Track legacy operator-study row data; extend generated tables

Pulls the training-set-size series, snapshot-location sweep, stress
grid, scalar-gain comparison, oracle diagnostic, and derivative-probe
rows from the experiment machine, and adds three generated fragments
(train size, snapshot location, stress grid) used by the appendix.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

2 files changed, 626 insertions, 0 deletions

diff --git a/outputs/early_directional_predictors_T50_width64_N256/early_kernel_predictors.csv b/outputs/early_directional_predictors_T50_width64_N256/early_kernel_predictors.csv
new file mode 100644
index 0000000..729db1e
--- /dev/null
+++ b/outputs/early_directional_predictors_T50_width64_N256/early_kernel_predictors.csv
@@ -0,0 +1,25 @@
+init_seed,feedback_seed,target_steps,early_steps,empirical_bp_loss,empirical_fa_loss,empirical_gap,fixed_bp_loss,fixed_fa_loss,fixed_gap,directional_bp_loss,directional_fa_loss,directional_gap,kfa_fro_drift,kbp_fro_drift,fa_bp_overlap_0,fa_bp_overlap_s,fa_bp_overlap_slope,fa_directional_gain_s,bp_directional_gain_s,fa_directional_drift_s,bp_directional_drift_s

+10000,100000,50,1,2.5704680254566754,2.6773099946553027,0.10684196919862732,2.5486201412594696,2.674726176946598,0.12610603568712841,3.8658371527254456,3.385159624196853,-0.48067752852859247,0.0057212510189920025,0.006585346078790702,0.9806851555329678,0.9808363020643607,0.00015114653139292056,1984.410700810208,2733.7296720154964,-0.034063049097849143,-0.05215199954950663

+10000,100000,50,2,2.5704680254566754,2.6773099946553027,0.10684196919862732,2.5486201412594696,2.674726176946598,0.12610603568712841,3.8658371527254456,3.360130877294943,-0.5057062754305024,0.010124591256342299,0.008699609326803939,0.9806851555329678,0.9808992673810625,0.0001070559240473612,1915.9827975592555,2592.6428733031407,-0.06737119453158721,-0.10107009171436698

+10000,100000,50,5,2.5704680254566754,2.6773099946553027,0.10684196919862732,2.5486201412594696,2.674726176946598,0.12610603568712841,3.8658371527254456,3.2794281627249147,-0.5864089900005309,0.01727182382675466,0.018494600675005555,0.9806851555329678,0.9810806118710773,7.909126762191132e-05,1721.0739716728158,2208.8212378124035,-0.16224552518491306,-0.23415002769110577

+10000,100001,50,1,2.5704680254566754,2.6761942818704343,0.10572625641375888,2.5486201412594696,2.686715285479813,0.13809514422034352,3.8658371527254456,3.286064270733585,-0.5797728819918606,0.010256676589880142,0.006585346078790702,0.9793427016451279,0.9795685241560856,0.00022582251095770722,2048.4181412163634,2733.7296720154964,-0.03279969120450552,-0.05215199954950663

+10000,100001,50,2,2.5704680254566754,2.6761942818704343,0.10572625641375888,2.5486201412594696,2.686715285479813,0.13809514422034352,3.8658371527254456,3.2869459097168434,-0.5788912430086022,0.012153573967221653,0.008699609326803939,0.9793427016451279,0.9797325684797786,0.0001949334173253492,1978.896136276908,2592.6428733031407,-0.06562585266663484,-0.10107009171436698

+10000,100001,50,5,2.5704680254566754,2.6761942818704343,0.10572625641375888,2.5486201412594696,2.686715285479813,0.13809514422034352,3.8658371527254456,3.254444649138838,-0.6113925035866075,0.020756394173052927,0.018494600675005555,0.9793427016451279,0.9801603686588448,0.00016353340274337657,1775.6058888550517,2208.8212378124035,-0.16161328127082417,-0.23415002769110577

