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<!DOCTYPE html>
<!--
DESIGN DIRECTION — LOCKED
Concept: Spectral field report — a calm indigo technical sheet with warm audit accents.
Hero: one full-width outcome banner carrying the four decisive reproduction numbers.
Canvas: 60in x 36in landscape. Density: normal. No organization logo.
Template: posterly/templates/landscape_4col_neutral.html.
-->
<!--
Vendored + adapted into posterly from ARIS (Auto-claude-code-research-in-sleep),
skill paper-poster-html. Origin: https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep
Upstream tokenization: MIT (c) 2026 wanshuiyin -- ../LICENSES/aris-MIT.txt
This is the tokenized form of posterly's own neutral template; the class names and
content are posterly's own (c) 2026 Ruishuo Chen. As an adapted derivative this file
ships as part of posterly under AGPL-3.0. See ../NOTICE.md.
-->
<!--
============================================================
TEMPLATE: landscape_4col (ARIS fork)
CANVAS: 60in × 36in landscape (ICML / NeurIPS / generic landscape)
LAYOUT: header → optional banner → 4 body columns → optional takeaways → footer
USE WHEN: standard ML conference poster with 3-5 content cards per column,
mix of figures + equations + small tables.
HOW TO USE:
1. Copy this file to your working directory as `poster.html`.
2. Edit the DESIGN TOKENS in `:root` to your lab/venue colors.
3. Replace TODO content placeholders (search for "TODO").
4. Run `python tools/run_gates.py poster.html --tokens design_tokens.json` (the default driver: preflight -> style -> measure -> polish; design_tokens.json is the design-direction pack written at lock time -- SKILL.md Step 2.5) to align columns and check style/structure.
5. Run `python tools/render_preview.py poster.html` to produce the PDF.
NOTE: as shipped, this scaffold passes `preflight` (structure) but is
EXPECTED to FAIL `measure`/`polish` -- figures are commented out and copy
is TODO stubs, so columns only fill the top of the canvas. Those two gates
judge a FILLED poster; balance them once you've added real content. See
templates/README.md ("Scaffolds, not finished posters").
MEASURE ROLES: every layout-critical element carries `data-measure-role`.
Generic measurement scripts depend on these — do not remove.
CANVAS RETARGETING: to print at another size, change the canvas in exactly
TWO places that must stay in sync -- the `@page { size: ... }` rule and the
`.poster { width/height }` (also the `@media print .poster { width/height }`).
Example: ICLR 2026 main conference uses 185cm 90cm landscape (official print
service spec) -- set @page to `185cm 90cm`, width to `1850 * var(--u)` and
height to `900 * var(--u)` (and the print-override .poster to `185cm`/`90cm`).
Adapted from posterly (MIT, © 2026 Ruishuo Chen) — see LICENSES/ & NOTICE.md;
ARIS modifications: flat de-gradient, --fs token scale, zero-inline-style
utilities, data-source/data-color-exempt contracts.
============================================================
-->
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="generator" content="posterly">
<title>What Makes a Strong Model? — ICML 2026 Reproduction</title>
<!-- MathJax v3 for inline equations. CDN by default when the file is
opened by hand; the posterly check tools (measure/polish/pack/…)
intercept this request and serve the skill's bundled copy
(assets/mathjax/tex-svg.js, MathJax 3.2.2), so gates render math
deterministically even offline. To make a hand-opened poster
offline too, copy that bundle next to the poster and point the
<script> `src` at it. -->
<script>
window.MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']],
displayMath: [['$$', '$$'], ['\\[', '\\]']],
packages: {'[+]': ['ams']}
},
svg: { fontCache: 'global' }
};
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
<style>
/* =========================================================
CANVAS — 60" × 36" landscape
========================================================= */
@page { size: 60in 36in; margin: 0; }
:root {
/* ===== DESIGN TOKENS ===== */
/* Primary accent (header underline, card-highlight bar, section nums, .keyword) */
--accent: #315D8A;
--accent-deep: #1D3F60;
--accent-light: #E7F0F8;
--accent-soft: #D2E2F0;
--accent-ink: #FFFFFF; /* ink ON the accent (chips, callout, thead) */
/* Emphasis register for "ours / best" (table .ours row, "★" callouts).
