export m2/answer-distance
Browse files- exports/m2/answer-distance/_assets/lost-cube-dark.png +3 -0
- exports/m2/answer-distance/_assets/lost-cube-light.png +3 -0
- exports/m2/answer-distance/_assets/lost-histograms-dark.png +3 -0
- exports/m2/answer-distance/_assets/lost-histograms-light.png +3 -0
- exports/m2/answer-distance/_assets/lost-lines-dark.png +3 -0
- exports/m2/answer-distance/_assets/lost-lines-light.png +3 -0
- exports/m2/answer-distance/_assets/nonred-distance-dark.png +3 -0
- exports/m2/answer-distance/_assets/nonred-distance-light.png +3 -0
- exports/m2/answer-distance/_assets/provenance.json +22 -0
- exports/m2/answer-distance/_assets/removal-distance-dark.png +3 -0
- exports/m2/answer-distance/_assets/removal-distance-light.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/lost-cube-dark.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/lost-cube-light.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/lost-histograms-dark.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/lost-histograms-light.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/lost-lines-dark.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/lost-lines-light.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/nonred-distance-dark.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/nonred-distance-light.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/removal-distance-dark.png +3 -0
- exports/m2/answer-distance/_assets/thumbs/removal-distance-light.png +3 -0
- exports/m2/answer-distance/index.html +955 -0
- exports/m2/answer-distance/index.md +157 -0
exports/m2/answer-distance/_assets/lost-cube-dark.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/lost-cube-light.png
ADDED
|
Git LFS Details
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exports/m2/answer-distance/_assets/lost-histograms-dark.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/lost-histograms-light.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/lost-lines-dark.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/lost-lines-light.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/nonred-distance-dark.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/nonred-distance-light.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/provenance.json
ADDED
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@@ -0,0 +1,22 @@
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| 1 |
+
{
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| 2 |
+
"refs": {
|
| 3 |
+
"reports/m2/answer-distance/arrays": {
|
| 4 |
+
"experiment": "answer-distance",
|
| 5 |
+
"git_describe": "5a63b5c-dirty",
|
| 6 |
+
"git_dirty": true,
|
| 7 |
+
"git_sha": "5a63b5cea85b103b8b745dc6510e7c5b000fc79e",
|
| 8 |
+
"run_at": "2026-09-25T16:23:25.784773+00:00",
|
| 9 |
+
"task": "publish_results-ce4deb4c0cf6",
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| 10 |
+
"written_at": "2026-09-25T16:42:07.098320+00:00"
|
| 11 |
+
},
|
| 12 |
+
"reports/m2/answer-distance/metrics": {
|
| 13 |
+
"experiment": "answer-distance",
|
| 14 |
+
"git_describe": "5a63b5c-dirty",
|
| 15 |
+
"git_dirty": true,
|
| 16 |
+
"git_sha": "5a63b5cea85b103b8b745dc6510e7c5b000fc79e",
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| 17 |
+
"run_at": "2026-09-25T16:23:25.784773+00:00",
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| 18 |
+
"task": "publish_results-ce4deb4c0cf6",
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| 19 |
+
"written_at": "2026-09-25T16:42:08.098260+00:00"
|
| 20 |
+
}
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| 21 |
+
}
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| 22 |
+
}
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exports/m2/answer-distance/_assets/removal-distance-dark.png
ADDED
|
Git LFS Details
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exports/m2/answer-distance/_assets/removal-distance-light.png
ADDED
|
Git LFS Details
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exports/m2/answer-distance/_assets/thumbs/lost-cube-dark.png
ADDED
|
Git LFS Details
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exports/m2/answer-distance/_assets/thumbs/lost-cube-light.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/thumbs/lost-histograms-dark.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/thumbs/lost-histograms-light.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/thumbs/lost-lines-dark.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/thumbs/lost-lines-light.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/thumbs/nonred-distance-dark.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/thumbs/nonred-distance-light.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/thumbs/removal-distance-dark.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/_assets/thumbs/removal-distance-light.png
ADDED
|
Git LFS Details
|
exports/m2/answer-distance/index.html
ADDED
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@@ -0,0 +1,955 @@
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|
| 1 |
+
<!doctype html>
|
| 2 |
+
<html lang="en">
|
| 3 |
+
<head>
|
| 4 |
+
<meta name="mini-thumbnails" content="_assets/thumbs/" />
|
| 5 |
+
<link rel="alternate" type="text/markdown" href="index.md" />
|
| 6 |
+
<meta charset="utf-8">
|
| 7 |
+
<meta name="viewport" content="width=device-width, initial-scale=1">
|
| 8 |
+
<title>How far the answer moves: an RGB-distance readout beside expected exact match</title>
|
| 9 |
+
<link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=Lora:wght@400..700&family=PT+Sans:wght@400;700&family=Fira+Mono:wght@400;500;700&display=swap">
|
| 10 |
+
<style>
|
| 11 |
+
/* The base sheet: what a woven report page and the site's Markdown pages share —
|
| 12 |
+
* tokens, type, code, tables, images, quotes, heading anchors. It reaches a page three
|
| 13 |
+
* ways: mini.lit.page inlines it ahead of lit.css (the report frame); scripts/build_site.py
|
| 14 |
+
* concatenates it ahead of scripts/md.css into the md.css the site serves; and VS Code's
|
| 15 |
+
* Markdown preview lists both files (.vscode/settings.json). A value changed here
|
| 16 |
+
* changes every page, so the report-only and site-only rules live in those two sheets. */
|
| 17 |
+
|
| 18 |
+
:root {
|
| 19 |
+
color-scheme: light dark;
|
| 20 |
+
--bg: #ffffff;
|
| 21 |
+
--fg: #1a1a1a;
|
| 22 |
+
--fg-muted: #555555;
|
| 23 |
+
--link: #0066cc;
|
| 24 |
+
--border: #dddddd;
|
| 25 |
+
--code-bg: #f5f5f5;
|
| 26 |
+
--code-accent: #0066cc;
|
| 27 |
+
--mark: #fff3a8;
|
| 28 |
+
/* Table rules, in the booktabs manner: the text colour, eased off a little. */
|
| 29 |
+
--rule: color-mix(in srgb, var(--fg) 75%, transparent);
|
| 30 |
+
/* The faces, loaded by the one Google Fonts <link> every page shares
|
| 31 |
+
* (mini.lit.page.FONTS). Inline SVG figures read --font-mono too (src/subline). */
|
| 32 |
+
--font-sans: "PT Sans", ui-sans-serif, system-ui, sans-serif;
|
| 33 |
+
--font-serif: "Lora", serif;
|
| 34 |
+
--font-mono:
|
| 35 |
+
"Fira Mono", ui-monospace, SFMono-Regular, Menlo, Consolas, monospace;
|
| 36 |
+
}
|
| 37 |
+
@media (prefers-color-scheme: dark) {
|
| 38 |
+
:root {
|
| 39 |
+
--bg: #1f1f1f;
|
| 40 |
+
--fg: #ffffff;
|
| 41 |
+
--fg-muted: #aaaaaa;
|
| 42 |
+
--link: #6cb6ff;
|
| 43 |
+
--border: #5a5a5a;
|
| 44 |
+
--code-bg: #2d2d2d;
|
| 45 |
+
--code-accent: #66d9aa;
|
| 46 |
+
--mark: #6b5d00;
|
| 47 |
+
}
|
| 48 |
+
}
|
| 49 |
+
|
| 50 |
+
body {
|
| 51 |
+
background-color: var(--bg);
|
| 52 |
+
color: var(--fg);
|
| 53 |
+
font-family: var(--font-sans);
|
| 54 |
+
/* Prose lands at ~14.4px (a 90% base), the size the reports settled on. */
|
| 55 |
+
font-size: 0.9rem;
|
| 56 |
+
line-height: 1.6;
|
| 57 |
+
}
|
| 58 |
+
|
| 59 |
+
a {
|
| 60 |
+
color: var(--link);
|
| 61 |
+
text-decoration: none;
|
| 62 |
+
}
|
| 63 |
+
a:hover {
|
| 64 |
+
text-decoration: underline;
|
| 65 |
+
}
|
| 66 |
+
|
| 67 |
+
h1,
|
| 68 |
+
h2,
|
| 69 |
+
h3,
|
| 70 |
+
h4,
|
| 71 |
+
h5,
|
| 72 |
+
h6 {
|
| 73 |
+
font-family: var(--font-serif);
|
| 74 |
+
/* Lora at the regular weight rather than the browser-default bold, with ligatures
|
| 75 |
+
* on — otherwise the variable font shows its 700 master. */
|
| 76 |
+
font-weight: 400;
|
| 77 |
+
font-feature-settings:
|
| 78 |
+
"rlig" 1,
|
| 79 |
+
"calt" 1;
|
| 80 |
+
margin-top: 1.5em;
|
| 81 |
+
margin-bottom: 0.5em;
|
| 82 |
+
line-height: 1.3;
|
| 83 |
+
}
|
| 84 |
+
h1 {
|
| 85 |
+
margin-top: 0;
|
| 86 |
+
font-size: 2.25em;
|
| 87 |
+
}
|
| 88 |
+
h2 {
|
| 89 |
+
margin-top: 4em;
|
| 90 |
+
}
|
| 91 |
+
p {
|
| 92 |
+
margin-block: 1em;
|
| 93 |
+
}
|
| 94 |
+
|
| 95 |
+
code,
|
| 96 |
+
pre,
|
| 97 |
+
kbd {
|
| 98 |
+
font-family: var(--font-mono);
|
| 99 |
+
font-size: 0.875em;
|
| 100 |
+
}
|
| 101 |
+
code {
|
| 102 |
+
background-color: var(--code-bg);
|
| 103 |
+
padding: 0.1em 0.3em;
|
| 104 |
+
border-radius: 3px;
|
| 105 |
+
}
|
| 106 |
+
pre {
|
| 107 |
+
background-color: var(--code-bg);
|
| 108 |
+
padding: 1em;
|
| 109 |
+
border-radius: 4px;
|
| 110 |
+
border-left: 3px solid var(--code-accent);
|
| 111 |
+
overflow-x: auto;
|
| 112 |
+
margin-block: 1.5em;
|
| 113 |
+
}
|
| 114 |
+
pre code {
|
| 115 |
+
background: none;
|
| 116 |
+
padding: 0;
|
| 117 |
+
border-radius: 0;
|
| 118 |
+
font-size: 1em;
|
| 119 |
+
}
|
| 120 |
+
|
| 121 |
+
/* Anchor links on headings. */
|
| 122 |
+
a.anchor-link {
|
| 123 |
+
opacity: 0;
|
| 124 |
+
color: var(--fg-muted);
|
| 125 |
+
transition: opacity 0.2s ease;
|
| 126 |
+
}
|
| 127 |
+
a.anchor-link::after {
|
| 128 |
+
content: "#";
|
| 129 |
+
font-size: 0.8em;
|
| 130 |
+
margin-inline: 0.4em;
|
| 131 |
+
}
|
| 132 |
+
:hover > a.anchor-link {
|
| 133 |
+
opacity: 1;
|
| 134 |
+
}
|
| 135 |
+
|
| 136 |
+
/* Tables in the booktabs manner: horizontal rules only — one above the headings, one
|
| 137 |
+
* under them, one under the last row — and no boxes around cells. Ragged right by
|
| 138 |
+
* default; a numeric column opts in with `---:` in the Markdown. Top-aligned: a row
|
| 139 |
+
* whose prose cell wraps to four lines would otherwise leave its short cells floating
|
| 140 |
+
* in the middle. */
|
| 141 |
+
table {
|
| 142 |
+
border-collapse: collapse;
|
| 143 |
+
margin-block: 1.5em;
|
| 144 |
+
margin-inline: auto;
|
| 145 |
+
}
|
| 146 |
+
th,
|
| 147 |
+
td {
|
| 148 |
+
padding: 0.35em 0.8em;
|
| 149 |
+
border: 0;
|
| 150 |
+
text-align: left;
|
| 151 |
+
vertical-align: top;
|
| 152 |
+
}
|
| 153 |
+
th {
|
| 154 |
+
font-weight: 600;
|
| 155 |
+
}
|
| 156 |
+
/* \toprule, \midrule, \bottomrule. The rules are on the cells rather than the table
|
| 157 |
+
* so that they travel with the content when a wide table scrolls inside its own box. */
|
| 158 |
+
:is(thead, tbody:first-child) > tr:first-child > :is(th, td) {
|
| 159 |
+
border-top: 2px solid var(--rule);
|
| 160 |
+
}
|
| 161 |
+
thead > tr:last-child > :is(th, td) {
|
| 162 |
+
border-bottom: 1px solid var(--rule);
|
| 163 |
+
padding-bottom: 0.5em;
|
| 164 |
+
}
|
| 165 |
+
tbody > tr:first-child > :is(th, td) {
|
| 166 |
+
padding-top: 0.5em;
|
| 167 |
+
}
|
| 168 |
+
tbody > tr:last-child > :is(th, td) {
|
| 169 |
+
border-bottom: 2px solid var(--rule);
|
| 170 |
+
}
|
| 171 |
+
|
| 172 |
+
img,
|
| 173 |
+
video {
|
| 174 |
+
max-width: 100%;
|
| 175 |
+
height: auto;
|
| 176 |
+
}
|
| 177 |
+
|
| 178 |
+
blockquote {
|
| 179 |
+
margin-inline: 0;
|
| 180 |
+
padding-inline: 1em;
|
| 181 |
+
border-left: 3px solid var(--border);
|
| 182 |
+
color: var(--fg-muted);
|
| 183 |
+
}
|
| 184 |
+
|
| 185 |
+
/* The page frame for a woven document, on top of base.css (tokens, type, code, tables).
