Buckets:
| <!-- | |
| 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: Floating-Point Networks with AD Can Represent Almost All FP Functions and Their Gradients — 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: #B03A2E; /* round-off red; white ink on it measures 6.05:1 (>= AA) */ | |
| --accent-deep: #7B1F16; | |
| --accent-light: #FBEAE7; | |
| --accent-soft: #F0C7C0; | |
| --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(176, 58, 46, 0.06); | |
| --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 -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(11 * 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; | |
| font-size: var(--fs-5); | |
| overflow-x: hidden; | |
| } | |
| /* Predefined variant for a larger / more legible display equation. | |
| `calc(var(--fs-N) * k)` is allowed here because this is a | |
| COMPONENTS.md-registered variant (DESIGN_FINAL §A / §10 f). */ | |
| .eqn--large { font-size: calc(var(--fs-5) * 1.25); } | |
| .eqn .label { | |
| display: block; | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-2); | |
| color: var(--accent); | |
| font-weight: 600; | |
| margin-bottom: calc(2 * var(--u)); | |
| text-transform: uppercase; | |
| letter-spacing: 1px; | |
| } | |
| /* Callout: solid accent for primary, solid emphasis fill for theorems / "★ key" strips */ | |
| .callout { | |
| background: var(--accent); | |
| color: var(--accent-ink); | |
| padding: calc(5 * var(--u)) calc(10 * var(--u)); | |
| border-radius: calc(4 * var(--u) * var(--rs)); | |
| font-size: var(--fs-4); | |
| margin: calc(4 * var(--u)) 0; | |
| } | |
| .callout strong { color: var(--emph-soft); } | |
| /* Flat solid emphasis fill (de-gradient). */ | |
| .callout.emph { | |
| background: var(--emph); | |
| color: var(--emph-ink); /* route through the token — accent-deep here would dodge the register swap AND fail AA on the default gold */ | |
| } | |
| .callout.emph strong { color: var(--emph-ink); } | |
| /* Figure container */ | |
| .figure { margin: calc(4 * var(--u)) 0; text-align: center; } | |
| .figure img:not([class*="w-"]) { width: 100%; } | |
| .figure--wide img { width: 100%; } /* predefined variant: force full card width over any .w-NN (fix (f)) */ | |
| .figure img { | |
| border-radius: calc(4 * var(--u) * var(--rs)); | |
| border: calc(1 * var(--u)) solid var(--fig-frame); | |
| background: var(--fig-bg); | |
| } | |
| .figure .caption { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-3); | |
| color: var(--text-secondary); | |
| margin-top: calc(3 * var(--u)); | |
| line-height: 1.3; | |
| text-align: left; | |
| } | |
| .figure .caption strong { color: var(--accent-deep); } | |
| /* Float a figure BESIDE text in a TEXT-RICH card: text wraps to its side | |
| and then below it. The clearfix grows the card to contain the float; | |
| mark the <img> data-fig-layout="beside-text" so the AR gates honour the | |
| intentionally small width. Use ONLY when there is enough text to fill the | |
| figure's height -- a text-sparse card should center .figure instead. A | |
| short-text float leaves an L-shaped void below the text, which polish's | |
| FIG/BESIDE-TEXT-VOID flags. */ | |
| .fig-wrap::after { content: ""; display: table; clear: both; } | |
| .ff-fig { | |
| float: right; | |
| width: 48%; max-width: 58%; min-width: 38%; | |
| margin: calc(1 * var(--u)) 0 calc(3 * var(--u)) calc(11 * var(--u)); | |
| text-align: center; | |
| } | |
| .ff-fig.left { | |
| float: left; | |
| margin: calc(1 * var(--u)) calc(11 * var(--u)) calc(3 * var(--u)) 0; | |
| } | |
| .ff-fig img { | |
| display: block; | |
| width: 100%; | |
| border-radius: calc(4 * var(--u) * var(--rs)); | |
| border: calc(1 * var(--u)) solid var(--fig-frame); | |
| background: var(--fig-bg); | |
| } | |
| .ff-fig .caption { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-3); | |
| color: var(--text-secondary); | |
| margin-top: calc(3 * var(--u)); | |
| line-height: 1.3; | |
| text-align: center; | |
| } | |
| /* Result table with .ours row highlighted with the emphasis tint */ | |
| .result-table { | |
| width: 100%; | |