Default is the warm gold; a redesign may choose any register that
keeps 4.5:1 with --emph-ink (see templates/THEMES.md Mechanism 1). */
--emph: #B45F22;
--emph-soft: #FFF0E5;
--emph-ink: #38200F; /* ink ON the emphasis fill. NOT var(--accent-deep):
#1D3F60 on the default gold measures 4.16:1 (< AA);
#38200F measures 5.58:1 (>= 4.5:1). */
/* Text */
--text-primary: #1A1A1A;
--text-secondary: #555555;
--text-muted: #888888;
/* Backgrounds */
--bg-page: #F4F1ED;
--bg-card: #FFFFFF;
--bg-card-tint: #FAFAFB;
--bg-emphasis: var(--accent-light);
/* Borders */
--border-soft: #D8D8D8;
--border-strong: var(--accent);
/* Screen-only dark mat behind the poster (the off-canvas viewport
background). Print resets html/body to white, so this never reaches
paper; kept as a token so no color literal lives outside this block. */
--bg-viewport: #2B2B2B;
/* Base unit. Print: 1mm; screen preview: 1.6px (~3.78px = 1mm at 96dpi). */
--u: 1.6px;
/* Font-size scale (9 archetypes). Every `font-size` in this template
references one of these. `calc(var(--fs-N) * k)` is permitted ONLY for
a COMPONENTS.md-defined variant (e.g. `.eqn--large`). */
--fs-1: calc(9 * var(--u)); /* micro label */
--fs-2: calc(10 * var(--u)); /* small caption */
--fs-3: calc(11 * var(--u)); /* caption / table */
--fs-4: calc(12 * var(--u)); /* body text */
--fs-5: calc(13 * var(--u)); /* equation / emphasis */
--fs-6: calc(15 * var(--u)); /* subtitle */
--fs-7: calc(16 * var(--u)); /* section title */
--fs-8: calc(22 * var(--u)); /* banner number */
--fs-9: calc(32 * var(--u)); /* main title */
/* Fonts. Override at :root if your venue mandates a specific family. */
--font-serif: "Charter", "Source Serif Pro", "Georgia", serif;
--font-sans: "Inter", "Helvetica Neue", sans-serif;
/* Shadows & watermark ink — tokenized so rules 1/3 stay literal-free
(the faint radial page tint is the ONE allowed literal outside this
block; rule 5 validates it WHEN ENABLED -- the style gate ships with rules 4-5 off). */
--shadow-screen: 0 0 60px rgba(0, 0, 0, 0.5);
--shadow-card: 0 calc(2 * var(--u)) calc(6 * var(--u)) rgba(45, 95, 139, 0.05);
--ornament-ink: rgba(45, 95, 139, 0.06);
/* Identity mark ink — the corner-signature ⊕ adopts the LOCAL accent so it
reads native (the woven-signature instead inherits its host's ink). The
glyph GEOMETRY, not the hue, is the posterly signature. Re-theme with the
palette like any other token. */
--ps-mark-ink: var(--accent-deep);
/* Corner-radius scale. Every border-radius calc() multiplies by this;
1 = the shipped soft look, 0 = square/flat (see templates/THEMES.md). */
--rs: 1;
/* Figure mount: the ground behind paper figures (transparent PNGs sit on
it) and the keyline around them (.figure img / .ff-fig img). Re-theme
with the Axis 6 frame decision so figures sit mounted in the design
instead of pasted on it; --fig-frame: transparent = frameless mount.
QR backgrounds stay literal white -- that's scannability, not styling. */
--fig-bg: white;
--fig-frame: var(--border-soft);
/* ===== END DESIGN TOKENS ===== */
}
/* =========================================================
RESET + BASE
========================================================= */
* { box-sizing: border-box; margin: 0; padding: 0; }
/* =========================================================
BASE DEFENSES -- wrap & ink safety. KEEP this block in ANY
skeleton, including a fully custom one (copy it over and
EXTEND the selector lists with your own prose/display
classes -- a hand-rolled skeleton that drops it strands
single-word widows and ragged titles; polish warns as
TEXT-WRAP).
- pretty: fills each line, protects the last-line orphan
(single-word widow). Safe on all prose.
- balance: evens CENTERED display text only -- never pair
it with left-aligned multi-sentence prose (SKILL.md wrap
rules).
- Any inline class you add that paints a background (a
.mark highlight, a keyword chip) must declare its own
`color` (Gate G -- never inherit ink across a ground
change) plus `box-decoration-break: clone;
-webkit-box-decoration-break: clone;` so a wrapped
highlight keeps its padding on both fragments (then it
never needs &nbsp;-gluing to hold one line).
