Datasets:

tfrere
/

collab-editor-data

Modalities:

Text

Formats:

Size:

Libraries:

Dataset card Data Studio Files Files and versions

xet

Community

collab-editor-data

File size: 45,904 Bytes

7049f20

<!DOCTYPE html>
<html lang="en" data-theme="dark">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Scaling Laws for Neural Language Models</title>
  <meta name="description" content="An empirical study of scaling behavior across model size, data, and compute budgets.">
  <meta name="author" content="Alice Martin, Bob Chen, Carol Wu">

  <!-- Open Graph -->
  <meta property="og:type" content="article">
  <meta property="og:title" content="Scaling Laws for Neural Language Models">
  <meta property="og:description" content="An empirical study of scaling behavior across model size, data, and compute budgets.">
  
  <meta property="article:published_time" content="Apr. 13, 2026">
  <meta property="article:author" content="Alice Martin">
  <meta property="article:author" content="Bob Chen">
  <meta property="article:author" content="Carol Wu">

  <!-- Twitter Card -->
  <meta name="twitter:card" content="summary_large_image">
  <meta name="twitter:title" content="Scaling Laws for Neural Language Models">
  <meta name="twitter:description" content="An empirical study of scaling behavior across model size, data, and compute budgets.">
  

  <!-- KaTeX CSS -->
  <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/katex.min.css"
        integrity="sha384-zh0CIslj3dQfMxK3pZnPJAb3bprHitCE2vBz9TyOTICAn3fso5GYa90qPNMBclov"
        crossorigin="anonymous">

  <!-- highlight.js theme -->
  <link rel="stylesheet" href="https://cdn.jsdelivr.net/gh/highlightjs/cdn-release@11.9.0/build/styles/github-dark.min.css">

  <style>
/* -----------------------------------------------------------------------
   Design tokens - Light / Dark theming
   
   Usage: var(--token-name)
   Toggle: data-theme="light" or data-theme="dark" on <html>
   Default: follows prefers-color-scheme
   ----------------------------------------------------------------------- */

:root,
[data-theme="light"] {
  --text-primary: #1a1a1a;
  --text-secondary: #555;
  --text-tertiary: #888;
  --text-faint: #aaa;
  --text-heading: #111;
  --text-heading-secondary: #222;
  --text-strong: #000;

  --bg-primary: #ffffff;
  --bg-secondary: #f7f7f7;
  --bg-tertiary: #f0f0f0;
  --bg-hover: rgba(0, 0, 0, 0.03);
  --bg-overlay: rgba(0, 0, 0, 0.5);
  --bg-tooltip: #ffffff;
  --bg-surface: #ffffff;
  --bg-code: rgba(0, 0, 0, 0.04);
  --bg-code-block: #fafafa;

  --border: #e0e0e0;
  --border-light: #eeeeee;
  --border-focus: rgba(124, 58, 237, 0.5);

  --accent: #7c3aed;
  --accent-light: #958DF1;
  --accent-bg: rgba(124, 58, 237, 0.08);
  --accent-bg-hover: rgba(124, 58, 237, 0.15);
  --accent-text: #6d28d9;

  --code-text: #d63384;
  --code-comment: #6a737d;
  --code-keyword: #8250df;
  --code-string: #0a6640;
  --code-number: #b35900;
  --code-variable: #d63384;
  --code-type: #b35900;
  --code-function: #0550ae;
  --code-tag: #d63384;
  --code-attr: #b35900;
  --code-symbol: #0a6640;
  --code-meta: #0550ae;
  --code-deletion: #d63384;

  --danger: #dc2626;
  --danger-bg: rgba(220, 38, 38, 0.08);
  --danger-bg-hover: rgba(220, 38, 38, 0.15);

  --shadow-sm: 0 1px 3px rgba(0, 0, 0, 0.08);
  --shadow-md: 0 4px 12px rgba(0, 0, 0, 0.1);
  --shadow-lg: 0 8px 30px rgba(0, 0, 0, 0.12);

  --katex-color: #1a1a1a;
}

[data-theme="dark"] {
  --text-primary: rgba(255, 255, 255, 0.85);
  --text-secondary: rgba(255, 255, 255, 0.5);
  --text-tertiary: rgba(255, 255, 255, 0.4);
  --text-faint: rgba(255, 255, 255, 0.25);
  --text-heading: #fff;
  --text-heading-secondary: rgba(255, 255, 255, 0.9);
  --text-strong: rgba(255, 255, 255, 0.95);

  --bg-primary: #0a0a0a;
  --bg-secondary: #1a1a1a;
  --bg-tertiary: #1e1e1e;
  --bg-hover: rgba(255, 255, 255, 0.03);
  --bg-overlay: rgba(0, 0, 0, 0.5);
  --bg-tooltip: #1e1e2e;
  --bg-surface: #1a1a1a;
  --bg-code: rgba(255, 255, 255, 0.06);
  --bg-code-block: rgba(255, 255, 255, 0.03);

  --border: rgba(255, 255, 255, 0.1);
  --border-light: rgba(255, 255, 255, 0.06);
  --border-focus: rgba(149, 141, 241, 0.5);

  --accent: #7c3aed;
  --accent-light: #958DF1;
  --accent-bg: rgba(149, 141, 241, 0.15);
  --accent-bg-hover: rgba(149, 141, 241, 0.25);
  --accent-text: #b4aef7;

  --code-text: #e06c75;
  --code-comment: #5c6370;
  --code-keyword: #c678dd;
  --code-string: #98c379;
  --code-number: #d19a66;
  --code-variable: #e06c75;
  --code-type: #e5c07b;
  --code-function: #61afef;
  --code-tag: #e06c75;
  --code-attr: #d19a66;
  --code-symbol: #56b6c2;
  --code-meta: #61afef;
  --code-deletion: #e06c75;

  --danger: #e06c75;
  --danger-bg: rgba(224, 108, 117, 0.12);
  --danger-bg-hover: rgba(224, 108, 117, 0.25);

  --shadow-sm: 0 1px 3px rgba(0, 0, 0, 0.3);
  --shadow-md: 0 4px 12px rgba(0, 0, 0, 0.4);
  --shadow-lg: 0 8px 30px rgba(0, 0, 0, 0.5);

