Variable */
.highlight pre .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */
.highlight pre .w { color: #bbbbbb } /* Text.Whitespace */
.highlight pre .mb { color: #666666 } /* Literal.Number.Bin */
.highlight pre .mf { color: #666666 } /* Literal.Number.Float */
.highlight pre .mh { color: #666666 } /* Literal.Number.Hex */
.highlight pre .mi { color: #666666 } /* Literal.Number.Integer */
.highlight pre .mo { color: #666666 } /* Literal.Number.Oct */
.highlight pre .sa { color: #BA2121 } /* Literal.String.Affix */
.highlight pre .sb { color: #BA2121 } /* Literal.String.Backtick */
.highlight pre .sc { color: #BA2121 } /* Literal.String.Char */
.highlight pre .dl { color: #BA2121 } /* Literal.String.Delimiter */
.highlight pre .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */
.highlight pre .s2 { color: #BA2121 } /* Literal.String.Double */
.highlight pre .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */
.highlight pre .sh { color: #BA2121 } /* Literal.String.Heredoc */
.highlight pre .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */
.highlight pre .sx { color: #008000 } /* Literal.String.Other */
.highlight pre .sr { color: #BB6688 } /* Literal.String.Regex */
.highlight pre .s1 { color: #BA2121 } /* Literal.String.Single */
.highlight pre .ss { color: #19177C } /* Literal.String.Symbol */
.highlight pre .bp { color: #008000 } /* Name.Builtin.Pseudo */
.highlight pre .fm { color: #0000FF } /* Name.Function.Magic */
.highlight pre .vc { color: #19177C } /* Name.Variable.Class */
.highlight pre .vg { color: #19177C } /* Name.Variable.Global */
.highlight pre .vi { color: #19177C } /* Name.Variable.Instance */
.highlight pre .vm { color: #19177C } /* Name.Variable.Magic */
.highlight pre .il { color: #666666 } /* Literal.Number.Integer.Long */
Gated Multimodal Units for Information Fusion¶
Deep learning has proven its superiority in many domains, in a variety of tasks such as image classification and text generation. Dealing with tasks that involve inputs from multiple modalities is an interesting research area.
The Gated Multimodal Unit (GMU) is a new building block proposed by a recent paper, which is presented in ICLR 2017 as a workshop. The goal of this building block is to fuse information from multiple different modalities in a smart way.
In this post I’ll describe the GMU, and illustrate how it works on a toy data set.
The architecture¶
Given two representations of different modalities, $x_v$ and $x_t$ (visual and textual modalities for instance), the GMU block performs a form of self attention:
The equations describing the GMU are relatively simple:
(1) $h_v = tanh(W_v \cdot x_v)$
(2) $h_t = tanh(W_t \cdot x_t)$
(3) $z = \sigma(W_z \cdot [x_v, x_t])$
(4) $h = z \cdot h_v + (1 – z) \cdot h_t$
(1) + (2) are transforming the representations into different representations, which are then attended in (4) according to $z$ which is calculated in (3). Since $z$ is a function of $x_v$ and $x_t$, it means we’re dealing with a self attention mechanism.
The intuition behind the GMU is that it uses the representations themselves to understand which of the modalities should affect the prediction. Consider the task of predicting the gender of a photographed person accompanied by a recording of his voice. If the recording of a given example is too noisy, the model should learn to use only the image in that example.
Synthetic data¶
In the paper they describe a nice synthetic data set which demonstrates how the GMU works.
Here we’ll implement the same data set, and find out for ourselves whether or not the GMU actually works (spoiler alert: it does).
First, let’s do the imports:
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(41)
tf.set_random_seed(41)
%matplotlib inline
Generate the data¶
Don’t let the graph scare you – later on you’ll find a visualization of the data generated by this graph.
Basically what the graph says is that the target class $C$ depicts the values of the modalities $y_v$ and $y_t$ – with some randomness of course.
In the next step the random variable $M$ decides which of the inputs $y_v$, $y_t$ to ignore, and instead to use a source of noise $\hat{y}_v$, $\hat{y}_t$.
