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diff --git a/RECOVERY_RESULTS.md b/RECOVERY_RESULTS.md new file mode 100644 index 0000000..00125df --- /dev/null +++ b/RECOVERY_RESULTS.md @@ -0,0 +1,179 @@ +# Blind recovery on gate-passing states: the search phase + +Run date: 2026-07-29 + +## Question + +The basin audit licenses recovery: on content-projected VG states the true +assignment sits 5--19% below every quench, so a search that reaches the +bottom of the landscape would recover it. This experiment asks whether +three search families get there without any pair information. The text +side enters through a hidden shuffle; hidden truth scores outcomes only. + +## Arms + +- Parallel tempering: eight-replica Metropolis over permutations with + exact closed-form swap deltas and neighbor exchange, 60,000 rounds. +- Entropic Sinkhorn annealing: soft coupling, barycentric states, + temperature and entropy schedules, four restarts. +- Spectral-band homotopy: the Sinkhorn arm warm-started through + progressively finer content bands (4 to full dimensions), a spectral + proxy for band-limited continuation on the symmetric group. + +## Result: the energy is right and the search is the wall + +On all three gate-passing conditions (512 nodes, subset seed 0): + +| Condition | Gate margin | Tempering: E over true / accuracy | Sinkhorn | Homotopy | +|---|---:|---:|---:|---:| +| VG isolated, k=256 | +7.8--12.0% | +9.4% / 3.1% | +72% / 0.4% | +62% / 0.4% | +| VG isolated, k=128 | +5.1--10.8% | +10.1% / 2.1% | +100% / 0.2% | +76% / 0.6% | +| VG in-context, k=128 | +11.6--18.5% | +19.8% / 1.0% | +99% / 0.8% | +78% / 0.0% | + +Tempering equilibrates into exactly the quench band of the gate report -- +the glass's low shelf -- and never enters the true funnel; chance is 0.2%, +so 1--3% accuracy is a population-level shift, not recovery. The soft +arms stall far higher; their couplings put no verified mass anywhere +(top-margin-decile precision 0.000 in all runs, mutual-NN precision below +1.2%). Continuous relaxation loses to discrete annealing everywhere, and +discrete annealing loses to the landscape. + +The picture matches the hard phase of planted-assignment problems: the +configuration is information-theoretically identifiable (the gate), while +local dynamics equilibrate into an exponential shelf of wrong states +whose energies sit just above the planted one. The distance between the +statistical and the algorithmic threshold is now the project's central +quantity. + +## What moves the algorithmic threshold + +Ordered by expected yield, per the tool inventory of +`STRUCTURE_DESIGN.md`: + +1. Constraint density per node: the N-scaling probe below, and at fixed N + the view-level recursion and R8 intervention constraints, which + sharpen the funnel rather than the search. +2. Side information: gauge-free unary anchors (counting, mm-space + observable invariants) that bias the sampler into the funnel; in + planted problems even weak unary priors change the search class. +3. Message passing: cavity/BP dynamics for planted matching reach partial + recovery at densities where annealing fails; this is the queued + spin-glass tool. + +## N-scaling probe + +Tempering-only runs at N=1024 and N=2048 with a fixed 80,000-round budget +test whether the phase boundary approaches with constraint density. Best +replica by energy: + +| N | E over true | Accuracy | Chance | +|---:|---:|---:|---:| +| 512 | +9.4% | 3.1% | 0.20% | +| 1,024 | +5.2% | 2.5% | 0.10% | +| 2,048 | +15.0% | 0.05% | 0.05% | + +Doubling to 1,024 cuts the energy gap by nearly half at constant budget. +The under-equilibrated 2,048 point is budget-confounded, so an +equal-moves-per-node rerun with 320,000 rounds was run: + +| N | Moves per node | E over true | Accuracy | +|---:|---:|---:|---:| +| 512 | ~117 | +9.4% | 3.1% | +| 1,024 | ~78 | +5.2% | 2.5% | +| 2,048 | ~156 | +10.4% | 0.05% | + +At matched per-node budget the reachable shelf returns to the same ++9--10% band as N=512, and the small accuracy signal present at 512 and +1,024 vanishes entirely. One seed per point, so the 1,024 dip may be +noise; what the curve rules out is the optimistic reading -- **no +algorithmic threshold is approached by density alone within the tested +range** (N up to 2,048, 320k rounds). The recovery bottleneck stands, and +the priority order shifts to the other two levers: gauge-free unary side +information and cavity-style message passing, with constraint sharpening +(view-level