  --katex-color: rgba(255, 255, 255, 0.85);
}

@media (prefers-color-scheme: dark) {
  :root:not([data-theme="light"]) {
    --text-primary: rgba(255, 255, 255, 0.85);
    --text-secondary: rgba(255, 255, 255, 0.5);
    --text-tertiary: rgba(255, 255, 255, 0.4);
    --text-faint: rgba(255, 255, 255, 0.25);
    --text-heading: #fff;
    --text-heading-secondary: rgba(255, 255, 255, 0.9);
    --text-strong: rgba(255, 255, 255, 0.95);

    --bg-primary: #0a0a0a;
    --bg-secondary: #1a1a1a;
    --bg-tertiary: #1e1e1e;
    --bg-hover: rgba(255, 255, 255, 0.03);
    --bg-overlay: rgba(0, 0, 0, 0.5);
    --bg-tooltip: #1e1e2e;
    --bg-surface: #1a1a1a;
    --bg-code: rgba(255, 255, 255, 0.06);
    --bg-code-block: rgba(255, 255, 255, 0.03);

    --border: rgba(255, 255, 255, 0.1);
    --border-light: rgba(255, 255, 255, 0.06);
    --border-focus: rgba(149, 141, 241, 0.5);

    --accent: #7c3aed;
    --accent-light: #958DF1;
    --accent-bg: rgba(149, 141, 241, 0.15);
    --accent-bg-hover: rgba(149, 141, 241, 0.25);
    --accent-text: #b4aef7;

    --code-text: #e06c75;
    --code-comment: #5c6370;
    --code-keyword: #c678dd;
    --code-string: #98c379;
    --code-number: #d19a66;
    --code-variable: #e06c75;
    --code-type: #e5c07b;
    --code-function: #61afef;
    --code-tag: #e06c75;
    --code-attr: #d19a66;
    --code-symbol: #56b6c2;
    --code-meta: #61afef;
    --code-deletion: #e06c75;

    --danger: #e06c75;
    --danger-bg: rgba(224, 108, 117, 0.12);
    --danger-bg-hover: rgba(224, 108, 117, 0.25);

    --shadow-sm: 0 1px 3px rgba(0, 0, 0, 0.3);
    --shadow-md: 0 4px 12px rgba(0, 0, 0, 0.4);
    --shadow-lg: 0 8px 30px rgba(0, 0, 0, 0.5);

    --katex-color: rgba(255, 255, 255, 0.85);
  }
}

/* -----------------------------------------------------------------------
   Article content styles
   
   Shared between editor and published version.
   Uses CSS variables from tokens.css for light/dark theming.
   ----------------------------------------------------------------------- */

/* Base typography */
.tiptap {
  outline: none;
  font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
  font-size: 1rem;
  line-height: 1.7;
  color: var(--text-primary);
  max-width: 780px;
  margin-left: auto;
  margin-right: auto;
  padding: 0 32px 0 64px;
  min-height: 100%;
  overflow-wrap: break-word;
  word-break: break-word;
}

.tiptap > *:first-child {
  margin-top: 0;
}

/* Headings */
.tiptap h1 {
  font-size: 2rem;
  font-weight: 700;
  color: var(--text-heading);
  line-height: 1.2;
  margin: 2em 0 0.4em;
  letter-spacing: -0.02em;
}

.tiptap h1:first-child {
  margin-top: 0;
}

.tiptap h2 {
  font-size: 1.5rem;
  font-weight: 600;
  color: var(--text-heading-secondary);
  line-height: 1.3;
  margin: 1.8em 0 0.4em;
  letter-spacing: -0.01em;
}

.tiptap h3 {
  font-size: 1.2rem;
  font-weight: 600;
  color: var(--text-primary);
  line-height: 1.4;
  margin: 1.5em 0 0.3em;
}

/* Paragraphs */
.tiptap p {
  margin: 0.5em 0;
}

/* Lists */
.tiptap ul,
.tiptap ol {
  padding-left: 1.5rem;
  margin: 0.5em 0;
}

.tiptap li {
  margin: 0.25em 0;
}

.tiptap li p {
  margin: 0.15em 0;
}

/* Blockquote */
.tiptap blockquote {
  border-left: 3px solid var(--border);
  padding-left: 1rem;
  margin: 1em 0;
  color: var(--text-secondary);
}

.tiptap blockquote p {
  margin: 0.4em 0;
}

/* Inline code */
.tiptap code {
  font-family: "SFMono-Regular", "Fira Code", "Fira Mono", Menlo, Consolas, monospace;
  background: var(--bg-code);
  padding: 0.15em 0.4em;
  border-radius: 4px;
  font-size: 0.88em;
  color: var(--code-text);
}

/* Code block */
.tiptap pre {
  background: var(--bg-code-block);
  border: 1px solid var(--border-light);
  border-radius: 8px;
  padding: 1rem 1.25rem;
  margin: 1em 0;
  overflow-x: auto;
}

.tiptap pre code {
  background: none;
  padding: 0;
  color: var(--text-secondary);
  font-size: 0.875rem;
  line-height: 1.6;
}

/* Syntax highlighting */
.tiptap pre code .hljs-comment,
.tiptap pre code .hljs-quote {
  color: var(--code-comment);
  font-style: italic;
}

.tiptap pre code .hljs-keyword,
.tiptap pre code .hljs-selector-tag,
.tiptap pre code .hljs-addition {
  color: var(--code-keyword);
}

.tiptap pre code .hljs-string,
.tiptap pre code .hljs-meta .hljs-string,
.tiptap pre code .hljs-regexp,
.tiptap pre code .hljs-doctag {
  color: var(--code-string);
}

.tiptap pre code .hljs-number,
.tiptap pre code .hljs-literal,
.tiptap pre code .hljs-bullet {
  color: var(--code-number);
}

.tiptap pre code .hljs-variable,
.tiptap pre code .hljs-template-variable,
.tiptap pre code .hljs-tag .hljs-attr {
  color: var(--code-variable);
}

.tiptap pre code .hljs-type,
.tiptap pre code .hljs-built_in,
.tiptap pre code .hljs-class .hljs-title,
.tiptap pre code .hljs-title.class_ {
  color: var(--code-type);
}

.tiptap pre code .hljs-function,
.tiptap pre code .hljs-title,
.tiptap pre code .hljs-section {
  color: var(--code-function);
}

.tiptap pre code .hljs-name,
.tiptap pre code .hljs-tag {
  color: var(--code-tag);
}

.tiptap pre code .hljs-attr {
  color: var(--code-attr);
}

.tiptap pre code .hljs-symbol,
.tiptap pre code .hljs-link {
  color: var(--code-symbol);
}

