{ "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": "mean-phrase-0.716", "size": 256, "correlation": 0.7157944505313559, "visual_effective_rank": 39.69132496762981, "text_effective_rank": 47.98422953390366, "shared_directions_cos_gt_0.7": 16, "shuffled_null": 1.0, "shared_above_null": 15.0, "principal_cosines_top8": [ 0.987, 0.978, 0.96, 0.941, 0.934, 0.922, 0.899, 0.89 ], "spectrum_profile": [ { "index": 0, "best_text_overlap": 0.8406807387214822 }, { "index": 1, "best_text_overlap": 0.6748753041856854 }, { "index": 2, "best_text_overlap": 0.7174150319587717 }, { "index": 3, "best_text_overlap": 0.4742164704027202 }, { "index": 4, "best_text_overlap": 0.7105187496542062 }, { "index": 5, "best_text_overlap": 0.5435228035336661 }, { "index": 6, "best_text_overlap": 0.5173316630294161 }, { "index": 7, "best_text_overlap": 0.3720956303455928 }, { "index": 8, "best_text_overlap": 0.4031225977235423 }, { "index": 9, "best_text_overlap": 0.5909531802492844 }, { "index": 10, "best_text_overlap": 0.373881786434362 }, { "index": 11, "best_text_overlap": 0.2816693575587397 }, { "index": 12, "best_text_overlap": 0.21822240451244762 }, { "index": 13, "best_text_overlap": 0.3929212823566225 }, { "index": 14, "best_text_overlap": 0.4024276537497661 }, { "index": 15, "best_text_overlap": 0.2659834432053085 } ] }, { "label": "structured-wv64", "size": 256, "correlation": 0.7246401498403082, "visual_effective_rank": 39.69132496762981, "text_effective_rank": 39.044391234462196, "shared_directions_cos_gt_0.7": 15, "shuffled_null": 1.0, "shared_above_null": 14.0, "principal_cosines_top8": [ 0.991, 0.979, 0.957, 0.94, 0.924, 0.913, 0.884, 0.877 ], "spectrum_profile": [ { "index": 0, "best_text_overlap": 0.8699128451599867 }, { "index": 1, "best_text_overlap": 0.5919394988285451 }, { "index": 2, "best_text_overlap": 0.664910963201995 }, { "index": 3, "best_text_overlap": 0.5718467670534315 }, { "index": 4, "best_text_overlap": 0.6155246177540001 }, { "index": 5, "best_text_overlap": 0.520789559417958 }, { "index": 6, "best_text_overlap": 0.5726871443670466 }, { "index": 7, "best_text_overlap": 0.359948345526124 }, { "index": 8, "best_text_overlap": 0.3629235665536516 }, { "index": 9, "best_text_overlap": 0.3191775375612409 }, { "index": 10, "best_text_overlap": 0.23839966477101518 }, { "index": 11, "best_text_overlap": 0.3902646088886306 }, { "index": 12, "best_text_overlap": 0.2525566443339542 }, { "index": 13, "best_text_overlap": 0.4143287992176083 }, { "index": 14, "best_text_overlap": 0.35641603055069626 }, { "index": 15, "best_text_overlap": 0.1905065808689813 } ] }, { "label": "structured-wv128", "size": 256, "correlation": 0.7252267991153296, "visual_effective_rank": 39.69132496762981, "text_effective_rank": 48.61469812212951, "shared_directions_cos_gt_0.7": 16, "shuffled_null": 1.0, "shared_above_null": 15.0, "principal_cosines_top8": [ 0.987, 0.978, 0.956, 0.936, 0.933, 0.919, 0.908, 0.882 ], "spectrum_profile": [ { "index": 0, "best_text_overlap": 0.8836896656200444 }, { "index": 1, "best_text_overlap": 0.6662527722108562 }, { "index": 2, "best_text_overlap": 0.6895209294138209 }, { "index": 3, "best_text_overlap": 0.5068523620638157 }, { "index": 4, "best_text_overlap": 0.6826302737796026 }, { "index": 5, "best_text_overlap": 0.5697249361142291 }, { "index": 6, "best_text_overlap": 0.5326573257977141 }, { "index": 7, "best_text_overlap": 0.37933461331439877 }, { "index": 8, "best_text_overlap": 0.3322445785255883 }, { "index": 9, "best_text_overlap": 0.5083883525562566 }, { "index": 10, "best_text_overlap": 0.3237366787528124 }, { "index": 11, "best_text_overlap": 0.38425794698324 }, { "index": 12, "best_text_overlap": 0.1960410706899702 }, { "index": 13, "best_text_overlap": 0.4644524929154713 }, { "index": 14, "best_text_overlap": 0.2559185730403851 }, { "index": 15, "best_text_overlap": 0.2515038306148867 } ] } ], "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." }