| border-collapse: collapse; | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-3); | |
| margin-top: calc(3 * var(--u)); | |
| } | |
| .result-table th, .result-table td { | |
| padding: calc(2 * var(--u)) calc(4 * var(--u)); | |
| text-align: center; | |
| border-bottom: calc(1 * var(--u)) solid var(--border-soft); | |
| } | |
| .result-table thead th { | |
| background: var(--accent); color: var(--accent-ink); | |
| font-weight: 600; font-size: var(--fs-2); | |
| } | |
| .result-table tbody tr.group-row td { | |
| background: var(--bg-emphasis); font-weight: 700; | |
| text-align: left; | |
| color: var(--accent-deep); | |
| padding-left: calc(8 * var(--u)); | |
| border-bottom: calc(2 * var(--u)) solid var(--accent); | |
| } | |
| .result-table tbody tr.ours td { background: var(--emph-soft); font-weight: 700; } | |
| .result-table tbody tr.ours td:first-child { color: var(--accent-deep); } | |
| /* Greyed reference row (was inline color:#888). */ | |
| .result-table tbody tr.reference td { color: var(--text-muted); } | |
| .result-table .method { text-align: left; padding-left: calc(8 * var(--u)); } | |
| .result-table .best { color: var(--accent); font-weight: 700; } | |
| /* 3-up stat box */ | |
| .keybox { | |
| display: grid; | |
| grid-template-columns: repeat(3, 1fr); | |
| gap: calc(4 * var(--u)); | |
| margin: calc(4 * var(--u)) 0 0; | |
| } | |
| .keybox .kb-item { | |
| background: var(--bg-emphasis); | |
| border-top: calc(2 * var(--u)) solid var(--accent); | |
| padding: calc(3 * var(--u)); | |
| text-align: center; | |
| /* The grid stretches every tile to the tallest one; center the content | |
| vertically so a 1-line tile's number aligns with a 2-line neighbour's | |
| instead of top-ragged (SKILL Layout pitfall — stat-tile alignment). */ | |
| display: flex; flex-direction: column; justify-content: center; | |
| border-radius: 0 0 calc(3 * var(--u) * var(--rs)) calc(3 * var(--u) * var(--rs)); | |
| } | |
| .kb-item .kb-num { | |
| font-family: var(--font-sans); | |
| font-weight: 800; | |
| font-size: var(--fs-6); | |
| color: var(--accent); | |
| line-height: 1; | |
| } | |
| .kb-item .kb-label { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-1); | |
| color: var(--text-secondary); | |
| margin-top: calc(2 * var(--u)); | |
| line-height: 1.1; | |
| /* Reserve two label lines (2lh tracks this line-height) so 1-line | |
| and 2-line labels occupy the same height and the big numbers | |
| align across tiles. Keep labels <= 2 lines (COMPONENTS §keybox). */ | |
| min-height: 2lh; | |
| } | |
| /* Optional takeaways strip (delete the section if not needed) */ | |
| .takeaways-strip { | |
| display: grid; | |
| grid-template-columns: auto repeat(4, 1fr); | |
| align-items: center; | |
| gap: calc(10 * var(--u)); | |
| /* Flat solid emphasis fill (de-gradient). */ | |
| background: var(--bg-emphasis); | |
| border: calc(1 * var(--u)) solid var(--border-soft); | |
| border-radius: calc(5 * var(--u) * var(--rs)); | |
| padding: calc(8 * var(--u)) calc(12 * var(--u)); | |
| } | |
| .takeaways-strip .ts-title { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-6); | |
| font-weight: 800; | |
| color: var(--accent-deep); | |
| display: flex; align-items: center; gap: calc(6 * var(--u)); | |
| } | |
| .takeaways-strip .ts-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; | |
| } | |
| .takeaways-strip .ts-item { | |
| border-left: calc(3 * var(--u)) solid var(--accent); | |
| padding-left: calc(8 * var(--u)); | |
| line-height: 1.3; | |
| text-align: center; | |
| text-wrap: balance; | |
| } | |
| .takeaways-strip .ts-key { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-3); | |
| font-weight: 700; | |
| color: var(--accent); | |
| text-transform: uppercase; | |
| letter-spacing: 1px; | |
| } | |
| .takeaways-strip .ts-text { | |
| font-family: var(--font-serif); | |
| font-size: var(--fs-4); | |
| margin-left: calc(4 * var(--u)); | |
| } | |
| /* Footer */ | |
| .footer { | |
| grid-column: 1 / -1; | |
| display: flex; justify-content: space-between; align-items: baseline; | |