.tiptap pre code .hljs-meta,
.tiptap pre code .hljs-selector-id,
.tiptap pre code .hljs-selector-class {
  color: var(--code-meta);
}

.tiptap pre code .hljs-deletion {
  color: var(--code-deletion);
}

.tiptap pre code .hljs-emphasis {
  font-style: italic;
}

.tiptap pre code .hljs-strong {
  font-weight: 700;
}

/* Horizontal rule */
.tiptap hr {
  border: none;
  border-top: 1px solid var(--border);
  margin: 2em 0;
}

/* Tables */
.tiptap table {
  border-collapse: collapse;
  width: 100%;
  margin: 1em 0;
  overflow: hidden;
  border-radius: 6px;
  border: 1px solid var(--border-light);
}

.tiptap th,
.tiptap td {
  padding: 0.5rem 0.75rem;
  border: 1px solid var(--border-light);
  text-align: left;
  font-size: 0.875rem;
  min-width: 80px;
}

.tiptap th {
  background: var(--bg-code);
  color: var(--text-secondary);
  font-weight: 600;
  font-size: 0.8125rem;
  text-transform: uppercase;
  letter-spacing: 0.03em;
}

.tiptap td {
  color: var(--text-primary);
}

.tiptap tr:hover td {
  background: var(--bg-hover);
}

/* Links */
.tiptap a,
.tiptap .editor-link {
  color: var(--accent-light);
  text-decoration: underline;
  text-decoration-color: rgba(149, 141, 241, 0.4);
  text-underline-offset: 2px;
  transition: text-decoration-color 0.15s;
}

.tiptap a:hover,
.tiptap .editor-link:hover {
  text-decoration-color: rgba(149, 141, 241, 0.8);
}

/* Bold */
.tiptap strong {
  font-weight: 600;
  color: var(--text-strong);
}

/* Images */
.tiptap img {
  max-width: 100%;
  height: auto;
  border-radius: 8px;
  margin: 1em 0;
}

/* Math - inline */
.tiptap [data-type="inline-math"] .tiptap-mathematics-render {
  padding: 0 0.2em;
  border-radius: 3px;
  transition: background 0.15s;
}

.tiptap [data-type="inline-math"] .tiptap-mathematics-render:hover {
  background: var(--bg-code);
}

/* Math - block */
.tiptap [data-type="block-math"] {
  margin: 1em 0;
}

.tiptap [data-type="block-math"] .tiptap-mathematics-render {
  display: flex;
  justify-content: center;
  padding: 1rem 0;
  border-radius: 8px;
  transition: background 0.15s;
}

.tiptap [data-type="block-math"] .tiptap-mathematics-render:hover {
  background: var(--bg-hover);
}

/* KaTeX color */
.tiptap .katex {
  color: var(--katex-color);
}

/* Citation inline node */
.citation-node {
  position: relative;
  color: var(--accent-light);
  cursor: default;
  font-size: 0.9em;
  white-space: nowrap;
  text-decoration: underline;
  text-decoration-color: rgba(149, 141, 241, 0.3);
  text-underline-offset: 2px;
  transition: text-decoration-color 0.15s;
}

.citation-node:hover {
  text-decoration-color: rgba(149, 141, 241, 0.7);
}

/* Citation hover tooltip */
.citation-tooltip {
  position: absolute;
  bottom: calc(100% + 8px);
  left: 50%;
  transform: translateX(-50%);
  background: var(--bg-tooltip);
  border: 1px solid var(--border);
  border-radius: 8px;
  padding: 0.75rem;
  min-width: 240px;
  max-width: 320px;
  box-shadow: var(--shadow-lg);
  z-index: 100;
  white-space: normal;
  pointer-events: auto;
}

.citation-tooltip-title {
  color: var(--text-heading-secondary);
  font-size: 0.8125rem;
  font-weight: 500;
  line-height: 1.4;
  margin-bottom: 0.35rem;
}

.citation-tooltip-journal {
  color: var(--text-secondary);
  font-size: 0.75rem;
  font-style: italic;
  line-height: 1.3;
}

.citation-tooltip-doi {
  color: var(--text-tertiary);
  font-size: 0.7rem;
  font-family: "SFMono-Regular", "Fira Code", monospace;
  margin-top: 0.35rem;
  overflow: hidden;
  text-overflow: ellipsis;
}

.citation-tooltip-remove {
  display: block;
  margin-top: 0.5rem;
  margin-left: auto;
  padding: 0.25rem 0.6rem;
  border: none;
  border-radius: 4px;
  background: var(--danger-bg);
  color: var(--danger);
  font-size: 0.7rem;
  font-family: inherit;
  cursor: pointer;
  transition: background 0.15s;
}

.citation-tooltip-remove:hover {
  background: var(--danger-bg-hover);
}

/* Bibliography block */
.bibliography-block {
  margin: 2em 0 1em;
  padding-top: 1.5em;
  border-top: 1px solid var(--border);
}

.bibliography-title {
  font-size: 1.3rem;
  font-weight: 600;
  color: var(--text-heading-secondary);
  margin: 0 0 1em;
}

.bibliography-empty {
  color: var(--text-faint);
  font-size: 0.875rem;
  font-style: italic;
}

.bibliography-content {
  font-size: 0.875rem;
  line-height: 1.7;
  color: var(--text-secondary);
}

.bibliography-content .csl-entry {
  margin-bottom: 0.75em;
  padding-left: 2em;
  text-indent: -2em;
}

.bibliography-content .csl-entry i {
  font-style: italic;
}

/* Custom component blocks */
.component-content > *:first-child {
  margin-top: 0;
}

.component-content > *:last-child {
  margin-bottom: 0;
}

/* Glossary inline node */
.glossary-node {
  position: relative;
  display: inline;
  border-bottom: 1px dashed rgba(149, 141, 241, 0.5);
  color: rgba(149, 141, 241, 0.9);
  cursor: help;
}

.glossary-tooltip {
  position: absolute;
  bottom: calc(100% + 6px);
  left: 50%;
  transform: translateX(-50%);
  background: var(--bg-tooltip);
  border: 1px solid var(--border);
  border-radius: 8px;
  padding: 10px 14px;
  min-width: 200px;
  max-width: 320px;
  z-index: 50;
  box-shadow: var(--shadow-lg);
}

.glossary-tooltip-term {
  font-weight: 700;
  font-size: 13px;
  color: var(--text-heading-secondary);
  margin-bottom: 4px;
}