+10000,100002,50,1,2.5704680254566754,2.665831997258412,0.09536397180173672,2.5486201412594696,2.6570973933324966,0.10847725207302705,3.8658371527254456,3.8658371527254456,0.0,0.0059185583886561645,0.006585346078790702,0.9805923675370241,0.9806074823235712,1.5114786547143488e-05,2215.901012008652,2733.7296720154964,-0.042220850924819996,-0.05215199954950663

+10000,100002,50,2,2.5704680254566754,2.665831997258412,0.09536397180173672,2.5486201412594696,2.6570973933324966,0.10847725207302705,3.8658371527254456,3.8658371527254456,0.0,0.008730339488493308,0.008699609326803939,0.9805923675370241,0.9806190733718962,1.335291743609357e-05,2123.8438979838074,2592.6428733031407,-0.08201070789912063,-0.10107009171436698

+10000,100002,50,5,2.5704680254566754,2.665831997258412,0.09536397180173672,2.5486201412594696,2.6570973933324966,0.10847725207302705,3.8658371527254456,3.7228115256666987,-0.14302562705874688,0.019503100852995645,0.018494600675005555,0.9805923675370241,0.98059528222392,5.829373791899072e-07,1861.1186010308454,2208.8212378124035,-0.19556849319388608,-0.23415002769110577

+10000,100003,50,1,2.5704680254566754,2.665868768518039,0.0954007430613637,2.5486201412594696,2.6694883149629254,0.12086817370345582,3.8658371527254456,3.8658371527254456,0.0,0.007221673320200367,0.006585346078790702,0.9773423620210906,0.9774137712707848,7.14092496941765e-05,2313.194200327081,2733.7296720154964,-0.042705235300988985,-0.05215199954950663

+10000,100003,50,2,2.5704680254566754,2.665868768518039,0.0954007430613637,2.5486201412594696,2.6694883149629254,0.12086817370345582,3.8658371527254456,3.8658371527254456,0.0,0.010905745405402506,0.008699609326803939,0.9773423620210906,0.9774462865458688,5.1962262389126934e-05,2213.9016326765113,2592.6428733031407,-0.0837965778142862,-0.10107009171436698

+10000,100003,50,5,2.5704680254566754,2.665868768518039,0.0954007430613637,2.5486201412594696,2.6694883149629254,0.12086817370345582,3.8658371527254456,3.7750787437205657,-0.09075840900487986,0.01593493947748635,0.018494600675005555,0.9773423620210906,0.9774743013922653,2.6387874234945487e-05,1935.6582715355592,2208.8212378124035,-0.19894510831588735,-0.23415002769110577

+10001,101000,50,1,2.570334573821084,2.697143412487514,0.1268088386664301,2.5510676448481027,2.6946737310587165,0.14360608621061388,4.066101667089287,4.066101667089287,0.0,0.006484177311394147,0.006384612514262938,0.976951289661455,0.9770480161704411,9.672650898617796e-05,2558.0484494675547,3642.853516902313,-0.04312301540828878,-0.06369219976030034

+10001,101000,50,2,2.570334573821084,2.697143412487514,0.1268088386664301,2.5510676448481027,2.6946737310587165,0.14360608621061388,4.066101667089287,4.066101667089287,0.0,0.009943291504341702,0.009896827277091172,0.976951289661455,0.9770564468965752,5.2578617560139485e-05,2447.8190839515664,3410.877842279085,-0.08435598850164468,-0.12331596245287509

+10001,101000,50,5,2.570334573821084,2.697143412487514,0.1268088386664301,2.5510676448481027,2.6946737310587165,0.14360608621061388,4.066101667089287,3.990204808513375,-0.07589685857591189,0.016559323111176562,0.017483644584136898,0.976951289661455,0.977089676811308,2.7677429970607292e-05,2137.5969318534508,2782.9928969587368,-0.20039930953998655,-0.284698672251328