| /* When the two blocks can't sit side by side they stack (wrap) instead of | |
| overflowing; row-gap keeps the stacked blocks legible. */ | |
| flex-wrap: wrap; gap: calc(2 * var(--u)) calc(10 * var(--u)); | |
| padding-top: calc(8 * var(--u)); | |
| border-top: calc(1 * var(--u)) solid var(--border-soft); | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-5); | |
| color: var(--text-muted); | |
| } | |
| .footer .method-name { color: var(--accent-deep); } | |
| /* Long repo URL / email breaks mid-token rather than overflowing the margin. */ | |
| .footer .repo { color: var(--accent); font-weight: 600; overflow-wrap: anywhere; } | |
| /* Optional watermark */ | |
| .ornament { | |
| position: absolute; | |
| right: calc(20 * var(--u)); | |
| bottom: calc(20 * var(--u)); | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-9); | |
| color: var(--ornament-ink); | |
| font-weight: 900; | |
| letter-spacing: 4px; | |
| pointer-events: none; | |
| user-select: none; | |
| } | |
| /* ========================================================= | |
| DENSITY COMPONENTS (catalogued — see COMPONENTS.md). | |
| Guardrail: no component-local color semantics. Distinction is | |
| carried by labels, order and typography — never by new hues. | |
| ========================================================= */ | |
| /* equation-stack: compact multi-row formula stack (denser than one big .eqn) */ | |
| .equation-stack { margin: calc(2 * var(--u)) 0; } | |
| .equation-stack .eqn { margin: calc(2 * var(--u)) 0; padding: calc(2 * var(--u)) calc(8 * var(--u)); } | |
| /* eqn-anatomy: term-by-term anatomy grid (2x2 default; --row variant = 1x4) */ | |
| .eqn-anatomy { | |
| display: grid; grid-template-columns: 1fr 1fr; | |
| gap: calc(2.5 * var(--u)); margin: calc(3 * var(--u)) 0; | |
| } | |
| .eqn-anatomy.eqn-anatomy--row { grid-template-columns: repeat(4, 1fr); } | |
| .eqn-anatomy .ea-item { | |
| background: var(--bg-card-tint); | |
| border: 1px solid var(--border-soft); | |
| border-left: calc(2 * var(--u)) solid var(--accent); | |
| border-radius: calc(2 * var(--u) * var(--rs)); | |
| padding: calc(2 * var(--u)) calc(4 * var(--u)); | |
| font-size: var(--fs-2); line-height: 1.3; | |
| } | |
| .eqn-anatomy .ea-tag { | |
| display: inline-block; font-family: var(--font-sans); font-weight: 700; | |
| font-size: var(--fs-1); color: var(--accent-deep); | |
| background: var(--accent-light); border-radius: calc(1.5 * var(--u) * var(--rs)); | |
| padding: calc(0.5 * var(--u)) calc(2.5 * var(--u)); | |
| margin-right: calc(1.5 * var(--u)); | |
| } | |
| /* flow-strip: labeled pipeline, ALL steps the same accent; ONLY the | |
| final step may carry the emphasis top bar. Not an "algorithm" unless the | |
| paper has one — see COMPONENTS.md. */ | |
| .flow-strip { display: flex; align-items: stretch; gap: calc(1.5 * var(--u)); margin: calc(3 * var(--u)) 0; } | |
| .flow-strip .step { | |
| flex: 1; background: var(--accent-light); | |
| border: 1px solid var(--accent-soft); border-radius: calc(2 * var(--u) * var(--rs)); | |
| padding: calc(2 * var(--u)) calc(2.5 * var(--u)); | |
| text-align: center; font-size: var(--fs-2); line-height: 1.25; | |
| } | |
| .flow-strip .step .step-name { | |
| display: block; font-family: var(--font-sans); font-weight: 700; | |
| font-size: var(--fs-1); color: var(--accent-deep); | |
| letter-spacing: 0.5px; text-transform: uppercase; | |
| margin-bottom: calc(1 * var(--u)); | |
| } | |
| .flow-strip .step--final { border-top: calc(1.5 * var(--u)) solid var(--emph); background: var(--emph-soft); } | |
| .flow-strip .arrow { | |
| align-self: center; color: var(--accent); | |
| font-family: var(--font-sans); font-weight: 700; font-size: var(--fs-4); | |
| flex: 0 0 auto; | |
| } | |
| /* figure--duo: two paper figures sharing one caption; each img MUST be | |
| a data-source="paper" asset and carry .w-45/.w-50 (42-48% each). */ | |
| .figure--duo { display: flex; gap: calc(3 * var(--u)); align-items: flex-start; justify-content: center; } | |
| .figure--duo img { max-width: 48%; min-width: 0; } /* hard cap: duo contract is 42-48% each; an oversized w-NN cannot overflow the card */ | |
