| { | |
| "analysis": "A3 basin-approach dynamics", | |
| "date": "2026-08-08", | |
| "plan": "history/plans/2026-08-08_analysis_phase.md A3", | |
| "method": { | |
| "data": "VAL scalars val/cos_to_target and val/erank from hub tensorboard event files (multi-file runs merged by step, later file wins on duplicates)", | |
| "model": "y(t) = y_inf - (y_inf - y0) * exp(-(t - t_first)/tau), scipy curve_fit; fit_full = all points (first val at step 1000); fit_late_ge2000 = steps >= 2000 (past warmup)", | |
| "model_free": "t50/t90/t95 = first step crossing y0 + frac*(final5mean - y0), linear interp; robust to the fit instability below", | |
| "note": "single exponential systematically under-models every curve: observed t90/t50 = 5.27-7.66 across all 8 trunks vs 3.32 for a pure exponential. The approach is two-timescale (fast half-depth lock by ~2-3.4k steps, heavy consolidation tail). Late-phase fits reach R2 >= .95 for 11/16 curves; a2_dense-s0 is unfittable (R2 .5452 full / .4374 late) despite a smooth monotone curve - model misfit, not noise. Cross-run comparisons therefore use the model-free crossings." | |
| }, | |
| "runs": { | |
| "alephlm0-a1_anchored-s0": { | |
| "arm": "a1_anchored", | |
| "seed": "s0", | |
| "source_repo": "AbstractPhil/alephlm-0", | |
| "event_files": [ | |
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| "gauges": { | |
| "val/cos_to_target": { | |
| "n_points": 62, | |
| "step_range": [ | |
| 1000.0, | |
| 62000.0 | |
| ], | |
| "y_at_step1000": 0.6886, | |
| "final_value": 0.8393, | |
| "fit_full": { | |
| "y_inf": 0.8353, | |
| "y0": 0.7164, | |
| "tau_steps": 5998.0, | |
| "r2": 0.9404, | |
| "t_offset": 1000.0, | |
| "n_points": 62 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 0.8378, | |
| "y0": 0.7562, | |
| "tau_steps": 9037.0, | |
| "r2": 0.9672, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 3235.0, | |
| "t90_steps": 18940.0, | |
| "t95_steps": 27690.0, | |
| "t90_over_t50": 5.853 | |
| }, | |
| "fit_quality": "late_ok" | |
| }, | |
| "val/erank": { | |
| "n_points": 62, | |
| "step_range": [ | |
| 1000.0, | |
| 62000.0 | |
| ], | |
| "y_at_step1000": 52.78, | |
| "final_value": 98.59, | |
| "fit_full": { | |
| "y_inf": 97.29, | |
| "y0": 61.8, | |
| "tau_steps": 6249.0, | |
| "r2": 0.9305, | |
| "t_offset": 1000.0, | |
| "n_points": 62 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 98.18, | |
| "y0": 73.88, | |
| "tau_steps": 9795.0, | |
| "r2": 0.959, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 3245.0, | |
| "t90_steps": 19620.0, | |
| "t95_steps": 31030.0, | |
| "t90_over_t50": 6.045 | |
| }, | |
| "fit_quality": "late_ok" | |
| } | |
| } | |
| }, | |
| "alephlm0-a1_anchored-s1": { | |
| "arm": "a1_anchored", | |
| "seed": "s1", | |
| "source_repo": "AbstractPhil/alephlm-0", | |
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| "n_points": 62, | |
| "step_range": [ | |
| 1000.0, | |
| 62000.0 | |
| ], | |
| "y_at_step1000": 0.6843, | |
| "final_value": 0.8391, | |
| "fit_full": { | |
| "y_inf": 0.8351, | |
| "y0": 0.7121, | |
| "tau_steps": 5498.0, | |
| "r2": 0.9418, | |
| "t_offset": 1000.0, | |
| "n_points": 62 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 0.8373, | |
| "y0": 0.7551, | |
| "tau_steps": 8341.0, | |
| "r2": 0.9704, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 2678.0, | |
| "t90_steps": 17870.0, | |
| "t95_steps": 25240.0, | |
| "t90_over_t50": 6.673 | |
| }, | |
| "fit_quality": "late_ok" | |
| }, | |
| "val/erank": { | |
| "n_points": 62, | |
| "step_range": [ | |
| 1000.0, | |
| 62000.0 | |
| ], | |
| "y_at_step1000": 54.23, | |
| "final_value": 98.57, | |
| "fit_full": { | |
| "y_inf": 97.34, | |
| "y0": 62.28, | |
| "tau_steps": 6162.0, | |
| "r2": 0.9446, | |