+10001,101001,50,1,2.570334573821084,2.678819805545933,0.10848523172484903,2.5510676448481027,2.6851718899206034,0.13410424507250074,4.066101667089287,4.066101667089287,0.0,0.007918613299755812,0.006384612514262938,0.9828127818056384,0.982929851452701,0.00011706964706259537,2764.8865641420475,3642.853516902313,-0.04339146607993533,-0.06369219976030034

+10001,101001,50,2,2.570334573821084,2.678819805545933,0.10848523172484903,2.5510676448481027,2.6851718899206034,0.13410424507250074,4.066101667089287,4.066101667089287,0.0,0.010209082104582094,0.009896827277091172,0.9828127818056384,0.9829953623325879,9.129026347476366e-05,2640.0805951102316,3410.877842279085,-0.08657242569266566,-0.12331596245287509

+10001,101001,50,5,2.570334573821084,2.678819805545933,0.10848523172484903,2.5510676448481027,2.6851718899206034,0.13410424507250074,4.066101667089287,4.066101667089287,0.0,0.01545339741556104,0.017483644584136898,0.9828127818056384,0.9831641204628632,7.026773144496179e-05,2287.162854386855,2782.9928969587368,-0.20867657525387207,-0.284698672251328

+10001,101002,50,1,2.570334573821084,2.684839622758295,0.11450504893721103,2.5510676448481027,2.6900721075509733,0.1390044627028706,4.066101667089287,4.066101667089287,0.0,0.004696247795133425,0.006384612514262938,0.9828061326343368,0.9828344264937947,2.82938594579063e-05,2817.025852575887,3642.853516902313,-0.047765096434622456,-0.06369219976030034

+10001,101002,50,2,2.570334573821084,2.684839622758295,0.11450504893721103,2.5510676448481027,2.6900721075509733,0.1390044627028706,4.066101667089287,4.066101667089287,0.0,0.011615547485972856,0.009896827277091172,0.9828061326343368,0.9828370787349955,1.5473050329339877e-05,2681.6012528700435,3410.877842279085,-0.09354246497504826,-0.12331596245287509

+10001,101002,50,5,2.570334573821084,2.684839622758295,0.11450504893721103,2.5510676448481027,2.6900721075509733,0.1390044627028706,4.066101667089287,4.066101667089287,0.0,0.016755592275579465,0.017483644584136898,0.9828061326343368,0.98286698124195,1.2169721522647947e-05,2302.9660340708997,2782.9928969587368,-0.22153194392497408,-0.284698672251328

+10001,101003,50,1,2.570334573821084,2.681052714285519,0.11071814046443507,2.5510676448481027,2.6833566536237186,0.1322890087756159,4.066101667089287,4.066101667089287,0.0,0.004897653710957696,0.006384612514262938,0.9792574873433338,0.9793685321860623,0.00011104484272850268,2642.014618440444,3642.853516902313,-0.04286501182071257,-0.06369219976030034

+10001,101003,50,2,2.570334573821084,2.681052714285519,0.11071814046443507,2.5510676448481027,2.6833566536237186,0.1322890087756159,4.066101667089287,4.066101667089287,0.0,0.00887689134694127,0.009896827277091172,0.9792574873433338,0.9794836801266967,0.00011309639168144425,2527.264099032341,3410.877842279085,-0.08443621898612716,-0.12331596245287509

+10001,101003,50,5,2.570334573821084,2.681052714285519,0.11071814046443507,2.5510676448481027,2.6833566536237186,0.1322890087756159,4.066101667089287,4.003389756543286,-0.06271191054600056,0.015809691563003,0.017483644584136898,0.9792574873433338,0.9798000976433185,0.00010852205999694054,2205.1230693187536,2782.9928969587368,-0.20113975594421707,-0.284698672251328

