From f4fa8343cbd20bce75aa9591db3d7fa75251398b Mon Sep 17 00:00:00 2001 From: Yuren Hao Date: Sat, 1 Aug 2026 14:31:20 -0500 Subject: Candidate register: five factors, ordered by expected movement The natural-data obstruction decomposes into field correlation, landscape shape, search strength, problem size, and orthogonal signal, and every candidate attacks exactly one. Records what is measured, what is running, and what is specified but unstarted, so branches can be eliminated in cost order rather than by preference. Co-Authored-By: Claude --- CANDIDATE_REGISTER.md | 126 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 126 insertions(+) create mode 100644 CANDIDATE_REGISTER.md diff --git a/CANDIDATE_REGISTER.md b/CANDIDATE_REGISTER.md new file mode 100644 index 0000000..31906ff --- /dev/null +++ b/CANDIDATE_REGISTER.md @@ -0,0 +1,126 @@ +# Candidate register + +The obstruction on natural data decomposes into five factors, and every +candidate attacks exactly one of them. Field correlation stands at 0.656 +against the 0.9 that polynomial recovery needs, so the register is +ordered by expected movement per unit of effort rather than by elegance. + +Status is one of: **done** (measured, number recorded), **running**, +**queued** (specified, not started), **open** (idea, not specified). + +## A. Raise the field correlation + +The binding constraint. Everything else is worth less than a tenth of +what this is worth if it moves. + +| Candidate | Cost | Status | +|---|---|---| +| Continuous states instead of class codes | low | done: 0.166 to 0.489 | +| Content projection, between-scene over within-scene | low | done: 0.489 to 0.656 | +| Augmentation orbits, four views | medium | done: no gain, 0.6559 either way | +| Larger vision backbone (DINOv2-large, -giant) | medium | queued | +| Multi-scale patch features, several receptive fields | medium | queued | +| Corpus-trained text encoder instead of PPMI vectors | medium | queued | +| Structured phrase encoding: head and modifiers apart | low | queued | +| Intervention responses: occlude a region, re-encode, use the change | high | queued | +| Native multi-view corpora: product photographs, video frames | high | queued | +| Nonlinear content projection (kernel discriminant) | low | open | +| Adaptive segment count with quality filtering | low | open | + +The intervention row is the one the closed world argued for hardest and +the one never run on natural data. It needs real forward passes -- masked +re-encoding on both sides -- not cached-feature algebra, which is a +tautology. + +## B. Reshape the landscape + +Decoys exist because they match second-order statistics. Either raise +them or widen the true basin. + +| Candidate | Cost | Status | +|---|---|---| +| Third-order terms, tr(M^3) | low | done: deepens truth and decoys alike | +| Rank-truncation ladder, coarse to sharp | low | running | +| Convex-concave path following (PATH, FAQ family) | medium | queued | +| Entropic doubly-stochastic relaxation | low | done: stalls far above truth | +| Degree normalisation of the fields | low | queued | +| Hubness correction (CSLS) on field similarities | low | queued | +| Sparsified fields, top-k neighbours only | low | queued | +| Functional term: held-out generalisation of the induced map | medium | running | + +Path following is the canonical landscape-deformation method for +quadratic assignment and has never been tried here. The functional term +is landscape reshaping by orthogonal information: a decoy that copies +relational statistics still has to induce a map that generalises. + +## C. Search harder + +| Candidate | Cost | Status | +|---|---|---| +| Spectral initialisation plus exact refinement | low | done: 53.5% to 95.3% composed | +| Parallel tempering with exact swap deltas | medium | done: equilibrates into the decoy shelf | +| Multiple spectral inits over eta, keep best by energy | low | queued | +| Seeded expansion from high-confidence pairs | medium | queued | +| Belief propagation on the assignment factor graph | high | queued | +| Cluster moves: swap blocks rather than single pairs | low | queued | +| Path relinking and crossover over permutations | medium | open | +| Branch and bound, exact on small blocks | medium | open | +| Sum-of-squares or low-degree hierarchies | high | open | + +Accepting exponential cost does not rescue the hard phase at fixed size: +tempering already is exponential-time and fails by equilibrating, not by +running out of budget. Exponential methods pay only where the block is +small enough to finish, which is why C and D are the same programme seen +from two sides. + +## D. Shrink the problem + +The phase boundary is joint in correlation and population size, so a +corpus need not be matched at once. + +| Candidate | Cost | Status | +|---|---|---| +| Largest recoverable N at the natural field quality | low | running | +| Diversity-selected bootstrap subset instead of random | low | queued | +| Hierarchical: cluster first, match within cluster | medium | queued | +| Many small blocks, merge by consistency voting | medium | queued | + +Diversity selection is the cheapest idea in the register and possibly +the best value: decoys arise from scenes that resemble each other, and +choosing a mutually dissimilar bootstrap set thins them at no +algorithmic cost. It composes with small blocks by construction, since +if only a few hundred pairs are needed they should be the most +distinguishable few hundred. + +## E. Add orthogonal signal + +| Candidate | Cost | Status | +|---|---|---| +| Held-out generalisation of the induced map | medium | running | +| Intervention response consistency | high | queued | +| Counting and cardinality, gauge-free by construction | low | queued | +| Higher-order joint tables (colour by shape by count) | low | queued | +| Temporal or sequential structure where corpora carry it | high | open | + +## F. Change the formulation + +Real corpora are not in bijection, so the permutation formulation is a +scaffold that has to be replaced eventually regardless of performance. + +| Candidate | Cost | Status | +|---|---|---| +| Unbalanced coupling: partial mass, unmatched items allowed | medium | queued | +| Many-to-many soft assignment | medium | open | +| Part-level matching across the corpus rather than scene-level | medium | open | +| Joint factor-level and scene-level, alternating | medium | open | + +## Order of attempt + +Cheap and untried first, because the register's value is in eliminating +branches quickly: diversity selection, degree normalisation, hubness +correction, sparsified fields, multiple spectral inits, structured phrase +encoding, higher-order joint tables. Then the medium tier led by path +following and the functional term. The two expensive rows worth pre- +committing to are intervention responses and a natively multi-view +corpus, because the closed world named both as protocol requirements +rather than optimisations. -- cgit v1.2.3