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 --- .../vg512_visible_relations_seed0_bundle.json | 1103 ++++++++++++++++++++ 1 file changed, 1103 insertions(+) create mode 100644 artifacts/manifold_gate/vg512_visible_relations_seed0_bundle.json (limited to 'artifacts/manifold_gate/vg512_visible_relations_seed0_bundle.json') diff --git a/artifacts/manifold_gate/vg512_visible_relations_seed0_bundle.json b/artifacts/manifold_gate/vg512_visible_relations_seed0_bundle.json new file mode 100644 index 0000000..21c0cc4 --- /dev/null +++ b/artifacts/manifold_gate/vg512_visible_relations_seed0_bundle.json @@ -0,0 +1,1103 @@ +{ + "protocol": "Assignments permute real frozen text states; hidden pairs are used only to place the true assignment in the ranking. The energy terms are the cross-modal relation MSE and conditional KL; the language-only terms of the falsified free-particle energy are permutation-invariant on this space.", + "meta": { + "dataset": "visual_genome_5k", + "tier": "visible_relations", + "samples": 512, + "subset_seed": 0, + "bundle_channels": true + }, + "args": { + "dataset": "vg", + "text_orbits": "artifacts/text_orbits_qwen0p5b.pt", + "text_mode": "orbit_mean", + "vg_vision": "artifacts/vg_5k/vision_features.pt", + "vg_text": "artifacts/vg_5k_tiers/text_features_visible_relations.pt", + "vg_ground_truth": "artifacts/vg_5k/ground_truth.private.jsonl", + "vg_bundle_channels": true, + "split": "test", + "samples": 512, + "subset_seed": 0, + "random_perms": 1000, + "derangement_samples": 200, + "descent_restarts": 2, + "descent_max_steps": 200000, + "descent_objective": "m30_total", + "descent_verify_top": 64, + "device": "cpu", + "seed": 20260729, + "output": "artifacts/manifold_gate/vg512_visible_relations_seed0_bundle.json", + "trajectory_output": null + }, + "channel_names": [ + "mean", + "std", + "q10", + "q90" + ], + "gate_a_global_ranking": { + "true": { + "mse": 1.8361814201873075, + "mse_channels": [ + 1.8361814201873075, + 2.0092065496306146, + 1.8682381883198815, + 1.6745829951895506 + ], + "mse_channel_mean": 1.8470522883318385, + "conditional_kl": 5.968007727757813, + "m30_total": 4.865964385926178 + }, + "similarity_shift": { + "mse": 1.8282155900618504, + "mse_channels": [ + 1.8282155900618504, + 2.040174771117967, + 1.855414617038681, + 1.939644997614589 + ], + "mse_channel_mean": 1.9158624939582718, + "conditional_kl": 6.148225399493324, + "m30_total": 4.8860762600223655 + }, + "random": { + "mse": { + "mean": 2.002326488494873, + "std": 0.06357469409704208, + "min": 1.8082175254821777, + "true_z": 2.6133840084075928, + "true_rank_among_random": 4, + "count": 1000 + }, + "mse_channel_mean": { + "mean": 2.000269651412964, + "std": 0.03424125537276268, + "min": 1.9081450700759888, + "true_z": 4.474640846252441, + "true_rank_among_random": 0, + "count": 1000 + }, + "conditional_kl": { + "mean": 6.156534194946289, + "std": 0.00829392485320568, + "min": 6.131365776062012, + "true_z": 22.730690002441406, + "true_rank_among_random": 0, + "count": 1000 + }, + "m30_total": { + "mean": 5.235959053039551, + "std": 0.12760761380195618, + "min": 4.843794345855713, + "true_z": 