{ "protocol": "Effective rank from the participation ratio of each field's spectrum; shared directions from principal angles between the two leading eigenspaces. No pairing enters beyond the alignment the fields already carry.", "width": 32, "rows": [ { "label": "synth-RECOVERS", "size": 256, "correlation": 0.9284809883663888, "visual_effective_rank": 14.50854049599196, "text_effective_rank": 11.832081486516831, "shared_directions_cos_gt_0.7": 27, "principal_cosines_top8": [ 1.0, 1.0, 1.0, 1.0, 1.0, 0.999, 0.999, 0.999 ], "spectrum_profile": [ { "index": 0, "best_text_overlap": 0.9988184979219944 }, { "index": 1, "best_text_overlap": 0.9038254548424662 }, { "index": 2, "best_text_overlap": 0.7738637793117231 }, { "index": 3, "best_text_overlap": 0.7898924505967239 }, { "index": 4, "best_text_overlap": 0.9633572761985347 }, { "index": 5, "best_text_overlap": 0.9667594083538564 }, { "index": 6, "best_text_overlap": 0.8581068112833727 }, { "index": 7, "best_text_overlap": 0.7720408457258224 }, { "index": 8, "best_text_overlap": 0.9451869286586472 }, { "index": 9, "best_text_overlap": 0.9346387523699597 }, { "index": 10, "best_text_overlap": 0.9744620235608439 }, { "index": 11, "best_text_overlap": 0.8287855141725994 }, { "index": 12, "best_text_overlap": 0.8450929971524885 }, { "index": 13, "best_text_overlap": 0.7475087759782241 }, { "index": 14, "best_text_overlap": 0.5363062788775304 }, { "index": 15, "best_text_overlap": 0.5851587348701632 } ] }, { "label": "nat-6seg", "size": 256, "correlation": 0.6922159706308013, "visual_effective_rank": 39.69132496762981, "text_effective_rank": 31.7662539087451, "shared_directions_cos_gt_0.7": 15, "principal_cosines_top8": [ 0.989, 0.978, 0.956, 0.938, 0.916, 0.892, 0.881, 0.87 ], "spectrum_profile": [ { "index": 0, "best_text_overlap": 0.7532219338133863 }, { "index": 1, "best_text_overlap": 0.618182152081914 }, { "index": 2, "best_text_overlap": 0.6411572047678387 }, { "index": 3, "best_text_overlap": 0.5609614131227192 }, { "index": 4, "best_text_overlap": 0.5786521313263311 }, { "index": 5, "best_text_overlap": 0.6212040366073345 }, { "index": 6, "best_text_overlap": 0.6014409101136969 }, { "index": 7, "best_text_overlap": 0.3241154791286174 }, { "index": 8, "best_text_overlap": 0.33772536144199544 }, { "index": 9, "best_text_overlap": 0.46886651280081304 }, { "index": 10, "best_text_overlap": 0.339879585332424 }, { "index": 11, "best_text_overlap": 0.2697704959742108 }, { "index": 12, "best_text_overlap": 0.3089464131279491 }, { "index": 13, "best_text_overlap": 0.34824951852897246 }, { "index": 14, "best_text_overlap": 0.26546032832701905 }, { "index": 15, "best_text_overlap": 0.17108445671033506 } ] }, { "label": "nat-16seg", "size": 256, "correlation": 0.6794444345566248, "visual_effective_rank": 40.32463000927306, "text_effective_rank": 31.7662539087451, "shared_directions_cos_gt_0.7": 14, "principal_cosines_top8": [ 0.991, 0.979, 0.955, 0.937, 0.917, 0.897, 0.882, 0.87 ], "spectrum_profile": [ { "index": 0, "best_text_overlap": 0.7366894502381554 }, { "index": 1, "best_text_overlap": 0.6371340906520718 }, { "index": 2, "best_text_overlap": 0.6670233369588643 }, { "index": 3, "best_text_overlap": 0.7305683273676973 }, { "index": 4, "best_text_overlap": 0.5178189484095195 }, { "index": 5, "best_text_overlap": 0.6108081877127542 }, { "index": 6, "best_text_overlap": 0.5743712616080214 }, { "index": 7, "best_text_overlap": 0.30576250785088804 }, { "index": 8, "best_text_overlap": 0.31705130049377683 }, { "index": 9, "best_text_overlap": 0.434975496479508 }, { "index": 10, "best_text_overlap": 0.2627438939568967 }, { "index": 11, "best_text_overlap": 0.22483152594639236 }, { "index": 12, "best_text_overlap": 0.24208088194854407 }, { "index": 13, "best_text_overlap": 0.2850328753356361 }, { "index": 14, "best_text_overlap": 0.24894409456686264 }, { "index": 15, "best_text_overlap": 0.3923832160325988 } ] }, { "label": "nat-oracle-regions", "size": 256, "correlation": 0.702748890720233, "visual_effective_rank": 39.32779841860138, "text_effective_rank": 31.7662539087451, "shared_directions_cos_gt_0.7": 15, "principal_cosines_top8": [ 0.99, 0.978, 0.959, 0.939, 0.921, 0.899, 0.89, 0.876 ], "spectrum_profile": [ { "index": 0, "best_text_overlap": 0.7416685704809811 }, { "index": 1, "best_text_overlap": 0.6591035296451755 }, { "index": 2, "best_text_overlap": 0.6730514886891261 }, { "index": 3, "best_text_overlap": 0.5813764120097434 }, { "index": 4, "best_text_overlap": 0.5492379792963318 }, { "index": 5, "best_text_overlap": 0.6616657410048805 }, { "index": 6, "best_text_overlap": 0.5607722465245946 }, { "index": 7, "best_text_overlap": 0.3913414443532297 }, { "index": 8, "best_text_overlap": 0.3431217610653001 }, { "index": 9, "best_text_overlap": 0.39446274885223964 }, { "index": 10, "best_text_overlap": 0.2624025040480312 }, { "index": 11, "best_text_overlap": 0.31050951747572164 }, { "index": 12, "best_text_overlap": 0.37391245736141376 }, { "index": 13, "best_text_overlap": 0.2550412331810302 }, { "index": 14, "best_text_overlap": 0.29254528024572746 }, { "index": 15, "best_text_overlap": 0.3608253612065695 } ] } ], "reading": "The narrow modality is the one to upgrade. A shared count far below both effective ranks means each side is rich but they are rich about different things." }