| "t_offset": 1000.0, | |
| "n_points": 62 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 97.98, | |
| "y0": 73.46, | |
| "tau_steps": 8896.0, | |
| "r2": 0.9688, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 2794.0, | |
| "t90_steps": 18580.0, | |
| "t95_steps": 26770.0, | |
| "t90_over_t50": 6.65 | |
| }, | |
| "fit_quality": "late_ok" | |
| } | |
| } | |
| }, | |
| "alephlm0-a2_dense-s0": { | |
| "arm": "a2_dense", | |
| "seed": "s0", | |
| "source_repo": "AbstractPhil/alephlm-0", | |
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| 1000.0, | |
| 62000.0 | |
| ], | |
| "y_at_step1000": 0.6535, | |
| "final_value": 0.8418, | |
| "fit_full": { | |
| "y_inf": 0.8405, | |
| "y0": 0.709, | |
| "tau_steps": 7833.0, | |
| "r2": 0.5452, | |
| "t_offset": 1000.0, | |
| "n_points": 62 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 0.8431, | |
| "y0": 0.7504, | |
| "tau_steps": 11070.0, | |
| "r2": 0.4374, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 2155.0, | |
| "t90_steps": 14790.0, | |
| "t95_steps": 23660.0, | |
| "t90_over_t50": 6.861 | |
| }, | |
| "fit_quality": "poor_single_exp" | |
| }, | |
| "val/erank": { | |
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| "step_range": [ | |
| 1000.0, | |
| 62000.0 | |
| ], | |
| "y_at_step1000": 50.12, | |
| "final_value": 99.18, | |
| "fit_full": { | |
| "y_inf": 98.93, | |
| "y0": 62.38, | |
| "tau_steps": 9340.0, | |
| "r2": 0.6222, | |
| "t_offset": 1000.0, | |
| "n_points": 62 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 99.6, | |
| "y0": 71.23, | |
| "tau_steps": 11960.0, | |
| "r2": 0.5415, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 2608.0, | |
| "t90_steps": 18190.0, | |
| "t95_steps": 29510.0, | |
| "t90_over_t50": 6.973 | |
| }, | |
| "fit_quality": "poor_single_exp" | |
| } | |
| } | |
| }, | |
| "alephlm0-a2_dense-s1": { | |
| "arm": "a2_dense", | |
| "seed": "s1", | |
| "source_repo": "AbstractPhil/alephlm-0", | |
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| "y_at_step1000": 0.6574, | |
| "final_value": 0.842, | |
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| "tau_steps": 4173.0, | |
| "r2": 0.9137, | |
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| "r2": 0.9464, | |
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| "n_points": 61 | |
| }, | |
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| "t90_steps": 14770.0, | |
| "t95_steps": 22750.0, | |
| "t90_over_t50": 6.002 | |
| }, | |
| "fit_quality": "poor_single_exp" | |
| }, | |
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| "y_at_step1000": 50.2, | |
| "final_value": 99.18, | |
| "fit_full": { | |
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| "y0": 60.31, | |
| "tau_steps": 6057.0, | |
| "r2": 0.9126, | |
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| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 98.83, | |
| "y0": 73.87, | |
| "tau_steps": 10030.0, | |
| "r2": 0.9397, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
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| "t90_steps": 16990.0, | |
| "t95_steps": 27450.0, | |
| "t90_over_t50": 6.131 | |
| }, | |
| "fit_quality": "poor_single_exp" | |
| } | |
| } | |
| }, | |
| "alephlm0-a3_random-s0": { | |
| "arm": "a3_random_frozen", | |
| "seed": "s0", | |
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| "y_at_step1000": 0.6842, | |
| "final_value": 0.8392, | |
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| "y_inf": 0.8349, | |
| "y0": 0.7101, | |
| "tau_steps": 4872.0, | |
| "r2": 0.9422, | |
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| }, | |
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| "y0": 0.7577, | |
| "tau_steps": 7833.0, | |