========================================================= */
p, li, dd, figcaption,
.body-text, .caption, .callout, .section-title { text-wrap: pretty; }
.title { text-wrap: balance; }
/* Case-safety: lowercase Greek under text-transform:uppercase paints
as its capital (α -> Α, a Latin-A lookalike -- "SHARPEN α>1" prints
as "SHARPEN A>1"). Wrap the symbol: <span class="tt-none">α</span>.
polish flags misses as SYMBOL-CASE. */
.tt-none { text-transform: none; }
html, body {
background: var(--bg-viewport);
font-family: var(--font-serif);
color: var(--text-primary);
-webkit-font-smoothing: antialiased;
}
/* =========================================================
UTILITY CLASSES — replace inline `style=` in the body markup.
The template (and any finished poster) must carry ZERO `style=`
attributes. Use these classes instead. Two documented exceptions
exist ONLY as examples and may appear in comments, never live:
- a logo/seal SVG flagged data-color-exempt="logo"
- a paper figure `<img ... data-source="paper" style="width: NN%">`
(AR width tweak; prefer the .w-NN classes below where possible)
========================================================= */
/* Poster container — exact print dimensions; data-measure-role="poster" so poster_check.py
can verify the canvas size. */
.poster {
width: calc(1524 * var(--u));
height: calc(914 * var(--u));
background: var(--bg-page);
/* Page tint kept (radial only, all color stops alpha <= 0.06 per the
de-gradient policy: linear-gradient is banned, this low-alpha radial
wash is the single allowed exception). */
background-image:
radial-gradient(ellipse at top left, rgba(45, 95, 139, 0.06), transparent 40%),
radial-gradient(ellipse at bottom right, rgba(201, 162, 74, 0.05), transparent 50%);
margin: 20px auto;
padding: calc(10 * var(--u)) calc(14 * var(--u));
display: grid;
grid-template-columns: minmax(0, 1fr); /* column-axis twin of the minmax(0,1fr) body-row defense: without it the implicit `auto` column grows to a wide child's max-content and a full-width row overflows the canvas (measure's canvas-overflow gate). Keep on any custom skeleton. */
grid-template-rows: auto auto minmax(0, 1fr) auto auto; /* header | banner | body | takeaways | footer. minmax(0,1fr) (not bare 1fr): an over-tall body compresses instead of pushing takeaways/footer off-canvas */
gap: calc(6 * var(--u));
box-shadow: var(--shadow-screen);
position: relative;
overflow: hidden;
}
/* Decorative top bar — flat solid accent (de-gradient). */
.poster::before {
content: "";
position: absolute; top: 0; left: 0; right: 0;
height: calc(8 * var(--u));
background: var(--accent);
}
/* =========================================================
HEADER
========================================================= */
.header {
display: grid;
grid-template-columns: 1fr minmax(50%, auto) 1fr; /* equal side tracks (1fr) -> the title track is centred on the poster, not just between the side blocks; the centre track is floored at 50% so a one-line title still fills it (else a short title measures narrow and trips a false HEADER/TITLE-SQUEEZED). Best-effort: a side block wide enough to clamp its 1fr track can still pull the title off-centre. */
align-items: center;
gap: calc(16 * var(--u));
padding: calc(2 * var(--u)) calc(4 * var(--u)) calc(5 * var(--u));
border-bottom: calc(2 * var(--u)) solid var(--accent);
}
.venue-badge {
justify-self: start; /* anchor to the far-left edge so the centre track stays centred */
display: flex; flex-direction: column;
align-items: center; justify-content: center;
min-width: calc(95 * var(--u));
text-align: center;
border-right: calc(1 * var(--u)) solid var(--border-soft);
padding-right: calc(12 * var(--u));
}
.venue-badge .vb-venue {
font-family: var(--font-sans);
font-weight: 800;
font-size: var(--fs-9);
color: var(--accent-deep);
line-height: 1;
letter-spacing: -0.5px;
}
.venue-badge .vb-year {
font-family: var(--font-sans);
font-size: var(--fs-5);
color: var(--text-secondary);
margin-top: calc(3 * var(--u));
letter-spacing: 1.2px;
}
.venue-badge .vb-tag {
font-family: var(--font-sans);
font-size: var(--fs-2);
color: var(--accent);
font-weight: 700;
margin-top: calc(2 * var(--u));