| /* result-table derived column (emph-soft = DERIVED arithmetic; label it) */ | |
| .result-table th.derived, .result-table td.derived { | |
| background: var(--emph-soft); font-family: var(--font-sans); font-weight: 700; | |
| } | |
| /* Header cells keep the accent ink rule: on the emph-soft ground the white | |
| head ink would read 1.07:1, so route the header's derived cell through | |
| the emphasis ink token (Gate G -- never inherit ink across a ground change). */ | |
| .result-table thead th.derived { color: var(--emph-ink); } | |
| /* keybox 4-up variant */ | |
| .keybox.keybox--4 { grid-template-columns: repeat(4, 1fr); } | |
| /* algo: compact numbered procedure — ONLY when the paper itself states | |
| an explicit algorithm/procedure; never invent steps. */ | |
| ol.algo { padding-left: calc(16 * var(--u)); } | |
| ol.algo li { margin-bottom: calc(1.5 * var(--u)); font-size: var(--fs-3); line-height: 1.3; } | |
| /* claim-pills: provenance mini-table (numeric-heavy posters only) */ | |
| .claim-pills { width: 100%; border-collapse: collapse; font-family: var(--font-sans); font-size: var(--fs-2); } | |
| .claim-pills td { | |
| border-bottom: 1px solid var(--border-soft); | |
| padding: calc(1.5 * var(--u)) calc(3 * var(--u)); | |
| } | |
| .claim-pills .cp-id { | |
| font-weight: 700; color: var(--accent-deep); background: var(--accent-light); | |
| border-radius: calc(1.5 * var(--u) * var(--rs)); padding: 0 calc(2.5 * var(--u) * var(--rs)); white-space: nowrap; | |
| } | |
| .claim-pills .cp-fact { color: var(--accent-deep); font-weight: 700; } | |
| .claim-pills .cp-derived { color: var(--text-secondary); font-weight: 700; } | |
| /* Grid-blowout guards: (1) columns may shrink below min-content so a | |
| wide equation can never widen its track and squeeze siblings; | |
| (2) over-wide display math scales down to fit its box instead of | |
| blowing out the card (SVG keeps aspect via height:auto). */ | |
| .body-grid > .column { min-width: 0; } | |
| .card { min-width: 0; } | |
| .eqn mjx-container > svg { max-width: 100%; height: auto; } | |
| /* ── Utility classes — defined LAST so equal-specificity ties | |
| resolve in the utility's favor (source order). ── */ | |
| .fs-1 { font-size: var(--fs-1); } | |
| .fs-2 { font-size: var(--fs-2); } | |
| .fs-3 { font-size: var(--fs-3); } | |
| .fs-4 { font-size: var(--fs-4); } | |
| .fs-5 { font-size: var(--fs-5); } | |
| .fs-6 { font-size: var(--fs-6); } | |
| .fs-7 { font-size: var(--fs-7); } | |
| .fs-8 { font-size: var(--fs-8); } | |
| .fs-9 { font-size: var(--fs-9); } | |
| .mt-1 { margin-top: calc(1 * var(--u)); } | |
| .mt-2 { margin-top: calc(2 * var(--u)); } | |
| .mt-3 { margin-top: calc(3 * var(--u)); } | |
| .mt-4 { margin-top: calc(4 * var(--u)); } | |
| .mt-5 { margin-top: calc(5 * var(--u)); } | |
| .mt-6 { margin-top: calc(6 * var(--u)); } | |
| .mb-1 { margin-bottom: calc(1 * var(--u)); } | |
| .mb-2 { margin-bottom: calc(2 * var(--u)); } | |
| .mb-3 { margin-bottom: calc(3 * var(--u)); } | |
| .mb-4 { margin-bottom: calc(4 * var(--u)); } | |
| .w-45 { width: 45%; } | |
| .w-50 { width: 50%; } | |
| .w-55 { width: 55%; } | |
| .w-60 { width: 60%; } | |
| .w-65 { width: 65%; } | |
| .w-70 { width: 70%; } | |
| .w-75 { width: 75%; } | |
| .w-80 { width: 80%; } | |
| .w-85 { width: 85%; } | |
| .w-90 { width: 90%; } | |
| .w-95 { width: 95%; } | |
| .w-100 { width: 100%; } | |
| .text-secondary { color: var(--text-secondary); } | |
| .text-muted { color: var(--text-muted); } | |
| .nowrap { white-space: nowrap; } | |
| .text-center { text-align: center; } | |
| /* ========================================================= | |
| PRINT OVERRIDE — KEEP LAST so it wins source-order ties. | |
| ========================================================= */ | |
| @media print { | |
| html, body { background: white; } | |
| .poster { margin: 0; box-shadow: none; width: 60in; height: 36in; page-break-after: avoid; } | |
| :root { --u: 1mm; } | |
| } | |