| "r2": 0.9728, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
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| "t90_steps": 17720.0, | |
| "t95_steps": 27410.0, | |
| "t90_over_t50": 6.469 | |
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| }, | |
| "val/erank": { | |
| "n_points": 62, | |
| "step_range": [ | |
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| 62000.0 | |
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| "y_at_step1000": 53.24, | |
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| "fit_late_ge2000": { | |
| "y_inf": 98.22, | |
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| "tau_steps": 9206.0, | |
| "r2": 0.9663, | |
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| }, | |
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| "t90_steps": 19220.0, | |
| "t95_steps": 29840.0, | |
| "t90_over_t50": 6.817 | |
| }, | |
| "fit_quality": "late_ok" | |
| } | |
| } | |
| }, | |
| "alephlm0-a3_random-s1": { | |
| "arm": "a3_random_frozen", | |
| "seed": "s1", | |
| "source_repo": "AbstractPhil/alephlm-0", | |
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| "y_at_step1000": 0.6877, | |
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| "tau_steps": 5448.0, | |
| "r2": 0.9518, | |
| "t_offset": 1000.0, | |
| "n_points": 62 | |
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| "fit_late_ge2000": { | |
| "y_inf": 0.8374, | |
| "y0": 0.7518, | |
| "tau_steps": 7860.0, | |
| "r2": 0.9681, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 3374.0, | |
| "t90_steps": 18810.0, | |
| "t95_steps": 26600.0, | |
| "t90_over_t50": 5.575 | |
| }, | |
| "fit_quality": "late_ok" | |
| }, | |
| "val/erank": { | |
| "n_points": 62, | |
| "step_range": [ | |
| 1000.0, | |
| 62000.0 | |
| ], | |
| "y_at_step1000": 53.47, | |
| "final_value": 98.56, | |
| "fit_full": { | |
| "y_inf": 97.09, | |
| "y0": 61.25, | |
| "tau_steps": 5961.0, | |
| "r2": 0.9415, | |
| "t_offset": 1000.0, | |
| "n_points": 62 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 97.85, | |
| "y0": 73.11, | |
| "tau_steps": 8970.0, | |
| "r2": 0.9621, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 3261.0, | |
| "t90_steps": 19760.0, | |
| "t95_steps": 27970.0, | |
| "t90_over_t50": 6.061 | |
| }, | |
| "fit_quality": "late_ok" | |
| } | |
| } | |
| }, | |
| "captionbert-8192-v2": { | |
| "arm": "captionbert_v2_trunk", | |
| "seed": "-", | |
| "source_repo": "AbstractPhil/captionbert-8192-v2", | |
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| "gauges": { | |
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| 1000.0, | |
| 52000.0 | |
| ], | |
| "y_at_step1000": 0.6631, | |
| "final_value": 0.841, | |
| "fit_full": { | |
| "y_inf": 0.836, | |
| "y0": 0.6871, | |
| "tau_steps": 3412.0, | |
| "r2": 0.9402, | |
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| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 0.839, | |
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| "tau_steps": 6332.0, | |
| "r2": 0.9756, | |
| "t_offset": 2000.0, | |
| "n_points": 51 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 2267.0, | |
| "t90_steps": 11950.0, | |
| "t95_steps": 20900.0, | |
| "t90_over_t50": 5.273 | |
| }, | |
| "fit_quality": "late_ok" | |
| }, | |
| "val/erank": { | |
| "n_points": 52, | |
| "step_range": [ | |
| 1000.0, | |
| 52000.0 | |
| ], | |
| "y_at_step1000": 51.52, | |
| "final_value": 102.9, | |
| "fit_full": { | |
| "y_inf": 101.7, | |
| "y0": 59.51, | |
| "tau_steps": 4628.0, | |
| "r2": 0.9483, | |
| "t_offset": 1000.0, | |
| "n_points": 52 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 102.5, | |
| "y0": 75.28, | |
| "tau_steps": 7132.0, | |
| "r2": 0.9762, | |
| "t_offset": 2000.0, | |
