From f75e1f0877c7d1b57299a68507d30eeb16bf3b4d Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Sat, 1 Aug 2026 17:02:43 -0500 Subject: Correction, same session: the width statistic does not survive its control The replacement gate proposed this morning is refuted by a control run this afternoon. Independent noise lowers the correlation to 0.828 without narrowing the underlying signal and reaches the same measured width as a field whose captions omit one factor -- 15.7 against 15.0 -- with recovery at 94.7% and 5.6%. A second instrument built specifically to fix that, counting canonical directions that generalise to held-out scenes, fails the same way and rates Visual Genome highest of the three failing fields. Established: the correlation does not govern recovery, in both directions. Corpus overlap does control it -- the caption-suppression ladder is monotone from 96.4% to 0.0%. Not established: any statistic that predicts recovery cheaply. Documents corrected accordingly rather than quietly rephrased; the refuted claim stood for four hours and is recorded as such. Co-Authored-By: Claude --- EXTENDED_ABSTRACT.md | 56 ++++++++++++++++++++++++++++++++-------------------- 1 file changed, 35 insertions(+), 21 deletions(-) (limited to 'EXTENDED_ABSTRACT.md') diff --git a/EXTENDED_ABSTRACT.md b/EXTENDED_ABSTRACT.md index 1e96cae..7dec8f8 100644 --- a/EXTENDED_ABSTRACT.md +++ b/EXTENDED_ABSTRACT.md @@ -86,11 +86,18 @@ The theory said so in advance and we misread it. Matching thresholds are derived for exchangeable full-rank noise, where each of the N²/2 field entries constrains the pairing independently; a rank-*r* shared component supplies about *rN*, an eighth as many at 256 scenes with *r* near ten. -The corrected gate is a joint condition on the correlation and on the -width of the shared spectrum — the number of directions along which the -two modalities agree, measured by principal angles against a -scene-shuffled null. Neither alone suffices: 18 shared directions at -correlation 0.508 fails, and 11 at 0.902 fails. + +What replaces the correlation is an open question, and we report two +failed answers rather than one plausible one. The obvious candidate is +the width of the shared spectrum, and it does not survive its own +control: independent noise that lowers the correlation to 0.828 without +narrowing the underlying signal reaches the same measured width as a +field whose captions omit one factor — 15.7 against 15.0 — with recovery +at 94.7% and 5.6% respectively. A second instrument built to fix that, +counting canonical directions that generalise to held-out scenes, rates +the three failing fields at 16.6 to 17.2 and ranks the worst of them +highest. **What is established is that the correlation is not the +governing statistic; what is not established is what is.** ## A closed world settles the mechanism @@ -132,9 +139,9 @@ frequency rankings diverge in the tail. Ported to Visual Genome under the same recipe — DINOv2 patch features, spectral segmentation, distributional word statistics — the field -correlation reaches 0.716 and the shared spectrum 15 directions, against -0.928 and 26 for the synthetic world that recovers. The trajectory that -got there is more informative than either number. +correlation reaches 0.731 against 0.928 for the synthetic world, and +blind search returns 0.0000 against a chance rate of 0.0039. The +trajectory that got there is more informative than the number. Discretisation cost more than half the signal: hard class codes give 0.166 where continuous states give 0.489, because fields need only @@ -149,19 +156,26 @@ underperform corpus-fitted statistics, 0.19 against 0.656, so in-context features beat isolated crops and corpus-specific vectors beat a language model's pooled states. -The width diagnosis localises the remaining gap somewhere the correlation -alone never pointed. Both modalities are individually rich on -photographs — vision effective rank 40, text 48 — and they agree on 15 -directions, so **each side is rich about something and they are rich -about different things.** That intersection barely moves under anything -tunable on the vision side: near-tripling the segments costs one shared -direction, and handing the pipeline annotated boxes instead of -unsupervised segmentation buys one. The text side moves it from 10 to 17 -and saturates. Enlarging the population does not help either, 23 to 19 -shared directions from 256 to 1024 scenes. The ceiling behaves like a -property of what the two corpora are about rather than of how either is -encoded, which makes corpus choice a first-class variable: the closed -world reaches 26 because its captions state exactly the world state. +What does localise the gap is an intervention rather than a statistic. +In the closed world the caption is encoded in separate factor blocks, so +one can be suppressed — the caption stops stating a property while vision +still sees it, and nothing else changes. Deleting a single word class +takes recovery from 96.4% to 5.6% at a correlation of 0.830, higher than +anything we reach on photographs, and the full ladder is monotone in how +much the caption states. **Corpus overlap controls recovery**, whatever +the mediating quantity turns out to be. + +Encoder-side changes do not. Five interventions on the vision side — +near-tripling the segments, substituting annotated boxes for unsupervised +segmentation, third-order moments in the set kernel, and doubling the +backbone to DINOv2-large — each raise the vision field's own effective +rank and leave both the correlation and every width measure where they +were. The gains that did arrive came from the projection, the text +vectors and the phrase encoding, and total 0.075 in correlation. This +makes corpus choice a first-class variable rather than a fallback: a +region description does not say as much about a photograph as the closed +world's captions say about their scenes, and no vision encoder repairs +that. ## What is not shown -- cgit v1.2.3