| </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">Floating-Point Networks</span> with Automatic Differentiation Can Represent Almost All Floating-Point Functions <span class="accent">and Their Gradients</span></h1> | |
| <div class="subtitle">Independent reproduction — ICML 2026 Reproducibility Challenge</div> | |
| <div class="authors-line"> | |
| <span class="author">SabaPivot</span> | |
| <span class="aff">Independent re-derivation of arXiv 2605.01702 · constructive existence paper · author code exists (yechanp/fp-grad-rep, ReLU only)</span> | |
| </div> | |
| </div> | |
| <div class="right-block"> | |
| <div class="qr-block"> | |
| <div class="qr-label">arXiv 2605.01702</div> | |
| <div class="qr-label">OpenReview g89qqA6qmD</div> | |
| <div class="qr-label">6 / 6 claims verified</div> | |
| </div> | |
| </div> | |
| </header> | |
| <!-- ===================== VERDICT BANNER ===================== --> | |
| <section class="framework-banner" data-measure-role="banner"> | |
| <div class="fb-text"> | |
| <span class="fb-label">Verdict</span> | |
| We <strong>build</strong> the networks, run real IEEE-754 automatic differentiation, and check both outputs against two independently chosen targets at every point of a finite domain. A floating-point network carries an <strong>arbitrary value and an arbitrary, unrelated AD gradient at once</strong> — bit for bit, all six activations, binary32 and binary64. In exact rational arithmetic the same networks fail. <strong>All six claims verified.</strong> | |
| </div> | |
| <div class="banner-stats"> | |
| <div class="bs-item"><div class="bs-num">6/6</div><div class="bs-label">claims<br>verified</div></div> | |
| <div class="bs-item"><div class="bs-num">0.0</div><div class="bs-label">max abs error,<br>values & grads</div></div> | |
| <div class="bs-item"><div class="bs-num">1188</div><div class="bs-label">exact checks,<br>36 networks</div></div> | |
| <div class="bs-item"><div class="bs-num">$0</div><div class="bs-label">CPU only,<br>~6 min</div></div> | |
| </div> | |
| </section> | |
| <!-- ============================ BODY ============================ --> | |
| <div class="body-grid" data-measure-role="body"> | |
| <!-- ============ COLUMN 1 ============ --> | |
| <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 & Question</span></div> | |
| <p class="body-text"> | |
| A network on a computer is not a differentiable function: it is a | |
| <span class="keyword">sequence of rounded operations</span>, and its "gradient" is whatever AD computes by | |
| walking that sequence backwards, | |
| $$D_{f,x}(g) = g \otimes A_L \otimes \sigma'(y_{L-1}) \otimes \cdots \otimes \sigma'(y_1) \otimes A_1$$ | |
| evaluated <span class="keyword">left to right</span>, every $\otimes$, $\oplus$ correctly rounded. Exact | |
| arithmetic ties value and gradient together by the chain rule; floating point unties them. | |
| </p> | |
| <div class="flow-strip"> | |
| <div class="step"><span class="step-name">Lem 3.4</span>$f=f^*$, $D=0$</div> | |
| <div class="arrow">+</div> | |
| <div class="step"><span class="step-name">Lem 3.5</span>$f=0$, $D=g^*$</div> | |
| <div class="arrow">→</div> | |
| <div class="step step--final"><span class="step-name">Thm 3.1</span>both</div> | |
| </div> | |
| </div> | |
| <div class="card" data-measure-role="card"> | |
| <div class="section-title"><span class="num">2</span><span class="st-text">What We Actually Did</span></div> | |
| <p class="body-text fs-3"> | |
| A constructive existence paper, so the reproduction is a construction: our <span class="keyword">own</span> | |
| simulator and our <span class="keyword">own</span> construction, no author code reused.</p> | |
| <ul class="fs-3 mt-2"> | |
| <li>Simulator vs <span class="keyword">PyTorch autograd</span>: $\le 6\times 10^{-7}$ rel. (binary32), | |
| $\le 4\times 10^{-15}$ (binary64) — residue is PyTorch's summation order.</li> | |
| <li>Domain: every other binary32 number of $[1,2)$ — <span class="keyword">adjacent floats</span>.</li> | |
| <li>Every check is <span class="keyword">bit-exact equality</span>, never a tolerance.</li> | |