| "n_points": 51 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 2627.0, | |
| "t90_steps": 15870.0, | |
| "t95_steps": 19690.0, | |
| "t90_over_t50": 6.042 | |
| }, | |
| "fit_quality": "late_ok" | |
| } | |
| } | |
| }, | |
| "captionbert-8192-v2-B": { | |
| "arm": "captionbert_v2B_trunk", | |
| "seed": "-", | |
| "source_repo": "AbstractPhil/captionbert-8192-v2-B", | |
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| "y_at_step1000": 0.6626, | |
| "final_value": 0.8421, | |
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| "r2": 0.9023, | |
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| "n_points": 62 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 0.8405, | |
| "y0": 0.7655, | |
| "tau_steps": 7982.0, | |
| "r2": 0.9561, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 1986.0, | |
| "t90_steps": 13890.0, | |
| "t95_steps": 20930.0, | |
| "t90_over_t50": 6.996 | |
| }, | |
| "fit_quality": "late_ok" | |
| }, | |
| "val/erank": { | |
| "n_points": 62, | |
| "step_range": [ | |
| 1000.0, | |
| 62000.0 | |
| ], | |
| "y_at_step1000": 50.99, | |
| "final_value": 103.1, | |
| "fit_full": { | |
| "y_inf": 101.6, | |
| "y0": 60.67, | |
| "tau_steps": 4285.0, | |
| "r2": 0.9149, | |
| "t_offset": 1000.0, | |
| "n_points": 62 | |
| }, | |
| "fit_late_ge2000": { | |
| "y_inf": 102.6, | |
| "y0": 79.3, | |
| "tau_steps": 8482.0, | |
| "r2": 0.9653, | |
| "t_offset": 2000.0, | |
| "n_points": 61 | |
| }, | |
| "crossings_model_free": { | |
| "t50_steps": 2234.0, | |
| "t90_steps": 17120.0, | |
| "t95_steps": 24550.0, | |
| "t90_over_t50": 7.666 | |
| }, | |
| "fit_quality": "late_ok" | |
| } | |
| } | |
| } | |
| }, | |
| "verdict": { | |
| "same_attractor": "yes - endpoint band cos .8390-.8420, erank 98.56-99.21 (E1 six) with captionbert trunks landing the high-erank corner 102.9/103.2", | |
| "same_path_shape": "yes - all 8 trunks share the two-timescale approach (t90/t50 5.27-7.66, all far above the 3.32 of a single exponential); no trunk takes a qualitatively different route", | |
| "anchored_vs_dense": "REVERSED vs small-bed expectation: dense reaches 90% basin depth FASTER. t90(cos) a2_dense 14785/14770 (seeds s0/s1) vs a1_anchored 18936/17870 and a3_random 17717/18811. Same ordering on erank (a2 18186/16990 vs a1 19616/18580, a3 19224/19763). The small-bed anchored sample-efficiency advantage (.9055 vs .7790 @2ep) is a CAPABILITY-gauge fact; on the TRAINING gauge at full scale, routing costs ~3-4k steps of basin depth. Consistent with A2: routed function accrues LATE - the router is still organizing while dense is already settling", | |
| "learned_vs_frozen_anchors": "indistinguishable paths: a1 seed-mean t90(cos) 18403 vs a3 18264 (0.8% apart); anchor learnability does not change basin approach", | |
| "seed_consistency": "high, arm-dominated: t90(cos) seed spread a2 0.1%, a1 5.8%, a3 6.0%; every arm's two seeds are closer to each other than to any other arm", | |
| "captionbert_trunks": "fastest approach of all 8 (t90 cos 11952/13894) and higher erank asymptote (final 102.9/103.2) - the 5-teacher consensus bed both accelerates the approach and lands a wider basin corner", | |
| "tau_table_late_fit_cos": { | |
| "a1_anchored-s0": 9037, | |
| "a1_anchored-s1": 8341, | |
| "a2_dense-s0": "unreliable (R2 .44)", | |
| "a2_dense-s1": 8243, | |
| "a3_random-s0": 7833, | |
| "a3_random-s1": 7860, | |
| "captionbert-v2": 6332, | |
| "captionbert-v2-B": 7982 | |
| }, | |
| "tau_table_late_fit_erank": { | |
| "a1_anchored-s0": 9795, | |
| "a1_anchored-s1": 8896, | |
| "a2_dense-s0": "unreliable (R2 .54)", | |
| "a2_dense-s1": 10030, | |
| "a3_random-s0": 9206, | |
| "a3_random-s1": 8970, | |
| "captionbert-v2": 7132, | |
| "captionbert-v2-B": 8482 | |
| } | |
| } | |
| } |