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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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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 <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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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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