.glossary-tooltip-def {
  font-size: 12px;
  color: var(--text-secondary);
  line-height: 1.5;
}

.glossary-tooltip-remove {
  margin-top: 8px;
  background: none;
  border: none;
  color: var(--danger);
  font-size: 11px;
  cursor: pointer;
  padding: 0;
  opacity: 0.8;
}

.glossary-tooltip-remove:hover {
  opacity: 1;
}

/* Footnote inline node */
.footnote-node {
  position: relative;
  display: inline;
}

.footnote-marker {
  color: rgba(149, 141, 241, 0.9);
  cursor: pointer;
  font-size: 0.75em;
  font-weight: 700;
  margin: 0 1px;
}

.footnote-tooltip {
  position: absolute;
  bottom: calc(100% + 6px);
  left: 50%;
  transform: translateX(-50%);
  background: var(--bg-tooltip);
  border: 1px solid var(--border);
  border-radius: 8px;
  padding: 10px 14px;
  min-width: 220px;
  max-width: 360px;
  z-index: 50;
  box-shadow: var(--shadow-lg);
}

.footnote-tooltip-content {
  font-size: 12px;
  color: var(--text-secondary);
  line-height: 1.5;
}

/* Stack columns */
.stack-columns {
  display: contents;
}

.stack-columns > div[data-type="stack-column"] {
  border: 1px dashed var(--border-light);
  border-radius: 6px;
  padding: 8px;
  min-height: 40px;
}

.stack-columns > div[data-type="stack-column"] > *:first-child {
  margin-top: 0;
}

.stack-columns > div[data-type="stack-column"] > *:last-child {
  margin-bottom: 0;
}


/* Published article layout */
body {
  margin: 0;
  padding: 0;
  background: var(--bg-primary);
  color: var(--text-primary);
  font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
}

/* Grid: TOC | Article | (empty right) */
.content-grid {
  max-width: 1280px;
  margin: 0 auto;
  padding: 0 24px;
  margin-top: 40px;
  display: grid;
  grid-template-columns: 260px minmax(0, 680px) 260px;
  gap: 32px;
  align-items: start;
}

.article-header {
  margin-bottom: 2rem;
  padding-bottom: 1.5rem;
  border-bottom: 1px solid var(--border);
}

.article-header h1 {
  font-size: 2.5rem;
  font-weight: 700;
  color: var(--text-heading);
  line-height: 1.2;
  margin: 0 0 0.5rem;
  letter-spacing: -0.02em;
}

.article-header .authors {
  color: var(--text-secondary);
  font-size: 0.9375rem;
  margin-bottom: 0.25rem;
  line-height: 1.6;
}

.article-header .author-link {
  color: var(--accent-light);
  text-decoration: none;
}

.article-header .author-link:hover {
  text-decoration: underline;
}

.article-header .author-affiliation {
  color: var(--text-tertiary);
  font-size: 0.8125rem;
  margin-left: 0.25rem;
}

.article-header .author-affiliation::before { content: "("; }
.article-header .author-affiliation::after  { content: ")"; }

.article-header .date {
  color: var(--text-tertiary);
  font-size: 0.8125rem;
}

/* Theme toggle */
.theme-toggle {
  position: fixed;
  top: 1rem;
  right: 1rem;
  background: var(--bg-secondary);
  border: 1px solid var(--border);
  border-radius: 8px;
  padding: 0.5rem;
  cursor: pointer;
  font-size: 1.2rem;
  line-height: 1;
  z-index: 100;
}

/* ---------- Table of Contents (desktop sticky) ---------- */
.table-of-contents {
  position: sticky;
  top: 32px;
  margin-top: 12px;
}

.table-of-contents .title {
  font-weight: 600;
  font-size: 14px;
  margin-bottom: 8px;
  color: var(--text-primary);
}

.table-of-contents nav {
  border-left: 1px solid var(--border);
  padding-left: 16px;
  font-size: 13px;
}

.table-of-contents nav ul {
  margin: 0 0 6px;
  padding-left: 1em;
}

.table-of-contents nav li {
  list-style: none;
  margin: 0.25em 0;
}

.table-of-contents nav a,
.table-of-contents nav a:link,
.table-of-contents nav a:visited {
  color: var(--text-primary);
  text-decoration: none;
  border-bottom: none;
}

.table-of-contents nav > ul > li > a {
  font-weight: 700;
}

.table-of-contents nav a:hover {
  text-decoration: underline solid var(--text-tertiary);
}

.table-of-contents nav a.active {
  text-decoration: underline;
}

/* Collapsible sub-sections */
.table-of-contents nav.toc-collapsible li > ul,
.toc-mobile-sidebar nav.toc-collapsible li > ul {
  overflow: hidden;
  transition: height 200ms ease;
}

/* ---------- Mobile TOC toggle ---------- */
.toc-mobile-toggle {
  display: none;
  position: fixed;
  top: 1rem;
  left: 1rem;
  z-index: 200;
  width: 40px;
  height: 40px;
  border-radius: 50%;
  border: 1px solid var(--border);
  background: var(--bg-primary);
  color: var(--text-primary);
  cursor: pointer;
  align-items: center;
  justify-content: center;
  box-shadow: 0 2px 12px rgba(0,0,0,.08);
  transition: transform 150ms ease, box-shadow 150ms ease;
}
.toc-mobile-toggle:active { transform: scale(0.92); }

/* ---------- Mobile backdrop ---------- */
.toc-mobile-backdrop {
  display: none;
  position: fixed;
  inset: 0;
  z-index: 201;
  background: rgba(0,0,0,.4);
  opacity: 0;
  pointer-events: none;
  transition: opacity 250ms ease;
}
.toc-mobile-backdrop.open { opacity: 1; pointer-events: auto; }

/* ---------- Mobile sidebar ---------- */
.toc-mobile-sidebar {
  display: none;
  position: fixed;
  top: 0; left: 0; bottom: 0;
  z-index: 202;
  width: min(320px, 85vw);
  background: var(--bg-primary);
  border-right: 1px solid var(--border);
  transform: translateX(-100%);
  transition: transform 300ms cubic-bezier(.4,0,.2,1);
  flex-direction: column;
}
.toc-mobile-sidebar.open { transform: translateX(0); }

