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DINOv2-large, twice the depth of base and wider, leaves the shared count
at exactly 15 and moves the correlation by less than the segmentation
noise floor. Four vision-side interventions now raise the vision field's
own rank and leave the intersection alone.
The cheap tier of the register is exhausted. What remains is a corpus
chosen for naturally wide overlap, promoted to the central bet, and the
unbalanced formulation, promoted to the critical path since such a
corpus is unlikely to arrive in bijection.
Co-Authored-By: Claude <noreply@anthropic.com>
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Four tests around today's additions. Two failed on first run and both
were worth having.
The degree decomposition left an O(1/n) residual on a field that is
purely additive: excluding the diagonal makes the two-way design
unbalanced, so one pass of row and column means does not remove a pure
degree effect. Swept to convergence instead. At N=256 the correction
moves the reported variance shares by under 0.001, so the refutation of
the hubness hypothesis stands unchanged -- but the instrument that
produced it now does what it claims.
The other failure was the test's own scale: two random 16-dimensional
subspaces of R^64 overlap above 0.7 by chance, which is why the real
measurements are made at N=256 where the null sits at 1.0.
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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Four random resized crops per Visual Genome image, segmented
independently with their fields averaged, leave the correlation at
0.6559. Closed-world re-renders resample layout, which is nuisance by
construction, so averaging removes modality-private variation; random
crops perturb framing that self-supervised patch features already
absorb, leaving nothing to cancel.
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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