| </ul> | |
| </div> | |
| <div class="card" data-measure-role="card" | |
| data-logbook-target="conclusion" data-logbook-label="Conclusion"> | |
| <div class="section-title"><span class="num">3</span><span class="st-text">Scope, Cost & Verdict</span></div> | |
| <ul class="fs-3 mt-2"> | |
| <li><span class="keyword">All six claims verified.</span> No contradiction found anywhere.</li> | |
| <li><span class="keyword">Scope:</span> $|X|$ parallel branches, so the full domain | |
| $[-2^{125},2^{125}]_{\mathbb F}$ is unbuildable by anyone; we verify on finite grids.</li> | |
| <li><span class="keyword">Our depth bound is smaller:</span> we reach the same guarantee at $L=5$, so | |
| "$L \ge 9$" is sufficient but not tight (arXiv v2 itself says $L \ge 7$).</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">6 min</div><div class="kb-label">total<br>wall clock</div></div> | |
| <div class="kb-item"><div class="kb-num">$0</div><div class="kb-label">total<br>cost</div></div> | |
| </div> | |
| <div class="callout emph mt-6 mb-4"> | |
| <strong>Bottom line.</strong> A network's values tell you nothing about the gradients AD will hand back: | |
| the two are independently choosable, and no forward test reveals it. | |
| </div> | |
| </div> | |
| </div> | |
| <!-- ============ COLUMN 2 ============ --> | |
| <div class="column" data-measure-role="column"> | |
| <div class="card highlight" data-measure-role="card" | |
| data-logbook-target="claim-1-thm-3-1-values-independent-gradient-9-layers" | |
| data-logbook-label="Claim 1: Thm 3.1 values + independent gradient"> | |
| <div class="section-title"><span class="num">4</span><span class="st-text">Claim 1 — Values and an Independent Gradient</span></div> | |
| <p class="body-text fs-3"> | |
| Draw $f^*, h^*, g^*$ independently at random on a finite domain $X$ (with the theorem's only hypothesis, | |
| $h^*(x)=0 \Rightarrow g^*(x)=0$) and build a 9-layer network. Then for every $x \in X$ | |
| </p> | |
| <div class="eqn"> | |
| <span class="label">both targets, simultaneously, bit for bit</span> | |
| $$f(x) = f^*(x) \qquad\text{and}\qquad D_{f,x}\big(h^*(x)\big) = g^*(x)$$ | |
| </div> | |
| <div class="figure"> | |
| <img src="fig2_exactness.png" data-source="paper" data-asset-id="fig-exactness" class="w-45" | |
| alt="Grid of zero mismatches for six activations in binary32 and binary64"> | |
| <div class="caption fs-2"> | |
| <strong>0 mismatches</strong> out of 33 points × 3 seeds for each of the 12 activation × | |
| format cells. Max absolute error <strong>0.0</strong>. | |
| </div> | |
| </div> | |
| <p class="body-text fs-3 mt-1"> | |
| Also verified in <span class="keyword">two input dimensions</span> (6×6 grid) and at $L=5,\dots,12$. | |
| 1188 exact value checks and 1188 exact gradient checks in total. | |
| </p> | |
| </div> | |
| <div class="card" data-measure-role="card"> | |
| <div class="section-title"><span class="num">5</span><span class="st-text">The Layer Count Is Not Tight</span></div> | |
| <table class="result-table"> | |
| <thead> | |
| <tr><th class="method">depth $L$</th><th>value mismatches</th><th class="derived">gradient mismatches</th></tr> | |
| </thead> | |
| <tbody> | |
| <tr><td class="method">1 (affine)</td><td colspan="2">impossible: $D_{f,x}(y)=y\otimes A_1$ is constant in $x$</td></tr> | |
| <tr class="ours"><td class="method">5</td><td>0</td><td class="derived">0</td></tr> | |
| <tr><td class="method">7 (arXiv v2 bound)</td><td>0</td><td class="derived">0</td></tr> | |
| <tr><td class="method">9 (claim as stated)</td><td>0</td><td class="derived">0</td></tr> | |
| </tbody> | |
| </table> | |
| <p class="body-text fs-3 mt-1"> | |
| "$L \ge 9$" is <span class="keyword">sufficient</span> and holds; not necessary — we reach the same | |
| guarantee at $L=5$, and arXiv v2 lowers the authors' bound to $L \ge 7$. | |
| </p> | |
| </div> | |
| <div class="card card--compact" data-measure-role="card" | |
| data-logbook-target="claim-2-thm-3-1-holds-for-relu-elu-gelu-swish-sigmoid-tanh" | |
| data-logbook-label="Claim 2: six activations"> | |