letter-spacing: 1.2px;
}
.title-block { text-align: center; min-width: 0; }
.title {
font-family: var(--font-sans);
font-weight: 800;
font-size: var(--fs-9);
line-height: 1.05;
color: var(--accent-deep);
letter-spacing: -0.5px;
}
.title .accent { color: var(--emph); }
.subtitle {
font-family: var(--font-sans);
font-weight: 500;
font-size: var(--fs-6);
color: var(--text-secondary);
margin-top: calc(2 * var(--u));
font-style: italic;
}
.authors-line {
font-family: var(--font-sans);
font-size: var(--fs-4);
color: var(--accent);
font-weight: 600;
margin-top: calc(3 * var(--u));
}
.authors-line .author { margin: 0 calc(4 * var(--u)); }
.authors-line sup { font-size: 0.7em; color: var(--accent); }
.authors-line .aff {
color: var(--text-secondary);
font-weight: 400;
display: block;
margin-top: calc(2 * var(--u));
font-size: var(--fs-4);
}
.right-block {
justify-self: end; /* keep logo+QR in the far-right corner */
display: flex; align-items: center;
gap: calc(10 * var(--u));
}
.qr-block { display: flex; flex-direction: column; align-items: center; gap: calc(2 * var(--u)); }
.qr-block img {
width: calc(85 * var(--u));
height: calc(85 * var(--u));
border: calc(2 * var(--u)) solid var(--accent);
border-radius: calc(4 * var(--u) * var(--rs));
background: white;
padding: calc(2 * var(--u));
}
.qr-label {
font-family: var(--font-sans);
font-size: var(--fs-3);
color: var(--accent);
font-weight: 600;
}
/* Optional logo slot — drop your lab logo here. Keep its rendered height
close to the QR (~85u) so the header doesn't grow disproportionately.
A raster logo needs no exemption. An inline-SVG logo with brand colors
must carry data-color-exempt="logo" so style_check skips its fills, e.g.:
<svg data-color-exempt="logo" ...> ... </svg> */
.logo-slot img { height: calc(85 * var(--u)); width: auto; max-width: calc(360 * var(--u)); object-fit: contain; display: block; }
/* Logo size classes on .logo-slot -- pick from the file's aspect ratio (SKILL.md Gate E).
tall/square sit at the QR-matched slot height; wide is intentionally shorter (~68% of the
QR) and width-capped so a long wordmark doesn't out-mass the title. Do NOT combine these
with logo-stack (that row is width-normalized, below). */
.logo-slot.logo-tall img,
.logo-slot.logo-square img { height: calc(85 * var(--u)); }
.logo-slot.logo-wide img { height: calc(58 * var(--u)); max-width: calc(300 * var(--u)); }
/* Logo chip: a solid backing that keeps a transparent / edge-white logo legible on a
colored/dark header (white chip) or a light header (.logo-chip-dark); the padding + radius
fold a stray white box into a deliberate rounded tile (SKILL.md Gate E, Background). */
.logo-chip {
display: inline-flex; align-items: center; justify-content: center;
background: var(--bg-card); border-radius: calc(3 * var(--u) * var(--rs));
padding: calc(3 * var(--u)) calc(5 * var(--u));
}
.logo-chip.logo-chip-dark { background: var(--text-primary); }
/* logo-row: institution logos in the header right block (REAL logos the
user provided — never fabricate a seal). Each img MUST carry
data-color-exempt="logo"; height pairs with the QR. */
.logo-row { display: flex; align-items: center; gap: calc(5 * var(--u)); }
.logo-row img { height: calc(68 * var(--u)); width: auto; display: block; }
/* --boxed variant: each logo in a labeled tile (logo + institution name) —
more presence at poster distance; white tile + soft border, no new hues. */
.logo-row .lr-item {
display: flex; flex-direction: column; align-items: center;
gap: calc(2 * var(--u));
background: var(--bg-card);
border: 1px solid var(--border-soft);
border-radius: calc(3 * var(--u) * var(--rs));
padding: calc(4 * var(--u)) calc(6 * var(--u));
}
.logo-row .lr-item img { height: calc(58 * var(--u)); }
.logo-row .lr-label {
font-family: var(--font-sans); font-weight: 600; font-size: var(--fs-1);
color: var(--text-secondary); text-align: center; line-height: 1.15;
}
/* logo-stack variant: WIDE WORDMARKS (AR >= ~2) normalized to EQUAL WIDTH
and stacked vertically, left-aligned. Use when two wide wordmarks of
different aspect ratio read unbalanced height-matched in a row (equal
width lets the less-wide mark grow taller and aligns a clean block).