|
| 186 |
+
*
|
| 187 |
+
* Where the rest of the CSS lives, and how each reaches a page:
|
| 188 |
+
* base.css (beside this) shared with the site's Markdown pages; mini.lit.page inlines
|
| 189 |
+
* base + this + the Pygments styles into every page it renders
|
| 190 |
+
* docs/report.css report polish and the print block; inlined after this at
|
| 191 |
+
* render, export and site build (mini.reports.set_report_styles),
|
| 192 |
+
* so an edit there reaches published reports without a re-export
|
| 193 |
+
* scripts/md.css the site's Markdown pages only (base + md, concatenated by
|
| 194 |
+
* scripts/build_site.py; VS Code's preview reads both files)
|
| 195 |
+
* mini/chips.css the nav and provenance chips the site build injects
|
| 196 |
+
* mini/lightbox.css the click-to-enlarge overlay, injected with its script
|
| 197 |
+
* subline/theme.css inside each subline SVG, reading this page's tokens
|
| 198 |
+
*/
|
| 199 |
+
|
| 200 |
+
:root {
|
| 201 |
+
/* The reading measure, and the page's own side inset. Every block in the content
|
| 202 |
+
* column is capped at --measure and centred; the print stylesheet redefines it in
|
| 203 |
+
* absolute units (see docs/report.css). */
|
| 204 |
+
--measure: 40rem;
|
| 205 |
+
--gutter: 1.5rem;
|
| 206 |
+
--subfigure-gap: 1.5rem;
|
| 207 |
+
}
|
| 208 |
+
|
| 209 |
+
/* The page is a vertical flexbox, so the nav and data-provenance chips that
|
| 210 |
+
* `mini.reports` injects sit above and below the content column in normal flow. */
|
| 211 |
+
body {
|
| 212 |
+
margin: 0;
|
| 213 |
+
display: flex;
|
| 214 |
+
flex-direction: column;
|
| 215 |
+
min-height: 100dvh;
|
| 216 |
+
}
|
| 217 |
+
|
| 218 |
+
/* The content column. `main.lit` spans the page and each block *inside* it is capped
|
| 219 |
+
* at the reading measure and centred — rather than capping the column as a whole —
|
| 220 |
+
* which is what lets a figure or a table opt out and take the full page width. */
|
| 221 |
+
main.lit {
|
| 222 |
+
flex: 1 0 auto;
|
| 223 |
+
padding-inline: var(--gutter);
|
| 224 |
+
padding-block: 2rem;
|
| 225 |
+
}
|
| 226 |
+
main.lit > * {
|
| 227 |
+
max-width: var(--measure);
|
| 228 |
+
margin-inline: auto;
|
| 229 |
+
}
|
| 230 |
+
/* Figures and tables run the full width of the page, out into the column's margins:
|
| 231 |
+
* a wide plot or a many-column table gets the room, and anything narrower than the
|
| 232 |
+
* measure still centres on it. Element selectors, so no report has to opt in. */
|
| 233 |
+
main.lit > :is(figure, table) {
|
| 234 |
+
max-width: none;
|
| 235 |
+
margin-block: 3rem;
|
| 236 |
+
}
|
| 237 |
+
|
| 238 |
+
/* Highlighted code (Pygments, appended to this sheet by mini.lit.page). */
|
| 239 |
+
.highlight pre { background-color: var(--code-bg); }
|
| 240 |
+
.highlight { background: none; }
|
| 241 |
+
|
| 242 |
+
/* What a cell printed, and what went wrong in one. */
|
| 243 |
+
pre.stdout { border-left-color: var(--fg-muted); color: var(--fg-muted); }
|
| 244 |
+
pre.error { border-left-color: #c33; white-space: pre-wrap; }
|
| 245 |
+
|
| 246 |
+
/* The cell the live server is waiting on; the page below it is provisional. */
|
| 247 |
+
pre.running { border-left-color: var(--link); color: var(--fg-muted); animation: lit-pulse 1.2s ease-in-out infinite alternate; }
|
| 248 |
+
@keyframes lit-pulse { from { opacity: 0.5; } to { opacity: 1; } }
|
| 249 |
+
|
| 250 |
+
/* A value the document could not compute yet: a name used after `stop()`. */
|
| 251 |
+
mark.pending { background: var(--mark); padding: 0 0.2em; border-radius: 2px; font-size: 0.85em; }
|
| 252 |
+
code mark.pending { font-size: inherit; }
|
| 253 |
+
|
| 254 |
+
/* Figures: the box runs the full page width (above), and the body centres within it,
|
| 255 |
+
* so anything smaller than the page sits over the reading column. Sub-figures sit side
|
| 256 |
+
* by side and reflow to a stack on a narrow viewport. Captions are muted italic. */
|
| 257 |
+
figure {
|
| 258 |
+
margin-inline: 0; text-align: center;
|
| 259 |
+
}
|
| 260 |
+
figure img {
|
| 261 |
+
margin-inline: auto; display: block;
|
| 262 |
+
}
|
| 263 |
+
figure:has(> figure) {
|
| 264 |
+
display: flex;
|
| 265 |
+
flex-wrap: wrap; /* for a browser without `balance` */
|
| 266 |
+
flex-wrap: balance;
|
| 267 |
+
justify-content: center;
|
| 268 |
+
gap: var(--subfigure-gap) 0.5rem;
|
| 269 |
+
}
|
| 270 |
+
figure:has(> figure) > figure {
|
| 271 |
+
margin: 0;
|
| 272 |
+
}
|
| 273 |
+
/* A caption is prose, so it keeps the reading measure even under a full-width figure.
