From a62cf4d2a99b4a7985c61b2a7feb92a82a8218b7 Mon Sep 17 00:00:00 2001 From: Yuren Hao Date: Sat, 1 Aug 2026 14:10:03 -0500 Subject: 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 --- worldalign/synth_precision_gate.py | 279 +++++++++++++++++++++++++++++++++++++ 1 file changed, 279 insertions(+) create mode 100644 worldalign/synth_precision_gate.py (limited to 'worldalign/synth_precision_gate.py') diff --git a/worldalign/synth_precision_gate.py b/worldalign/synth_precision_gate.py new file mode 100644 index 0000000..46887fa --- /dev/null +++ b/worldalign/synth_precision_gate.py @@ -0,0 +1,279 @@ +"""Channel-matched (precision-weighted) relational energy for the synth world. + +Planted-problem theory: search is glassy when the energy mismatches the +generative channel. The orbit provides the channel unimodally -- the +variance of each vision relation entry across re-rendered views measures +exactly how corrupted that entry is (segmentation errors are the dominant +noise and are view-dependent), so entries are weighted by their orbit +precision. Text fields are parse-deterministic and enter unweighted. + +The weighted energy loses the all-pairs closed form (the quadratic terms +no longer cancel), but each swap delta is still O(N) and vectorizes over +sampled pairs; gates and tempering below use that form. Hidden pairs +score orderings only. +""" + +from __future__ import annotations + +import argparse +import json +from pathlib import Path + +import torch +import torch.nn.functional as F +from tqdm import tqdm + +from .common import read_json, seed_everything, write_json +from .synth_cc_battery import ( + component_descriptors, + moment_field, + onehot_descriptors, + phrase_bow_sets, +) + + +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("--precision-floor", type=float, default=1e-4) + parser.add_argument("--random-perms", type=int, default=300) + parser.add_argument("--transposition-samples", type=int, default=100000) + parser.add_argument("--descent-restarts", type=int, default=5) + parser.add_argument("--descent-max-steps", type=int, default=5000) + parser.add_argument("--replicas", type=int, default=8) + parser.add_argument("--tempering-rounds", type=int, default=60000) + parser.add_argument("--temp-high", type=float, default=3e-3) + parser.add_argument("--temp-low", type=float, default=1e-5) + parser.add_argument("--exchange-every", type=int, default=20) + parser.add_argument("--device", default="cuda:3") + parser.add_argument("--seed", type=int, default=20260731) + parser.add_argument( + "--output", default="artifacts/synth_v0/precision_gate.json" + ) + return parser.parse_args() + + +def standardized(field: torch.Tensor) -> torch.Tensor: + mask = ~torch.eye(len(field), dtype=torch.bool) + values = field[mask] + out = (field - values.mean()) / values.std().clamp_min(1e-9) + return out.masked_fill(~mask, 0.0) + + +def weighted_energy( + text: torch.Tensor, visual: torch.Tensor, weights: torch.Tensor, + permutations: torch.Tensor, +) -> torch.Tensor: + fields = text[permutations[:, :, None], permutations[:, None, :]] + difference = (fields - visual) ** 2 * weights + mask = ~torch.eye(text.shape[-1], dtype=torch.bool, device=text.device) + return difference[:, mask].sum(-1) / weights[mask].sum() + + +def swap_deltas( + permuted_text: torch.Tensor, + visual: torch.Tensor, + weights: torch.Tensor, + pairs_p: torch.Tensor, + pairs_q: torch.Tensor, +) -> torch.Tensor: + """Weighted swap deltas, O(N) per proposal, batched over replicas. + + permuted_text: [R, N, N]; pairs: [R, P]. Row and column contributions + are equal by symmetry of all three matrices; the k in {p, q} terms are + excluded because the (p, q) entry itself is unchanged by the swap. + """ + replica_index = torch.arange(len(permuted_text), device=permuted_text.device) + rows_p = permuted_text[replica_index[:, None], pairs_p] + rows_q = permuted_text[replica_index[:, None], pairs_q] + visual_p, visual_q = visual[pairs_p], visual[pairs_q] + weight_p, weight_q = weights[pairs_p], weights[pairs_q] + new_p = (rows_q - visual_p) ** 2 * weight_p + old_p = (rows_p - visual_p) ** 2 * weight_p + new_q = (rows_p - visual_q) ** 2 * weight_q + old_q = (rows_q - visual_q) ** 2 * weight_q + total = (new_p - old_p + new_q - old_q).sum(-1) + columns = torch.stack([pairs_p, pairs_q], -1) + correction = torch.zeros_like(total) + for slot in range(2): + chosen = columns[..., slot] + correction = correction + ( + (rows_q.gather(-1, chosen[..., None]) - visual_p.gather(-1, chosen[..., None])) ** 2 + - (rows_p.gather(-1, chosen[..., None]) - visual_p.gather(-1, chosen[..., None])) ** 2 + ).squeeze(-1) * weight_p.gather(-1, chosen[..., None]).squeeze(-1) + correction = correction + ( + (rows_p.gather(-1, chosen[..., None]) - visual_q.gather(-1, chosen[..., None])) ** 2 + - (rows_q.gather(-1, chosen[..., None]) - visual_q.gather(-1, chosen[..., None])) ** 2 + ).squeeze(-1) * weight_q.gather(-1, chosen[..., None]).squeeze(-1) + mask_count = weights[~torch.eye(len(visual), dtype=torch.bool, device=visual.device)].sum() + return 2.0 * (total - correction) / mask_count + + +def main() -> None: + args = parse_args() + seed_everything(args.seed) + manifest = read_json(Path(args.data_dir, "manifest.json")) + captions = read_json(Path(args.data_dir, "captions.json"))["captions"] + rows = manifest[args.split][: args.samples] + image_dir = Path(manifest["image_dir"]) + from .synth_towers import load_image + + per_view = [] + for view in range(args.vision_views): + raw = [] + for row in tqdm(rows, desc=f"cc v{view}"): + sprites, _ = component_descriptors( + load_image(image_dir / f"scene{row:06d}_v{view}.png"), + args.merge_distance, + ) + raw.append(sprites) + sets = [F.normalize(v, dim=-1) for v in onehot_descriptors(raw)] + per_view.append(moment_field(sets)) + stack = torch.stack(per_view) + visual_field = stack.mean(0) + variance = stack.var(0) + weights = 1.0 / (variance + args.precision_floor) + weights = weights / weights.mean() + + text_sets = phrase_bow_sets(rows, captions, manifest["vocabulary"]) + text_field = moment_field(text_sets) + + 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) + text_input = standardized(text_field[hidden][:, hidden].double()).float().to(device) + visual = standardized(visual_field.double()).float().to(device) + weight_map = weights.float().to(device) + + identity = torch.arange(size, device=device) + true_energy = float( + weighted_energy(text_input, visual, weight_map, truth[None].to(device))[0] + ) + random_perms = torch.stack( + [torch.argsort(torch.rand(size, generator=generator)) for _ in range(args.random_perms)] + ).to(device) + random_energies = weighted_energy(text_input, visual, weight_map, random_perms) + gate_a = { + "true": true_energy, + "random_mean": float(random_energies.mean()), + "random_std": float(random_energies.std()), + "true_z": float((random_energies.mean() - true_energy) / random_energies.std().clamp_min(1e-12)), + } + + samples = min(args.transposition_samples, size * (size - 1) // 2) + pairs_p = torch.randint(0, size, (1, samples), generator=generator).to(device) + pairs_q = torch.randint(0, size, (1, samples), generator=generator).to(device) + valid = (pairs_p != pairs_q).squeeze(0) + fields_true = text_input[truth.to(device)][:, truth.to(device)][None] + deltas = swap_deltas(fields_true, visual, weight_map, pairs_p, pairs_q).squeeze(0)[valid] + gate_b = { + "sampled": int(valid.sum()), + "improving_fraction": float((deltas < 0).float().mean()), + } + + def descent(start: torch.Tensor) -> dict: + current = start.clone() + energy = float(weighted_energy(text_input, visual, weight_map, current[None])[0]) + for _ in range(args.descent_max_steps): + fields = text_input[current][:, current][None] + cp = torch.randint(0, size, (1, 4096), generator=generator).to(device) + cq = torch.randint(0, size, (1, 4096), generator=generator).to(device) + dd = swap_deltas(fields, visual, weight_map, cp, cq).squeeze(0) + best = int(dd.argmin()) + if float(dd[best]) >= -1e-12: + break + p, q = int(cp[0, best]), int(cq[0, best]) + current[[p, q]] = current[[q, p]] + energy += float(dd[best]) + return { + "accuracy": float((current.cpu() == truth).float().mean()), + "energy": float(weighted_energy(text_input, visual, weight_map, current[None])[0]), + } + + from_true = descent(truth.to(device)) + restarts = [ + descent(torch.argsort(torch.rand(size, generator=generator)).to(device)) + for _ in range(args.descent_restarts) + ] + best_random = min(r["energy"] for r in restarts) + + # Tempering recovery with the weighted deltas. + temperatures = torch.logspace( + torch.log10(torch.tensor(args.temp_low)), + torch.log10(torch.tensor(args.temp_high)), + args.replicas, + ).to(device) + permutations = torch.stack( + [torch.randperm(size, generator=generator).to(device) for _ in range(args.replicas)] + ) + energies = weighted_energy(text_input, visual, weight_map, permutations) + for round_index in range(args.tempering_rounds): + fields = text_input[permutations[:, :, None], permutations[:, None, :]] + cp = torch.randint(0, size, (args.replicas, 24), generator=generator).to(device) + cq = torch.randint(0, size, (args.replicas, 24), generator=generator).to(device) + dd = swap_deltas(fields, visual, weight_map, cp, cq) + noise = torch.rand(args.replicas, 24, generator=generator).to(device) + ok = (dd < -temperatures[:, None] * noise.clamp_min(1e-12).log()) & (cp != cq) + for replica in range(args.replicas): + hits = torch.nonzero(ok[replica]) + if not len(hits): + continue + first = int(hits[0, 0]) + p, q = int(cp[replica, first]), int(cq[replica, first]) + permutations[replica][[p, q]] = permutations[replica][[q, p]] + energies[replica] = energies[replica] + dd[replica, first] + if round_index % args.exchange_every == 0: + for replica in range(args.replicas - 1): + gap = (energies[replica] - energies[replica + 1]) * ( + 1.0 / temperatures[replica] - 1.0 / temperatures[replica + 1] + ) + if gap > 0 or torch.rand(1, generator=generator).item() < float(gap.exp()): + permutations[[replica, replica + 1]] = permutations[[replica + 1, replica]] + energies[[replica, replica + 1]] = energies[[replica + 1, replica]] + if round_index % 10000 == 0: + energies = weighted_energy(text_input, visual, weight_map, permutations) + energies = weighted_energy(text_input, visual, weight_map, permutations) + accuracies = (permutations.cpu() == truth[None]).float().mean(-1) + cold = int(energies.argmin()) + + report = { + "protocol": ( + "Relation entries are weighted by orbit-derived precision " + "(variance of the vision field across re-rendered views); " + "weights are unimodal statistics. Hidden pairs score only." + ), + "samples": size, + "weight_stats": { + "min": float(weights.min()), + "median": float(weights.median()), + "max": float(weights.max()), + }, + "gate_a": gate_a, + "gate_b": gate_b, + "descent_from_true": from_true, + "descent_from_random": restarts, + "tempering": { + "cold_energy": float(energies[cold]), + "cold_accuracy": float(accuracies[cold]), + "best_accuracy": float(accuracies.max()), + }, + "verdict": { + "true_energy": true_energy, + "best_random_descent": best_random, + "counterfeit_found": bool(best_random < true_energy and min(r["accuracy"] for r in restarts) < 0.5), + "recovery_accuracy": float(accuracies.max()), + }, + } + print(json.dumps({"verdict": report["verdict"], "gate_b": gate_b, "from_true": from_true})) + write_json(args.output, report) + print(f"Wrote {args.output}") + + +if __name__ == "__main__": + main() -- cgit v1.2.3