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, 129 insertions, 0 deletions

diff --git a/worldalign/synth_probes.py b/worldalign/synth_probes.py
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+++ b/worldalign/synth_probes.py
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+"""Ground-truth factor probes for synthetic-world representations.
+
+Linear probes from a representation to the discrete scene factors measure
+which world variables survive the encoder and its pooling. Probes are
+fitted per modality on that modality's own training split and evaluated
+on held-out scenes; scene truth is generator metadata, so this is a
+within-modality diagnostic, not a cross-modal signal.
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+from pathlib import Path
+
+import numpy as np
+import torch
+
+from .common import read_json, write_json
+from .synth_world import COLORS, SHAPES
+
+
+def parse_args() -> argparse.Namespace:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--data-dir", default="artifacts/synth_v0")
+    parser.add_argument("--features", required=True)
+    parser.add_argument(
+        "--side", choices=["vision", "text"], required=True,
+        help="Selects the training split whose scenes fit the probes.",
+    )
+    parser.add_argument("--ridge", type=float, default=1.0)
+    parser.add_argument("--output", required=True)
+    return parser.parse_args()
+
+
+def scene_targets(scene: dict) -> dict[str, np.ndarray | float]:
+    color_presence = np.zeros(len(COLORS))
+    shape_presence = np.zeros(len(SHAPES))
+    for group in scene["groups"]:
+        color_presence[list(COLORS).index(group["color"])] = 1.0
+        shape_presence[SHAPES.index(group["shape"])] = 1.0
+    return {
+        "color_presence": color_presence,
+        "shape_presence": shape_presence,
+        "group_count": float(len(scene["groups"])),
+        "object_total": float(sum(g["count"] for g in scene["groups"])),
+        "relation_count": float(len(scene["relations"])),
+    }
+
+
+def ridge_fit(
+    x: np.ndarray, y: np.ndarray, ridge: float
+) -> tuple[np.ndarray, np.ndarray]:
+    x = np.concatenate([x, np.ones((len(x), 1))], axis=1)
+    gram = x.T @ x + ridge * np.eye(x.shape[1])
+    weights = np.linalg.solve(gram, x.T @ y)
+    return weights, x @ weights
+
+
+def evaluate(
+    features_train: np.ndarray,
+    features_test: np.ndarray,
+    train_targets: np.ndarray,
+    test_targets: np.ndarray,
+    ridge: float,
+    binary: bool,
+) -> dict:
+    weights, _ = ridge_fit(features_train, train_targets, ridge)
+    prediction = (
+        np.concatenate([features_test, np.ones((len(features_test), 1))], axis=1)
+        @ weights
+    )
+    if binary:
+        accuracy = float(((prediction > 0.5) == (test_targets > 0.5)).mean())
+        balanced = []
+        for column in range(test_targets.shape[1]):
+            truth = test_targets[:, column] > 0.5
+            if truth.any() and (~truth).any():
+                hit = (prediction[:, column] > 0.5) == truth
+                balanced.append(
+                    (hit[truth].mean() + hit[~truth].mean()) / 2.0
+                )
+        return {
+            "accuracy": accuracy,
+            "balanced_accuracy": float(np.mean(balanced)),
+        }
+    residual = prediction[:, 0] - test_targets[:, 0]
+    variance = test_targets[:, 0].var()
+    return {
+        "r2": float(1.0 - residual.var() / max(variance, 1e-9)),
+        "mae": float(np.abs(residual).mean()),
+    }
+
+
+def main() -> None:
+    args = parse_args()
+    manifest = read_json(Path(args.data_dir, "manifest.json"))
+    scenes = read_json(Path(args.data_dir, "scenes.private.json"))["scenes"]
+    state = torch.load(args.features, map_location="cpu", weights_only=False)
+    lookup = {int(row): i for i, row in enumerate(state["rows"])}
+    features = state["features"].float().numpy()
+
+    split_key = "vision_only_train" if args.side == "vision" else "text_only_train"
+    train_rows = [row for row in manifest[split_key] if row in lookup][:8000]
+    test_rows = [row for row in manifest["test"] if row in lookup]
+
+    x_train = features[[lookup[row] for row in train_rows]]
+    x_test = features[[lookup[row] for row in test_rows]]
+    report = {"features": args.features, "side": args.side, "targets": {}}
+    for name in ("color_presence", "shape_presence"):
+        y_train = np.stack([scene_targets(scenes[row])[name] for row in train_rows])
+        y_test = np.stack([scene_targets(scenes[row])[name] for row in test_rows])
+        report["targets"][name] = evaluate(
+            x_train, x_test, y_train, y_test, args.ridge, binary=True
+        )
+    for name in ("group_count", "object_total", "relation_count"):
+        y_train = np.array(
+            [[scene_targets(scenes[row])[name]] for row in train_rows]
+        )
+        y_test = np.array([[scene_targets(scenes[row])[name]] for row in test_rows])
+        report["targets"][name] = evaluate(
+            x_train, x_test, y_train, y_test, args.ridge, binary=False
+        )
+    write_json(args.output, report)
+    print(json.dumps(report, indent=2))
+
+
+if __name__ == "__main__":
+    main()