|
| 274 |
+
* `100%` is the ceiling for a sub-figure, whose own box is narrower than that. */
|
| 275 |
+
figcaption {
|
| 276 |
+
max-width: min(var(--measure), 100%);
|
| 277 |
+
margin-top: 0.6em;
|
| 278 |
+
margin-inline: auto;
|
| 279 |
+
font-size: 0.9em;
|
| 280 |
+
font-style: italic;
|
| 281 |
+
opacity: 0.75;
|
| 282 |
+
text-wrap: balance;
|
| 283 |
+
text-align: center;
|
| 284 |
+
}
|
| 285 |
+
/* The main caption of a sub-figure group is a flex item: a full row of its own (a
|
| 286 |
+
* `max-width` would cap the basis and let a sub-figure share the row, so the measure is
|
| 287 |
+
* padding here), and the row gap above it comes off, so it sits under the figures as
|
| 288 |
+
* any caption does. */
|
| 289 |
+
figure:has(> figure) > figcaption {
|
| 290 |
+
flex-basis: 100%;
|
| 291 |
+
box-sizing: border-box;
|
| 292 |
+
max-width: none;
|
| 293 |
+
padding-inline: max(0px, calc((100% - var(--measure)) / 2));
|
| 294 |
+
margin-top: calc(0.6em - var(--subfigure-gap));
|
| 295 |
+
}
|
| 296 |
+
/* A caption rendered from Markdown arrives in a <p>; its margins would pad the caption. */
|
| 297 |
+
figcaption > :is(:first-child, :last-child) {
|
| 298 |
+
margin-block: 0;
|
| 299 |
+
}
|
| 300 |
+
|
| 301 |
+
/* A themed figure (mini.vis.figures.themed) carries both renders of the plot, and the
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| 302 |
+
* page shows one: an explicit theme on the body element wins, and the OS preference
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| 303 |
+
* applies only where the body states none. The print rules in docs/report.css pin the
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| 304 |
+
* light one. */
|
| 305 |
+
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|
| 306 |
+
.mini-themed-figure .mini-themed-img-light { display: block; }
|
| 307 |
+
body[data-theme="dark"] .mini-themed-figure,
|
| 308 |
+
body.dark .mini-themed-figure,
|
| 309 |
+
body.dark-theme .mini-themed-figure {
|
| 310 |
+
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|
| 311 |
+
.mini-themed-img-light { display: none; }
|
| 312 |
+
}
|
| 313 |
+
@media (prefers-color-scheme: dark) {
|
| 314 |
+
body:not([data-theme="dark"]):not([data-theme="light"]):not(.dark):not(.dark-theme):not(.light):not(.light-theme)
|
| 315 |
+
.mini-themed-figure {
|
| 316 |
+
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|
| 317 |
+
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|
| 318 |
+
}
|
| 319 |
+
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| 320 |
+
|
| 321 |
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|
| 322 |
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|
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+
margin-block: 1.5em;
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| 324 |
+
padding: 0.6em 1em;
|
| 325 |
+
border-left: 3px solid var(--link);
|
| 326 |
+
background: var(--code-bg);
|
| 327 |
+
border-radius: 4px;
|
| 328 |
+
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|
| 329 |
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|
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| 332 |
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|
| 334 |
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.admonition > :last-child { margin-bottom: 0; }
|
| 335 |
+
|
| 336 |
+
/* Footnotes. */
|
| 337 |
+
.footnote { font-size: 0.9em; color: var(--fg-muted); border-top: 1px solid var(--border); margin-top: 3em; }
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+
.footnote > hr { display: none; } /* the border above is the rule; python-markdown writes an <hr> too */
|
| 339 |
+
.footnote-backref { text-decoration: none; }
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| 340 |
+
|
| 341 |
+
/* Colour swatches (see the style-fig skill). */
|
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+
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.sw-open { background: none; border-color: var(--sw); }
|
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+
|
| 346 |
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/* Definition lists. */
|
| 347 |
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dl > dt { font-weight: 600; margin-top: 0.8em; }
|
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+
|
| 349 |
+
/* Print: only what the frame needs on its own. The page size, type and page breaks
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+
* are docs/report.css's print block, which every rendered report carries. */
|
| 351 |
+
@media print {
|
| 352 |
+
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|
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+
/* Paper has no viewport to fill, and the chips are hidden, so the flexbox comes off. */
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+
body { display: block; min-height: 0; }
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/* The page's own margins are the gutter here (`@page` in the report stylesheet), so
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+
* the column rules above carry over unchanged: prose is capped at --measure, and a
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| 357 |
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* figure or table reaches past it to the full width of the printed page. */
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+
main.lit { padding: 0; }
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a { color: inherit; }
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+
a.anchor-link { display: none; }
|
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+
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| 362 |
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|
| 363 |
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pre { line-height: 125%; }
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td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
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span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
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span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
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| 372 |
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.highlight .il { color: #666 } /* Literal.Number.Integer.Long */
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pre { line-height: 125%; }
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span.linenos.special { color: #e6edf3; background-color: #6e7681; padding-left: 5px; padding-right: 5px; }
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<details data-mini-provenance><summary>Data provenance</summary><div><strong>answer-distance</strong> · <code>5a63b5c-dirty</code> (dirty) · run 2026-09-25<div>via reports/m2/answer-distance/arrays, reports/m2/answer-distance/metrics</div></div></details>
|
| 842 |
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<main class="lit">
|
| 843 |
+
<h1 id="how-far-the-answer-moves-an-rgb-distance-readout-beside-expected-exact-match">How far the answer moves: an RGB-distance readout beside expected exact match<a class="anchor-link" href="#how-far-the-answer-moves-an-rgb-distance-readout-beside-expected-exact-match" title="Link to this heading">¶</a></h1>
|
| 844 |
+
<div class="admonition tip">
|
| 845 |
+
<!-- tl;dr -->
|
| 846 |
+
<p>We re-scored ex-2.2.11's 54 checkpoints with a distance on the color grid beside expected exact match, to see where the answers go when the anchored direction is removed. On <code>handover</code> the removed answers are near misses, two to three grid steps from the right color and well short of a random guess, and the non-red lines move less than the control's own lines do under the same operator.</p>
|
| 847 |
+
</div>
|
| 848 |
+
<h2 id="observations">Observations<a class="anchor-link" href="#observations" title="Link to this heading">¶</a></h2>
|
| 849 |
+
<ul>
|
| 850 |
+
<li><a href="#the-removal-lines-by-distance">The removal lines, by distance</a>: under <code>projection</code>, the greedy guess on <code>handover</code> moves from the floor (0 to 0.5 steps, a perfect answer) to 1.8 steps on <code>mix</code> and 3.4 on <code>value-hsv</code>, between 44% and 77% of the way to chance. The control stays at the floor. The mean, median, and expected distances agree with the greedy one within 0.3 steps.</li>
|
| 851 |
+
<li><a href="#kept-and-lost">Kept and lost</a>: the operator loses 77% to 99% of the removal lines. The kept lines stay at the floor; the lost lines sit 1.8 (<code>mix</code>) to 3.7 (<code>value-hsv</code>) steps from the answer, and reach chance only on <code>value-hsv</code>.</li>
|
| 852 |
+
<li><a href="#the-lost-answers-on-the-cube">The lost answers on the cube</a>: on <code>mix</code>, nine in ten lost answers are one or two steps off. On <code>hue-hsv</code> the guesses keep their saturation and move in hue; on <code>darken</code> they land darker than the answer.</li>
|
| 853 |
+
<li><a href="#a-counterfactual-answer">A counterfactual answer</a>: the lost answers are not the op applied to a de-reddened operand. The nearest such answer is a little closer to the guess than the true one on most ops, but the guess lands in its box on under a quarter of the lines on all ops but <code>lighten</code>.</li>
|
| 854 |
+
<li><a href="#the-non-red-lines">The non-red lines</a>: on <code>handover</code> the exact match deficit stays under 0.01 and the mean of the distribution moves under 0.03 steps on every op. The control's own lines move as much or more under the same operator.</li>
|
| 855 |
+
<li><a href="#between-seeds">Between seeds</a>: the seed spread of the distances is 6% to 20% of the mean, against 33% to 127% for the kept share of exact match.</li>
|
| 856 |
+
</ul>
|
| 857 |
+
<h2 id="scope">Scope<a class="anchor-link" href="#scope" title="Link to this heading">¶</a></h2>
|
| 858 |
+
<p>This is a re-score of stored checkpoints, planned in the <a href="/todo/science/rgb-distance-readout-beside-exact-match.md">backlog item</a>. There is no training, no gates, and no verdicts.</p>
|
| 859 |
+
<p>Every removal and selectivity number in D2.2 is <em>expected exact match</em>: the probability mass the model puts on the colors that a line's answer can be. It gives no partial credit, so a guess one grid step from the answer scores the same as a guess of black.</p>
|
| 860 |
+
<p>So when <code>handover</code> keeps 24% of exact match on the <code>hue-hsv</code> removal lines, that could mean a quarter of the lines answered perfectly and the rest sent anywhere, or every line nudged one step over. Likewise, a non-red deficit of 0.01 could be one line in a hundred lost outright, or the mass of every line leaning a little.</p>
|
| 861 |
+
<p>We add a distance on the color grid, in grid steps. One step is the spacing between the six levels of each channel, and the far corner of the cube is 5√3 ≈ 8.7 steps from black. The target of a line is its <em>raw answer</em> (the unrounded value of the op), which is also the expected value of the answer distribution under stochastic rounding.<sup id="fnref:stochastic"><a class="footnote-ref" href="#fn:stochastic">1</a></sup></p>
|
| 862 |
+
<p>Four quantities are measured from the raw answer. Three are central points of the model's distribution over the 216 grid colors: the <em>greedy</em> guess (the most likely color), the <em>mean</em>, and the channel-wise <em>median</em>. The fourth is the <em>expected</em> distance of a color drawn from the distribution.</p>
|
| 863 |
+
<p>The greedy and expected distances are the ones to compare with exact match. The mean is the one that moves when mass leans toward a neighbor while the guess stays the same.</p>
|
| 864 |
+
<p>Every distance comes with two references. The <em>floor</em> is the distance from the raw answer to the best possible grid answer (the mode of the answer distribution): zero when the answer lands on the grid, and up to half a step per channel otherwise. A distance at the floor is a perfect answer.</p>
|
| 865 |
+
<p><em>Chance</em> is the mean distance of a color drawn uniformly from the grid: about 3 steps for a target near the middle of the cube, and more for one near a corner. A distance at chance means the answer no longer depends on the line.</p>
|
| 866 |
+
<p>The distances and exact match are measured under the same three passes as ex-2.2.11:
|
| 867 |
+
(a) the clean forward pass,
|
| 868 |
+
(b) <code>projection</code>, with e₁ removed at every slice and position, and
|
| 869 |
+
(c) <code>operands</code>, with e₁ removed at the operand positions only.