2.8994715213775635, + "true_rank_among_random": 1, + "count": 1000 + } + } + }, + "gate_b_transpositions": { + "pairs": 130816, + "improving_pairs": 42471, + "improving_fraction": 0.32466212084148727, + "delta_mean": 0.0009241115345120619, + "delta_min": -0.023728921363780353, + "identity_is_local_min_mse": false, + "worst_improving_swaps": [ + { + "pair": [ + 150, + 334 + ], + "delta_mse": -0.023728921363780353, + "text_cosine": 0.9716231382004907, + "visual_cosine": 0.05834248860413824 + }, + { + "pair": [ + 133, + 295 + ], + "delta_mse": -0.023698267967706303, + "text_cosine": 0.9648793499512175, + "visual_cosine": 0.18205207859587322 + }, + { + "pair": [ + 133, + 248 + ], + "delta_mse": -0.02264878127326141, + "text_cosine": 0.9627004751833519, + "visual_cosine": 0.24336934029158566 + }, + { + "pair": [ + 30, + 248 + ], + "delta_mse": -0.02233376355178191, + "text_cosine": 0.987872123747108, + "visual_cosine": 0.2777819889987811 + }, + { + "pair": [ + 30, + 295 + ], + "delta_mse": -0.02106105663706159, + "text_cosine": 0.9832236378697833, + "visual_cosine": 0.17619941884729287 + }, + { + "pair": [ + 133, + 398 + ], + "delta_mse": -0.020000674756893978, + "text_cosine": 0.9539023891100868, + "visual_cosine": 0.16937273182784013 + }, + { + "pair": [ + 150, + 406 + ], + "delta_mse": -0.019785022723425694, + "text_cosine": 0.9711140124786037, + "visual_cosine": 0.08323255310799109 + }, + { + "pair": [ + 57, + 150 + ], + "delta_mse": -0.019765571316395496, + "text_cosine": 0.9734208466006409, + "visual_cosine": 0.10226345267775054 + }, + { + "pair": [ + 30, + 69 + ], + "delta_mse": -0.01975097730261382, + "text_cosine": 0.9876766905001162, + "visual_cosine": 0.26779431955666283 + }, + { + "pair": [ + 102, + 334 + ], + "delta_mse": -0.019587814793411613, + "text_cosine": 0.9866491719494747, + "visual_cosine": 0.19200126724411806 + }, + { + "pair": [ + 334, + 392 + ], + "delta_mse": -0.019393103233296058, + "text_cosine": 0.9771122574342217, + "visual_cosine": 0.10414264614190519 + }, + { + "pair": [ + 143, + 334 + ], + "delta_mse": -0.019377392431435474, + "text_cosine": 0.981428698694982, + "visual_cosine": 0.18685970256839998 + }, + { + "pair": [ + 30, + 398 + ], + "delta_mse": -0.01918613845607458, + "text_cosine": 0.9865944763859051, + "visual_cosine": 0.3199654341613582 + }, + { + "pair": [ + 392, + 433 + ], + "delta_mse": -0.018889355004655477, + "text_cosine": 0.9603847980862464, + "visual_cosine": 0.18498394025619516 + }, + { + "pair": [ + 133, + 392 + ], + "delta_mse": -0.018818120308154416, + "text_cosine": 0.9598765587349306, + "visual_cosine": 0.04400789354357283 + }, + { + "pair": [ + 334, + 378 + ], + "delta_mse": -0.018404405330439848, + "text_cosine": 0.981577157364069, + "visual_cosine": 0.26979077914374316 + }, + { + "pair": [ + 258, + 334 + ], + "delta_mse": -0.017883181745420924, + "text_cosine": 0.9861746810877529, + "visual_cosine": 0.19498707579060517 + }, + { + "pair": [ + 30, + 392 + ], + "delta_mse": -0.017783365345781555, + "text_cosine": 0.988289708337802, + "visual_cosine": 0.13529230274348428 + }, + { + "pair": [ + 69, + 133 + ], + "delta_mse": -0.017413607719125708, + "text_cosine": 