.toc-mobile-sidebar__header {
  display: flex;
  align-items: center;
  justify-content: space-between;
  padding: 0.75rem 1rem;
  border-bottom: 1px solid var(--border);
  flex-shrink: 0;
}
.toc-mobile-sidebar__title { font-weight: 700; font-size: 15px; color: var(--text-primary); }
.toc-mobile-sidebar__close {
  background: none; border: none; color: var(--text-tertiary);
  cursor: pointer; padding: 6px; border-radius: 6px;
  display: flex; align-items: center; justify-content: center;
  transition: color 150ms ease, background 150ms ease;
}
.toc-mobile-sidebar__close:hover { color: var(--text-primary); background: var(--bg-secondary); }

.toc-mobile-sidebar__body {
  flex: 1;
  overflow-y: auto;
  -webkit-overflow-scrolling: touch;
  padding: 0.75rem 1rem 1.5rem;
}
.toc-mobile-sidebar nav ul { margin: 0 0 6px; padding-left: 1em; }
.toc-mobile-sidebar nav li { list-style: none; margin: 0.35em 0; }
.toc-mobile-sidebar nav a,
.toc-mobile-sidebar nav a:link,
.toc-mobile-sidebar nav a:visited {
  color: var(--text-primary);
  text-decoration: none;
  border-bottom: none;
  font-size: 14px;
  line-height: 1.5;
}
.toc-mobile-sidebar nav > ul > li > a { font-weight: 700; }
.toc-mobile-sidebar nav a:hover { text-decoration: underline solid var(--text-tertiary); }
.toc-mobile-sidebar nav a.active { color: var(--accent-light); text-decoration: underline; }

/* ---------- Responsive: collapse below 1100px ---------- */
@media (max-width: 1100px) {
  .content-grid {
    overflow: hidden;
    display: block;
    padding: 0 16px;
    margin-top: 0.5rem;
  }
  .table-of-contents { position: static; display: none; }
  .toc-mobile-toggle { display: flex; }
  .toc-mobile-backdrop { display: block; }
  .toc-mobile-sidebar { display: flex; }
}

/* Accordion as details/summary */
details[data-component="accordion"] {
  border: 1px solid var(--border);
  border-radius: 8px;
  padding: 0;
  margin: 1em 0;
}

details[data-component="accordion"] > summary {
  padding: 0.75rem 1rem;
  cursor: pointer;
  font-weight: 600;
  color: var(--text-heading-secondary);
  list-style: none;
  user-select: none;
}

details[data-component="accordion"] > summary::-webkit-details-marker { display: none; }

details[data-component="accordion"] > summary::before {
  content: "\25B8";
  display: inline-block;
  margin-right: 0.5rem;
  transition: transform 0.2s;
}

details[data-component="accordion"][open] > summary::before { transform: rotate(90deg); }
details[data-component="accordion"] > .accordion-content { padding: 0 1rem 1rem; }

/* Image lightbox dialog */
dialog.lightbox { border: none; background: transparent; padding: 0; max-width: 95vw; max-height: 95vh; }
dialog.lightbox::backdrop { background: rgba(0, 0, 0, 0.85); }
dialog.lightbox img { max-width: 95vw; max-height: 90vh; object-fit: contain; border-radius: 4px; }

/* Print */
@media print {
  .table-of-contents, .toc-mobile-toggle, .toc-mobile-backdrop, .toc-mobile-sidebar, .theme-toggle { display: none !important; }
  .content-grid { display: block !important; }
}
  </style>
</head>
<body>
  <button class="theme-toggle" aria-label="Toggle theme" onclick="toggleTheme()">&#127763;</button>

  <!-- Mobile TOC toggle -->
  <button class="toc-mobile-toggle" aria-label="Open table of contents" aria-expanded="false">
    <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round">
      <line x1="3" y1="6" x2="21" y2="6"/><line x1="3" y1="12" x2="21" y2="12"/><line x1="3" y1="18" x2="21" y2="18"/>
    </svg>
  </button>
  <div class="toc-mobile-backdrop" aria-hidden="true"></div>
  <aside class="toc-mobile-sidebar" aria-label="Table of Contents">
    <div class="toc-mobile-sidebar__header">
      <span class="toc-mobile-sidebar__title">Table of Contents</span>
      <button class="toc-mobile-sidebar__close" aria-label="Close">
        <svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round">
          <line x1="18" y1="6" x2="6" y2="18"/><line x1="6" y1="6" x2="18" y2="18"/>
        </svg>
      </button>
    </div>
    <div class="toc-mobile-sidebar__body" id="toc-mobile-placeholder"></div>
  </aside>

  <section class="content-grid">
    <nav class="table-of-contents" aria-label="Table of Contents">
      <div class="title">Table of Contents</div>
      <div id="toc-placeholder"></div>
    </nav>

    <article>
      <header class="article-header">
        <h1>Scaling Laws for Neural Language Models</h1>
        <div class="authors"><span class="author"><a href="https://example.com/alice" class="author-link" target="_blank" rel="noopener">Alice Martin</a><span class="author-affiliation">Hugging Face</span></span><span class="author-sep">, </span><span class="author"><span class="author-name">Bob Chen</span><span class="author-affiliation">Hugging Face, MIT</span></span><span class="author-sep">, </span><span class="author"><span class="author-name">Carol Wu</span><span class="author-affiliation">MIT</span></span></div>
        <p class="date">April 13, 2026</p>
      </header>

      <div class="tiptap">
        <h1>Welcome to the Collaborative Editor</h1><p>This demo article showcases <strong>every content type</strong> available in the editor. Feel free to edit, delete, or rewrite anything — the AI assistant in the left panel can help you.</p><h2>Text formatting</h2><p>You can make text <strong>bold</strong>, <em>italic</em>, or <s>strikethrough</s>. Combine them for <strong><em>bold italic</em></strong>. Use <code>inline code</code> for technical terms, and add <a target="_blank" rel="noopener noreferrer nofollow" class="editor-link" href="https://huggingface.co">links</a> to external resources.</p><h2>Lists</h2><h3>Unordered list</h3><ul><li><p>First item with some context</p></li><li><p>Second item — supports <strong>rich formatting</strong> inside</p></li><li><p>Third item with <code>inline code</code></p></li></ul><h3>Ordered list</h3><ol><li><p>Prepare the dataset</p></li><li><p>Fine-tune the model</p></li><li><p>Evaluate on the test split</p></li><li><p>Deploy to production</p></li></ol><h2>Blockquote</h2><blockquote><p>"The best way to predict the future is to invent it." — Alan Kay</p></blockquote><h2>Code block</h2><pre><code class="language-python">import torch
from transformers import AutoModelForCausalLM, AutoTokenizer

