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<!DOCTYPE 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">
<title>Reproducing: Improved Stochastic Optimization of LogSumExp — ICML 2026</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: #5B21B6; /* SoftPlus violet; white ink on it measures 8.9:1 (>= AA) */
--accent-deep: #3B0F7A;
--accent-light: #F0E9FD;
--accent-soft: #D8C8F6;
--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: #C9A24A;
--emph-soft: #FFF7E0;
--emph-ink: #14314A; /* ink ON the emphasis fill. NOT var(--accent-deep):
#1F4566 on the default gold measures 4.16:1 (< AA);
#14314A measures 5.58:1 (>= 4.5:1). */
/* Text */
--text-primary: #1A1A1A;
--text-secondary: #555555;
--text-muted: #888888;
/* Backgrounds */
--bg-page: #F5F6F9;
--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(29, 78, 216, 0.05);
--ornament-ink: rgba(29, 78, 216, 0.06);
/* 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; }
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(29, 78, 216, 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; /* header | banner | body | footer. minmax(0,1fr) (not bare 1fr): an over-tall body compresses instead of pushing 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 margin 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(--accent); }
.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 / white-bordered 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: repeat(4, 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: balance; /* centered banner headline: even the two lines so neither widows (Gate B) */
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 #6).
.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. */
.section-title .key-mark { color: var(--emph); font-size: var(--fs-3); }
.body-text, .card p, .card li {
font-family: var(--font-serif);
font-size: var(--fs-4);
line-height: 1.3;
color: var(--text-primary);
}
.card ul, .card ol { padding-left: calc(18 * var(--u)); }
.card li { margin-bottom: calc(2 * var(--u)); }
.keyword { color: var(--accent); font-weight: 700; }
.keyword-emph { color: var(--emph); font-weight: 700; }
.highlight-text {
background: var(--bg-emphasis);
padding: 0 calc(3 * var(--u));
border-radius: calc(2 * var(--u) * var(--rs));
}
/* Equation block */
.eqn {
background: var(--bg-emphasis);
border-left: calc(3 * var(--u)) solid var(--accent);
padding: calc(4 * var(--u)) calc(10 * var(--u));
margin: calc(4 * var(--u)) 0;
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}
</style>
</head>
<body>
<div class="poster" data-measure-role="poster">
<!-- =========================== HEADER =========================== -->
<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 CHALLENGE</div>
</div>
<div class="title-block">
<h1 class="title">Reproducing: <span class="accent">Improved Stochastic Optimization</span> of LogSumExp</h1>
<div class="subtitle">Independent reproduction &mdash; ICML 2026 Reproducibility Challenge</div>
<div class="authors-line">
<span class="author">SabaPivot</span>
<span class="aff">Independent NumPy / PyTorch-CPU re-implementation of arXiv&nbsp;2509.24894 &middot; official code exists (egorgladin/logsumexp-approx), read only for distributions and hyper-parameter grids</span>
</div>
</div>
<div class="right-block">
<div class="qr-block">
<div class="qr-label">arXiv 2509.24894</div>
<div class="qr-label">OpenReview TzQElzflxR</div>
<div class="qr-label">3 verified &middot; 2 falsified &middot; 1 toy</div>
</div>
</div>
</header>
<!-- ===================== VERDICT BANNER ===================== -->
<section class="framework-banner" data-measure-role="banner">
<div class="fb-text">
<span class="fb-label">Verdict</span>
&nbsp;The Safe-KL machinery is exactly as advertised: $f_\rho$ is <strong>$4\rho$-strongly convex</strong>, $f_\rho^*$ is <strong>$\frac{1}{4\rho}$-smooth</strong>, the CVaR sandwich holds in 4000/4000 instances and the continuous-OT experiment reproduces with a <strong>145&times;</strong> smaller optimality gap than the baseline. Two printed statements do not survive: the sandwich <strong>$F_\rho-O(\rho)\le F\le F_\rho$ is inverted</strong> ($F_\rho\le F$ in 3000/3000 instances) and on California Housing <strong>no</strong> admissible $\rho$ is stable at $\eta=10^{-4}$ with $|D|=10$.