0.9598239880334228, + "visual_cosine": 0.28479583279160214 + }, + { + "pair": [ + 119, + 334 + ], + "delta_mse": -0.01730024192581437, + "text_cosine": 0.9726405921477498, + "visual_cosine": 0.1312553545729741 + } + ] + }, + "derangement_curve": [ + { + "k": 2, + "delta_mean": 0.0007151878671720624, + "delta_std": 0.004676415119320154, + "improving_fraction": 0.285 + }, + { + "k": 4, + "delta_mean": 0.0018588155508041382, + "delta_std": 0.00784938782453537, + "improving_fraction": 0.4 + }, + { + "k": 8, + "delta_mean": 0.0039601074531674385, + "delta_std": 0.012014222331345081, + "improving_fraction": 0.33 + }, + { + "k": 16, + "delta_mean": 0.006842718925327063, + "delta_std": 0.015744848176836967, + "improving_fraction": 0.3 + }, + { + "k": 32, + "delta_mean": 0.014034444466233253, + "delta_std": 0.022500935941934586, + "improving_fraction": 0.275 + }, + { + "k": 64, + "delta_mean": 0.028988618403673172, + "delta_std": 0.0313674621284008, + "improving_fraction": 0.15 + }, + { + "k": 128, + "delta_mean": 0.0565815269947052, + "delta_std": 0.039167921990156174, + "improving_fraction": 0.08 + }, + { + "k": 256, + "delta_mean": 0.10482538491487503, + "delta_std": 0.05807621031999588, + "improving_fraction": 0.04 + }, + { + "k": 512, + "delta_mean": 0.17797137796878815, + "delta_std": 0.06258363276720047, + "improving_fraction": 0.0 + } + ], + "gate_c_descent_from_true": { + "start_accuracy": 1.0, + "final_accuracy": 0.05859375, + "final_objective": 2.8828200508854174, + "final_energy": { + "mse": 0.842092475394899, + "mse_channels": [ + 0.842092475394899, + 1.7121131998880907, + 0.9524185157696106, + 0.639278194828943 + ], + "mse_channel_mean": 1.0364755964703858, + "conditional_kl": 5.993175500478097, + "m30_total": 2.8828200508854174 + }, + "accepted_moves": 510, + "moved_fraction": 0.94140625, + "mse_local_min_certificate": false, + "trajectory": [ + { + "step": 0, + "objective": 4.76723068555389, + "accuracy": 0.99609375 + }, + { + "step": 50, + "objective": 3.749711605167353, + "accuracy": 0.80078125 + }, + { + "step": 100, + "objective": 3.325865716526354, + "accuracy": 0.611328125 + }, + { + "step": 150, + "objective": 3.1867501637571323, + "accuracy": 0.44921875 + }, + { + "step": 200, + "objective": 3.0719914702699826, + "accuracy": 0.3125 + }, + { + "step": 250, + "objective": 3.011496674783193, + "accuracy": 0.220703125 + }, + { + "step": 300, + "objective": 2.9707172102189814, + "accuracy": 0.15234375 + }, + { + "step": 350, + "objective": 2.9390738089276693, + "accuracy": 0.119140625 + }, + { + "step": 400, + "objective": 2.9171705781589825, + "accuracy": 0.095703125 + }, + { + "step": 450, + "objective": 2.897556763758914, + "accuracy": 0.06640625 + }, + { + "step": 500, + "objective": 2.8841153341920114, + "accuracy": 0.05859375 + } + ], + "final_permutation": [ + 50, + 236, + 379, + 381, + 182, + 185, + 269, + 374, + 161, + 384, + 212, + 11, + 221, + 369, + 291, + 293, + 89, + 59, + 338, + 26, + 446, + 131, + 30, + 109, + 104, + 65, + 349, + 300, + 28, + 29, + 125, + 433, + 282, + 429, + 34, + 474, + 36, + 312, + 77, + 115, + 40, + 13, + 49, + 192, + 490, + 166, + 390, + 47, + 307, + 44, + 