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"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": {
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"seed": "s0",
"source_repo": "AbstractPhil/alephlm-0",
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"y0": 0.7164,
"tau_steps": 5998.0,
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"t_offset": 1000.0,
"n_points": 62
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"tau_steps": 9037.0,
"r2": 0.9672,
"t_offset": 2000.0,
"n_points": 61
},
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"t90_over_t50": 5.853
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"fit_late_ge2000": {
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"t90_over_t50": 6.045
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}
}
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"captionbert-8192-v2-B": {
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"final_value": 103.1,
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},
"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
}
}
} |