|
| 870 |
+
Each is read on the line groups of ex-2.2.11: the removal lines (a red operand whose hue the op carries into the answer), the non-red lines, and the rest. As in the ex-2.2.11 report, the shaped operator is left out.</p>
|
| 871 |
+
<h2 id="the-runs">The runs<a class="anchor-link" href="#the-runs" title="Link to this heading">¶</a></h2>
|
| 872 |
+
<p>The runs are the 54 final checkpoints of ex-2.2.11: the un-anchored control (5 seeds), <code>handover</code> (20), and two arms that each undo one of the changes in <code>handover</code>, <code>handover-slot</code> (20) and <code>handover-tied</code> (9). The probe lines are the ones ex-2.2.11 scored: 5,832 per op, and twice that for the three order-sensitive ops.</p>
|
| 873 |
+
<p>The two scorers agree: the re-score reproduces ex-2.2.11's kept share of expected exact match on every op (24% on <code>hue-hsv</code>, 12% to 18% on the next four).</p>
|
| 874 |
+
<h2 id="the-removal-lines-by-distance">The removal lines, by distance<a class="anchor-link" href="#the-removal-lines-by-distance" title="Link to this heading">¶</a></h2>
|
| 875 |
+
<p>On the removal lines under <code>projection</code>, the answers behind the exact match that <code>handover</code> keeps are mostly near misses, rather than right answers among wrong ones. The figure puts the distance beside the kept share, per op.</p>
|
| 876 |
+
<p>The clean pass sits at the floor on every op and condition (the table below the figure gives it), so any distance above the floor under <code>projection</code> is caused by the operator.</p>
|
| 877 |
+
<figure class="mini-themed-figure">
|
| 878 |
+
<img class="mini-themed-img-light" src="_assets/removal-distance-light.png" alt="Under projection, handover's greedy distance on the removal lines rises from the floor to about halfway to chance on every op, while the control stays at the floor." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="removal-distance" />
|
| 879 |
+
<img class="mini-themed-img-dark" src="_assets/removal-distance-dark.png" alt="Under projection, handover's greedy distance on the removal lines rises from the floor to about halfway to chance on every op, while the control stays at the floor." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="removal-distance" />
|
| 880 |
+
<figcaption><p><strong>The removal lines under <code>projection</code>, per op and condition: exact match kept, and how far the answer moves.</strong> Top: the share of the clean expected exact match kept, as ex-2.2.11 reads it, dashed at its 20% gate. Middle: the distance in grid steps of the greedy guess from the raw answer; the dotted rule at each op is the floor (the best grid answer's distance) and the dashed rule is chance (a uniform draw from the grid). Bottom: the distance of the mean of the model's distribution from the raw answer; the dashed rule is the center of the cube, where a uniform distribution's mean sits. Each small dot is one seed, the larger mark the seed mean, and the thin bar the seed range.</p></figcaption></figure>
|
| 881 |
+
|
| 882 |
+
<p>The table gives the same measurements on <code>handover</code>, adds the clean and <code>operands</code> passes, and adds the hit rate (the share of lines whose greedy guess is one of the line's possible answers).</p>
|
| 883 |
+
<figure class="report-figure"><table class="report-table"><thead><tr><th>op</th><th class=num>removal lines</th><th class=num>exact match kept</th><th class=num>hit rate, clean</th><th class=num>hit rate, <code>projection</code></th><th class=num>greedy distance, clean</th><th class=num>greedy distance, <code>projection</code></th><th class=num>greedy distance, <code>operands</code></th><th class=num>floor</th><th class=num>chance</th></tr></thead><tbody><tr><td><code>mix</code></td><td class=num>365</td><td class=num>0.02 (0.0–0.1)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.01 (0.0–0.1)</td><td class=num>0.00 (0.0–0.0)</td><td class=num>1.77 (1.4–2.0)</td><td class=num>1.76 (1.4–2.0)</td><td class=num>0.00</td><td class=num>3.66</td></tr><tr><td><code>screen</code></td><td class=num>387</td><td class=num>0.14 (0.1–0.2)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.19 (0.1–0.3)</td><td class=num>0.24 (0.2–0.2)</td><td class=num>1.95 (1.5–2.5)</td><td class=num>1.94 (1.5–2.4)</td><td class=num>0.20</td><td class=num>4.14</td></tr><tr><td><code>multiply</code></td><td class=num>384</td><td class=num>0.15 (0.0–0.3)</td><td class=num>0.91 (0.9–0.9)</td><td class=num>0.15 (0.1–0.3)</td><td class=num>0.22 (0.2–0.2)</td><td class=num>2.09 (1.5–2.7)</td><td class=num>2.07 (1.5–2.8)</td><td class=num>0.20</td><td class=num>4.39</td></tr><tr><td><code>lighten</code></td><td class=num>386</td><td class=num>0.14 (0.1–0.3)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.15 (0.1–0.3)</td><td class=num>0.00 (0.0–0.0)</td><td class=num>2.07 (1.6–2.6)</td><td class=num>2.07 (1.6–2.5)</td><td class=num>0.00</td><td class=num>4.12</td></tr><tr><td><code>darken</code></td><td class=num>382</td><td class=num>0.18 (0.0–0.3)</td><td class=num>0.95 (0.9–0.9)</td><td class=num>0.17 (0.0–0.3)</td><td class=num>0.00 (0.0–0.0)</td><td class=num>2.20 (1.3–3.2)</td><td class=num>2.18 (1.3–3.2)</td><td class=num>0.00</td><td class=num>4.28</td></tr><tr><td><code>difference</code></td><td class=num>403</td><td class=num>0.06 (0.0–0.1)</td><td class=num>0.99 (1.0–1.0)</td><td class=num>0.07 (0.0–0.1)</td><td class=num>0.01 (0.0–0.0)</td><td class=num>2.75 (2.3–3.3)</td><td class=num>2.73 (2.2–3.3)</td><td class=num>0.00</td><td class=num>3.80</td></tr><tr><td><code>exclusion</code></td><td class=num>390</td><td class=num>0.12 (0.1–0.2)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.20 (0.1–0.3)</td><td class=num>0.21 (0.2–0.2)</td><td class=num>2.30 (1.8–2.8)</td><td class=num>2.25 (1.8–2.8)</td><td class=num>0.18</td><td class=num>3.67</td></tr><tr><td><code>hsvmix</code></td><td class=num>401</td><td class=num>0.05 (0.0–0.1)</td><td class=num>0.98 (1.0–1.0)</td><td class=num>0.09 (0.0–0.2)</td><td class=num>0.53 (0.5–0.6)</td><td class=num>2.61 (2.3–2.8)</td><td class=num>2.59 (2.2–2.8)</td><td class=num>0.48</td><td class=num>3.99</td></tr><tr><td><code>hue-hsv</code></td><td class=num>333</td><td class=num>0.24 (0.1–0.4)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.23 (0.0–0.5)</td><td class=num>0.17 (0.2–0.2)</td><td class=num>2.51 (1.7–3.4)</td><td class=num>2.38 (1.7–3.4)</td><td class=num>0.15</td><td class=num>4.00</td></tr><tr><td><code>sat-hsv</code></td><td class=num>377</td><td class=num>0.10 (0.0–0.2)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.17 (0.0–0.3)</td><td class=num>0.20 (0.2–0.2)</td><td class=num>2.85 (2.0–4.1)</td><td class=num>2.71 (2.0–3.4)</td><td class=num>0.18</td><td class=num>4.17</td></tr><tr><td><code>value-hsv</code></td><td class=num>389</td><td class=num>0.08 (0.0–0.2)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.11 (0.0–0.2)</td><td class=num>0.15 (0.1–0.2)</td><td class=num>3.36 (2.5–4.3)</td><td class=num>3.15 (2.1–3.9)</td><td class=num>0.13</td><td class=num>4.34</td></tr></tbody></table><figcaption><p><strong>The removal lines on <code>handover</code>, per op: seed mean (seed range).</strong> Distances in grid steps from the raw answer. The floor is the best grid answer's distance and chance a uniform draw's, both averaged over the op's removal lines.</p></figcaption></figure>
|
| 884 |
+
|
| 885 |
+
<h2 id="kept-and-lost">Kept and lost<a class="anchor-link" href="#kept-and-lost" title="Link to this heading">¶</a></h2>
|
| 886 |
+
<p>A distance averaged over a group mixes lines the operator leaves answered with lines it does not, so we split the lines by the greedy guess. Under a given pass, a line is:
|
| 887 |
+
(a) <em>kept</em> when the guess is one of the possible answers of the line,
|
| 888 |
+
(b) <em>lost</em> when the clean guess was a possible answer and the guess under the pass is not, and
|
| 889 |
+
(c) <em>never</em> when the clean guess already missed.
|
| 890 |
+
The distance of the lost lines tells us where a removed answer goes.</p>
|
| 891 |
+
<figure class="mini-themed-figure">
|
| 892 |
+
<img class="mini-themed-img-light" src="_assets/lost-lines-light.png" alt="Most of handover's removal lines are lost under projection; the lost lines sit two to three steps from the answer, short of chance on every op but value-hsv, while the kept lines stay at the floor." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="lost-lines" />
|
| 893 |
+
<img class="mini-themed-img-dark" src="_assets/lost-lines-dark.png" alt="Most of handover's removal lines are lost under projection; the lost lines sit two to three steps from the answer, short of chance on every op but value-hsv, while the kept lines stay at the floor." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="lost-lines" />
|
| 894 |
+
<figcaption><p><strong>The removal lines under <code>projection</code>, split by whether the greedy guess survives.</strong> Top: the share of each op's removal lines that are lost (answered on the clean pass, not under the operator). Middle: the greedy distance of the lost lines from the raw answer, in grid steps, with chance dashed. Bottom: the greedy distance of the kept lines, with the floor dotted. Each small dot is one seed, the larger mark the seed mean, and the thin bar the seed range; a condition with no lost line on a seed draws nothing for it.</p></figcaption></figure>
|
| 895 |
+
|
| 896 |
+
<p>Per line, as a distribution: in the histograms below, the bin at zero holds the kept lines and the other bins show where the lost answers go.</p>
|
| 897 |
+
<p>On <code>mix</code>, nine in ten of the moved answers sit one or two steps off, which is what treating the red channel as absent would give (on <code>mix</code> that shift is about 2.5 steps). <code>darken</code> decays from one step, <code>hue-hsv</code> spreads over two to four, and <code>value-hsv</code> is close to the shape a uniform guess gives.</p>
|
| 898 |
+
<figure class="mini-themed-figure">
|
| 899 |
+
<img class="mini-themed-img-light" src="_assets/lost-histograms-light.png" alt="Per-op histograms of guess distance: mix peaks at one to two steps, darken decays from one step, hue-hsv spreads over two to four, and value-hsv is close to the uniform-guess shape." width="818" height="548" style="max-width: 100%; height: auto;" data-asset-name="lost-histograms" />
|
| 900 |
+
<img class="mini-themed-img-dark" src="_assets/lost-histograms-dark.png" alt="Per-op histograms of guess distance: mix peaks at one to two steps, darken decays from one step, hue-hsv spreads over two to four, and value-hsv is close to the uniform-guess shape." width="818" height="548" style="max-width: 100%; height: auto;" data-asset-name="lost-histograms" />
|
| 901 |
+
<figcaption><p><strong>Where the removal-line answers land under <code>projection</code> on <code>handover</code>, per op.</strong> Bars: the share of the op's removal lines, pooled over twenty seeds, whose greedy guess sits each number of grid steps from the raw answer (rounded), under <code>projection</code>; in outline, the same under the clean pass. The dashed line is the distribution a uniform guess from the grid would give on the same lines.</p></figcaption></figure>
|
| 902 |
+
|
| 903 |
+
<h2 id="the-lost-answers-on-the-cube">The lost answers on the cube<a class="anchor-link" href="#the-lost-answers-on-the-cube" title="Link to this heading">¶</a></h2>
|
| 904 |
+
<p>The figure draws the lost removal lines of the two ops the backlog item names: <code>hue-hsv</code>, whose removal lines keep the most exact match, and <code>darken</code>, the near miss of ex-2.2.11.</p>
|
| 905 |
+
<figure class="mini-themed-figure">
|
| 906 |
+