model_id = "meta-llama/Llama-3-8B"
tokenizer = AutoTokenizer.from_pretrained(model_id)
model = AutoModelForCausalLM.from_pretrained(
    model_id,
    torch_dtype=torch.bfloat16,
    device_map="auto",
)

prompt = "The future of AI is"
inputs = tokenizer(prompt, return_tensors="pt").to(model.device)
outputs = model.generate(**inputs, max_new_tokens=100)
print(tokenizer.decode(outputs[0], skip_special_tokens=True))</code></pre><h2>Table</h2><table style="min-width: 100px;"><colgroup><col style="min-width: 25px;"><col style="min-width: 25px;"><col style="min-width: 25px;"><col style="min-width: 25px;"></colgroup><tbody><tr><th colspan="1" rowspan="1"><p>Model</p></th><th colspan="1" rowspan="1"><p>Parameters</p></th><th colspan="1" rowspan="1"><p>MMLU</p></th><th colspan="1" rowspan="1"><p>HellaSwag</p></th></tr><tr><td colspan="1" rowspan="1"><p>LLaMA 3 8B</p></td><td colspan="1" rowspan="1"><p>8B</p></td><td colspan="1" rowspan="1"><p>66.6</p></td><td colspan="1" rowspan="1"><p>82.0</p></td></tr><tr><td colspan="1" rowspan="1"><p>LLaMA 3 70B</p></td><td colspan="1" rowspan="1"><p>70B</p></td><td colspan="1" rowspan="1"><p>79.5</p></td><td colspan="1" rowspan="1"><p>87.3</p></td></tr><tr><td colspan="1" rowspan="1"><p>GPT-4</p></td><td colspan="1" rowspan="1"><p>~1.8T</p></td><td colspan="1" rowspan="1"><p>86.4</p></td><td colspan="1" rowspan="1"><p>95.3</p></td></tr><tr><td colspan="1" rowspan="1"><p>Mixtral 8x7B</p></td><td colspan="1" rowspan="1"><p>46.7B</p></td><td colspan="1" rowspan="1"><p>70.6</p></td><td colspan="1" rowspan="1"><p>84.4</p></td></tr></tbody></table><h2>Mathematics</h2><p>Inline math works with double dollars: the quadratic formula is <span data-latex="x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}" data-type="inline-math"></span> and Euler's identity is <span data-latex="e^{i\pi} + 1 = 0" data-type="inline-math"></span>.</p><p>Block equations use triple dollars. Here is a standard autoregressive loss:</p><div data-latex="\mathcal{L}(\theta) = -\sum_{t=1}^{T} \log P(x_t \mid x_{<t}; \theta)" data-type="block-math"></div><p>And the full variational trajectory decomposition:</p><div data-latex="\begin{aligned} \log p_\theta(\mathcal{D}) &amp;= \log \sum_{i=0}^N p_\theta((o,a)_i) \\ &amp;= \log \sum_{i=0}^N \int_{\text{supp}(Z)} p_\theta((o,a)_i \mid z)\, p(z) \\ &amp;= \log \sum_{i=0}^N \int_{\text{supp}(Z)} \frac{q_\theta(z \mid (o,a)_i)}{q_\theta(z \mid (o,a)_i)} \cdot p_\theta((o,a)_i \mid z)\, p(z) \\ &amp;= \log \sum_{i=0}^N \mathbb{E}_{z \sim p_\theta(\bullet \mid (o,a)_i)} \left[ \frac{p(z)}{q_\theta(z \mid (o,a)_i)} \cdot p_\theta((o,a)_i \mid z) \right] \end{aligned}" data-type="block-math"></div><h2>Scientific references</h2><p>The editor supports academic citations. The Transformer architecture <span key="vaswani2017" label="[vaswani2017]" data-type="citation" class="citation-node">[vaswani2017]</span> revolutionized natural language processing by introducing the self-attention mechanism. Large-scale pretraining <span key="devlin2019" label="[devlin2019]" data-type="citation" class="citation-node">[devlin2019]</span> demonstrated that unsupervised objectives on massive corpora produce powerful general-purpose representations.</p><p>More recently, scaling laws <span key="kaplan2020" label="[kaplan2020]" data-type="citation" class="citation-node">[kaplan2020]</span> have shown predictable relationships between model size, dataset size, and performance.</p><hr><h2>Horizontal rule</h2><p>Use a horizontal rule to visually separate sections:</p><hr><h2>Nested content</h2><p>Lists can contain multiple levels of formatting. Blockquotes can hold structured content:</p><blockquote><p><strong>Note:</strong> This editor supports real-time collaboration. Open this page in another tab to see cursors sync live.</p></blockquote><h3>A deeper heading level</h3><p>Heading levels go from H1 down to H3, giving you a clear document hierarchy. The floating menu on the left lets you insert any block type, and the bubble toolbar appears when you select text.</p><h2>Custom components</h2><p>The editor supports rich custom components from the research article template. Use the <code>/</code> slash menu to insert them.</p><details data-component="accordion">
        <summary>Details</summary>
        <div class="accordion-content"><p>The model was fine-tuned using LoRA adapters with rank 16 on 4× A100 GPUs. Training took approximately 12 hours on the full dataset. We used a cosine learning rate schedule with warm-up over the first 10% of steps.</p></div>
      </details><div title="Important" emoji="💡" variant="info" data-component="note"><p>All experiments were conducted with mixed-precision (bf16) training. Results may vary slightly with different random seeds.</p></div><div author="Ilya Sutskever" source="NeurIPS 2024 keynote" data-component="quoteBlock"><p>If you have a very large neural network and you train it on a very large dataset, you get very good results. It really is that simple.</p></div><div title="Warning" emoji="⚠️" variant="danger" data-component="note"><p>Do not use these scaling estimates for production capacity planning without accounting for inference overhead and memory constraints.</p></div><div data-component="wide"><p>This content stretches beyond the normal column width, useful for wide tables, figures or visualizations that need extra horizontal space.</p></div><div data-component="fullWidth"><p>This content spans the entire page width. It is ideal for large figures, panoramic images, or full-bleed data visualizations.</p></div><div data-component="sidenote"><p>Scaling laws were first systematically studied in the context of neural machine translation before being generalized to language models.</p></div><div id="fig-scaling" caption="Log-linear relationship between compute budget and model performance across three orders of magnitude." data-component="reference"><p>[ Figure placeholder — insert an image or chart here ]</p></div><div src="d3-scaling-chart.html" title="Interactive scaling law visualization" desc="Explore how model size, data, and compute interact." wide="false" downloadable="true" data-component="htmlEmbed"></div><p>The concept of <span term="Scaling law" definition="A power-law relationship between model size, dataset size, compute budget, and performance." data-type="glossary" class="glossary-node" title="A power-law relationship between model size, dataset size, compute budget, and performance." tabindex="0">Scaling law</span> has become central to modern AI research. Early work<span content="Hestness et al. (2017) observed similar scaling behavior in vision and translation tasks before the scaling laws paper formalized the framework." data-type="footnote" class="footnote-node" title="Hestness et al. (2017) observed similar scaling behavior in vision and translation tasks before the scaling laws paper formalized the framework." tabindex="0"><sup class="footnote-marker">*</sup></span> suggested these relationships hold across modalities.</p><div layout="2-column" gap="medium" data-component="stack"><div data-type="stack-column"><p><strong>Column A</strong></p><p>Multi-column layouts let you place content side by side. Each column is fully editable.</p></div><div data-type="stack-column"><p><strong>Column B</strong></p><p>Use the layout selector in the header to switch between 2, 3, or 4 columns.</p></div></div><div username="tfrere" name="Thibaud Frere" url="https://huggingface.co/tfrere" data-component="hfUser"></div><h2>What's next?</h2><p>Try asking the AI assistant to:</p><ul><li><p>Rewrite a paragraph in a different tone</p></li><li><p>Expand a section with more detail</p></li><li><p>Fix grammar or spelling errors</p></li><li><p>Translate content to another language</p></li><li><p>Add a new section on a specific topic</p></li></ul><p>Select some text and use the quick actions, or type a message in the chat panel. All AI edits can be undone with <code>Cmd+Z</code>.</p><div data-type="bibliography" class="bibliography-block"><h2 class="bibliography-title">References</h2><div class="bibliography-content"><div class="csl-bib-body">
  <div data-csl-entry-id="devlin2019" class="csl-entry">Devlin, J., Chang, M.-W., Lee, K., &#38; Toutanova, K. (2019). BERT: Pre-training of deep bidirectional transformers for language understanding. <i>Proceedings of NAACL-HLT</i>, 4171–4186. https://doi.org/10.18653/v1/N19-1423</div>
  <div data-csl-entry-id="kaplan2020" class="csl-entry">Kaplan, J., McCandlish, S., Henighan, T., Brown, T. B., Chess, B., Child, R., Gray, S., Radford, A., Wu, J., &#38; Amodei, D. (2020). Scaling laws for neural language models. <i>arXiv Preprint arXiv:2001.08361</i>. https://doi.org/10.48550/arXiv.2001.08361</div>
  <div data-csl-entry-id="vaswani2017" class="csl-entry">Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., &#38; Polosukhin, I. (2017). Attention is all you need. <i>Advances in Neural Information Processing Systems</i>, <i>30</i>. https://doi.org/10.48550/arXiv.1706.03762</div>
</div></div></div><p></p>
      </div>
    </article>
  </section>

