From f29c41e78da10d3c40afdd2deeb43c4d73f5eb43 Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Sat, 1 Aug 2026 17:15:26 -0500 Subject: A cheap gate that survives its controls: the anchor bound Three statistics failed the same way -- fields agreeing on the number and disagreeing on recovery -- because each was invented by staring at the fields rather than by asking what matching needs. The fourth asks directly: declare half the scenes anchors, hand over their correspondence, describe the rest by their field rows against the anchors, and match one-to-one by Hungarian assignment. Seconds to compute, and it upper-bounds blind recovery because blind recovery must also discover the anchor correspondence. Never violated across six fields spanning the full range of outcomes, and it separates every case the refuted statistics collapsed: synth full bound 0.989 blind 0.958 gap +0.03 synth noise 0.35 bound 0.984 blind 0.947 gap +0.04 synth omit size bound 0.997 blind 0.056 gap +0.94 synth rank 8 bound 0.930 blind 0.129 gap +0.80 Visual Genome bound 0.291 blind 0.000 gap +0.29 This corrects two claims from earlier today. Caption suppression does not destroy information -- its bound is 0.997 -- it destroys blind searchability, by making scenes interchangeable under permutation in a way given anchors break. And Visual Genome's problem was never spectral width: with the correspondence handed over, seven scenes in ten still cannot be identified. Co-Authored-By: Claude --- RANK_RESULTS.md | 67 +++++++++++++++++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 65 insertions(+), 2 deletions(-) (limited to 'RANK_RESULTS.md') diff --git a/RANK_RESULTS.md b/RANK_RESULTS.md index d520e5e..ffee8c9 100644 --- a/RANK_RESULTS.md +++ b/RANK_RESULTS.md @@ -1,7 +1,16 @@ # The gate was measuring the wrong thing -*2026-08-01. Supersedes the correlation threshold used as the project's -go/no-go statistic since the synthetic world results.* +*2026-08-01. Retires the correlation threshold that has been the project's +go/no-go statistic since the synthetic world results, records two replacement +statistics that were proposed and refuted the same day, and settles on a third +that survives its controls: an upper bound obtained by giving the solver half +the correspondence and asking it to recover the rest.* + +**Result in one line.** The correlation does not govern recovery in either +direction; what does is whether a representation can identify scenes at all, +measured by matching against anchors whose correspondence is given. Visual +Genome scores 0.291 on that bound against 0.98 for the synthetic world that +recovers, and its blind recovery is 0.0000 against 0.0039 chance. ## The correlation does not govern recovery @@ -102,6 +111,60 @@ than everything found (recoverable), tied with what is found (symmetry), or shallower than what is found (information deficit). The gate is running on both fields; the sections below should be read against this correction. +## Resolution: ask the matching question, and give one thing away + +Three statistics failed the same way — fields agreeing on the number and +disagreeing on recovery — and the pattern in the failures is that each was +invented by staring at the fields rather than by asking what matching needs. +The one that works asks directly, with a single concession. + +Declare half the scenes anchors and hand over their correspondence. Describe +every remaining scene, in each modality, by its field row against the anchors. +Match the two descriptions one-to-one by Hungarian assignment. Nothing is +searched; the answer is a linear program, and it costs seconds. + +This **upper-bounds blind recovery**, because blind recovery must additionally +discover the anchor correspondence. It held in every field measured: + +| Field | ρ | anchor bound | blind recovery | search gap | +|---|---|---|---|---| +| synthetic, full | 0.928 | 0.989 | 0.958 | +0.031 | +| synthetic, noise 0.35 | 0.828 | 0.984 | 0.947 | +0.037 | +| synthetic, caption omits size | 0.830 | **0.997** | 0.056 | **+0.941** | +| synthetic, rank 8 | 0.906 | 0.930 | 0.129 | +0.801 | +| Visual Genome, best | 0.731 | **0.291** | 0.000 | +0.291 | +| Visual Genome, baseline | 0.656 | 0.195 | 0.000 | +0.195 | + +**The bound splits the deficit in two, and the two halves call for opposite +work.** The bound itself says whether the representation identifies scenes at +all; the gap between bound and blind recovery says whether the search can find +what the representation contains. + +Read down the table and the three regimes are unmistakable. The two recovering +fields have a bound near one and a gap of three points — representation good, +search working. Caption-omission and rank-8 truncation have a bound of 0.93 to +**0.997** and lose almost everything to the search: the information is intact, +perfectly so in the omission case, and blind matching cannot reach it. Visual +Genome is the opposite failure — its bound is 0.291, so **even with the +correspondence handed over, seven scenes in ten cannot be identified**, and no +solver improvement addresses that. + +This corrects two things I wrote earlier today. The caption-suppression ladder +does not show information being destroyed; it shows blind searchability being +destroyed while the information stays. Suppressing a factor makes scenes that +differed only in that factor interchangeable *under permutation*, which the +given anchors break and blind matching does not. And Visual Genome's problem +was never the width of its shared spectrum — it is that a region description +and a patch descriptor, compared through relation profiles, identify a +photograph about 29% of the time. + +The bound is an empirical upper bound rather than a proven one: handing over +anchors removes search but also changes the estimation problem. It was not +violated in six fields spanning the full range of outcomes, and unlike the +three refuted statistics it separates every case they collapsed. It is now the +project's cheap gate, and a representation that cannot pass it should not be +searched. + ## What the shared spectrum measures Each field is eigendecomposed and the principal angles between the two leading -- cgit v1.2.3