World Alignment: unpaired cross-modal correspondence by relational 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>

1 files changed, 173 insertions, 0 deletions

diff --git a/worldalign/synth_triangle_recovery.py b/worldalign/synth_triangle_recovery.py
new file mode 100644
index 0000000..a9bca61
--- /dev/null
+++ b/worldalign/synth_triangle_recovery.py
@@ -0,0 +1,173 @@
+"""Blind recovery under the triangle energy.
+
+The triangle gate holds the true assignment at N=512 with no counterfeit
+below it. The search question is separate and now worth asking again:
+tempering with third-order swap deltas, from random starts, with the
+hidden order behind a shuffle. Recovery accuracy is the end-to-end world
+matching measurement.
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+from pathlib import Path
+
+import torch
+
+from .common import read_json, seed_everything, write_json
+from .synth_triangle_gate import TriangleEnergy, build_fields, standardized
+
+
+def parse_args() -> argparse.Namespace:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--data-dir", default="artifacts/synth_v0")
+    parser.add_argument("--split", choices=["val", "test"], default="test")
+    parser.add_argument("--samples", type=int, default=512)
+    parser.add_argument("--merge-distance", type=float, default=30.0)
+    parser.add_argument("--vision-views", type=int, default=4)
+    parser.add_argument("--triples", type=int, default=400000)
+    parser.add_argument("--pair-weight", type=float, default=1.0)
+    parser.add_argument("--triangle-weight", type=float, default=1.0)
+    parser.add_argument("--replicas", type=int, default=6)
+    parser.add_argument("--rounds", type=int, default=4000)
+    parser.add_argument("--proposals", type=int, default=48)
+    parser.add_argument("--temp-high", type=float, default=2e-2)
+    parser.add_argument("--temp-low", type=float, default=1e-4)
+    parser.add_argument("--exchange-every", type=int, default=20)
+    parser.add_argument("--greedy-rounds", type=int, default=3000)
+    parser.add_argument("--device", default="cuda:3")
+    parser.add_argument("--seed", type=int, default=20260731)
+    parser.add_argument(
+        "--output", default="artifacts/synth_v0/triangle_recovery.json"
+    )
+    return parser.parse_args()
+
+
+def main() -> None:
+    args = parse_args()
+    seed_everything(args.seed)
+    manifest = read_json(Path(args.data_dir, "manifest.json"))
+    rows = manifest[args.split][: args.samples]
+    visual_field, text_field = build_fields(args, rows, manifest)
+
+    device = torch.device(args.device)
+    size = len(rows)
+    generator = torch.Generator().manual_seed(args.seed)
+    hidden = torch.randperm(size, generator=generator)
+    truth = torch.argsort(hidden).to(device)
+    text = standardized(text_field[hidden][:, hidden].double().to(device)).float()
+    visual = standardized(visual_field.double().to(device)).float()
+
+    triples = torch.randint(0, size, (args.triples, 3), generator=generator)
+    triples = triples[
+        (triples[:, 0] != triples[:, 1])
+        & (triples[:, 1] != triples[:, 2])
+        & (triples[:, 0] != triples[:, 2])
+    ].to(device)
+    energy = TriangleEnergy(
+        text, visual, triples, args.pair_weight, args.triangle_weight
+    )
+    true_energy = energy.total(truth)
+
+    temperatures = torch.logspace(
+        torch.log10(torch.tensor(args.temp_low)),
+        torch.log10(torch.tensor(args.temp_high)),
+        args.replicas,
+    )
+    states = [
+        torch.argsort(torch.rand(size, generator=generator)).to(device)
+        for _ in range(args.replicas)
+    ]
+    energies = [energy.total(state) for state in states]
+    history = []
+    for round_index in range(args.rounds):
+        for replica in range(args.replicas):
+            temperature = float(temperatures[replica])
+            for _ in range(args.proposals):
+                p = int(torch.randint(0, size, (1,), generator=generator))
+                q = int(torch.randint(0, size, (1,), generator=generator))
+                if p == q:
+                    continue
+                delta = energy.swap_delta(states[replica], p, q)
+                threshold = -temperature * float(
+                    torch.rand(1, generator=generator).clamp_min(1e-12).log()
+                )
+                if delta < threshold:
+                    states[replica][[p, q]] = states[replica][[q, p]]
+                    energies[replica] += delta
+        if round_index % args.exchange_every == 0:
+            for replica in range(args.replicas - 1):
+                gap = (energies[replica] - energies[replica + 1]) * (
+                    1.0 / float(temperatures[replica])
+                    - 1.0 / float(temperatures[replica + 1])
+                )
+                if gap > 0 or float(torch.rand(1, generator=generator)) < min(
+                    1.0, float(torch.tensor(gap).exp())
+                ):
+                    states[replica], states[replica + 1] = (
+                        states[replica + 1],
+                        states[replica],
+                    )
+                    energies[replica], energies[replica + 1] = (
+                        energies[replica + 1],
+                        energies[replica],
+                    )
+        if round_index % 200 == 0:
+            cold = min(range(args.replicas), key=lambda r: energies[r])
+            record = {
+                "round": round_index,
+                "cold_energy": energies[cold],
+                "cold_accuracy": float(
+                    (states[cold].cpu() == truth.cpu()).float().mean()
+                ),
+                "energy_over_true": energies[cold] / true_energy - 1.0,
+            }
+            history.append(record)
+            print(json.dumps(record))
+
+    # Greedy polish of the coldest replica.
+    cold = min(range(args.replicas), key=lambda r: energies[r])
+    current = states[cold].clone()
+    for _ in range(args.greedy_rounds):
+        best_delta, best_pair = 0.0, None
+        for _ in range(96):
+            p = int(torch.randint(0, size, (1,), generator=generator))
+            q = int(torch.randint(0, size, (1,), generator=generator))
+            if p == q:
+                continue
+            delta = energy.swap_delta(current, p, q)
+            if delta < best_delta:
+                best_delta, best_pair = delta, (p, q)
+        if best_pair is None:
+            break
+        p, q = best_pair
+        current[[p, q]] = current[[q, p]]
+
+    final = {
+        "accuracy": float((current.cpu() == truth.cpu()).float().mean()),
+        "energy": energy.total(current),
+    }
+    final["energy_over_true"] = final["energy"] / true_energy - 1.0
+    report = {
+        "protocol": (
+            "Tempering on the pairwise-plus-triangle energy from random "
+            "starts; text order hidden behind a shuffle; hidden truth "
+            "scores the outcome only."
+        ),
+        "samples": size,
+        "true_energy": true_energy,
+        "chance_accuracy": 1.0 / size,
+        "history": history,
+        "final_polished": final,
+        "replica_accuracies": [
+            float((state.cpu() == truth.cpu()).float().mean()) for state in states
+        ],
+    }
+    print(json.dumps({"final": final}))
+    write_json(args.output, report)
+    print(f"Wrote {args.output}")
+
+
+if __name__ == "__main__":
+    main()