<img class="mini-themed-img-light" src="_assets/lost-cube-light.png" alt="On the color wheel, hue-hsv guesses fan out from the red-hued answers toward yellow-green and blue-purple at the same saturation, and darken guesses land darker than their answers." width="800" height="414" style="max-width: 100%; height: auto;" data-asset-name="lost-cube" />
|
| 907 |
+
<img class="mini-themed-img-dark" src="_assets/lost-cube-dark.png" alt="On the color wheel, hue-hsv guesses fan out from the red-hued answers toward yellow-green and blue-purple at the same saturation, and darken guesses land darker than their answers." width="800" height="414" style="max-width: 100%; height: auto;" data-asset-name="lost-cube" />
|
| 908 |
+
<figcaption><p><strong>Where the lost removal lines land, on <code>handover-s0</code> under <code>projection</code>.</strong> One panel per op, on the color wheel view of the cube. Each mark is the greedy guess of one lost line, in the guessed color; the ring is the line's raw answer and the stub joins the two. A random sample of the lost lines is drawn where there are more than fit.</p></figcaption></figure>
|
| 909 |
+
|
| 910 |
+
<h2 id="a-counterfactual-answer">A counterfactual answer<a class="anchor-link" href="#a-counterfactual-answer" title="Link to this heading">¶</a></h2>
|
| 911 |
+
<p>This is a post hoc check on the near misses. If the operator took the redness out of the red operand and left the op intact, the guess would be the op applied to a de-reddened operand. We try two versions of that operand:
|
| 912 |
+
(a) red channel set to zero, and
|
| 913 |
+
(b) red channel lowered to the larger of its green and blue, which keeps the other two channels and drops the saturation.</p>
|
| 914 |
+
<figure class="report-figure"><table class="report-table"><thead><tr><th>op</th><th class=num>to the answer</th><th class=num>to the zero-red answer</th><th class=num>to the grey-red answer</th><th class=num>in the grey-red box</th></tr></thead><tbody><tr><td><code>mix</code></td><td class=num>1.77</td><td class=num>1.98</td><td class=num>1.67</td><td class=num>5%</td></tr><tr><td><code>screen</code></td><td class=num>1.95</td><td class=num>2.32</td><td class=num>1.94</td><td class=num>17%</td></tr><tr><td><code>multiply</code></td><td class=num>2.09</td><td class=num>2.32</td><td class=num>2.02</td><td class=num>22%</td></tr><tr><td><code>lighten</code></td><td class=num>2.07</td><td class=num>1.68</td><td class=num>1.52</td><td class=num>36%</td></tr><tr><td><code>darken</code></td><td class=num>2.20</td><td class=num>3.03</td><td class=num>2.55</td><td class=num>10%</td></tr><tr><td><code>difference</code></td><td class=num>2.75</td><td class=num>2.90</td><td class=num>2.69</td><td class=num>5%</td></tr><tr><td><code>exclusion</code></td><td class=num>2.30</td><td class=num>2.45</td><td class=num>2.14</td><td class=num>20%</td></tr><tr><td><code>hsvmix</code></td><td class=num>2.61</td><td class=num>2.41</td><td class=num>2.22</td><td class=num>3%</td></tr><tr><td><code>hue-hsv</code></td><td class=num>2.51</td><td class=num>2.79</td><td class=num>2.03</td><td class=num>21%</td></tr><tr><td><code>sat-hsv</code></td><td class=num>2.85</td><td class=num>4.56</td><td class=num>4.14</td><td class=num>0%</td></tr><tr><td><code>value-hsv</code></td><td class=num>3.36</td><td class=num>3.77</td><td class=num>2.89</td><td class=num>8%</td></tr></tbody></table><figcaption><p><strong>Distance of the greedy guess on the removal lines, <code>handover</code> under <code>projection</code>, seed mean.</strong> The answer is the line's raw answer; the zero-red and grey-red answers are the op applied with the red operand's red channel set to zero, or to the larger of its green and blue. The last column is the share of lines whose guess is one of the grey-red answer's possible roundings.</p></figcaption></figure>
|
| 915 |
+
|
| 916 |
+
<p>Neither substitute is where the guesses go. The zero-red answer is farther from the guess than the true answer on every op but <code>lighten</code> and <code>hsvmix</code>. The grey-red answer is a little nearer on most ops (2.0 steps against 2.5 on <code>hue-hsv</code>), but the guess lands in its box on under a quarter of the lines on every op but <code>lighten</code> (36%).</p>
|
| 917 |
+
<p>So the lost answers sit between the answer and its de-reddened version, and no single substitute operand describes them.</p>
|
| 918 |
+
<h2 id="the-non-red-lines">The non-red lines<a class="anchor-link" href="#the-non-red-lines" title="Link to this heading">¶</a></h2>
|
| 919 |
+
<p>The non-red lines are the other side of selectivity: the operator should leave them alone. Ex-2.2.11 gates the exact match deficit on <code>mix</code> at {ex.ex2211.NONRED_DEFICIT_GATE:g}, and finds it near zero on every op. The distance shows whether the mass moves at all on those lines.</p>
|
| 920 |
+
<figure class="mini-themed-figure">
|
| 921 |
+
<img class="mini-themed-img-light" src="_assets/nonred-distance-light.png" alt="On the non-red lines every rise is small; handover and handover-slot rise less than the control on every op, and handover-tied rises above it on difference." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="nonred-distance" />
|
| 922 |
+
<img class="mini-themed-img-dark" src="_assets/nonred-distance-dark.png" alt="On the non-red lines every rise is small; handover and handover-slot rise less than the control on every op, and handover-tied rises above it on difference." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="nonred-distance" />
|
| 923 |
+
<figcaption><p><strong>The non-red lines (without a red answer) under <code>projection</code>, per op and condition: what the operator changes.</strong> Top: the deficit in expected exact match (clean minus <code>projection</code>), dashed at ex-2.2.11's 0.05 gate, which that report reads on <code>mix</code> alone. Middle: the rise in the greedy distance from the raw answer, in grid steps. Bottom: the rise in the distance of the mean of the model's distribution. Each small dot is one seed, the larger mark the seed mean, and the thin bar the seed range.</p></figcaption></figure>
|
| 924 |
+
|
| 925 |
+
<h2 id="between-seeds">Between seeds<a class="anchor-link" href="#between-seeds" title="Link to this heading">¶</a></h2>
|
| 926 |
+
<p>The distances vary far less between seeds than exact match does. A measurement used for a gate needs a seed spread small relative to the effect it measures; the table gives each removal measurement's spread across the twenty <code>handover</code> seeds as a share of its mean (the coefficient of variation, CV).</p>
|
| 927 |
+
<figure class="report-figure"><table class="report-table"><thead><tr><th>op</th><th class=num>exact match kept: mean</th><th class=num>seed CV</th><th class=num>greedy distance: mean</th><th class=num>seed CV</th><th class=num>mean-of-distribution distance: mean</th><th class=num>seed CV</th></tr></thead><tbody><tr><td><code>mix</code></td><td class=num>0.02</td><td class=num>127%</td><td class=num>1.77</td><td class=num>8%</td><td class=num>1.73</td><td class=num>9%</td></tr><tr><td><code>screen</code></td><td class=num>0.14</td><td class=num>35%</td><td class=num>1.95</td><td class=num>12%</td><td class=num>1.88</td><td class=num>10%</td></tr><tr><td><code>multiply</code></td><td class=num>0.15</td><td class=num>38%</td><td class=num>2.09</td><td class=num>15%</td><td class=num>2.01</td><td class=num>15%</td></tr><tr><td><code>lighten</code></td><td class=num>0.14</td><td class=num>33%</td><td class=num>2.07</td><td class=num>10%</td><td class=num>2.00</td><td class=num>8%</td></tr><tr><td><code>darken</code></td><td class=num>0.18</td><td class=num>44%</td><td class=num>2.20</td><td class=num>20%</td><td class=num>2.11</td><td class=num>19%</td></tr><tr><td><code>difference</code></td><td class=num>0.06</td><td class=num>56%</td><td class=num>2.75</td><td class=num>11%</td><td class=num>2.60</td><td class=num>11%</td></tr><tr><td><code>exclusion</code></td><td class=num>0.12</td><td class=num>35%</td><td class=num>2.30</td><td class=num>11%</td><td class=num>2.14</td><td class=num>10%</td></tr><tr><td><code>hsvmix</code></td><td class=num>0.05</td><td class=num>53%</td><td class=num>2.61</td><td class=num>6%</td><td class=num>2.53</td><td class=num>7%</td></tr><tr><td><code>hue-hsv</code></td><td class=num>0.24</td><td class=num>44%</td><td class=num>2.51</td><td class=num>20%</td><td class=num>2.46</td><td class=num>17%</td></tr><tr><td><code>sat-hsv</code></td><td class=num>0.10</td><td class=num>53%</td><td class=num>2.85</td><td class=num>19%</td><td class=num>2.65</td><td class=num>15%</td></tr><tr><td><code>value-hsv</code></td><td class=num>0.08</td><td class=num>58%</td><td class=num>3.36</td><td class=num>18%</td><td class=num>3.04</td><td class=num>13%</td></tr></tbody></table><figcaption><p><strong>Seed spread of the removal measurements on <code>handover</code> under <code>projection</code>, per op.</strong> CV is the standard deviation over the twenty seeds divided by the seed mean.</p></figcaption></figure>
|
| 928 |
+
|
| 929 |
+
<h2 id="what-we-make-of-it">What we make of it<a class="anchor-link" href="#what-we-make-of-it" title="Link to this heading">¶</a></h2>
|
| 930 |
+
<p>The kept exact match on the removal lines is not a quarter of the lines answered and the rest sent anywhere. It is closer to the other reading: nearly every line moves, and moves a short way. On <code>mix</code>, the op the D2.2 gates are scored on, the guess ends one or two steps from the answer nine times in ten.</p>
|
| 931 |
+
<p>The answers move toward what the line would give without its red, but not all the way: the counterfactual check says the model is not computing the op on a de-reddened operand.</p>
|
| 932 |
+
<p>That is the kind of side-effect this program wants to be able to describe. The intervention changes the answer on the lines that use the concept, by an amount that scales with how much the op relies on the red channel, and leaves the other lines alone.</p>
|
| 933 |
+
<p>The distance gives the removal measurement partial credit and a scale. On <code>mix</code>, exact match on <code>handover</code> sits near zero with a seed spread larger than its mean, while the distance on the same lines has a seed spread under a tenth of its mean.</p>
|
| 934 |
+
<p>That comparison flatters the distance: the CV favors a measurement with a large mean, and the distances have means an order of magnitude above the kept shares. In units of the seed spread, the two separate the conditions about equally well. The advantage of the distance is that it stays informative where exact match is near zero.</p>
|
| 935 |
+
<p>The distance also separates ops that exact match does not: <code>mix</code> and <code>value-hsv</code> both keep under a tenth of their exact match, but their guesses sit 1.8 and 3.4 steps away.</p>
|
| 936 |
+
<p>On the non-red lines, the mean of the distribution is the sensitive measurement, since it moves while the guess stays put. On <code>handover</code> every such move is under 0.03 steps, and the control's lines move as much or more, so the operator's cost on the lines it should leave alone is about what removing any direction costs.</p>
|
| 937 |
+
<p>For use in a gate, the backlog item asks for a preregistered direction before the measurement is adopted. This re-score supports two measurements:
|
| 938 |
+
(a) removal, as the normalized distance of the mean of the distribution on the removal lines, (distance − floor) / (chance − floor), rising under the operator, with the greedy distance beside it as the number a user of exact match would expect; and
|
| 939 |
+
(b) selectivity, as the non-red rise of the same mean staying at or under the rise of the control under the same operator.