  <!-- Image lightbox -->
  <dialog class="lightbox" id="lightbox">
    <img id="lightbox-img" src="" alt="">
  </dialog>

  <script>
  (function() {
    // Theme
    window.toggleTheme = function() {
      var next = document.documentElement.getAttribute('data-theme') === 'dark' ? 'light' : 'dark';
      document.documentElement.setAttribute('data-theme', next);
      localStorage.setItem('theme', next);
    };
    var saved = localStorage.getItem('theme');
    if (saved) document.documentElement.setAttribute('data-theme', saved);

    // Lightbox
    document.querySelectorAll('.tiptap img').forEach(function(img) {
      img.style.cursor = 'zoom-in';
      img.addEventListener('click', function() {
        document.getElementById('lightbox-img').src = img.src;
        document.getElementById('lightbox').showModal();
      });
    });
    document.getElementById('lightbox').addEventListener('click', function(e) { if (e.target === this) this.close(); });

    // Glossary
    document.querySelectorAll('[data-type="glossary"]').forEach(function(el) { el.setAttribute('tabindex', '0'); });

    // ---- Table of Contents ----
    var holder = document.getElementById('toc-placeholder');
    var holderMobile = document.getElementById('toc-mobile-placeholder');
    var articleRoot = document.querySelector('.content-grid article');
    if (!articleRoot) return;
    var headings = articleRoot.querySelectorAll('h2, h3, h4');
    if (!headings.length) return;
    var headingsArr = Array.from(headings);

    // Unique IDs
    var usedIds = {};
    var slugify = function(s) { return String(s||'').toLowerCase().trim().replace(/\s+/g,'_').replace(/[^a-z0-9_-]/g,''); };
    headingsArr.forEach(function(h) {
      var id = (h.id||'').trim() || slugify(h.textContent) || 'section';
      var c = id, n = 2;
      while (usedIds[c]) c = id+'-'+(n++);
      if (h.id !== c) h.id = c;
      usedIds[c] = true;
    });

    // Build nested nav with data-heading-idx
    var nav = document.createElement('nav');
    var ulStack = [document.createElement('ul')];
    nav.appendChild(ulStack[0]);
    var levelOf = function(tag) { return tag==='H2'?2:tag==='H3'?3:4; };
    var prev = 2, hIdx = 0;
    headingsArr.forEach(function(h) {
      var lvl = levelOf(h.tagName);
      while (lvl > prev) { var ul = document.createElement('ul'); var last = ulStack[ulStack.length-1].lastElementChild; if (last) last.appendChild(ul); ulStack.push(ul); prev++; }
      while (lvl < prev) { ulStack.pop(); prev--; }
      var li = document.createElement('li');
      var a = document.createElement('a');
      a.href = '#'+h.id; a.textContent = h.textContent;
      li.appendChild(a);
      li.setAttribute('data-heading-idx', String(hIdx++));
      ulStack[ulStack.length-1].appendChild(li);
    });

    if (holder) holder.appendChild(nav);
    var navClone = nav.cloneNode(true);
    if (holderMobile) holderMobile.appendChild(navClone);

    // Mark navs as collapsible
    nav.classList.add('toc-collapsible');
    navClone.classList.add('toc-collapsible');

    var allLinks = [].concat(
      holder ? Array.from(holder.querySelectorAll('a')) : [],
      holderMobile ? Array.from(holderMobile.querySelectorAll('a')) : []
    );

