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The caption-omitted field returned under 5% from every solver tried:
Umeyama, GRAMPA, five Gromov-Wasserstein variants, FAQ with and without
restarts, PATH convex-concave, a moment ladder, semirelaxed GW. The
measurements said the answer was not a sixteenth solver.
Descent on that field amplifies: a start 10% correct comes out 42%, one
20% correct comes out 78%. What no initialiser could do was clear the
entry price, since all of them land in the same wrong region. So run a
diverse pool of cheap descents, let them vote, round the vote matrix to a
permutation by Hungarian assignment rather than argmax, descend from
that, and rebuild the pool around the result. Each round feeds the
amplifier a better start.
0.044 -> 0.72 on the best run, 0.54 mean over two. Competitive elsewhere:
0.977 on the easy field against 0.961 for the best GW variant.
Also adds the diagnostics that led here: the basin-width probe (k=16
transpositions still returns to the exact truth 100% of the time) and the
capture-threshold curve that measures amplification directly.
Co-Authored-By: Claude <noreply@anthropic.com>
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a benchmark
The gate settles which failure mode each field is in, and refutes the
symmetry hypothesis I proposed. On the caption-omitted field the truth is
a STRICT local minimum -- descent started at the truth does not move at
all -- the anchor bound says the information is 99.7% intact, and our
solver stops 0.44 above it at 4.9% accuracy. That is a pure optimiser
failure. Natural data is the opposite: descent from the truth falls a
further 0.167, so the truth is not even locally optimal, which is the
information-deficit signature the 0.291 bound predicted.
Steepest descent was brute-forcing all 32,640 candidate permutations
through the full energy every step, including a batched cube trace with
the triangle term active -- 203 seconds per descent, which is why the
gates were hopeless. The pairwise term needs one matrix product for the
whole table: swapping p,q changes the alignment sum by
2(C_pq + C_qp - C_pp - C_qq + 2 A_pq B_pq) with C = A @ B. Verified
against brute force to 1e-9 before use, and the fast descent reaches the
same optimum. 203s -> 0.79s.
Adds a matching benchmark with known-reachable answers and the solver
families never tried on these fields: Gromov-Wasserstein, entropic GW
with an annealed regulariser, BAPG.
Co-Authored-By: Claude <noreply@anthropic.com>
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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 <noreply@anthropic.com>
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A controlled truncation refutes the project's central go/no-go rule.
Projecting the recovering synthetic fields to rank r holds the field
correlation at 0.902-0.929 while recovery moves 6.2% -> 12.9% -> 95.6%
across ranks 4, 8, 16. A field past the supposed 0.9 threshold recovers
13%, so correlation neither predicts nor forbids recovery and the width
of the shared spectrum is what moves it.
The gate becomes a joint condition on correlation and shared width,
measured by principal angles against a scene-shuffled null. Neither
suffices alone: 18 shared directions at 0.508 fails, 11 at 0.902 fails.
With the old gate retired, natural data was finally searched: 0.0000
against 0.0039 chance. The old verdict was right, its reasoning was not.
Also closes route D by measurement. rho_IT ~ sqrt(4 log N / N) rises as N
falls, and at N = 16 through 96 the deepest state a strong searcher
reaches is deeper than the truth in 3/3 replicates at every size.
Free gains: eigenvalue-weighted projection over a wide basis with
128-dim text vectors takes the correlation 0.656 -> 0.716 and shared
width 10 -> 16. Hubness refuted as an inflation hypothesis.
Moving the per-image segmentation eigendecomposition onto the GPU cut
batch time from 130s to 1.9s.
Co-Authored-By: Claude <noreply@anthropic.com>
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identifiability
Method: scene states are sets of part states; relation fields are built
within each modality and are invariant to how each side labels its own
features; the cross-modal bridge is a coupling searched under an energy
that is a closed-form functional of one matrix; solving is spectral
initialisation followed by exact local refinement.
Evidence: in a procedurally generated closed world, blind recovery of a
hidden image-caption correspondence reaches 95.3% at 256 scenes against
0.39% chance, and the recovered pairs transfer to 200 held-out scenes at
93.0% exact retrieval with random-pair and shuffled-image controls at or
near chance. Cross-modal value correspondence is derived from disjoint
corpora rather than declared. On Visual Genome the field correlation
reaches 0.656 against the 0.9 that polynomial recovery needs, with the
deficit attributed away from segmentation and discretisation.
Protocol: no image-text pair enters any objective, optimiser,
initialisation, or model selection; hidden pairs score orderings only.
Co-Authored-By: Claude <noreply@anthropic.com>
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