|
| 940 |
+
The next experiment should set the thresholds from its own control runs. Until one of the distances has been used in a gate, the greedy and mean distances should be quoted together.</p>
|
| 941 |
+
<p>The distance does not say whether an answer is right, except at the floor, so a gate that wants "answered" should keep the hit rate or exact match beside it.</p>
|
| 942 |
+
<h2 id="method">Method<a class="anchor-link" href="#method" title="Link to this heading">¶</a></h2>
|
| 943 |
+
<p>The distances are in <code>sca.answer_distance</code>, and the re-score in <a href="experiment.py"><code>experiment.py</code></a> beside this script. Each of the 54 final checkpoints of ex-2.2.11 is run over the same probe lines under the clean pass, <code>projection</code>, and <code>operands</code>, with one compiled forward pass per operator. The answer distribution at the pre-answer position is restricted to the 216 color tokens.</p>
|
| 944 |
+
<p>For each line, we compute against its raw answer: the greedy guess, the mean and channel-wise median of that distribution, its expected exact match and expected distance, and whether the guess is a hit. For each group and pass, these are averaged, split by kept, lost, and never, and binned by rounded greedy distance. On <code>handover</code> and the control, the per-line guess is published for every op, and the mean beside it for <code>hue-hsv</code> and <code>darken</code>; every other per-line array stays in the run's memo record.</p>
|
| 945 |
+
<div class="footnote">
|
| 946 |
+
<hr />
|
| 947 |
+
<ol>
|
| 948 |
+
<li id="fn:stochastic">
|
| 949 |
+
<p>Stochastic rounding picks the grid level above or below a value at random, weighted so that the average equals the unrounded value. <a class="footnote-backref" href="#fnref:stochastic" title="Back to text">↩</a></p>
|
| 950 |
+
</li>
|
| 951 |
+
</ol>
|
| 952 |
+
</div>
|
| 953 |
+
</main>
|
| 954 |
+
</body>
|
| 955 |
+
</html>
|
exports/m2/answer-distance/index.md
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|
| 1 |
+
# How far the answer moves: an RGB-distance readout beside expected exact match
|
| 2 |
+
|
| 3 |
+
/// tip |
|
| 4 |
+
<!-- tl;dr -->
|
| 5 |
+
We re-scored ex-2.2.11's 54 checkpoints with a distance on the color grid beside expected exact match, to see where the answers go when the anchored direction is removed. On `handover` the removed answers are near misses, two to three grid steps from the right color and well short of a random guess, and the non-red lines move less than the control's own lines do under the same operator.
|
| 6 |
+
///
|
| 7 |
+
|
| 8 |
+
## Observations
|
| 9 |
+
|
| 10 |
+
- [The removal lines, by distance](#the-removal-lines-by-distance): under `projection`, the greedy guess on `handover` moves from the floor (0 to 0.5 steps, a perfect answer) to 1.8 steps on `mix` and 3.4 on `value-hsv`, between 44% and 77% of the way to chance. The control stays at the floor. The mean, median, and expected distances agree with the greedy one within 0.3 steps.
|
| 11 |
+
- [Kept and lost](#kept-and-lost): the operator loses 77% to 99% of the removal lines. The kept lines stay at the floor; the lost lines sit 1.8 (`mix`) to 3.7 (`value-hsv`) steps from the answer, and reach chance only on `value-hsv`.
|
| 12 |
+
- [The lost answers on the cube](#the-lost-answers-on-the-cube): on `mix`, nine in ten lost answers are one or two steps off. On `hue-hsv` the guesses keep their saturation and move in hue; on `darken` they land darker than the answer.
|
| 13 |
+
- [A counterfactual answer](#a-counterfactual-answer): the lost answers are not the op applied to a de-reddened operand. The nearest such answer is a little closer to the guess than the true one on most ops, but the guess lands in its box on under a quarter of the lines on all ops but `lighten`.
|
| 14 |
+
- [The non-red lines](#the-non-red-lines): on `handover` the exact match deficit stays under 0.01 and the mean of the distribution moves under 0.03 steps on every op. The control's own lines move as much or more under the same operator.
|
| 15 |
+
- [Between seeds](#between-seeds): the seed spread of the distances is 6% to 20% of the mean, against 33% to 127% for the kept share of exact match.
|
| 16 |
+
|
| 17 |
+
## Scope
|
| 18 |
+
|
| 19 |
+
This is a re-score of stored checkpoints, planned in the [backlog item](/todo/science/rgb-distance-readout-beside-exact-match.md). There is no training, no gates, and no verdicts.
|
| 20 |
+
|
| 21 |
+
Every removal and selectivity number in D2.2 is *expected exact match*: the probability mass the model puts on the colors that a line's answer can be. It gives no partial credit, so a guess one grid step from the answer scores the same as a guess of black.
|
| 22 |
+
|
| 23 |
+
So when `handover` keeps 24% of exact match on the `hue-hsv` removal lines, that could mean a quarter of the lines answered perfectly and the rest sent anywhere, or every line nudged one step over. Likewise, a non-red deficit of 0.01 could be one line in a hundred lost outright, or the mass of every line leaning a little.
|
| 24 |
+
|
| 25 |
+
We add a distance on the color grid, in grid steps. One step is the spacing between the six levels of each channel, and the far corner of the cube is 5√3 ≈ 8.7 steps from black. The target of a line is its *raw answer* (the unrounded value of the op), which is also the expected value of the answer distribution under stochastic rounding.[^stochastic]
|
| 26 |
+
|
| 27 |
+
Four quantities are measured from the raw answer. Three are central points of the model's distribution over the 216 grid colors: the *greedy* guess (the most likely color), the *mean*, and the channel-wise *median*. The fourth is the *expected* distance of a color drawn from the distribution.
|
| 28 |
+
|
| 29 |
+
The greedy and expected distances are the ones to compare with exact match. The mean is the one that moves when mass leans toward a neighbor while the guess stays the same.
|
| 30 |
+
|
| 31 |
+
[^stochastic]: Stochastic rounding picks the grid level above or below a value at random, weighted so that the average equals the unrounded value.
|
| 32 |
+
|
| 33 |
+
Every distance comes with two references. The *floor* is the distance from the raw answer to the best possible grid answer (the mode of the answer distribution): zero when the answer lands on the grid, and up to half a step per channel otherwise. A distance at the floor is a perfect answer.
|
| 34 |
+
|
| 35 |
+
*Chance* is the mean distance of a color drawn uniformly from the grid: about 3 steps for a target near the middle of the cube, and more for one near a corner. A distance at chance means the answer no longer depends on the line.
|
| 36 |
+
|
| 37 |
+
The distances and exact match are measured under the same three passes as ex-2.2.11:
|
| 38 |
+
(a) the clean forward pass,
|
| 39 |
+
(b) `projection`, with e₁ removed at every slice and position, and
|
| 40 |
+
(c) `operands`, with e₁ removed at the operand positions only.
|
| 41 |
+
Each is read on the line groups of ex-2.2.11: the removal lines (a red operand whose hue the op carries into the answer), the non-red lines, and the rest. As in the ex-2.2.11 report, the shaped operator is left out.
|
| 42 |
+
|
| 43 |
+
## The runs
|
| 44 |
+
|
| 45 |
+
The runs are the 54 final checkpoints of ex-2.2.11: the un-anchored control (5 seeds), `handover` (20), and two arms that each undo one of the changes in `handover`, `handover-slot` (20) and `handover-tied` (9). The probe lines are the ones ex-2.2.11 scored: 5,832 per op, and twice that for the three order-sensitive ops.
|
| 46 |
+
|
| 47 |
+
The two scorers agree: the re-score reproduces ex-2.2.11's kept share of expected exact match on every op (24% on `hue-hsv`, 12% to 18% on the next four).
|
| 48 |
+
|
| 49 |
+
## The removal lines, by distance
|
| 50 |
+
|
| 51 |
+
On the removal lines under `projection`, the answers behind the exact match that `handover` keeps are mostly near misses, rather than right answers among wrong ones. The figure puts the distance beside the kept share, per op.
|
| 52 |
+
|
| 53 |
+
The clean pass sits at the floor on every op and condition (the table below the figure gives it), so any distance above the floor under `projection` is caused by the operator.
|
| 54 |
+
|
| 55 |
+
|
| 56 |
+
<figure class="mini-themed-figure">
|
| 57 |
+
<img class="mini-themed-img-light" src="_assets/removal-distance-light.png" alt="Under projection, handover's greedy distance on the removal lines rises from the floor to about halfway to chance on every op, while the control stays at the floor." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="removal-distance" />
|
| 58 |
+
<img class="mini-themed-img-dark" src="_assets/removal-distance-dark.png" alt="Under projection, handover's greedy distance on the removal lines rises from the floor to about halfway to chance on every op, while the control stays at the floor." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="removal-distance" />
|
| 59 |
+
<figcaption><p><strong>The removal lines under <code>projection</code>, per op and condition: exact match kept, and how far the answer moves.</strong> Top: the share of the clean expected exact match kept, as ex-2.2.11 reads it, dashed at its 20% gate. Middle: the distance in grid steps of the greedy guess from the raw answer; the dotted rule at each op is the floor (the best grid answer's distance) and the dashed rule is chance (a uniform draw from the grid). Bottom: the distance of the mean of the model's distribution from the raw answer; the dashed rule is the center of the cube, where a uniform distribution's mean sits. Each small dot is one seed, the larger mark the seed mean, and the thin bar the seed range.</p></figcaption></figure>
|
| 60 |
+
|
| 61 |
+
The table gives the same measurements on `handover`, adds the clean and `operands` passes, and adds the hit rate (the share of lines whose greedy guess is one of the line's possible answers).