461, + 364, + 395, + 481, + 171, + 55, + 205, + 421, + 151, + 70, + 324, + 153, + 209, + 129, + 159, + 383, + 146, + 311, + 290, + 94, + 139, + 64, + 225, + 423, + 308, + 385, + 424, + 372, + 81, + 31, + 0, + 16, + 211, + 501, + 260, + 396, + 399, + 87, + 366, + 422, + 479, + 298, + 217, + 112, + 195, + 62, + 98, + 248, + 96, + 486, + 187, + 72, + 406, + 103, + 288, + 127, + 43, + 179, + 426, + 476, + 167, + 7, + 234, + 488, + 12, + 503, + 140, + 272, + 360, + 434, + 295, + 60, + 190, + 243, + 177, + 276, + 493, + 237, + 68, + 402, + 450, + 482, + 242, + 202, + 358, + 442, + 56, + 363, + 101, + 392, + 404, + 66, + 231, + 114, + 172, + 170, + 418, + 216, + 438, + 394, + 57, + 88, + 478, + 51, + 117, + 155, + 333, + 168, + 475, + 245, + 176, + 339, + 391, + 67, + 228, + 319, + 257, + 321, + 304, + 267, + 249, + 149, + 262, + 173, + 86, + 355, + 158, + 252, + 186, + 509, + 334, + 52, + 157, + 329, + 305, + 303, + 454, + 24, + 353, + 335, + 226, + 189, + 71, + 95, + 194, + 58, + 253, + 397, + 54, + 53, + 388, + 409, + 200, + 63, + 336, + 387, + 271, + 297, + 464, + 480, + 489, + 17, + 193, + 184, + 5, + 314, + 357, + 430, + 284, + 420, + 1, + 154, + 320, + 326, + 342, + 160, + 48, + 270, + 346, + 229, + 38, + 465, + 113, + 174, + 84, + 279, + 471, + 277, + 375, + 419, + 218, + 203, + 148, + 412, + 495, + 233, + 183, + 247, + 259, + 316, + 46, + 265, + 449, + 196, + 254, + 255, + 425, + 264, + 330, + 18, + 373, + 79, + 492, + 467, + 431, + 258, + 352, + 227, + 498, + 457, + 2, + 120, + 92, + 138, + 280, + 22, + 82, + 380, + 198, + 499, + 376, + 25, + 377, + 348, + 135, + 199, + 286, + 317, + 362, + 142, + 208, + 299, + 152, + 145, + 505, + 133, + 296, + 347, + 180, + 210, + 27, + 207, + 302, + 39, + 287, + 213, + 261, + 403, + 105, + 78, + 230, + 452, + 459, + 111, + 508, + 411, + 147, + 365, + 175, + 126, + 415, + 281, + 156, + 445, + 477, + 122, + 437, + 136, + 256, + 309, + 469, + 331, + 502, + 99, + 74, + 393, + 283, + 4, + 504, + 90, + 83, + 440, + 162, + 510, + 250, + 21, + 164, + 451, + 6, + 278, + 337, + 444, + 441, + 33, + 354, + 76, + 273, + 37, + 323, + 340, + 108, + 359, + 414, + 137, + 61, + 427, + 220, + 370, + 268, + 435, + 436, + 97, + 292, + 306, + 313, + 246, + 178, + 32, + 500, + 106, + 9, + 3, + 132, + 10, + 266, + 75, + 432, + 386, + 413, + 439, + 251, + 215, + 460, + 294, + 35, + 345, + 405, + 240, + 14, + 361, + 400, + 134, + 506, + 494, + 453, + 343, + 241, + 407, + 408, + 327, + 118, + 410, + 123, + 497, + 472, + 222, + 110, + 232, + 23, + 239, + 42, + 443, + 289, + 73, + 318, + 496, + 144, + 197, + 428, + 100, + 473, + 341, + 301, + 119, + 466, + 458, + 378, + 448, + 456, + 389, + 382, + 398, + 116, + 121, + 350, + 315, + 244, + 219, + 85, + 124, + 143, + 102, + 91, + 107, + 416, + 455, + 191, + 141, + 447, + 344, + 206, + 484, + 462, + 130, + 214, + 80, + 356, + 204, + 507, + 468, + 223, + 201, + 45, + 351, + 487, + 367, + 128, + 401, + 19, + 8, + 93, + 417, + 69, + 483, + 163, + 485, + 322, + 150, + 275, + 263, + 238, + 20, + 285, + 188, + 491, + 165, + 332, + 274, + 368, + 235, + 15, + 181, + 328, + 325, + 310, + 371, + 169, + 463, + 224, + 511, + 41, + 470 + ] + }, + "gate_c_descent_from_random": [ + { + "start_accuracy": 0.001953125, + "final_accuracy": 0.00390625, + "final_objective": 2.9303655483316198, + "final_energy": { + "mse": 0.8656314177592489, + "mse_channels": [ + 0.8656314177592489, + 1.6933344407135478, + 0.9517652546922492, + 0.6532691575437677 + ], + "mse_channel_mean": 1.0410000676772033, + "conditional_kl": 5.995513564065609, + "m30_total": 2.9303655483316198 + }, + "accepted_moves": 548, + "moved_fraction": 0.970703125, + "mse_local_min_certificate": false, + "trajectory": [ + { + "step": 0, + "objective": 5.231871557664851, + "accuracy": 0.001953125 + }, + { + "step": 50, + "objective": 3.939486529925836, + "accuracy": 0.001953125 + }, + { + "step": 100, + "objective": 3.480004965058698, + "accuracy": 0.00390625 + }, + { + "step": 150, + "objective": 3.2682677091657433, + "accuracy": 0.001953125 + }, + { + "step": 200, + "objective": 3.1427037750210873, + "accuracy": 0.001953125 + }, + { + "step": 250, + "objective": 3.0845357320790776, + "accuracy": 0.0 + }, + { + "step": 300, + "objective": 3.0400212227132926, + "accuracy": 0.0 + }, + { + "step": 350, + "objective": 3.0143326988066264, + "accuracy": 0.0 + }, + { + "step": 400, + "objective": 2.9878172415724364, + "accuracy": 0.0 + }, + { + "step": 450, + "objective": 2.9651861380796474, + "accuracy": 0.001953125 + }, + { + "step": 500, + "objective": 2.9439573850467267, + "accuracy": 0.001953125 + } + ] + }, + { + "start_accuracy": 0.0, + "final_accuracy": 0.00390625, + "final_objective": 2.8745484556368206, + "final_energy": { + "mse": 0.8369162421728444, + "mse_channels": [ + 0.8369162421728444, + 1.7387372868040347, + 0.9422185149915435, + 0.6473588666945231 + ], + "mse_channel_mean": 1.0413077276657365, + "conditional_kl": 6.003579856455657, + "m30_total": 2.8745484556368206 + }, + "accepted_moves": 565, + "moved_fraction": 0.986328125, + "mse_local_min_certificate": false, + "trajectory": [ + { + "step": 0, + "objective": 5.289356698717435, + "accuracy": 0.0 + }, + { + "step": 50, + "objective": 3.88523261730883, + "accuracy": 0.0 + }, + { + "step": 100, + "objective": 3.46459092695601, + "accuracy": 0.0 + }, + { + "step": 150, + "objective": 3.24571979250769, + "accuracy": 0.0 + }, + { + "step": 200, + "objective": 3.1299263312184014, + "accuracy": 0.0 + }, + { + "step": 250, + "objective": 3.0544498218686087, + "accuracy": 0.0 + }, + { + "step": 300, + "objective": 3.0073097847589514, + "accuracy": 0.0 + }, + { + "step": 350, + "objective": 2.9732345073865596, + "accuracy": 0.0 + }, + { + "step": 400, + "objective": 2.94420206040994, + "accuracy": 0.001953125 + }, + { + "step": 450, + "objective": 2.918926758008375, + "accuracy": 0.001953125 + }, + { + "step": 500, + "objective": 2.8983945485064964, + "accuracy": 0.00390625 + }, + { + "step": 550, + "objective": 2.8782554002261094, + "accuracy": 0.00390625 + } + ] + } + ], + "verdict": { + "true_m30_total": 4.865964385926178, + "identity_is_local_min_mse": false, + "descent_from_true_stays": 0.05859375, + "on_manifold_counterfeit_found": true, + "best_random_descent_m30_total": 2.8745484556368206 + } +} \ No newline at end of file -- cgit v1.2.3