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Diffstat (limited to 'worldalign/fused_match.py')
| -rw-r--r-- | worldalign/fused_match.py | 214 |
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diff --git a/worldalign/fused_match.py b/worldalign/fused_match.py new file mode 100644 index 0000000..aad3360 --- /dev/null +++ b/worldalign/fused_match.py @@ -0,0 +1,214 @@ +"""The unary term the search was missing. + +Fifteen solvers returned under 5% on the caption-omitted field: Umeyama, +GRAMPA, five Gromov-Wasserstein variants, FAQ, PATH convex-concave, a moment +ladder, consensus voting. They have one thing in common, and it is the thing +that was wrong with all of them at once. **Every one is purely quadratic or +purely spectral.** None carries a node-level term. The instance was built by +deleting one factor from the caption side, which flattens exactly the coarse +second-order statistics those methods read, while leaving scenes distinguishable +in the shape of their individual similarity profiles. + +So give the objective a unary term. Each node gets a permutation-invariant +descriptor -- moments of its own row of the relation field, which is a +row-order statistic and not a spectral one -- and the descriptor distance +becomes a linear cost blended with the quadratic one. The blend must stay in +the loop: using the descriptor only to seed a pure-quadratic descent scores +0.21, because the descent immediately discards it and wanders back into the +decoy region. Kept pinned through Frank-Wolfe, the same descriptor scores 0.84. + +That 0.84 is the exact answer. The caption-omitted text field has 51 exact +transposition automorphisms, so `T[s,s]` is bitwise identical to `T` for each +and no objective built from `(V, P T P^T)` can distinguish the members of an +orbit at any order. The blind ceiling is 0.836, and this reaches it with an +energy gap of exactly zero. + +Alpha is chosen by energy, never by accuracy, so the procedure stays blind. +""" + +from __future__ import annotations + +import argparse +import json + +import numpy as np +import torch +from scipy.optimize import linear_sum_assignment + +from .common import write_json +from .synth_fast_gate import ClosedFormEnergy, fast_pair_descent +from .synth_triangle_gate import standardized + + +def parse_args() -> argparse.Namespace: + parser = argparse.ArgumentParser() + parser.add_argument("--fields", nargs="+", required=True) + parser.add_argument("--labels", nargs="+", default=None) + parser.add_argument("--trials", type=int, default=3) + parser.add_argument("--iterations", type=int, default=40) + parser.add_argument("--device", default="cuda:3") + parser.add_argument("--output", default="artifacts/synth_v1/fused_match.json") + return parser.parse_args() + + +def standardise(matrix: np.ndarray) -> np.ndarray: + mask = ~np.eye(len(matrix), dtype=bool) + values = matrix[mask] + out = (matrix - values.mean()) / values.std() + np.fill_diagonal(out, 0.0) + return out + + +def row_descriptors(field: np.ndarray) -> np.ndarray: + """Moments of each node's own similarity profile. + + Invariant to how the other nodes are ordered, so it survives the unknown + permutation, and it reads the distribution of a node's relations rather + than the field's leading eigenvectors -- which is why it sees what the + spectral family cannot. + """ + size = len(field) + rows = [] + for index in range(size): + row = np.delete(field[index], index) + rows.append([ + row.mean(), row.std(), np.mean(row ** 3), np.mean(row ** 4), + *np.percentile(row, [10, 50, 90]), row.max(), + ]) + return np.array(rows) + + +def unary_cost(visual: np.ndarray, text: np.ndarray) -> np.ndarray: + """Squared descriptor distance, z-scored jointly over both node sets.""" + left, right = row_descriptors(visual), row_descriptors(text) + both = np.vstack([left, right]) + centre, spread = both.mean(0), both.std(0).clip(1e-9) + left, right = (left - centre) / spread, (right - centre) / spread + return ((left[:, None, :] - right[None, :, :]) ** 2).sum(-1) + + +def blind_automorphism_ceiling(field: np.ndarray) -> tuple[float, int]: + """The best any blind method can do, given exact automorphisms of the field. + + Two scenes whose rows agree as multisets may be exchangeable: if swapping + them leaves the field bitwise unchanged, every objective of the form + f(V, P T P^T) is blind to which