|
| 62 |
+
|
| 63 |
+
|
| 64 |
+
<figure class="report-figure"><table class="report-table"><thead><tr><th>op</th><th class=num>removal lines</th><th class=num>exact match kept</th><th class=num>hit rate, clean</th><th class=num>hit rate, <code>projection</code></th><th class=num>greedy distance, clean</th><th class=num>greedy distance, <code>projection</code></th><th class=num>greedy distance, <code>operands</code></th><th class=num>floor</th><th class=num>chance</th></tr></thead><tbody><tr><td><code>mix</code></td><td class=num>365</td><td class=num>0.02 (0.0–0.1)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.01 (0.0–0.1)</td><td class=num>0.00 (0.0–0.0)</td><td class=num>1.77 (1.4–2.0)</td><td class=num>1.76 (1.4–2.0)</td><td class=num>0.00</td><td class=num>3.66</td></tr><tr><td><code>screen</code></td><td class=num>387</td><td class=num>0.14 (0.1–0.2)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.19 (0.1–0.3)</td><td class=num>0.24 (0.2–0.2)</td><td class=num>1.95 (1.5–2.5)</td><td class=num>1.94 (1.5–2.4)</td><td class=num>0.20</td><td class=num>4.14</td></tr><tr><td><code>multiply</code></td><td class=num>384</td><td class=num>0.15 (0.0–0.3)</td><td class=num>0.91 (0.9–0.9)</td><td class=num>0.15 (0.1–0.3)</td><td class=num>0.22 (0.2–0.2)</td><td class=num>2.09 (1.5–2.7)</td><td class=num>2.07 (1.5–2.8)</td><td class=num>0.20</td><td class=num>4.39</td></tr><tr><td><code>lighten</code></td><td class=num>386</td><td class=num>0.14 (0.1–0.3)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.15 (0.1–0.3)</td><td class=num>0.00 (0.0–0.0)</td><td class=num>2.07 (1.6–2.6)</td><td class=num>2.07 (1.6–2.5)</td><td class=num>0.00</td><td class=num>4.12</td></tr><tr><td><code>darken</code></td><td class=num>382</td><td class=num>0.18 (0.0–0.3)</td><td class=num>0.95 (0.9–0.9)</td><td class=num>0.17 (0.0–0.3)</td><td class=num>0.00 (0.0–0.0)</td><td class=num>2.20 (1.3–3.2)</td><td class=num>2.18 (1.3–3.2)</td><td class=num>0.00</td><td class=num>4.28</td></tr><tr><td><code>difference</code></td><td class=num>403</td><td class=num>0.06 (0.0–0.1)</td><td class=num>0.99 (1.0–1.0)</td><td class=num>0.07 (0.0–0.1)</td><td class=num>0.01 (0.0–0.0)</td><td class=num>2.75 (2.3–3.3)</td><td class=num>2.73 (2.2–3.3)</td><td class=num>0.00</td><td class=num>3.80</td></tr><tr><td><code>exclusion</code></td><td class=num>390</td><td class=num>0.12 (0.1–0.2)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.20 (0.1–0.3)</td><td class=num>0.21 (0.2–0.2)</td><td class=num>2.30 (1.8–2.8)</td><td class=num>2.25 (1.8–2.8)</td><td class=num>0.18</td><td class=num>3.67</td></tr><tr><td><code>hsvmix</code></td><td class=num>401</td><td class=num>0.05 (0.0–0.1)</td><td class=num>0.98 (1.0–1.0)</td><td class=num>0.09 (0.0–0.2)</td><td class=num>0.53 (0.5–0.6)</td><td class=num>2.61 (2.3–2.8)</td><td class=num>2.59 (2.2–2.8)</td><td class=num>0.48</td><td class=num>3.99</td></tr><tr><td><code>hue-hsv</code></td><td class=num>333</td><td class=num>0.24 (0.1–0.4)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.23 (0.0–0.5)</td><td class=num>0.17 (0.2–0.2)</td><td class=num>2.51 (1.7–3.4)</td><td class=num>2.38 (1.7–3.4)</td><td class=num>0.15</td><td class=num>4.00</td></tr><tr><td><code>sat-hsv</code></td><td class=num>377</td><td class=num>0.10 (0.0–0.2)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.17 (0.0–0.3)</td><td class=num>0.20 (0.2–0.2)</td><td class=num>2.85 (2.0–4.1)</td><td class=num>2.71 (2.0–3.4)</td><td class=num>0.18</td><td class=num>4.17</td></tr><tr><td><code>value-hsv</code></td><td class=num>389</td><td class=num>0.08 (0.0–0.2)</td><td class=num>1.00 (1.0–1.0)</td><td class=num>0.11 (0.0–0.2)</td><td class=num>0.15 (0.1–0.2)</td><td class=num>3.36 (2.5–4.3)</td><td class=num>3.15 (2.1–3.9)</td><td class=num>0.13</td><td class=num>4.34</td></tr></tbody></table><figcaption><p><strong>The removal lines on <code>handover</code>, per op: seed mean (seed range).</strong> Distances in grid steps from the raw answer. The floor is the best grid answer's distance and chance a uniform draw's, both averaged over the op's removal lines.</p></figcaption></figure>
|
| 65 |
+
|
| 66 |
+
## Kept and lost
|
| 67 |
+
|
| 68 |
+
A distance averaged over a group mixes lines the operator leaves answered with lines it does not, so we split the lines by the greedy guess. Under a given pass, a line is:
|
| 69 |
+
(a) *kept* when the guess is one of the possible answers of the line,
|
| 70 |
+
(b) *lost* when the clean guess was a possible answer and the guess under the pass is not, and
|
| 71 |
+
(c) *never* when the clean guess already missed.
|
| 72 |
+
The distance of the lost lines tells us where a removed answer goes.
|
| 73 |
+
|
| 74 |
+
|
| 75 |
+
<figure class="mini-themed-figure">
|
| 76 |
+
<img class="mini-themed-img-light" src="_assets/lost-lines-light.png" alt="Most of handover's removal lines are lost under projection; the lost lines sit two to three steps from the answer, short of chance on every op but value-hsv, while the kept lines stay at the floor." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="lost-lines" />
|
| 77 |
+
<img class="mini-themed-img-dark" src="_assets/lost-lines-dark.png" alt="Most of handover's removal lines are lost under projection; the lost lines sit two to three steps from the answer, short of chance on every op but value-hsv, while the kept lines stay at the floor." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="lost-lines" />
|
| 78 |
+
<figcaption><p><strong>The removal lines under <code>projection</code>, split by whether the greedy guess survives.</strong> Top: the share of each op's removal lines that are lost (answered on the clean pass, not under the operator). Middle: the greedy distance of the lost lines from the raw answer, in grid steps, with chance dashed. Bottom: the greedy distance of the kept lines, with the floor dotted. Each small dot is one seed, the larger mark the seed mean, and the thin bar the seed range; a condition with no lost line on a seed draws nothing for it.</p></figcaption></figure>
|
| 79 |
+
|
| 80 |
+
Per line, as a distribution: in the histograms below, the bin at zero holds the kept lines and the other bins show where the lost answers go.
|
| 81 |
+
|
| 82 |
+
On `mix`, nine in ten of the moved answers sit one or two steps off, which is what treating the red channel as absent would give (on `mix` that shift is about 2.5 steps). `darken` decays from one step, `hue-hsv` spreads over two to four, and `value-hsv` is close to the shape a uniform guess gives.
|
| 83 |
+
|
| 84 |
+
|
| 85 |
+
<figure class="mini-themed-figure">
|
| 86 |
+
<img class="mini-themed-img-light" src="_assets/lost-histograms-light.png" alt="Per-op histograms of guess distance: mix peaks at one to two steps, darken decays from one step, hue-hsv spreads over two to four, and value-hsv is close to the uniform-guess shape." width="818" height="548" style="max-width: 100%; height: auto;" data-asset-name="lost-histograms" />
|
| 87 |
+
<img class="mini-themed-img-dark" src="_assets/lost-histograms-dark.png" alt="Per-op histograms of guess distance: mix peaks at one to two steps, darken decays from one step, hue-hsv spreads over two to four, and value-hsv is close to the uniform-guess shape." width="818" height="548" style="max-width: 100%; height: auto;" data-asset-name="lost-histograms" />
|
| 88 |
+
<figcaption><p><strong>Where the removal-line answers land under <code>projection</code> on <code>handover</code>, per op.</strong> Bars: the share of the op's removal lines, pooled over twenty seeds, whose greedy guess sits each number of grid steps from the raw answer (rounded), under <code>projection</code>; in outline, the same under the clean pass. The dashed line is the distribution a uniform guess from the grid would give on the same lines.</p></figcaption></figure>
|
| 89 |
+
|
| 90 |
+
## The lost answers on the cube
|
| 91 |
+
|
| 92 |
+
The figure draws the lost removal lines of the two ops the backlog item names: `hue-hsv`, whose removal lines keep the most exact match, and `darken`, the near miss of ex-2.2.11.
|
| 93 |
+
|
| 94 |
+
|
| 95 |
+
<figure class="mini-themed-figure">
|
| 96 |
+
<img class="mini-themed-img-light" src="_assets/lost-cube-light.png" alt="On the color wheel, hue-hsv guesses fan out from the red-hued answers toward yellow-green and blue-purple at the same saturation, and darken guesses land darker than their answers." width="800" height="414" style="max-width: 100%; height: auto;" data-asset-name="lost-cube" />
|
| 97 |
+
<img class="mini-themed-img-dark" src="_assets/lost-cube-dark.png" alt="On the color wheel, hue-hsv guesses fan out from the red-hued answers toward yellow-green and blue-purple at the same saturation, and darken guesses land darker than their answers." width="800" height="414" style="max-width: 100%; height: auto;" data-asset-name="lost-cube" />
|
| 98 |
+
<figcaption><p><strong>Where the lost removal lines land, on <code>handover-s0</code> under <code>projection</code>.</strong> One panel per op, on the color wheel view of the cube. Each mark is the greedy guess of one lost line, in the guessed color; the ring is the line's raw answer and the stub joins the two. A random sample of the lost lines is drawn where there are more than fit.</p></figcaption></figure>
|
| 99 |
+
|
| 100 |
+
## A counterfactual answer
|
| 101 |
+
|
| 102 |
+
This is a post hoc check on the near misses. If the operator took the redness out of the red operand and left the op intact, the guess would be the op applied to a de-reddened operand. We try two versions of that operand:
|
| 103 |
+
(a) red channel set to zero, and
|
| 104 |
+
(b) red channel lowered to the larger of its green and blue, which keeps the other two channels and drops the saturation.