NOT for a square seal or tall mark (equal width blows it up — keep those
height-matched). Do NOT also apply the logo-wide/tall/square classes. */
.logo-row.logo-stack { flex-direction: column; align-items: flex-start; gap: calc(8 * var(--u)); }
.logo-row.logo-stack img { width: calc(170 * var(--u)); height: auto; }
/* venue badge may carry the official venue logo above its text line */
.venue-badge img { height: calc(62 * var(--u)); width: auto; display: block; margin: 0 auto calc(2 * var(--u)); }
.venue-badge .vb-title { font-family: var(--font-sans); font-weight: 800; font-size: var(--fs-5); color: var(--accent-deep); letter-spacing: 0.5px; }
/* =========================================================
OPTIONAL FRAMEWORK BANNER (delete this whole section if you don't need it)
========================================================= */
.framework-banner {
display: flex;
align-items: center;
gap: calc(16 * var(--u));
/* Flat solid emphasis fill (de-gradient). */
background: var(--bg-emphasis);
border: calc(1 * var(--u)) solid var(--border-soft);
border-left: calc(6 * var(--u)) solid var(--accent);
border-radius: calc(6 * var(--u) * var(--rs));
padding: calc(6 * var(--u)) calc(14 * var(--u));
}
.framework-banner img { height: calc(120 * var(--u)); width: auto; display: block; }
.framework-banner .banner-stats {
flex: 1;
display: grid;
grid-template-columns: 1fr 1fr;
gap: calc(6 * var(--u));
}
.framework-banner .bs-item {
background: white;
border: calc(1 * var(--u)) solid var(--border-soft);
border-left: calc(3 * var(--u)) solid var(--accent);
border-radius: calc(3 * var(--u) * var(--rs));
padding: calc(2 * var(--u)) calc(8 * var(--u));
text-align: center;
}
.framework-banner .bs-num {
font-family: var(--font-sans);
font-weight: 800;
font-size: var(--fs-8);
color: var(--accent);
line-height: 1;
}
.framework-banner .bs-label {
font-family: var(--font-sans);
font-size: var(--fs-3);
color: var(--text-secondary);
margin-top: calc(2 * var(--u));
line-height: 1.2;
}
.framework-banner .fb-text {
flex: 1.6;
font-family: var(--font-serif);
font-size: var(--fs-6);
line-height: 1.5;
text-wrap: pretty; /* prose: fill each line, protect last-line orphan. NOT balance — on multi-sentence prose balance shortens+hyphenates line 1 (crammed-left, gap-right). */
text-align: center;
}
.framework-banner .fb-text strong { color: var(--accent-deep); }
.framework-banner .fb-label {
display: inline-block;
background: var(--accent);
color: var(--accent-ink);
font-family: var(--font-sans);
font-size: var(--fs-5);
font-weight: 700;
padding: calc(2 * var(--u)) calc(8 * var(--u));
border-radius: calc(4 * var(--u) * var(--rs));
text-transform: uppercase;
letter-spacing: 1px;
vertical-align: middle;
line-height: 1;
position: relative;
top: calc(-1 * var(--u));
}
/* Method-overview figure for the banner (banner-figure component,
catalogued in COMPONENTS.md). Usually CAPTIONLESS -- the banner text
block beside it is the figure's explanation. width:min-content collapses
the slot to the IMAGE (a captionless figure's slot IS the image); if a
short caption is used it wraps at the image box and can NEVER set the
flex-item width; margin-inline centres a block image (text-align does
not); overflow-wrap guards a long unbreakable token. Do NOT hand-roll a
.fb-fig wrapper or a bare <img class="w-100"> here. */
.framework-banner .banner-figure {
flex: 0 0 auto;
width: min-content;
margin: 0;
text-align: center;
}
.framework-banner .banner-figure img {
height: calc(120 * var(--u));
width: auto;
display: block;
margin-inline: auto;
}
.framework-banner .banner-figure figcaption {
width: 100%;
margin-top: calc(2 * var(--u));
font-family: var(--font-sans);
font-size: var(--fs-2);
line-height: 1.2;
color: var(--text-secondary);
text-align: center;
text-wrap: pretty;
overflow-wrap: anywhere;
}
.framework-banner .banner-figure figcaption strong { color: var(--accent-deep); }
/* =========================================================
BODY: 4 columns, variable-width hint via fr values
========================================================= */
.body-grid {
display: grid;
grid-template-columns: 1fr 1.05fr 1.05fr 1fr;
gap: calc(10 * var(--u));
/* No overflow:hidden here — it would clip card shadows (pitfall #7).