recursion, interventions) as the structural route. + +## Unary anchors, first wave: coarse anchors do not move the search + +The C5 battery extracted gauge-free unary anchors with no model passes: +numeral content, color-lexicon histograms, chromatic fraction, size and +light words on the text side; hue-band histograms, chromatic fraction, +luminance, and box areas on the vision side, with the lexicon-to-physics +maps frozen before evaluation. The combined anchor field has real +population-level signal at the true pairing (z = 17.2) and no per-pair +reliability: median truth rank 1,969 of 5,000, top-1%-margin precision +2%, mutual-NN precision 0.17%. + +Injected into the tempering energy as a dense unary field, it strictly +degrades recovery, monotonically in the weight (best-by-relational-energy +replica): + +| Unary weight | Init | Accuracy | Relational E over true | +|---:|---|---:|---:| +| 0 (baseline) | random | 3.1% | +9.4% | +| 0.5 | random | 1.6% | +30.2% | +| 2.0 | random | 2.0% | +76.2% | +| 2.0 | anchor-Hungarian | 1.0% | +82.6% | +| 8.0 | random | 1.0% | +115.2% | + +The mechanism echoes the spectral audit: scene-level color, luminance, +and size are coarse attributes that already live inside the shared +topical subspace, so the field adds a noisy copy of information the +relational energy has, plus its own wrong optima for the sampler to +compromise with. Side information can move a hard phase only if it is +per-pair reliable (sparse verified seeds -- there are none to sparsify +here) or statistically independent of the relational field. Pixel and +lexicon statistics at node level are neither. + +The constructive redirect: fine-grained anchors live at view level, where +region phrases carry numerals and spatial predicates about individual +regions, boxes carry geometry, and the candidate set is sixteen rather +than five hundred. The second anchor wave belongs inside the view-level +recursion, not the node-level search; message passing with priors remains +the queued search-side tool. + +## Unary anchors, second wave: view-level anchors yield the first seeds + +Per-view anchors -- twelve-class color lexicon against crop pixel classes +(white, black, gray, and brown rules on value and saturation carry most +of the coverage), size words against within-scene box-area ranks, light +words against crop luminance, position words against box centers -- give +the first per-pair-reliable signal of the project: + +- frame-free view matching 11.5% against 6.25% chance; 16.9% on the + 35,484 views whose phrase carries an attribute (2.7x); +- **seed calibration: 35.6% precision on the top-1%-margin views** (354 + seeds at 5.7x chance), against 0--4% for every prior high-confidence + channel; +- position words are nearly absent from region phrases (coverage under + 1.1%), so color and light do the work. + +Aggregated to node level (Hungarian value of the per-pair 16-view anchor +matrix as node affinity, three subset seeds at 512): retrieval R@10 +8.6--9.6% against 1.95% chance (4.4--4.9x, the best frame-free node +signal to date; graph signatures reached 3.1--3.5x), z = 16--17, median +rank 113--123 of 512. Node-level seed precision stays at 2--6%: one +order below seeding threshold. Adding fixed-assignment relational +agreement trades recall for precision without changing the order. + +Pixel and lexicon statistics are now exhausted at both levels. The two +open moves are the numeral-to-repetition anchor (patch-level extraction, +untested) and the aggregation everything above points to: a factor graph +over node and view assignments with anchor unaries and relational +pairwise terms, solved by message passing, so that 35%-precision view +seeds, 5x node affinities, and the gate-passing relational energy +reinforce globally instead of being consumed by independent per-node +Hungarians. + +## Main artifacts + +- `artifacts/manifold_gate/recovery_vg_k{128,256}_seed0.json` +- `artifacts/manifold_gate/recovery_vg_ctx_k128_seed0.json` +- `artifacts/manifold_gate/recovery_scale_n{1024,2048}.json` +- `artifacts/manifold_gate/recovery_scale_n2048_long.json` +- `artifacts/manifold_gate/anchor_battery.json` +- `artifacts/manifold_gate/anchor_unary.pt` +- `artifacts/manifold_gate/recovery_unary_lam{0.5,2.0,8.0}.json` +- `artifacts/manifold_gate/recovery_unary_lam2_unaryinit.json` +- `artifacts/manifold_gate/view_anchor_battery_v{2,3}.json` +- `artifacts/manifold_gate/view_anchor_features.pt` +- `artifacts/manifold_gate/view_anchor_affinity{,_v2}.json` |