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, 200 insertions, 0 deletions

diff --git a/worldalign/vg_diagnose.py b/worldalign/vg_diagnose.py
new file mode 100644
index 0000000..4c6d4a8
--- /dev/null
+++ b/worldalign/vg_diagnose.py
@@ -0,0 +1,200 @@
+from __future__ import annotations
+
+import argparse
+import json
+from pathlib import Path
+
+import numpy as np
+from scipy.stats import spearmanr
+import torch
+
+from .common import normalized, write_json
+
+
+def parse_args() -> argparse.Namespace:
+    p = argparse.ArgumentParser()
+    p.add_argument("--vision", default="artifacts/vg/vision_features.pt")
+    p.add_argument("--text", default="artifacts/vg/text_features.pt")
+    p.add_argument(
+        "--truth", default="artifacts/vg/ground_truth.private.jsonl"
+    )
+    p.add_argument("--max-nodes", type=int, default=5_000)
+    p.add_argument("--quantiles", type=int, default=33)
+    p.add_argument("--output", default="artifacts/vg/diagnostics.json")
+    return p.parse_args()
+
+
+def read_jsonl(path: str) -> list[dict]:
+    with open(path, encoding="utf-8") as handle:
+        return [json.loads(line) for line in handle if line.strip()]
+
+
+def bundle_signature(
+    features: torch.Tensor, quantiles: int = 33
+) -> torch.Tensor:
+    """Permutation- and rotation-invariant signature of a bag of views."""
+    x = normalized(features.float())
+    gram = x @ x.transpose(1, 2)
+    views = x.shape[1]
+    i, j = torch.triu_indices(views, views, offset=1)
+    pairwise = gram[:, i, j]
+    q = torch.linspace(0, 1, quantiles)
+    distribution = torch.quantile(pairwise, q, dim=1).T
+    eigenvalues = torch.linalg.eigvalsh(gram).flip(-1) / max(views, 1)
+    return torch.cat([distribution, eigenvalues], dim=-1)
+
+
+def rank_normalize_columns(x: torch.Tensor) -> torch.Tensor:
+    order = torch.argsort(x, dim=0)
+    ranks = torch.argsort(order, dim=0).float()
+    ranks = ranks / max(x.shape[0] - 1, 1)
+    return (ranks - 0.5) * 2
+
+
+def aligned_text_indices(
+    vision_ids: list[str], text_ids: list[str], truth_path: str
+) -> torch.Tensor:
+    truth = read_jsonl(truth_path)
+    mapping = {
+        item["vision_node_id"]: item["text_node_id"] for item in truth
+    }
+    text_lookup = {node_id: idx for idx, node_id in enumerate(text_ids)}
+    return torch.tensor([text_lookup[mapping[node_id]] for node_id in vision_ids])
+
+
+def arbitrary_target_retrieval(
+    queries: torch.Tensor, candidates: torch.Tensor, targets: torch.Tensor
+) -> dict:
+    similarity = normalized(queries) @ normalized(candidates).T
+    target_score = similarity[
+        torch.arange(len(queries)), targets.to(similarity.device)
+    ]
+    ranks = (similarity > target_score[:, None]).sum(-1) + 1
+    top_values, top_indices = similarity.topk(
+        min(2, similarity.shape[1]), dim=1
+    )
+    prediction = top_indices[:, 0]
+    correct = prediction == targets.to(prediction.device)
+    if top_values.shape[1] == 2:
+        margin = top_values[:, 0] - top_values[:, 1]
+    else:
+        margin = top_values[:, 0]
+    confidence_order = torch.argsort(margin, descending=True)
+    confidence_precision = {}
+    for count in (10, 50, 100, 500, 1_000):
+        if count <= len(queries):
+            selected = confidence_order[:count]
+            confidence_precision[str(count)] = {
+                "correct": int(correct[selected].sum()),
+                "precision": float(correct[selected].float().mean()),
+            }
+
+    reverse_prediction = similarity.argmax(dim=0)
+    mutual = (
+        reverse_prediction[prediction]
+        == torch.arange(len(queries), device=prediction.device)
+    )
+    mutual_count = int(mutual.sum())
+    result = {
+        "r@1": float((ranks <= 1).float().mean()),