.poster already clips at the page boundary; min-height:0 is the
grid-blowout guard. */
min-height: 0;
}
.column {
display: flex; flex-direction: column;
gap: calc(6 * var(--u));
min-height: 0;
height: 100%;
padding-bottom: calc(4 * var(--u)); /* shadow breathing room above takeaways */
}
/* =========================================================
CARDS
========================================================= */
.card {
background: var(--bg-card);
border-radius: calc(5 * var(--u) * var(--rs));
padding: calc(4 * var(--u)) calc(9 * var(--u));
border: calc(1 * var(--u)) solid var(--border-soft);
box-shadow: var(--shadow-card);
position: relative;
}
.card.tinted { background: var(--bg-card-tint); }
.card.card--compact { padding: calc(3 * var(--u)) calc(6 * var(--u)); } /* predefined variant: tighter padding (fix (f)) */
.card.highlight {
border-left: calc(6 * var(--u)) solid var(--accent);
/* Flat emphasis tint (de-gradient). */
background: var(--bg-emphasis);
}
.section-title {
font-family: var(--font-sans);
font-weight: 700;
font-size: var(--fs-7);
color: var(--accent-deep);
margin-bottom: calc(3 * var(--u));
display: flex; align-items: center;
gap: calc(5 * var(--u));
}
/* Title text + any ★ marker share ONE .st-text span, so the heading wraps as
natural text (hanging indent) instead of flex-wrapping atomic items: the
number badge is never stranded on its own line and the ★ never widows. */
.section-title .st-text { flex: 1; min-width: 0; line-height: 1.18; }
/* Graceful fallback if a title is NOT wrapped in .st-text: float the badge so
bare inline text still wraps beside it rather than dropping below it. */
.section-title:not(:has(.st-text)) { display: block; line-height: 1.18; }
.section-title:not(:has(.st-text)) .num { float: left; margin-right: calc(5 * var(--u)); }
.section-title .num {
display: inline-flex; align-items: center; justify-content: center;
width: calc(22 * var(--u)); height: calc(22 * var(--u));
background: var(--accent); color: var(--accent-ink);
border-radius: 50%;
font-size: var(--fs-5); font-weight: 700;
flex-shrink: 0;
}
/* Inline "★ KEY" / "★ Headline" marker beside a section title. */
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/* =========================================================
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/* ── Utility classes — defined LAST so equal-specificity ties
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/* =========================================================
PRINT OVERRIDE — KEEP LAST so it wins source-order ties.
========================================================= */
@media print {
html, body { background: white; }
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:root { --u: 1mm; }
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/* Reproduction-specific, token-only additions. */
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</style>
</head>
<body>
<div class="poster" data-measure-role="poster" data-posterly-contract="identity-v1" data-ps-identity="on">
<svg class="ps-sprite" data-color-exempt="logo" aria-hidden="true"><defs>
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</symbol>
</defs></svg>
<header class="header" data-measure-role="header">
<div class="venue-badge">
<div class="vb-venue">ICML</div><div class="vb-year">2026</div><div class="vb-tag">REPRO</div>
</div>
<div class="title-block">
<h1 class="title">What Makes a <span class="accent">Strong Model?</span></h1>
<div class="subtitle">A unified spectral analysis of knowledge transfer over high-dimensional linear regression</div>
<div class="authors-line">
<span class="author">Wendao Wu</span> · <span class="author">Fangqing Zhang</span> ·
<span class="author">Haihan Zhang</span> · <span class="author">Cong Fang</span>
<span class="aff">Independent reproduction · paper #23301 · arXiv:2606.01292</span>
</div>
</div>
<div class="right-block">
<div class="qr-block">
<img data-color-exempt="logo" src="assets/logbook-qr.png" alt="QR code to the published reproduction logbook">
<div class="qr-label">Open evidence logbook</div>
</div>
</div>
</header>
<section class="framework-banner" data-measure-role="banner">
<div class="fb-text"><span class="fb-label">Outcome</span>&nbsp;
<strong>The spectral mechanism reproduces.</strong> Learned modes inherit teacher error; expanded horizons improve sample efficiency; selected checkpoints denoise a stronger student. Full real-world task training remains outside this scaled audit.
