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, 204 insertions, 0 deletions

diff --git a/worldalign/natural_pipeline.py b/worldalign/natural_pipeline.py
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+++ b/worldalign/natural_pipeline.py
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+"""Natural-data field pipeline: continuous states and content projection.
+
+Produces the field correlation reported for Visual Genome. Two choices
+carry most of it, both measured. States stay continuous -- quantising
+segments and phrases into class codes costs more than half the signal,
+because relation fields need scene similarity and nothing else. And each
+side is projected onto the directions that separate scenes rather than
+parts, fitted per modality on scenes outside the evaluated set.
+
+Vision states come from `natural_objects`; language states are
+positive-PMI context vectors of the corpus, averaged per phrase. Hidden
+pairs are read only to report the correlation.
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import re
+from collections import Counter
+from pathlib import Path
+
+import numpy as np
+import torch
+import torch.nn.functional as F
+from scipy.linalg import eigh
+from sklearn.decomposition import TruncatedSVD
+
+from .common import read_json, seed_everything, write_json
+from .natural_families import load_phrases, statistics
+from .synth_cc_battery import moment_field
+
+
+def parse_args() -> argparse.Namespace:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--vg-dir", default="artifacts/vg_5k")
+    parser.add_argument("--objects", default="artifacts/vg_5k/natural_objects.pt")
+    parser.add_argument("--samples", type=int, default=256)
+    parser.add_argument("--fit-scenes", type=int, default=1200)
+    parser.add_argument("--word-vectors", type=int, default=48)
+    parser.add_argument("--min-count", type=int, default=60)
+    parser.add_argument("--max-vocabulary", type=int, default=600)
+    parser.add_argument("--context-window", type=int, default=2)
+    parser.add_argument("--keep", type=int, default=8)
+    parser.add_argument("--shrinkage", type=float, default=0.05)
+    parser.add_argument("--views", type=int, default=1)
+    parser.add_argument("--seed", type=int, default=0)
+    parser.add_argument("--output", default="artifacts/vg_5k/natural_pipeline.pt")
+    return parser.parse_args()
+
+
+def word_vectors(
+    phrases: list[list[str]], args: argparse.Namespace
+) -> dict[str, np.ndarray]:
+    """Positive-PMI context vectors, reduced by truncated SVD."""
+    counts = Counter(token for tokens in phrases for token in set(tokens))
+    vocabulary = [
+        word
+        for word, count in counts.most_common(args.max_vocabulary)
+        if count >= args.min_count
+    ]
+    _, _, context = statistics(phrases, set(vocabulary), args.context_window)
+    features = sorted({key for word in vocabulary for key in context[word]})
+    index = {key: position for position, key in enumerate(features)}
+    matrix = np.zeros((len(vocabulary), len(features)))
+    for row, word in enumerate(vocabulary):
+        for key, value in context[word].items():
+            matrix[row, index[key]] = value
+    total = matrix.sum()
+    expected = matrix.sum(1, keepdims=True) * matrix.sum(0, keepdims=True) / total
+    pmi = np.log(np.maximum(matrix, 1e-9) / np.maximum(expected, 1e-9))
+    pmi[matrix == 0] = 0.0
+    embedding = TruncatedSVD(args.word_vectors, random_state=args.seed).fit_transform(
+        np.maximum(pmi, 0.0)
+    )
+    embedding /= np.linalg.norm(embedding, axis=1, keepdims=True).clip(1e-9)
+    return {word: embedding[row] for row, word in enumerate(vocabulary)}
+
+
+def content_directions(
+    sets: list[np.ndarray], shrinkage: float
+) -> tuple[np.ndarray, np.ndarray]:
+    """Directions separating scenes more than they separate parts."""