In the end, $x_v$ and $x_t$ contain either the real source of information which can describe the target class $C$, or random noise.
The goal of the GMU block is to successfully find out which one of the sources is the informative one given a specific example, and to give all the attention to that source.
n = 400
p_c = 0.5
p_m = 0.5
mu_v_0 = 1.0
mu_v_1 = 8.0
mu_v_noise = 17.0
mu_t_0 = 13.0
mu_t_1 = 19.0
mu_t_noise = 10.0
c = np.random.binomial(n=1, p=p_c, size=n)
m = np.random.binomial(n=1, p=p_m, size=n)
y_v = np.random.randn(n) + np.where(c == 0, mu_v_0, mu_v_1)
y_t = np.random.randn(n) + np.where(c == 0, mu_t_0, mu_t_1)
y_v_noise = np.random.randn(n) + mu_v_noise
y_t_noise = np.random.randn(n) + mu_t_noise
x_v = m * y_v + (1 - m) * y_v_noise
x_t = m * y_t_noise + (1 - m) * y_t
# if we don't normalize the inputs the model will have hard time training
x_v = x_v - x_v.mean()
x_t = x_t - x_t.mean()
plt.scatter(x_v, x_t, c=np.where(c == 0, 'blue', 'red'))
plt.xlabel('visual modality')
plt.ylabel('textual modality');
Create the model¶
I’ll implement a basic version of the GMU – just to make it easier to comprehend.
Generalizing the code to handle more than two modalities is straightforward.
NUM_CLASSES = 2
HIDDEN_STATE_DIM = 1 # using 1 as dimensionality makes it easy to plot z, as we'll do later on
visual = tf.placeholder(tf.float32, shape=[None])
textual = tf.placeholder(tf.float32, shape=[None])
target = tf.placeholder(tf.int32, shape=[None])
h_v = tf.layers.dense(tf.reshape(visual, [-1, 1]),
HIDDEN_STATE_DIM,
activation=tf.nn.tanh)
h_t = tf.layers.dense(tf.reshape(textual, [-1, 1]),
HIDDEN_STATE_DIM,
activation=tf.nn.tanh)
z = tf.layers.dense(tf.stack([visual, textual], axis=1),
HIDDEN_STATE_DIM,
activation=tf.nn.sigmoid)
h = z * h_v + (1 - z) * h_t
logits = tf.layers.dense(h, NUM_CLASSES)
prob = tf.nn.sigmoid(logits)
loss = tf.losses.sigmoid_cross_entropy(multi_class_labels=tf.one_hot(target, depth=2),
logits=logits)
optimizer = tf.train.AdamOptimizer(learning_rate=0.1)
train_op = optimizer.minimize(loss)
Train the model¶
sess = tf.Session()
def train(train_op, loss):
sess.run(tf.global_variables_initializer())
losses = []
for epoch in xrange(100):
_, l = sess.run([train_op, loss], {visual: x_v,
textual: x_t,
target: c})
losses.append(l)
plt.plot(losses, label='loss')
plt.title('loss')
train(train_op, loss)
Inspect results¶
The loss is looking good.
Let’s look what $z$ and the predictions look like. The following visualizations appear in the paper as well.
