diff options
| -rw-r--r-- | CANDIDATE_REGISTER.md | 126 |
1 files changed, 126 insertions, 0 deletions
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. |