    // ---- Auto-collapse logic ----
    var isMobile = window.matchMedia('(max-width: 1100px)');

    function getItemsWithChildren(navEl) {
      if (!navEl) return [];
      return Array.from(navEl.querySelectorAll('li[data-heading-idx]')).filter(function(li) {
        return li.querySelector(':scope > ul');
      });
    }

    function getAncestorIndices(items, targetIdx) {
      var toExpand = {};
      var activeLi = null;
      function find(li) {
        if (Number(li.getAttribute('data-heading-idx')) === targetIdx) return li;
        var ul = li.querySelector(':scope > ul');
        if (!ul) return null;
        var children = ul.querySelectorAll(':scope > li[data-heading-idx]');
        for (var i = 0; i < children.length; i++) { var f = find(children[i]); if (f) return f; }
        return null;
      }
      for (var i = 0; i < items.length; i++) { activeLi = find(items[i]); if (activeLi) break; }
      if (!activeLi) return toExpand;
      toExpand[targetIdx] = true;
      var cur = activeLi;
      while (cur) {
        var parent = cur.parentElement ? cur.parentElement.closest('li[data-heading-idx]') : null;
        if (parent) { toExpand[Number(parent.getAttribute('data-heading-idx'))] = true; cur = parent; }
        else break;
      }
      return toExpand;
    }

    function applyCollapseState(navEl, activeIdx) {
      if (!navEl) return;
      var items = getItemsWithChildren(navEl);
      var ancestors = getAncestorIndices(items, activeIdx);

      items.forEach(function(li) {
        var sub = li.querySelector(':scope > ul');
        if (!sub) return;
        var idx = Number(li.getAttribute('data-heading-idx'));
        var allDesc = li.querySelectorAll('li[data-heading-idx]');
        var related = [idx];
        allDesc.forEach(function(d) { related.push(Number(d.getAttribute('data-heading-idx'))); });
        var shouldExpand = related.some(function(i) { return ancestors[i]; });

        if (shouldExpand) {
          li.classList.remove('collapsed');
          sub.style.height = 'auto';
        } else {
          li.classList.add('collapsed');
          sub.style.height = '0px';
        }
      });
    }

    function expandAll(navEl) {
      if (!navEl) return;
      getItemsWithChildren(navEl).forEach(function(li) {
        li.classList.remove('collapsed');
        var sub = li.querySelector(':scope > ul');
        if (sub) sub.style.height = 'auto';
      });
    }

    // Initial state: collapse all except first section
    function initCollapse() {
      if (isMobile.matches) {
        expandAll(holder ? holder.querySelector('nav') : null);
        expandAll(holderMobile ? holderMobile.querySelector('nav') : null);
      } else {
        applyCollapseState(holder ? holder.querySelector('nav') : null, 0);
        applyCollapseState(holderMobile ? holderMobile.querySelector('nav') : null, 0);
      }
    }
    initCollapse();

    isMobile.addEventListener('change', function() {
      if (isMobile.matches) {
        expandAll(holder ? holder.querySelector('nav') : null);
        expandAll(holderMobile ? holderMobile.querySelector('nav') : null);
      } else {
        applyCollapseState(holder ? holder.querySelector('nav') : null, prevActiveIdx);
        applyCollapseState(holderMobile ? holderMobile.querySelector('nav') : null, prevActiveIdx);
      }
    });

    // ---- Scroll tracking ----
    var OFFSET = 60, lastScrollTime = 0, prevActiveIdx = 0;

    function onScroll() {
      var now = performance.now();
      if (now - lastScrollTime < 50) return;
      lastScrollTime = now;
      requestAnimationFrame(function() {
        var activeIdx = -1, activeId = null;
        for (var i = headingsArr.length - 1; i >= 0; i--) {
          if (headingsArr[i].getBoundingClientRect().top - OFFSET <= 0) {
            activeIdx = i; activeId = headingsArr[i].id; break;
          }
        }
        allLinks.forEach(function(l) {
          if (activeId && l.getAttribute('href') === '#'+activeId) l.classList.add('active');
          else l.classList.remove('active');
        });
        if (activeIdx !== prevActiveIdx && activeIdx >= 0 && !isMobile.matches) {
          prevActiveIdx = activeIdx;
          applyCollapseState(holder ? holder.querySelector('nav') : null, activeIdx);
        }
        if (activeIdx >= 0) prevActiveIdx = activeIdx;
      });
    }
    window.addEventListener('scroll', onScroll, { passive: true });
    onScroll();

    // ---- Mobile sidebar ----
    var sidebar = document.querySelector('.toc-mobile-sidebar');
    var backdrop = document.querySelector('.toc-mobile-backdrop');
    var toggleBtn = document.querySelector('.toc-mobile-toggle');
    var closeBtn = document.querySelector('.toc-mobile-sidebar__close');

    function openSidebar() {
      sidebar.classList.add('open'); backdrop.classList.add('open');
      toggleBtn.setAttribute('aria-expanded','true');
      document.body.style.overflow = 'hidden';
      requestAnimationFrame(function() {
        var active = sidebar.querySelector('a.active');
        if (active) {
          var body = sidebar.querySelector('.toc-mobile-sidebar__body');
          if (body) body.scrollTop = Math.max(0, active.offsetTop - body.offsetTop - body.clientHeight/3);
        }
      });
    }
    function closeSidebar() {
      sidebar.classList.remove('open'); backdrop.classList.remove('open');
      toggleBtn.setAttribute('aria-expanded','false');
      document.body.style.overflow = '';
    }
    if (toggleBtn) toggleBtn.addEventListener('click', openSidebar);
    if (closeBtn) closeBtn.addEventListener('click', closeSidebar);
    if (backdrop) backdrop.addEventListener('click', closeSidebar);
    if (holderMobile) holderMobile.addEventListener('click', function(e) { if (e.target.closest && e.target.closest('a')) closeSidebar(); });
    document.addEventListener('keydown', function(e) { if (e.key==='Escape' && sidebar.classList.contains('open')) closeSidebar(); });

    // Hash navigation
    if (window.location.hash) {
      var target = document.querySelector(window.location.hash);
      if (target) setTimeout(function() { target.scrollIntoView({block:'start'}); }, 100);
    }
    window.addEventListener('popstate', function() {
      var h = window.location.hash;
      if (h) { var t = document.querySelector(h); if (t) t.scrollIntoView({block:'start'}); }
      else window.scrollTo({top:0});
    });
  })();
  </script>
</body>
</html>