</div>
<div class="banner-stats">
<div class="bs-item"><div class="bs-num">≤0.00996</div><div class="bs-label">tail inheritance<br>at δ² = 0.01</div></div>
<div class="bs-item"><div class="bs-num">κ = 0.1667</div><div class="bs-label">DER slope<br>theory = fitted</div></div>
<div class="bs-item"><div class="bs-num">5 / 5</div><div class="bs-label">signal widths<br>student beats teacher</div></div>
<div class="bs-item"><div class="bs-num">Δ = 0.5333</div><div class="bs-label">PGR slope<br>theory = fitted</div></div>
</div>
</section>
<div class="body-grid" data-measure-role="body">
<div class="column" data-measure-role="column">
<div class="card highlight" data-measure-role="card">
<div class="section-title"><span class="num">1</span><span class="st-text">Spectral transfer, mode by mode</span></div>
<p class="body-text">Diagonalizing the student dynamics turns distillation into a filter. Modes within the student's horizon copy the teacher; unresolved tail modes are strongly attenuated.</p>
<div class="eqn"><span class="label">Theorem 1 anatomy</span>
$$R = \underbrace{E_T}{\text{teacher error}} + \underbrace{E_S}{\text{optimization}} + \underbrace{B_\mathrm{align}}{\text{alignment bias}}$$
</div>
<div class="callout"><strong>Prediction:</strong> one-to-one inheritance in learned modes; $O(\delta^2)$ inheritance in unlearned modes.</div>
</div>
<div class="card" data-measure-role="card" data-logbook-target="claim-1-theorem-1-provides-a-teacher-to-student-risk-decomposition-into-propagated-teacher-error-student-optimization-er">
<div class="section-title"><span class="num">2</span><span class="st-text">Claim 1 · risk inheritance</span></div>
<span class="scope-tag">Exact diagonal instantiation</span>
<div class="figure claim1-large"><img src="assets/claim1.png" alt="Mode-wise teacher error inheritance against student learning factor"><div class="caption">At $\delta=0.1$, head ≥0.9827 while tail ≤0.009956, satisfying $\delta^2=0.01$.</div></div>
<div class="verdict">Supported mechanistically</div>
</div>
</div>
<div class="column" data-measure-role="column">
<div class="card highlight" data-measure-role="card" data-logbook-target="claim-2-theorem-3-shows-that-under-model-mis-specification-the-distillation-efficiency-ratio-der-diverges-at-rate-omega">
<div class="section-title"><span class="num">3</span><span class="st-text">Claim 2 · horizon expansion</span></div>
<span class="scope-tag">Analytic proxy · exponent check</span>
<div class="eqn"><span class="label">Theorem 3</span>
$$\mathrm{DER}=\widetilde\Omega(N^\kappa),\quad \kappa=(\alpha_T-1-\beta)(1/\alpha_T-1/\alpha_S)=1/6$$
</div>
<div class="figure tight"><img src="assets/claim2.png" alt="DER and spectral horizon ratio as sample size grows"><div class="caption">Proxy slope is 0.166667 and DER reaches 46.4 at $N=10^{10}$; this checks the exponent only.</div></div>
</div>
<div class="card" data-measure-role="card" data-logbook-target="claim-4-theorem-5-quantifies-weak-to-strong-performance-recovery-via-performance-gap-recovered-pgr-1-o-tilde-k-dagger-2">
<div class="section-title"><span class="num">4</span><span class="st-text">Claim 4 · spectral denoising</span></div>
<div class="eqn"><span class="label">Theorem 5 / Eq. 7</span>
$$1-\mathrm{PGR}=\widetilde O\!\left((k^\dagger)^{\frac{2\alpha_S}{2\alpha_S+1}}N^{-\Delta}\right),\quad \Delta=0.5333$$
</div>
<div class="figure tight"><img src="assets/claim4.png" alt="Performance gap recovered converges to one"><div class="caption">Fitted $\Delta=0.533333$; PGR = 0.999952 at the largest grid point.</div></div>
</div>
</div>
<div class="column" data-measure-role="column">
<div class="card highlight" data-measure-role="card" data-logbook-target="claim-3-theorem-4-establishes-a-weak-to-strong-generalization-guarantee-a-strong-student-model-provably-surpasses-a-weak">
<div class="section-title"><span class="num">5</span><span class="st-text">Claim 3 · weak → strong</span></div>
