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 --- tests/test_core.py | 236 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 236 insertions(+) create mode 100644 tests/test_core.py (limited to 'tests/test_core.py') diff --git a/tests/test_core.py b/tests/test_core.py new file mode 100644 index 0000000..50d3aad --- /dev/null +++ b/tests/test_core.py @@ -0,0 +1,236 @@ +import numpy as np +import torch + +from worldalign.common import retrieval_metrics, sliced_wasserstein +from worldalign.energy import ( + log_sinkhorn, + relation_field_energy, + standardized_relation, +) +from worldalign.gw import gw_pseudo_targets +from worldalign.models import Bridge, PrefixAdapter +from worldalign.vg_diagnose import bundle_signature + + +def test_shapes_and_retrieval(): + bridge = Bridge(8, 12, hidden_dim=16) + prefix = PrefixAdapter(12, 20, prefix_length=4, hidden_dim=16) + x = torch.randn(5, 8) + y = bridge(x) + assert y.shape == (5, 12) + assert prefix(y).shape == (5, 4, 20) + metrics = retrieval_metrics(y, y) + assert metrics["i2t_r@1"] == 1.0 + + +def test_sliced_wasserstein_identity(): + x = torch.randn(32, 16) + assert sliced_wasserstein(x, x).item() < 1e-10 + + +def test_gw_recovers_structure_without_pairs(): + rng = np.random.default_rng(7) + z = rng.normal(size=(600, 6)).astype(np.float32) + q, _ = np.linalg.qr(rng.normal(size=(6, 6))) + x = torch.from_numpy(z) + y = torch.from_numpy((z @ q).astype(np.float32))[torch.randperm(len(z))] + result = gw_pseudo_targets(x, y, clusters=12, seed=3, max_iter=50) + assert result["coupling"].shape == (12, 12) + assert np.isfinite(result["gw_distance"]) + + +def test_bundle_signature_is_view_permutation_and_rotation_invariant(): + torch.manual_seed(5) + x = torch.randn(7, 8, 12) + q, _ = torch.linalg.qr(torch.randn(12, 12)) + permuted = (x @ q)[:, torch.randperm(8)] + first = bundle_signature(x) + second = bundle_signature(permuted) + assert torch.allclose(first, second, atol=2e-5) + + +def test_log_sinkhorn_has_unit_marginals(): + logits = torch.randn(9, 9) + coupling = log_sinkhorn(logits, temperature=0.7, iterations=30) + assert torch.allclose(coupling.sum(0), torch.ones(9), atol=1e-4) + assert torch.allclose(coupling.sum(1), torch.ones(9), atol=1e-4) + + +def test_transposition_delta_matches_brute_force(): + from worldalign.manifold_gate import ( + all_transposition_delta_mse, + build_channels, + permuted, + relation_mse, + ) + + generator = torch.Generator().manual_seed(11) + visual = torch.randn(24, 8, generator=generator)[:, None, :] + text = torch.randn(24, 10, generator=generator)[:, None, :] + text_channels, _ = build_channels(text, bundle=False) + visual_channels, _ = build_channels(visual, bundle=False) + delta = all_transposition_delta_mse(text_channels[0], visual_channels[0]) + base = relation_mse(text_channels[0], visual_channels[0]) + for p, q in [(0, 1), (3, 17), (5, 23), (10, 11)]: + permutation = torch.arange(24) + permutation[[p, q]] = permutation[[q, p]] + brute = ( + relation_mse(permuted(text_channels[0], permutation), visual_channels[0]) + - base + ) + assert torch.allclose(delta[p, q], brute, atol=1e-10) + assert torch.allclose(delta[q, p], brute, atol=1e-10) + + +def test_gate_energy_matches_energy_module(): + from worldalign.manifold_gate import assignment_energy, build_channels + + generator = torch.Generator().manual_seed(3) + visual = torch.randn(16, 6, generator=generator) + text = torch.randn(16, 9, generator=generator) + text_channels, text_relation = build_channels(text[:, None, :], bundle=False) + visual_channels, visual_relation = build_channels(visual[:, None, :], bundle=False) + permutation = torch.randperm(16, generator=generator) + gate = assignment_energy( + text_channels, visual_channels, text_relation, visual_relation, permutation + ) + reference_relation, reference_standardized = standardized_relation(visual) + mse, kl = relation_field_energy( + reference_relation, reference_standardized, text[permutation] + ) + assert abs(gate["mse"] - float(mse)) < 1e-5 + assert abs(gate["conditional_kl"] - float(kl)) < 1e-4 + + +def test_k_derangement_moves_exactly_k(): + from worldalign.manifold_gate import k_derangement + + generator = torch.Generator().manual_seed(9) + for k in (2, 4, 16): + permutation = k_derangement(64, k, generator) + moved = (permutation != torch.arange(64)).sum() + assert int(moved) == k + + +def test_bundle_mean_channel_matches_view_mean_relation(): + from worldalign.manifold_gate import view_bundle_channels + + torch.manual_seed(4) + views = torch.nn.functional.normalize(torch.randn(6, 5, 8), dim=-1) + channels = view_bundle_channels(views) + assert channels.shape == (4, 6, 6) + means = views.double().mean(1) + assert torch.allclose(channels[0], means @ means.T, atol=1e-10) + + +def test_batched_transposition_delta_matches_single(): + from worldalign.manifold_gate import all_transposition_delta_mse + from worldalign.view_gate import batched_transposition_delta, standardized_field + + torch.manual_seed(2) + views_a = torch.nn.functional.normalize(torch.randn(3, 6, 5), dim=-1) + views_b = torch.nn.functional.normalize(torch.randn(3, 6, 7), dim=-1) + fields_a = standardized_field(views_a) + fields_b = standardized_field(views_b) + batched = batched_transposition_delta(fields_a, fields_b) + for item in range(3): + single = all_transposition_delta_mse(fields_a[item], fields_b[item]) + assert torch.allclose(batched[item], single, atol=1e-10) + + +def test_batched_descent_reaches_local_minimum(): + from worldalign.view_gate import ( + batched_descent, + batched_transposition_delta, + field_mse, + standardized_field, + ) + + torch.manual_seed(6) + visual = torch.nn.functional.normalize(torch.randn(4, 8, 5), dim=-1) + noise = torch.nn.functional.normalize( + visual + 0.1 * torch.randn(4, 8, 5), dim=-1 + ) + visual_fields = standardized_field(visual) + text_fields = standardized_field(noise) + starts = torch.stack([torch.randperm(8) for _ in range(4)]) + final_cost, permutations = batched_descent( + text_fields.clone(), visual_fields, starts.clone(), sweeps=100 + ) + index = torch.arange(4) + permuted = text_fields[ + index[:, None, None], permutations[:, :, None], permutations[:, None, :] + ] + assert torch.allclose(field_mse(permuted, visual_fields), final_cost, atol=1e-10) + delta = batched_transposition_delta(permuted, visual_fields) + assert (delta >= -1e-9).all() + + +def test_ricci_flow_returns_finite_symmetric_geometry(): + import numpy as np + + from worldalign.ricci_control import ollivier_ricci_apsp + + rng = np.random.default_rng(4) + points = rng.normal(size=(24, 3)) + distance = np.linalg.norm(points[:, None] - points[None, :], axis=-1) + + class FlowArgs: + neighbors = 5 + lazy_alpha = 0.5 + flow_step = 0.4 + + flowed = ollivier_ricci_apsp(distance, FlowArgs(), iterations=3) + assert np.isfinite(flowed).all() + assert np.allclose(flowed, flowed.T, atol=1e-9) + assert (np.diag(flowed) == 0).all() + + +def test_paired_relation_field_has_less_energy_than_permutation(): + generator = torch.Generator().manual_seed(7) + visual = torch.randn(32, 12, generator=generator) + paired = visual @ torch.randn(12, 20, generator=generator) + visual_relation, visual_standardized = standardized_relation(visual) + paired_energy = relation_field_energy( + visual_relation, visual_standardized, paired + )[0] + permutation = torch.randperm(32, generator=generator) + shuffled_energy = relation_field_energy( + visual_relation, visual_standardized, paired[permutation] + )[0] + assert paired_energy < shuffled_energy + + +def test_tier0_factor_vector_is_one_hot_per_factor(): + from worldalign.tier0_pipeline import factor_vector + + vector = factor_vector(3, 2, 0, classes=10) + assert vector.shape == (17,) + assert vector[:10].sum() == 1.0 and vector[3] == 1.0 + assert vector[10:14].sum() == 1.0 and vector[11] == 1.0 + assert vector[14:].sum() == 1.0 and vector[14] == 1.0 + + +def test_watershed_splits_touching_objects(): + from worldalign.tier0_pipeline import extract_objects, group_objects + + image = torch.full((3, 64, 64), 0.1) + # Two same-coloured discs whose supports touch at a single column. + ys, xs = torch.meshgrid(torch.arange(64), torch.arange(64), indexing="ij") + for centre in (22, 38): + disc = ((ys - 32) ** 2 + (xs - centre) ** 2) <= 8**2 + image[:, disc] = torch.tensor([0.9, 0.2, 0.2])[:, None] + objects = extract_objects(image, peak_distance=4) + assert len(objects) == 2 + groups = group_objects(objects, threshold=0.35) + assert len(groups) == 1 and groups[0]["members"] == 2 + + +def test_caption_encoding_matches_declared_factors(): + from worldalign.tier0_pipeline import encode_caption + + ranks = {"red": 0, "blue": 1} + states = encode_caption("there are three small red circles, a blue square.", ranks, 2) + assert states.shape == (2, 9) + assert states[0][0] > 0 and states[0][2 + 2] > 0 and states[0][2 + 4 + 0] > 0 + assert states[1][1] > 0 and states[1][2 + 0] > 0 and states[1][2 + 4 + 1] > 0 -- cgit v1.2.3