+        "r@5": float((ranks <= 5).float().mean()),
+        "r@10": float((ranks <= 10).float().mean()),
+        "mean_reciprocal_rank": float((1.0 / ranks.float()).mean()),
+        "median_rank": float(ranks.float().median()),
+        "chance_r@1": 1.0 / len(candidates),
+        "chance_r@5": min(5.0 / len(candidates), 1.0),
+        "chance_r@10": min(10.0 / len(candidates), 1.0),
+        "confidence_margin_precision": confidence_precision,
+        "mutual_nearest": {
+            "selected": mutual_count,
+            "correct": int(correct[mutual].sum()),
+            "precision": (
+                float(correct[mutual].float().mean())
+                if mutual_count
+                else 0.0
+            ),
+        },
+    }
+    return result
+
+
+def upper_triangle(x: torch.Tensor) -> np.ndarray:
+    i, j = torch.triu_indices(len(x), len(x), offset=1)
+    return x[i, j].cpu().numpy()
+
+
+def main() -> None:
+    args = parse_args()
+    vision = torch.load(args.vision, map_location="cpu", weights_only=False)
+    text = torch.load(args.text, map_location="cpu", weights_only=False)
+    n = min(args.max_nodes, len(vision["node_ids"]), len(text["node_ids"]))
+    vision_ids = vision["node_ids"][:n]
+    target_full = aligned_text_indices(
+        vision_ids, text["node_ids"], args.truth
+    )
+    candidate_indices = torch.unique(target_full, sorted=False)
+    if len(candidate_indices) != n:
+        raise ValueError("Ground truth is not a one-to-one permutation")
+    candidate_lookup = {
+        int(old): new for new, old in enumerate(candidate_indices.tolist())
+    }
+    targets = torch.tensor(
+        [candidate_lookup[int(old)] for old in target_full.tolist()]
+    )
+
+    v_views = vision["region_features"][:n]
+    t_views = text["region_features"][candidate_indices]
+    v_signature = rank_normalize_columns(
+        bundle_signature(v_views, args.quantiles)
+    )
+    t_signature = rank_normalize_columns(
+        bundle_signature(t_views, args.quantiles)
+    )
+    signature_retrieval = arbitrary_target_retrieval(
+        v_signature, t_signature, targets
+    )
+
+    paired_t_signature = t_signature[targets]
+    signature_cosine = (
+        normalized(v_signature) * normalized(paired_t_signature)
+    ).sum(-1)
+    generator = torch.Generator().manual_seed(20260728)
+    shuffled = paired_t_signature[torch.randperm(n, generator=generator)]
+    shuffled_cosine = (
+        normalized(v_signature) * normalized(shuffled)
+    ).sum(-1)
+
+    v_scene = vision["global_features"][:n]
+    t_scene = text["region_features"][candidate_indices].mean(1)[targets]
+    gv = normalized(v_scene) @ normalized(v_scene).T
+    gt = normalized(t_scene) @ normalized(t_scene).T
+    scene_rho = spearmanr(
+        upper_triangle(gv), upper_triangle(gt)
+    ).statistic
+
+    result = {
+        "nodes": n,
+        "views_per_node": int(v_views.shape[1]),
+        "vision_model": vision["model"],
+        "text_model": text["model"],
+        "text_tier": text["tier"],
+        "bundle_signature_retrieval": signature_retrieval,
+        "paired_bundle_signature_cosine_mean": float(
+            signature_cosine.mean()
+        ),
+        "shuffled_bundle_signature_cosine_mean": float(
+            shuffled_cosine.mean()
+        ),
+        "between_scene_pairwise_cosine_spearman": float(scene_rho),
+        "evaluation_note": (
+            "Ground-truth permutation is used only to score signatures and "
+            "relation geometry, never to fit them."
+        ),
+    }
+    Path(args.output).parent.mkdir(parents=True, exist_ok=True)
+    write_json(args.output, result)
+    print(json.dumps(result, indent=2))
+
+
+if __name__ == "__main__":
+    main()