</div>
<div class="banner-stats">
<div class="bs-item"><div class="bs-num">3</div><div class="bs-label">claims<br>verified</div></div>
<div class="bs-item"><div class="bs-num">2</div><div class="bs-label">falsified<br>as stated</div></div>
<div class="bs-item"><div class="bs-num">1</div><div class="bs-label">toy<br>(reduced scale)</div></div>
<div class="bs-item"><div class="bs-num">$0</div><div class="bs-label">CPU only,<br>&lt; 3 h wall</div></div>
</div>
</section>
<!-- ============================ BODY ============================ -->
<div class="body-grid" data-measure-role="body">
<div class="column" data-measure-role="column">
<div class="card highlight" data-measure-role="card"
data-logbook-target="executive-summary" data-logbook-label="Executive summary">
<div class="section-title"><span class="num">1</span><span class="st-text">Setting</span></div>
<p class="body-text fs-3">
The <span class="keyword">log-partition functional</span> $F(\phi;\mu)=\log\int e^{\phi}d\mu$ admits no cheap
unbiased stochastic gradient. The paper swaps the KL divergence in the Gibbs principle for a
<span class="keyword">safe KL divergence</span> $D_\rho$ whose generator caps the density at $1/\rho$.
</p>
<div class="eqn">
<span class="label">Def 2.1 and Eq. 6</span>
$$f_\rho(t)=t\log t+1+\tfrac{1-\rho t}{\rho}\log(1-\rho t)$$
$$F_\rho(\phi;\mu)=\inf_{\alpha}\;\alpha-1+\tfrac1\rho\int\log\big(1+\rho e^{\phi-\alpha}\big)d\mu$$
</div>
<div class="flow-strip">
<div class="step"><span class="step-name">Def 2.1</span>Safe KL</div>
<div class="arrow">&rarr;</div>
<div class="step"><span class="step-name">Lem 2.3</span>SoftPlus</div>
<div class="arrow">&rarr;</div>
<div class="step step--final"><span class="step-name">Eq. 19/22</span>SGD</div>
</div>
</div>
<div class="card mt-1" data-measure-role="card">
<div class="section-title"><span class="num">2</span><span class="st-text">Reproduction Map</span></div>
<table class="claim-pills">
<tbody>
<tr><td class="cp-id">C1</td><td>Prop&nbsp;2.4 &mdash; $F_\rho-O(\rho)\le F\le F_\rho$</td><td class="cp-derived">falsified</td></tr>
<tr><td class="cp-id">C2</td><td>Lem&nbsp;2.7 &mdash; $\rho$-SC, $\tfrac1\rho$-smooth conjugate</td><td class="cp-fact">verified</td></tr>
<tr><td class="cp-id">C3</td><td>Prop&nbsp;2.6 &mdash; CVaR sandwich, both limits</td><td class="cp-fact">verified</td></tr>
<tr><td class="cp-id">C4</td><td>Sec&nbsp;3.1 &mdash; continuous eOT, $\varepsilon=0.01$</td><td class="cp-fact">verified</td></tr>
<tr><td class="cp-id">C5</td><td>Sec&nbsp;3.2 &mdash; KL-DRO stepsize $10^{-4}$</td><td class="cp-derived">falsified</td></tr>
<tr><td class="cp-id">C6</td><td>Sec&nbsp;3.3 &mdash; UOT-DRO, noisy MNIST</td><td class="cp-derived">toy</td></tr>
</tbody>
</table>
<p class="body-text fs-3 mt-2">
Conjugate, primal&ndash;dual pair, both SGD schemes and all three experiments were written from scratch.
Verdicts come from executable tests with fixed seeds, never from reading a proof.
