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, 150 insertions, 0 deletions

diff --git a/worldalign/synth_decode.py b/worldalign/synth_decode.py
new file mode 100644
index 0000000..183e4a9
--- /dev/null
+++ b/worldalign/synth_decode.py
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+"""Close the loop: recovered pairs to a map to generated descriptions.
+
+Matching is transductive -- it aligns one fixed population. A usable
+system needs a map, so the recovered assignment is treated as pseudo-pair
+supervision for a small vision-to-text-state regressor, and the map is
+then applied to scenes that took no part in the matching. Descriptions
+are read out through the frozen text tower.
+
+Two controls decide whether the output is image-conditioned: the same
+pipeline with the recovered assignment replaced by a random one, and the
+same map applied to a shuffled image. Hidden pairs score; nothing here
+trains on them.
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+from pathlib import Path
+
+import numpy as np
+import torch
+import torch.nn.functional as F
+
+from .common import read_json, seed_everything, write_json
+
+
+def parse_args() -> argparse.Namespace:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--data-dir", default="artifacts/synth_v1")
+    parser.add_argument("--states", required=True,
+                        help=".pt with vision_states, text_states, rows for "
+                             "the matched population and the held-out split.")
+    parser.add_argument("--assignment", required=True,
+                        help=".pt with the recovered permutation and truth.")
+    parser.add_argument("--ridge", type=float, default=1.0)
+    parser.add_argument("--seed", type=int, default=0)
+    parser.add_argument("--output", default="artifacts/synth_v1/decode.json")
+    return parser.parse_args()
+
+
+def fit_map(source: np.ndarray, target: np.ndarray, ridge: float) -> np.ndarray:
+    source = np.concatenate([source, np.ones((len(source), 1))], axis=1)
+    gram = source.T @ source + ridge * np.eye(source.shape[1])
+    return np.linalg.solve(gram, source.T @ target)
+
+
+def apply_map(weights: np.ndarray, source: np.ndarray) -> np.ndarray:
+    source = np.concatenate([source, np.ones((len(source), 1))], axis=1)
+    return source @ weights
+
+
+def nearest_caption(
+    predicted: np.ndarray, bank: np.ndarray
+) -> np.ndarray:
+    predicted = predicted / np.linalg.norm(predicted, axis=1, keepdims=True).clip(1e-9)
+    bank = bank / np.linalg.norm(bank, axis=1, keepdims=True).clip(1e-9)
+    return (predicted @ bank.T).argmax(1)
+
+
+def factor_scores(
+    predicted_rows: list[int], truth_rows: list[int], scenes: list[dict]
+) -> dict:
+    """Do the retrieved descriptions state the right world facts?"""
+    colour_f1, count_ok, group_ok = [], [], []
+    for predicted, truth in zip(predicted_rows, truth_rows):
+        p, t = scenes[predicted], scenes[truth]
+        pc = {g["color"] for g in p["groups"]}
+        tc = {g["color"] for g in t["groups"]}
+        overlap = len(pc & tc)
+        precision = overlap / max(len(pc), 1)
+        recall = overlap / max(len(tc), 1)
+        colour_f1.append(
+            0.0 if precision + recall == 0 else 2 * precision * recall / (precision + recall)
+        )
+        count_ok.append(
+            sorted(g["count"] for g in p["groups"])
+            == sorted(g["count"] for g in t["groups"])
+        )
+        group_ok.append(len(p["groups"]) == len(t["groups"]))
+    return {
+        "colour_set_f1": float(np.mean(colour_f1)),
+        "count_multiset_exact": float(np.mean(count_ok)),
+        "group_count_exact": float(np.mean(group_ok)),
+    }
+
+
+def main() -> None:
+    args = parse_args()
+    seed_everything(args.seed)
+    scenes = read_json(Path(args.data_dir, "scenes.private.json"))["scenes"]
+    states = torch.load(args.states, map_location="cpu", weights_only=False)
+    recovered = torch.load(args.assignment, map_location="cpu", weights_only=False)
+
+    match_vision = states["match_vision"].double().numpy()
+    match_text = states["match_text"].double().numpy()
+    held_vision = states["held_vision"].double().numpy()
+    held_text = states["held_text"].double().numpy()
+    held_rows = states["held_rows"]
+
+    assignment = np.asarray(recovered["assignment"])
+    generator = np.random.default_rng(args.seed)
+    random_assignment = generator.permutation(len(assignment))
+
+    report = {
+        "protocol": (
+            "The recovered assignment supplies pseudo-pairs for a ridge "
+            "map from vision states to text states; the map is applied to "
+            "held-out scenes that took no part in matching. Random "
+            "assignment and shuffled-image controls bound the claim."
+        ),
+        "matched_population": len(assignment),
+        "held_out": len(held_rows),
+        "recovery_accuracy": float(
+            (assignment == np.arange(len(assignment))).mean()
+        ),
+        "conditions": {},
+    }
+
+    for label, permutation in (
+        ("recovered_pairs", assignment),
+        ("random_pairs", random_assignment),
+    ):
+        weights = fit_map(match_vision, match_text[permutation], args.ridge)
+        predicted = apply_map(weights, held_vision)
+        retrieved = nearest_caption(predicted, held_text)
+        exact = float((retrieved == np.arange(len(held_rows))).mean())
+        entry = {
+            "held_out_retrieval_exact": exact,
+            "chance": 1.0 / len(held_rows),
+            **factor_scores(
+                [held_rows[i] for i in retrieved], held_rows, scenes
+            ),
+        }
+        if label == "recovered_pairs":
+            shuffled = generator.permutation(len(held_vision))
+            predicted_shuffled = apply_map(weights, held_vision[shuffled])
+            retrieved_shuffled = nearest_caption(predicted_shuffled, held_text)
+            entry["shuffled_image_control"] = factor_scores(
+                [held_rows[i] for i in retrieved_shuffled], held_rows, scenes
+            )
+        report["conditions"][label] = entry
+        print(json.dumps({label: entry}))
+
+    write_json(args.output, report)
+    print(f"Wrote {args.output}")
+
+
+if __name__ == "__main__":
+    main()