<span class="scope-tag">Paper-scale synthetic dimensions · 64 seeds</span>
<p class="body-text">With $d=100$, $N=2000$ and $k^\dagger\in\{1,10,20,30,50\}$, the selected strong student beats its weak teacher and does so in all five tested signal settings.</p>
<table class="result-table">
<thead><tr><th class="method">$k^\dagger$</th><th>1</th><th>10</th><th>20</th><th>30</th><th>50</th></tr></thead>
<tbody><tr class="ours"><td class="method">best risk / teacher</td><td>0.145</td><td>0.524</td><td>0.714</td><td>0.818</td><td>0.928</td></tr>
<tr><td class="method">best step</td><td>11</td><td>51</td><td>80</td><td>115</td><td>182</td></tr></tbody>
</table>
<div class="callout emph mt-3"><strong>W2S observed:</strong> all five selected students surpass the teacher when intrinsic signal dimension is restricted.</div>
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<div class="card" data-measure-role="card" data-logbook-target="claim-5-figures-2-and-3-empirically-validate-the-risk-inheritance-and-early-stopping-predictions-using-both-synthetic-da">
<div class="section-title"><span class="num">6</span><span class="st-text">Claim 5 · stop before noise returns</span></div>
<div class="figure early-large"><img src="assets/claim3.png" alt="Student risk over training steps for five signal dimensions"><div class="caption">Every selected checkpoint beats the final checkpoint. Early stopping is beneficial across all five settings in this synthetic replication.</div></div>
<div class="verdict">Synthetic mechanism reproduced</div>
</div>
</div>
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<div class="card highlight" data-measure-role="card" data-logbook-target="claim-5-figures-2-and-3-empirically-validate-the-risk-inheritance-and-early-stopping-predictions-using-both-synthetic-da">
<div class="section-title"><span class="num">7</span><span class="st-text">Architecture spectra</span></div>
<span class="scope-tag">Scaled Figure 2(c) proxy</span>
<div class="figure arch-large"><img src="assets/architecture.png" alt="Log-log feature covariance spectra for three pretrained architectures on UTKFace"><div class="caption">1,000 UTKFace images; top-500 covariance eigenvalues. Fitted $\alpha$: ResNet18 1.986, ResNet50 1.551, ViT-B/16 1.628.</div></div>
<p class="body-text">Log–log fit $R^2$ ranges from 0.950 to 0.989, supporting approximate power-law decay in this scaled sample. This does not test downstream age-regression performance.</p>
</div>
<div class="card" data-measure-role="card">
<div class="section-title"><span class="num">8</span><span class="st-text">Audit boundary</span></div>
<table class="result-table">
<thead><tr><th class="method">Evidence</th><th>Scale</th><th>Verdict</th></tr></thead>
<tbody>
<tr class="ours"><td class="method">Claims 1–4</td><td>exact / synthetic</td><td>supported</td></tr>
<tr><td class="method">Figure 2 spectra</td><td>1k images, 3 nets</td><td>scaled support</td></tr>
<tr><td class="method">Full Figures 2–3</td><td>not rerun</td><td>partial</td></tr>
</tbody>
</table>
<div class="audit-note mt-3">The paper source links no official code. This independent audit publishes scripts, raw CSVs, jobs and seeds.</div>
</div>
</div>
</div>
<section class="takeaways-strip" data-measure-role="footer-strip">
<div class="ts-title"><span class="num">9</span> Evidence ladder</div>
<div class="ts-item"><span class="ts-key">Inheritance</span><span class="ts-text">head ≈ 1; tail ≤ δ²</span></div>
<div class="ts-item"><span class="ts-key">Expansion</span><span class="ts-text">DER ∝ N¹⁄⁶</span></div>
<div class="ts-item"><span class="ts-key">Denoising</span><span class="ts-text">PGR → 1</span></div>
<div class="ts-item"><span class="ts-key">Practice</span><span class="ts-text">selected beats final in 5/5</span></div>
</section>
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<div>Paper, commands, raw results and poster: <span class="repo">Hugging Face Trackio logbook</span></div>
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