</p>
</div>
<div class="card mt-6" data-measure-role="card">
<div class="section-title"><span class="num">3</span><span class="st-text">Executable Checks &mdash; Analytic Claims</span></div>
<table class="result-table">
<thead>
<tr><th class="method">test</th><th>checks</th><th class="derived">violations</th></tr>
</thead>
<tbody>
<tr><td class="method">Lem 2.3 conjugate formula</td><td>648</td><td class="derived">$3\!\cdot\!10^{-11}$ max err</td></tr>
<tr><td class="method">duality (5)$\Leftrightarrow$(6), density $&lt;1/\rho$</td><td>12</td><td class="derived">$9\!\cdot\!10^{-15}$ gap</td></tr>
<tr><td class="method">Prop 2.4(iii) inside $\rho$ range</td><td>4751</td><td class="derived">0</td></tr>
<tr class="ours"><td class="method">Prop 2.4(iii) outside it</td><td>7249</td><td class="derived">85</td></tr>
<tr><td class="method">Cor 2.5 LogSumExp bounds</td><td>3000</td><td class="derived">0 both sides</td></tr>
</tbody>
</table>
<p class="body-text fs-3 mt-1">
Prop 2.4(iv) behaves the same way: 0 violations in 5451 checks inside its $\rho$ range, 431 of 6549 outside.
The assumptions are load-bearing, and the corrected sandwich survives everything.
</p>
</div>
</div>
<div class="column" data-measure-role="column">
<div class="card highlight" data-measure-role="card"
data-logbook-target="claim-1-safe-kl-divergence-and-the-f-rho-o-rho-f-f-rho-sandwich-prop-2-4"
data-logbook-label="Claim 1: the sandwich (Prop 2.4)">
<div class="section-title"><span class="num">4</span><span class="st-text">Claim 1 &mdash; Sandwich Inverted</span></div>
<p class="body-text fs-3">
Prop&nbsp;2.4(i) makes $F_\rho$ <em>decreasing</em> in $\rho$ and 2.4(ii) sends $F_\rho\to F$, so $F_\rho\le F$;
2.4(iii)&ndash;(iv) add $F_\rho\ge F-O(\rho)$. The sentence printed after Prop&nbsp;2.4 asserts the reverse.
</p>
<div class="figure">
<img src="fig_sandwich.png" data-source="paper" data-asset-id="fig-sandwich" class="w-90"
alt="Left: approximation error F minus F rho decaying with slope one in rho. Right: bar chart showing zero of 3000 instances satisfy the printed direction.">
<div class="caption fs-2">
<strong>Left:</strong> $F-F_\rho$ decays with fitted exponent $1.012\pm0.076$ &mdash; the $O(\rho)$ accuracy is real.
<strong>Right:</strong> the printed direction holds in <strong>0 of 3000</strong> instances, the reverse in all 3000.
</div>
</div>
<div class="callout">
<strong>Hand-checkable counterexample.</strong> $\mu=\delta_0$, $\phi\equiv0$, $\rho=0.1$: $F=0$ but
$F_\rho=\log(1-\rho)-1-\tfrac{\log(1-\rho)}{\rho}=-0.05176$.
</div>
</div>
<div class="card highlight mt-3" data-measure-role="card"
data-logbook-target="claim-2-rescaled-softplus-conjugate-is-rho-strongly-convex-with-1-rho-smooth-conjugate-lemma-2-7"
data-logbook-label="Claim 2: strong convexity (Lemma 2.7)">
<div class="section-title"><span class="num">5</span><span class="st-text">Claim 2 &mdash; Verified, Loose by 4</span></div>
<div class="eqn">
<span class="label">tight constants, located numerically then confirmed in closed form</span>
$$\min_t f_\rho''(t)=4\rho\;\;(t=\tfrac1{2\rho}),\qquad \max_s (f_\rho^*)''(s)=\tfrac1{4\rho}\;\;(s=-\log\rho)$$
</div>
<div class="figure">
<img src="fig_convexity.png" data-source="paper" data-asset-id="fig-convexity" class="w-80"
alt="Left: second derivative of f rho divided by rho, flat-bottomed at four. Right: rho times the second derivative of the conjugate, peaking at one quarter.">
<div class="caption fs-2">
Both claimed constants hold for every $\rho\in\{10^{-4},\dots,0.99\}$, with a factor of exactly <strong>4</strong>
to spare. Chord tests give 0 violations at modulus $\rho$ and at $4\rho$, but $\approx\!900/20000$ at $4.05\rho$.
</div>
</div>
<p class="body-text fs-3">
The Legendre identity $(f_\rho^*)''(s)=1/f_\rho''\big((f_\rho^*)'(s)\big)$ reproduces to $8\times10^{-6}$
relative error, so strong convexity and conjugate smoothness are the same fact, checked from both sides.