# create a mesh of points which will be used for inference
resolution = 1000
vs = np.linspace(x_v.min(), x_v.max(), resolution)
ts = np.linspace(x_t.min(), x_t.max(), resolution)
vs, ts = np.meshgrid(vs, ts)
vs = np.ravel(vs)
ts = np.ravel(ts)
zs, probs = sess.run([z, prob], {visual: vs, textual: ts})
def plot_evaluations(evaluation, cmap, title, labels):
plt.scatter(((x_v - x_v.min()) * resolution / (x_v - x_v.min()).max()),
((x_t - x_t.min()) * resolution / (x_t - x_t.min()).max()),
c=np.where(c == 0, 'blue', 'red'))
plt.title(title, fontsize=14)
plt.xlabel('visual modality')
plt.ylabel('textual modality')
plt.imshow(evaluation.reshape([resolution, resolution]),
origin='lower',
cmap=cmap,
alpha=0.5)
cbar = plt.colorbar(ticks=[evaluation.min(), evaluation.max()])
cbar.ax.set_yticklabels(labels)
cbar.ax.tick_params(labelsize=13)
plt.figure(figsize=(20, 7))
plt.subplot(121)
plot_evaluations(zs,
cmap='binary_r',
title='which modality the model attends',
labels=['$x_t$ is important', '$x_v$ is important'])
plt.subplot(122)
plot_evaluations(probs[:, 1],
cmap='bwr',
title='$C$ prediction',
labels=['$C=0$', '$C=1$'])
We can see $z$ behaves exactly as we want (left figure). What’s nice about it is that the class of points that reside far from the boundary line are predicted using practically only one of the modalities. It means the model learned when to ignore the modality that contains pure unpredictive noise.
Why not to use simple FF (Feed Forward)?¶
If we ignore the data generating process and just look at the data points, clearly there are 4 distinct clusters.
These clusters aren’t linearly separable. While the GMU gives capacity to the model in order to explain this non-linear behaviour, one could just throw another layer to the mixture instead, thus solving the problem with plain feed-forward (FF) network.
The universal approximation theorem states that a feed-forward network with a single hidden layer containing a finite number of neurons, can approximate continuous functions… (Wikipedia)
So indeed, for this contrived example a simple FF will do the job. However, the point in introducing new architectures (GMU in this case) is to introduce inductive bias that allows the training process to take advantage of prior knowledge we have about the problem.
Conclusion¶
For real world problems involving multiple modalities, the authors claim the GMU achieves superior performance. They show cased their approach using the task of identifying a movie genre based on its plot and its poster.
GMU is easy to implement, and it may be worthwhile to keep it in your tool belt in case you need to train a model to use multiple modalities as input. To this end, you can create a sub network for each modality. The sub networks need not be the same – you can for instance use a CNN for a visual modality and LSTM for a textual one. What matters is that each sub network outputs a dense representation of its modality. Then, feed these representations into a GMU block in order to fuse the information into one representation. The fused representation will be fed into another sub network whose output will be the final prediction.
if (!document.getElementById(‘mathjaxscript_pelican_#%@#$@#’)) {
var mathjaxscript = document.createElement(‘script’);
mathjaxscript.id = ‘mathjaxscript_pelican_#%@#$@#’;
mathjaxscript.type=”text/javascript”;
mathjaxscript.src=”//cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML”;
mathjaxscript[(window.opera ? “innerHTML” : “text”)] =
“MathJax.Hub.Config({” +
” config: [‘MMLorHTML.js’],” +
” TeX: { extensions: [‘AMSmath.js’,’AMSsymbols.js’,’noErrors.js’,’noUndefined.js’], equationNumbers: { autoNumber: ‘AMS’ } },” +
” jax: [‘input/TeX’,’input/MathML’,’output/HTML-CSS’],” +
” extensions: [‘tex2jax.js’,’mml2jax.js’,’MathMenu.js’,’MathZoom.js’],” +
” displayAlign: ‘center’,” +
” displayIndent: ‘0em’,” +
” showMathMenu: true,” +
” tex2jax: { ” +
” inlineMath: [ [‘$’,’$’] ], ” +
” displayMath: [ [‘$$’,’$$’] ],” +
” processEscapes: true,” +
” preview: ‘TeX’,” +
” }, ” +
” ‘HTML-CSS’: { ” +
” linebreaks: { automatic: true, width: ‘95% container’ }, ” +
” styles: { ‘.MathJax_Display, .MathJax .mo, .MathJax .mi, .MathJax .mn’: {color: ‘black ! important’} }” +
” } ” +
“}); “;
(document.body || document.getElementsByTagName(‘head’)[0]).appendChild(mathjaxscript);
}
Discover more from reviewer4you.com
Subscribe to get the latest posts to your email.