|
| 105 |
+
|
| 106 |
+
|
| 107 |
+
<figure class="report-figure"><table class="report-table"><thead><tr><th>op</th><th class=num>to the answer</th><th class=num>to the zero-red answer</th><th class=num>to the grey-red answer</th><th class=num>in the grey-red box</th></tr></thead><tbody><tr><td><code>mix</code></td><td class=num>1.77</td><td class=num>1.98</td><td class=num>1.67</td><td class=num>5%</td></tr><tr><td><code>screen</code></td><td class=num>1.95</td><td class=num>2.32</td><td class=num>1.94</td><td class=num>17%</td></tr><tr><td><code>multiply</code></td><td class=num>2.09</td><td class=num>2.32</td><td class=num>2.02</td><td class=num>22%</td></tr><tr><td><code>lighten</code></td><td class=num>2.07</td><td class=num>1.68</td><td class=num>1.52</td><td class=num>36%</td></tr><tr><td><code>darken</code></td><td class=num>2.20</td><td class=num>3.03</td><td class=num>2.55</td><td class=num>10%</td></tr><tr><td><code>difference</code></td><td class=num>2.75</td><td class=num>2.90</td><td class=num>2.69</td><td class=num>5%</td></tr><tr><td><code>exclusion</code></td><td class=num>2.30</td><td class=num>2.45</td><td class=num>2.14</td><td class=num>20%</td></tr><tr><td><code>hsvmix</code></td><td class=num>2.61</td><td class=num>2.41</td><td class=num>2.22</td><td class=num>3%</td></tr><tr><td><code>hue-hsv</code></td><td class=num>2.51</td><td class=num>2.79</td><td class=num>2.03</td><td class=num>21%</td></tr><tr><td><code>sat-hsv</code></td><td class=num>2.85</td><td class=num>4.56</td><td class=num>4.14</td><td class=num>0%</td></tr><tr><td><code>value-hsv</code></td><td class=num>3.36</td><td class=num>3.77</td><td class=num>2.89</td><td class=num>8%</td></tr></tbody></table><figcaption><p><strong>Distance of the greedy guess on the removal lines, <code>handover</code> under <code>projection</code>, seed mean.</strong> The answer is the line's raw answer; the zero-red and grey-red answers are the op applied with the red operand's red channel set to zero, or to the larger of its green and blue. The last column is the share of lines whose guess is one of the grey-red answer's possible roundings.</p></figcaption></figure>
|
| 108 |
+
|
| 109 |
+
Neither substitute is where the guesses go. The zero-red answer is farther from the guess than the true answer on every op but `lighten` and `hsvmix`. The grey-red answer is a little nearer on most ops (2.0 steps against 2.5 on `hue-hsv`), but the guess lands in its box on under a quarter of the lines on every op but `lighten` (36%).
|
| 110 |
+
|
| 111 |
+
So the lost answers sit between the answer and its de-reddened version, and no single substitute operand describes them.
|
| 112 |
+
|
| 113 |
+
## The non-red lines
|
| 114 |
+
|
| 115 |
+
The non-red lines are the other side of selectivity: the operator should leave them alone. Ex-2.2.11 gates the exact match deficit on `mix` at {ex.ex2211.NONRED_DEFICIT_GATE:g}, and finds it near zero on every op. The distance shows whether the mass moves at all on those lines.
|
| 116 |
+
|
| 117 |
+
|
| 118 |
+
<figure class="mini-themed-figure">
|
| 119 |
+
<img class="mini-themed-img-light" src="_assets/nonred-distance-light.png" alt="On the non-red lines every rise is small; handover and handover-slot rise less than the control on every op, and handover-tied rises above it on difference." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="nonred-distance" />
|
| 120 |
+
<img class="mini-themed-img-dark" src="_assets/nonred-distance-dark.png" alt="On the non-red lines every rise is small; handover and handover-slot rise less than the control on every op, and handover-tied rises above it on difference." width="818" height="740" style="max-width: 100%; height: auto;" data-asset-name="nonred-distance" />
|
| 121 |
+
<figcaption><p><strong>The non-red lines (without a red answer) under <code>projection</code>, per op and condition: what the operator changes.</strong> Top: the deficit in expected exact match (clean minus <code>projection</code>), dashed at ex-2.2.11's 0.05 gate, which that report reads on <code>mix</code> alone. Middle: the rise in the greedy distance from the raw answer, in grid steps. Bottom: the rise in the distance of the mean of the model's distribution. Each small dot is one seed, the larger mark the seed mean, and the thin bar the seed range.</p></figcaption></figure>
|
| 122 |
+
|
| 123 |
+
## Between seeds
|
| 124 |
+
|
| 125 |
+
The distances vary far less between seeds than exact match does. A measurement used for a gate needs a seed spread small relative to the effect it measures; the table gives each removal measurement's spread across the twenty `handover` seeds as a share of its mean (the coefficient of variation, CV).
|
| 126 |
+
|
| 127 |
+
|
| 128 |
+
<figure class="report-figure"><table class="report-table"><thead><tr><th>op</th><th class=num>exact match kept: mean</th><th class=num>seed CV</th><th class=num>greedy distance: mean</th><th class=num>seed CV</th><th class=num>mean-of-distribution distance: mean</th><th class=num>seed CV</th></tr></thead><tbody><tr><td><code>mix</code></td><td class=num>0.02</td><td class=num>127%</td><td class=num>1.77</td><td class=num>8%</td><td class=num>1.73</td><td class=num>9%</td></tr><tr><td><code>screen</code></td><td class=num>0.14</td><td class=num>35%</td><td class=num>1.95</td><td class=num>12%</td><td class=num>1.88</td><td class=num>10%</td></tr><tr><td><code>multiply</code></td><td class=num>0.15</td><td class=num>38%</td><td class=num>2.09</td><td class=num>15%</td><td class=num>2.01</td><td class=num>15%</td></tr><tr><td><code>lighten</code></td><td class=num>0.14</td><td class=num>33%</td><td class=num>2.07</td><td class=num>10%</td><td class=num>2.00</td><td class=num>8%</td></tr><tr><td><code>darken</code></td><td class=num>0.18</td><td class=num>44%</td><td class=num>2.20</td><td class=num>20%</td><td class=num>2.11</td><td class=num>19%</td></tr><tr><td><code>difference</code></td><td class=num>0.06</td><td class=num>56%</td><td class=num>2.75</td><td class=num>11%</td><td class=num>2.60</td><td class=num>11%</td></tr><tr><td><code>exclusion</code></td><td class=num>0.12</td><td class=num>35%</td><td class=num>2.30</td><td class=num>11%</td><td class=num>2.14</td><td class=num>10%</td></tr><tr><td><code>hsvmix</code></td><td class=num>0.05</td><td class=num>53%</td><td class=num>2.61</td><td class=num>6%</td><td class=num>2.53</td><td class=num>7%</td></tr><tr><td><code>hue-hsv</code></td><td class=num>0.24</td><td class=num>44%</td><td class=num>2.51</td><td class=num>20%</td><td class=num>2.46</td><td class=num>17%</td></tr><tr><td><code>sat-hsv</code></td><td class=num>0.10</td><td class=num>53%</td><td class=num>2.85</td><td class=num>19%</td><td class=num>2.65</td><td class=num>15%</td></tr><tr><td><code>value-hsv</code></td><td class=num>0.08</td><td class=num>58%</td><td class=num>3.36</td><td class=num>18%</td><td class=num>3.04</td><td class=num>13%</td></tr></tbody></table><figcaption><p><strong>Seed spread of the removal measurements on <code>handover</code> under <code>projection</code>, per op.</strong> CV is the standard deviation over the twenty seeds divided by the seed mean.</p></figcaption></figure>
|
| 129 |
+
|
| 130 |
+
## What we make of it
|
| 131 |
+
|
| 132 |
+
The kept exact match on the removal lines is not a quarter of the lines answered and the rest sent anywhere. It is closer to the other reading: nearly every line moves, and moves a short way. On `mix`, the op the D2.2 gates are scored on, the guess ends one or two steps from the answer nine times in ten.
|
| 133 |
+
|
| 134 |
+
The answers move toward what the line would give without its red, but not all the way: the counterfactual check says the model is not computing the op on a de-reddened operand.
|
| 135 |
+
|
| 136 |
+
That is the kind of side-effect this program wants to be able to describe. The intervention changes the answer on the lines that use the concept, by an amount that scales with how much the op relies on the red channel, and leaves the other lines alone.
|
| 137 |
+
|
| 138 |
+
The distance gives the removal measurement partial credit and a scale. On `mix`, exact match on `handover` sits near zero with a seed spread larger than its mean, while the distance on the same lines has a seed spread under a tenth of its mean.
|
| 139 |
+
|
| 140 |
+
That comparison flatters the distance: the CV favors a measurement with a large mean, and the distances have means an order of magnitude above the kept shares. In units of the seed spread, the two separate the conditions about equally well. The advantage of the distance is that it stays informative where exact match is near zero.
|
| 141 |
+
|
| 142 |
+
The distance also separates ops that exact match does not: `mix` and `value-hsv` both keep under a tenth of their exact match, but their guesses sit 1.8 and 3.4 steps away.
|
| 143 |
+
|
| 144 |
+
On the non-red lines, the mean of the distribution is the sensitive measurement, since it moves while the guess stays put. On `handover` every such move is under 0.03 steps, and the control's lines move as much or more, so the operator's cost on the lines it should leave alone is about what removing any direction costs.
|
| 145 |
+
|
| 146 |
+
For use in a gate, the backlog item asks for a preregistered direction before the measurement is adopted. This re-score supports two measurements:
|
| 147 |
+
(a) removal, as the normalized distance of the mean of the distribution on the removal lines, (distance − floor) / (chance − floor), rising under the operator, with the greedy distance beside it as the number a user of exact match would expect; and
|
| 148 |
+
(b) selectivity, as the non-red rise of the same mean staying at or under the rise of the control under the same operator.
|
| 149 |
+
The next experiment should set the thresholds from its own control runs. Until one of the distances has been used in a gate, the greedy and mean distances should be quoted together.
|
| 150 |
+
|
| 151 |
+
The distance does not say whether an answer is right, except at the floor, so a gate that wants "answered" should keep the hit rate or exact match beside it.
|
| 152 |
+
|
| 153 |
+
## Method
|
| 154 |
+
|
| 155 |
+
The distances are in `sca.answer_distance`, and the re-score in [`experiment.py`](experiment.py) beside this script. Each of the 54 final checkpoints of ex-2.2.11 is run over the same probe lines under the clean pass, `projection`, and `operands`, with one compiled forward pass per operator. The answer distribution at the pre-answer position is restricted to the 216 color tokens.
|
| 156 |
+
|
| 157 |
+
For each line, we compute against its raw answer: the greedy guess, the mean and channel-wise median of that distribution, its expected exact match and expected distance, and whether the guess is a hit. For each group and pass, these are averaged, split by kept, lost, and never, and binned by rounded greedy distance. On `handover` and the control, the per-line guess is published for every op, and the mean beside it for `hue-hsv` and `darken`; every other per-line array stays in the run's memo record.
|