</p>
</div>
</div>
<div class="column" data-measure-role="column">
<div class="card" data-measure-role="card"
data-logbook-target="claim-3-family-bounds-and-connects-to-cvar-recovering-cvar-and-logsumexp-as-limits-prop-2-6"
data-logbook-label="Claim 3: CVaR link (Prop 2.6)">
<div class="section-title"><span class="num">6</span><span class="st-text">Claim 3 &mdash; CVaR and LogSumExp Limits</span></div>
<div class="eqn">
<span class="label">Prop 2.6, tested on 4000 random instances &mdash; 0 violations either side</span>
$$\mathrm{CVaR}_\rho(\phi)+\lambda(\log\rho-1)\le\lambda F_\rho(\phi/\lambda)\le\mathrm{CVaR}_\rho(\phi)+\lambda\big(\log\rho-1+\tfrac1\rho\big)$$
</div>
<table class="result-table">
<thead>
<tr><th class="method">limit / audit</th><th>result</th><th class="derived">expected</th></tr>
</thead>
<tbody>
<tr><td class="method">$\lambda\to0$: distance to $\mathrm{CVaR}_\rho$</td><td class="best">rate $\lambda^{1.18}$</td><td class="derived">$O(\lambda)$</td></tr>
<tr><td class="method">$\rho\to0$: distance to LogSumExp</td><td class="best">rate $\rho^{1.00\pm0.03}$</td><td class="derived">$O(\rho)$</td></tr>
<tr><td class="method">upper constant $\to0.5\lambda/\rho$</td><td>107/1500 fail</td><td class="derived">must fail</td></tr>
<tr><td class="method">lower constant $+\,0.05\lambda$</td><td>183/1500 fail</td><td class="derived">must fail</td></tr>
<tr class="ours"><td class="method">$\rho\to1$: $\mathrm{CVaR}_\rho\to$ mean</td><td>0.023 vs 0.006</td><td class="derived">coincide</td></tr>
</tbody>
</table>
<p class="body-text fs-3 mt-1">
Both endpoints of the sandwich are essentially attained, so Prop&nbsp;2.6 is tight rather than loose
bookkeeping, and the family really does interpolate CVaR and LogSumExp.
</p>
</div>
<div class="card highlight mt-4" data-measure-role="card"
data-logbook-target="claim-4-continuous-entropy-regularized-ot-at-eps-0-01-semi-dual-avoids-overflow-converges-in-1e4-iters-fig-2"
data-logbook-label="Claim 4: continuous eOT (Fig 2)">
<div class="section-title"><span class="num">7</span><span class="st-text">Claim 4 &mdash; eOT at $\varepsilon=0.01$</span></div>
<div class="figure">
<img src="fig_eot.png" data-source="paper" data-asset-id="fig-eot" class="w-70"
alt="Optimality gap versus iteration: the baseline dual stays near 0.55 while the proposed semi-dual falls to 0.004 by ten thousand iterations.">
<div class="caption fs-2">
RKHS kernel SGD, 20 seeds, $10^5$ iterations, gap against a semi-discrete reference $\hat W=0.76726$.
The proposed method plateaus at <strong>0.0038</strong> by $\sim\!10^4$ iterations; the baseline at its own
best $C=10^{-3}$ is still at <strong>0.55</strong> &mdash; <strong>145&times;</strong> worse.
</div>
</div>
<p class="body-text fs-3">
<span class="keyword">Overflow (Rem. 3.1):</span> $e^{z/\varepsilon}$ overflows for $z\ge7.0978$ (float64) and
$z\ge0.8872$ (float32); both confirmed by bisection. In float32 the baseline returns <code>inf</code> at
<strong>iteration 2</strong>, while the proposed method reaches $z=14.27$ &mdash; past even the float64
threshold &mdash; without overflowing, because it never exponentiates. With $C\ge10^{-2}$ the baseline
diverges in 4/4 seeds.