+    means = np.stack([item.mean(0) for item in sets])
+    centre = means.mean(0)
+    within = np.concatenate([item - item.mean(0, keepdims=True) for item in sets])
+    scatter_within = within.T @ within / max(len(within) - 1, 1)
+    centred = means - centre
+    scatter_between = centred.T @ centred / max(len(centred) - 1, 1)
+    trace = np.trace(scatter_within) / len(scatter_within)
+    values, vectors = eigh(
+        scatter_between, scatter_within + shrinkage * trace * np.eye(len(scatter_within))
+    )
+    return centre, vectors[:, np.argsort(values)[::-1]]
+
+
+def main() -> None:
+    args = parse_args()
+    seed_everything(args.seed)
+    vg_dir = Path(args.vg_dir)
+    truth = [
+        json.loads(line)
+        for line in (vg_dir / "ground_truth.private.jsonl")
+        .read_text(encoding="utf-8")
+        .splitlines()
+        if line.strip()
+    ]
+    records = {
+        json.loads(line)["node_id"]: json.loads(line)
+        for line in (vg_dir / "text_nodes.jsonl").read_text(encoding="utf-8").splitlines()
+        if line.strip()
+    }
+    state = torch.load(args.objects, map_location="cpu", weights_only=False)
+    per_view = state.get("view_segments") or [state["segments"]]
+    views = min(args.views, len(per_view))
+    index = {node: position for position, node in enumerate(state["node_ids"])}
+
+    vectors = word_vectors(load_phrases(vg_dir / "text_nodes.jsonl", "region_closed"), args)
+
+    def language_state(node: str) -> np.ndarray | None:
+        rows = []
+        for phrase in records[node]["region_closed"]:
+            hits = [vectors[token] for token in re.findall(r"[a-z]+", phrase.lower())
+                    if token in vectors]
+            if hits:
+                rows.append(np.mean(hits, axis=0))
+        return np.stack(rows) if rows else None
+
+    def vision_state(node: str, view: int) -> np.ndarray | None:
+        segments = per_view[view][index[node]]
+        return (
+            np.stack([item["feature"] for item in segments]).astype(np.float64)
+            if segments
+            else None
+        )
+
+    pairs = [
+        pair
+        for pair in truth
+        if pair["vision_node_id"] in index and pair["text_node_id"] in records
+    ]
+    fit = pairs[args.samples : args.samples + args.fit_scenes]
+    language_fit = [language_state(p["text_node_id"]) for p in fit]
+    language_fit = [item for item in language_fit if item is not None and len(item) > 1]
+    vision_fit = [vision_state(p["vision_node_id"], 0) for p in fit]
+    vision_fit = [item for item in vision_fit if item is not None and len(item) > 1]
+    language_centre, language_basis = content_directions(language_fit, args.shrinkage)
+    vision_centre, vision_basis = content_directions(vision_fit, args.shrinkage)
+
+    evaluated = [
+        pair for pair in pairs[: args.samples]
+        if language_state(pair["text_node_id"]) is not None
+    ]
+    keep = args.keep
+
+    def project(raw: np.ndarray, centre: np.ndarray, basis: np.ndarray) -> torch.Tensor:
+        width = min(keep, basis.shape[1])
+        return F.normalize(
+            torch.tensor((raw - centre) @ basis[:, :width], dtype=torch.float32), dim=-1
+        )
+
+    text_sets = [
+        project(language_state(p["text_node_id"]), language_centre, language_basis)
+        for p in evaluated
+    ]
+    view_fields = []
+    for view in range(views):
+        sets = [
+            project(vision_state(p["vision_node_id"], view), vision_centre, vision_basis)
+            for p in evaluated
+        ]
+        view_fields.append(moment_field(sets))
+    visual_field = torch.stack(view_fields).mean(0)
+    text_field = moment_field(text_sets)
+
+    mask = ~np.eye(len(evaluated), dtype=bool)
+    correlation = float(
+        np.corrcoef(
+            visual_field.double().numpy()[mask], text_field.double().numpy()[mask]
+        )[0, 1]
+    )
+    torch.save(
+        {"visual_field": visual_field, "text_field": text_field,
+         "nodes": [p["vision_node_id"] for p in evaluated]},
+        args.output,
+    )
+    summary = {
+        "protocol": (
+            "Continuous states, content projection fitted per modality on "
+            "scenes outside the evaluated set. Hidden pairs are read only "
+            "for the correlation."
+        ),
+        "samples": len(evaluated),
+        "views": views,
+        "kept_directions": keep,
+        "field_correlation_at_truth": correlation,
+        "recovery_threshold": 0.9,
+    }
+    print(json.dumps(summary))
+    write_json(str(args.output).replace(".pt", ".json"), summary)
+
+
+if __name__ == "__main__":
+    main()