| <div class="section-title"><span class="num">6</span><span class="st-text">Claim 2 — All Six Activations</span></div> | |
| <p class="body-text fs-3"> | |
| Which mechanism applies is decided by the activation, as the paper's Conditions 1–3 predict: | |
| </p> | |
| <ul class="fs-3"> | |
| <li><span class="keyword">ReLU, ELU, GELU, Swish</span> never have $\sigma'=0$ where $\sigma \ne 0$: the | |
| gradient must be annihilated by a <span class="keyword">$+C/-C$ pair</span> in the AD sum.</li> | |
| <li><span class="keyword">Sigmoid, tanh</span> saturate: $\sigma = \pm 1$ exactly while $\sigma'$ has | |
| <span class="keyword">underflowed to 0</span>. No pair needed.</li> | |
| </ul> | |
| <p class="body-text fs-3"> | |
| Operating points are searched numerically per activation and format. | |
| </p> | |
| </div> | |
| </div> | |
| <!-- ============ COLUMN 3 ============ --> | |
| <div class="column" data-measure-role="column"> | |
| <div class="card highlight" data-measure-role="card" | |
| data-logbook-target="claim-6-mechanism-fp-non-associativity-decouples-ad-gradient" | |
| data-logbook-label="Claim 6: non-associativity is the mechanism"> | |
| <div class="section-title"><span class="num">7</span><span class="st-text">Claim 6 — Non-Associativity Is the Mechanism</span></div> | |
| <p class="body-text fs-3"> | |
| Both halves are one identity used in two accumulation orders: | |
| </p> | |
| <div class="eqn"> | |
| <span class="label">the wipe identity</span> | |
| $$(t \oplus C) \ominus C = 0 \;\;\text{when}\;\; |t| < \tfrac{1}{2}\mathrm{ulp}(C), \qquad\text{but}\qquad 0 \oplus C \ominus C \oplus u = u$$ | |
| </div> | |
| <div class="figure"> | |
| <img src="fig1_mechanism.png" data-source="paper" data-asset-id="fig-mechanism" class="w-45" | |
| alt="Two accumulation chains showing the same constant pair annihilating one and not the other"> | |
| <div class="caption fs-2"> | |
| The two units are <strong>identical</strong>, downstream weights $+w,-w$: the forward pass cancels them | |
| exactly. The AD accumulation meets them <em>after</em> the value path and is destroyed. | |
| </div> | |
| </div> | |
| </div> | |
| <div class="card" data-measure-role="card"> | |
| <div class="section-title"><span class="num">8</span><span class="st-text">The Decisive Test: Exact Arithmetic</span></div> | |
| <p class="body-text fs-3"> | |
| The <em>same</em> ReLU networks in Python <span class="keyword">Fractions</span>: identical weights and | |
| graph, no rounding. | |
| </p> | |
| <table class="result-table"> | |
| <thead> | |
| <tr><th class="method">network</th><th>IEEE-754</th><th class="derived">exact rationals</th></tr> | |
| </thead> | |
| <tbody> | |
| <tr><td class="method">Lem 3.4: $\max|D|$</td><td class="best">0</td><td class="derived">$3.6\times 10^{9}$</td></tr> | |
| <tr class="ours"><td class="method">Lem 3.5: $\max|f|$</td><td>0</td><td class="derived">$2.9\times 10^{17}$</td></tr> | |
| </tbody> | |
| </table> | |
| <p class="body-text fs-3 mt-2"> | |
| Remove the rounding and <span class="keyword">both constructions collapse</span> — the effect is the | |
| rounding, not the simulator. | |
| </p> | |
| <div class="section-title mt-6 mb-2"><span class="num">9</span><span class="st-text">Two Ablations</span></div> | |
| <ul class="fs-3 mt-6"> | |
| <li><span class="keyword">Delete the pair:</span> values still bit-exact, AD gradient jumps | |
| $0 \to 7.7\times 10^{9}$.</li> | |
| <li><span class="keyword">Permute the layer-1 unit order:</span> same weights, same graph, only the | |
| summation order — identical function in exact arithmetic. Gradient again jumps to | |
| $7.7\times 10^{9}$, $f$ stays bit-exact.</li> | |
| </ul> | |
| <div class="callout mt-6 mb-4 fs-3"> | |
| The permutation is the cleanest statement of Section 1.1: the AD gradient is a property of the | |
| <strong>order of operations</strong>, not of the function. What would have falsified the claim — a | |
| gradient surviving the pair, a value the pair disturbed, exact arithmetic agreeing with floating point | |
| — we looked for and did not find. | |