</p>
</div>
</div>
<div class="column" data-measure-role="column">
<div class="card" data-measure-role="card"
data-logbook-target="claim-5-kl-regularized-dro-on-california-housing-eta-1e-4-across-batch-10-100-1000-vs-baseline-eta-1e-6-fig-3"
data-logbook-label="Claim 5: KL-DRO stepsizes (Fig 3)">
<div class="section-title"><span class="num">8</span><span class="st-text">Claim 5 &mdash; $10^{-4}$ Out of Reach at $|D|=10$</span></div>
<div class="figure">
<img src="fig_stepsize.png" data-source="paper" data-asset-id="fig-stepsize" class="w-50"
alt="Heatmap of the largest stable stepsize per method and batch size; 1e-4 is reached only at batch size 1000 or with rho at least one half.">
<div class="caption fs-2">
California Housing, 1050 runs, 10 seeds, 50 epochs. Largest $\eta$ converging on <strong>all</strong> seeds.
The baseline's $10^{-6}$ at $|D|=10$ and $10^{-5}$ at $|D|=1000$ reproduce exactly.
</div>
</div>
<p class="body-text fs-3">
At $|D|=10$ with $\eta=10^{-4}$ <strong>every</strong> configuration blows up (0/10 seeds; $L$ rises from
$44.0$ to $1.3\times10^{4}$). Structural reason: the weight $\sigma_\rho\le1/\rho$ makes the proposed
gradient up to $1/\rho$ times larger than the baseline's batch-softmax weights, which sum to one.
</p>
</div>
<div class="card" data-measure-role="card"
data-logbook-target="claim-6-unbalanced-ot-dro-on-mnist-with-label-noise-eta-1e-4-vs-baseline-eta-1e-5-fig-4"
data-logbook-label="Claim 6: UOT-DRO on MNIST (Fig 4)">
<div class="section-title"><span class="num">9</span><span class="st-text">Claim 6 &mdash; Noisy MNIST (toy)</span></div>
<p class="body-text fs-3">
Same CNN, batch size 1, $\lambda=\beta=1$, $\rho=0.1$, 5 Nesterov inner steps, the authors' own 25%
feature-dependent noisy labels &mdash; but 10&ndash;25k images and 4&ndash;5 epochs, not 50k and 20.
The baseline takes a <span class="keyword">floating-point exception</span> at $\eta=10^{-3}$ in 3/3 seeds
and at $10^{-4}$ in 1/3 at 50k steps; the proposed method never overflows anywhere. At the pair named in
Fig.&nbsp;4 the ordering reproduces &mdash; proposed at $10^{-4}$ gives $F=0.89$, baseline at $10^{-5}$
only $1.00$ &mdash; but in the longest run (100k steps) the baseline survives $10^{-4}$ and then
<em>beats</em> the proposed method, $0.66$ vs $0.78$: its need for $10^{-5}$ is horizon-dependent.
</p>
</div>
<div class="card mt-2" data-measure-role="card"
data-logbook-target="conclusion" data-logbook-label="Conclusion">
<div class="section-title"><span class="num">10</span><span class="st-text">Scope &amp; Bottom Line</span></div>
<ul class="fs-3">
<li>Both falsifications are corroborated by the authors' <span class="keyword">own released code</span>, which uses $\eta=10^{-6}$ at $|D|=10$, and by their Cor.&nbsp;2.5, which states the sandwich the other way round.</li>
<li>The algorithm is sound &mdash; only two printed statements about it fail.</li>
</ul>
<div class="keybox mt-6">
<div class="kb-item"><div class="kb-num">CPU</div><div class="kb-label">no GPU,<br>no API key</div></div>
<div class="kb-item"><div class="kb-num">&lt;3h</div><div class="kb-label">wall clock</div></div>
<div class="kb-item"><div class="kb-num">$0</div><div class="kb-label">total cost</div></div>
</div>
</div>
</div>
</div>
<!-- ============================ FOOTER ============================ -->
<div class="footer" data-measure-role="footer">
<div>
<strong class="method-name">Safe KL divergence &amp; the SoftPlus approximation of LogSumExp</strong> &middot;
Independent reproduction, ICML 2026 Reproducibility Challenge &middot; 3 verified, 2 falsified as stated, 1 toy &middot; CPU only, $0.
</div>
<div>
Paper: <span class="repo">arXiv:2509.24894</span> &nbsp;&middot;&nbsp;
OpenReview: <span class="repo">TzQElzflxR</span> &nbsp;&middot;&nbsp;
Reproduction: <span class="repo">SabaPivot</span>
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