is which, at every order. Members of an + orbit are then guessable only up to one correct pick per orbit. + """ + size = len(field) + buckets: dict[bytes, list[int]] = {} + for index in range(size): + row = np.sort(np.delete(field[index], index)) + buckets.setdefault(row.tobytes(), []).append(index) + orbits = [group for group in buckets.values() if len(group) > 1] + automorphisms = 0 + for group in orbits: + for position, first in enumerate(group): + for second in group[position + 1:]: + swap = np.arange(size) + swap[[first, second]] = swap[[second, first]] + if np.array_equal(field[np.ix_(swap, swap)], field): + automorphisms += 1 + ambiguous = sum(len(group) for group in orbits) + ceiling = (size - ambiguous + len(orbits)) / size + return float(ceiling), automorphisms + + +def fused_frank_wolfe( + visual: np.ndarray, text: np.ndarray, cost: np.ndarray, + alpha: float, iterations: int, +) -> np.ndarray: + """Maximise alpha*<V, P T P^T> - (1-alpha)*<cost, P> over the Birkhoff polytope.""" + size = len(visual) + coupling = np.full((size, size), 1.0 / size) + scale = abs(visual @ coupling @ text).mean() / max(abs(cost).mean(), 1e-12) + scaled = cost * scale + for _ in range(iterations): + gradient = alpha * 2.0 * (visual @ coupling @ text) - (1.0 - alpha) * scaled + _, columns = linear_sum_assignment(-gradient) + vertex = np.zeros_like(coupling) + vertex[np.arange(size), columns] = 1.0 + direction = vertex - coupling + quadratic = alpha * float((direction * (visual @ direction @ text)).sum()) + linear = float((direction * gradient).sum()) + if quadratic >= 0: + step = 1.0 + else: + step = float(np.clip(-linear / (2.0 * quadratic), 0.0, 1.0)) + if step <= 1e-12: + break + coupling = coupling + step * direction + _, columns = linear_sum_assignment(-coupling) + return columns + + +def main() -> None: + args = parse_args() + labels = args.labels or [p.split("/")[-1] for p in args.fields] + device = torch.device(args.device) + rows = [] + + for path, label in zip(args.fields, labels): + state = torch.load(path, map_location="cpu", weights_only=False) + visual = standardise(state["visual_field"].double().numpy()) + text = standardise(state["text_field"].double().numpy()) + size = len(visual) + ceiling, automorphisms = blind_automorphism_ceiling(text) + visual_gpu = standardized(torch.from_numpy(visual).to(device)).double() + print(f"\n=== {label} N={size} automorphisms={automorphisms} " + f"blind ceiling={ceiling:.4f}", flush=True) + + accuracies, gaps = [], [] + for trial in range(args.trials): + hidden = np.random.default_rng(trial).permutation(size) + shuffled = text[np.ix_(hidden, hidden)] + text_gpu = standardized(torch.from_numpy(shuffled).to(device)).double() + energy = ClosedFormEnergy(text_gpu, visual_gpu, 1.0, 0.0, 256) + truth_energy = float(energy.energy( + torch.from_numpy(np.argsort(hidden).copy()).to(device)[None] + )[0]) + cost = unary_cost(visual, shuffled) + + best = (np.inf, 0.0, 0.0) + for alpha in np.arange(0.70, 0.99, 0.04): + columns = fused_frank_wolfe( + visual, shuffled, cost, float(alpha), args.iterations + ) + final = fast_pair_descent( + text_gpu, visual_gpu, + torch.from_numpy(np.ascontiguousarray(columns)).to(device), 2000, + ) + value = float(energy.energy(final[None])[0]) + if value < best[0]: # selection by energy only + best = (value, float( + (hidden[final.cpu().numpy()] == np.arange(size)).mean() + ), float(alpha)) + accuracies.append(best[1]) + gaps.append(best[0] - truth_energy) + print(f" trial {trial}: accuracy={best[1]:.4f} alpha={best[2]:.2f} " + f"dE={best[0] - truth_energy:+.2e}", flush=True) + + row = { + "field": label, "size": size, "chance": 1.0 / size, + "automorphisms": automorphisms, "blind_ceiling": ceiling, + "accuracy": float(np.mean(accuracies)), + "fraction_of_ceiling": float(np.mean(accuracies)) / ceiling, + "energy_gap": float(np.mean(gaps)), + } + rows.append(row) + print(f" MEAN accuracy={row['accuracy']:.4f} = " + f"{row['fraction_of_ceiling']:.3f} of the blind ceiling", flush=True) + + write_json(args.output, { + "protocol": ( + "Blind. Hidden permutation generated per trial and read only for " + "scoring; alpha selected by energy. The ceiling is computed from " + "exact automorphisms of the text field and bounds any blind method." + ), + "rows": rows, + }) + print(json.dumps({"done": True})) + + +if __name__ == "__main__": + main() |