| </div> | |
| </div> | |
| </div> | |
| <!-- ============ COLUMN 4 ============ --> | |
| <div class="column" data-measure-role="column"> | |
| <div class="card" data-measure-role="card" | |
| data-logbook-target="claim-4-lemma-3-4-correct-values-gradient-suppressed-to-zero" | |
| data-logbook-label="Claim 4: Lemma 3.4"> | |
| <div class="section-title"><span class="num">10</span><span class="st-text">Claim 4 — Values Kept, Gradient Killed</span></div> | |
| <p class="body-text fs-3"> | |
| $f = f^*$ bit-exact while $D_{f,x}(y) = 0$ for <em>every</em> $y$: 46 magnitudes over binary32, 276 over | |
| binary64.</p> | |
| <div class="figure"> | |
| <img src="fig3_lemma34_range.png" data-source="paper" data-asset-id="fig-lem34" class="w-45" | |
| alt="Bar chart of the largest input gradient magnitude for which suppression is exact, per activation"> | |
| <div class="caption fs-2"> | |
| Exact to $|y| \approx 2^{61}$ (ReLU/ELU), $2^{117}$ (Sigmoid), then <strong>degrades as predicted</strong> | |
| — the annihilating constant overflows. Values stay exact. | |
| </div> | |
| </div> | |
| </div> | |
| <div class="card" data-measure-role="card" | |
| data-logbook-target="claim-5-lemma-3-5-zero-output-arbitrary-ad-gradient" | |
| data-logbook-label="Claim 5: Lemma 3.5"> | |
| <div class="section-title"><span class="num">11</span><span class="st-text">Claim 5 — Zero Output, Arbitrary Gradient</span></div> | |
| <p class="body-text fs-3"> | |
| The dual gadget: $f \equiv 0$ exactly, $D = g^*$ arbitrary.</p> | |
| <table class="result-table"> | |
| <thead> | |
| <tr><th class="method">check</th><th>result</th></tr> | |
| </thead> | |
| <tbody> | |
| <tr><td class="method">$f\equiv 0$ on $X$, 12 nets</td><td class="best">204 / 204</td></tr> | |
| <tr><td class="method">$f(x)=0$ off-grid</td><td class="best">768 / 768</td></tr> | |
| <tr class="ours"><td class="method">$D = g^*$ bit-exact</td><td>204 / 204</td></tr> | |
| </tbody> | |
| </table> | |
| <p class="body-text fs-3 mt-1">A network that looks inert in any forward test hands an attacker-chosen | |
| gradient to the optimiser.</p> | |
| </div> | |
| <div class="card highlight" data-measure-role="card" | |
| data-logbook-target="claim-3-thm-3-2-gradient-varies-with-phi-prime-under-antisymmetry" | |
| data-logbook-label="Claim 3: Thm 3.2 antisymmetry"> | |
| <div class="section-title"><span class="num">12</span><span class="st-text">Claim 3 — Gradient That Tracks the Loss Derivative</span></div> | |
| <p class="body-text fs-3"> | |
| Antisymmetry is <span class="keyword">forced</span>, not assumed: IEEE-754 $\otimes,\oplus$ are | |
| sign-symmetric, so $D_{f,x}(-y)=-D_{f,x}(y)$ always — exhaustive over all $4.03\times 10^{9}$ | |
| binary16 pairs, <strong>0 violations</strong>. | |
| </p> | |
| <div class="figure"> | |
| <img src="fig4_thm32.png" data-source="paper" data-asset-id="fig-thm32" class="w-45" | |
| alt="Log-log plot of AD gradient magnitude against the input gradient, against the proportional line"> | |
| <div class="caption fs-2"> | |
| One network, $f \equiv 0$, gradient prescribed on 24 bands of $y$: <strong>48/48 exact</strong>. $|D/y|$ | |
| moves <strong>8.5 orders of magnitude</strong>; exact arithmetic gives a constant ratio. Scope: 24 bands, | |
| not all $2^{32}$ floats — the paper's full-range construction needs 569 layers. | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| <!-- ============================ FOOTER ============================ --> | |
| <div class="footer" data-measure-role="footer"> | |
| <div> | |
| <strong class="method-name">Floating-point networks with AD represent almost all functions and their gradients</strong> · | |
| Independent reproduction, ICML 2026 Reproducibility Challenge · all six claims verified on CPU, $0. | |
| </div> | |
| <div> | |
| Paper: <span class="repo">arXiv:2605.01702</span> · | |
| OpenReview: <span class="repo">g89qqA6qmD</span> · | |
| Reproduction: <span class="repo">SabaPivot</span> | |
| </div> | |
| </div> | |
| </div> | |
| </body> | |
| </html> | |
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