diff --git a/outputs/early_directional_predictors_T50_width64_N256/summary.json b/outputs/early_directional_predictors_T50_width64_N256/summary.json
new file mode 100644
index 0000000..dd7a75e
--- /dev/null
+++ b/outputs/early_directional_predictors_T50_width64_N256/summary.json
@@ -0,0 +1,601 @@
+{
+  "config": {
+    "input_dim": 16,
+    "output_dim": 4,
+    "width": 64,
+    "train_samples": 256,
+    "test_samples": 512,
+    "target_steps": 50,
+    "early_steps": [
+      1,
+      2,
+      5
+    ],
+    "lr": 0.001,
+    "init_seeds": 2,
+    "feedback_seeds": 4,
+    "data_seed": 123,
+    "feedback_scale": "relu",
+    "device": "cpu",
+    "torch_threads": 8,
+    "outdir": "outputs/early_directional_predictors_T50_width64_N256"
+  },
+  "rows": [
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100000,
+      "target_steps": 50,
+      "early_steps": 1,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.6773099946553027,
+      "empirical_gap": 0.10684196919862732,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.674726176946598,
+      "fixed_gap": 0.12610603568712841,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.385159624196853,
+      "directional_gap": -0.48067752852859247,
+      "kfa_fro_drift": 0.0057212510189920025,
+      "kbp_fro_drift": 0.006585346078790702,
+      "fa_bp_overlap_0": 0.9806851555329678,
+      "fa_bp_overlap_s": 0.9808363020643607,
+      "fa_bp_overlap_slope": 0.00015114653139292056,
+      "fa_directional_gain_s": 1984.410700810208,
+      "bp_directional_gain_s": 2733.7296720154964,
+      "fa_directional_drift_s": -0.034063049097849143,
+      "bp_directional_drift_s": -0.05215199954950663
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100000,
+      "target_steps": 50,
+      "early_steps": 2,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.6773099946553027,
+      "empirical_gap": 0.10684196919862732,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.674726176946598,
+      "fixed_gap": 0.12610603568712841,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.360130877294943,
+      "directional_gap": -0.5057062754305024,
+      "kfa_fro_drift": 0.010124591256342299,
+      "kbp_fro_drift": 0.008699609326803939,
+      "fa_bp_overlap_0": 0.9806851555329678,
+      "fa_bp_overlap_s": 0.9808992673810625,
+      "fa_bp_overlap_slope": 0.0001070559240473612,
+      "fa_directional_gain_s": 1915.9827975592555,
+      "bp_directional_gain_s": 2592.6428733031407,
+      "fa_directional_drift_s": -0.06737119453158721,
+      "bp_directional_drift_s": -0.10107009171436698
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100000,
+      "target_steps": 50,
+      "early_steps": 5,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.6773099946553027,
+      "empirical_gap": 0.10684196919862732,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.674726176946598,
+      "fixed_gap": 0.12610603568712841,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.2794281627249147,
+      "directional_gap": -0.5864089900005309,
+      "kfa_fro_drift": 0.01727182382675466,
+      "kbp_fro_drift": 0.018494600675005555,
+      "fa_bp_overlap_0": 0.9806851555329678,
+      "fa_bp_overlap_s": 0.9810806118710773,
+      "fa_bp_overlap_slope": 7.909126762191132e-05,
+      "fa_directional_gain_s": 1721.0739716728158,
+      "bp_directional_gain_s": 2208.8212378124035,
+      "fa_directional_drift_s": -0.16224552518491306,
+      "bp_directional_drift_s": -0.23415002769110577
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100001,
+      "target_steps": 50,
+      "early_steps": 1,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.6761942818704343,
+      "empirical_gap": 0.10572625641375888,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.686715285479813,
+      "fixed_gap": 0.13809514422034352,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.286064270733585,
+      "directional_gap": -0.5797728819918606,
+      "kfa_fro_drift": 0.010256676589880142,
+      "kbp_fro_drift": 0.006585346078790702,
+      "fa_bp_overlap_0": 0.9793427016451279,
+      "fa_bp_overlap_s": 0.9795685241560856,
+      "fa_bp_overlap_slope": 0.00022582251095770722,
+      "fa_directional_gain_s": 2048.4181412163634,
+      "bp_directional_gain_s": 2733.7296720154964,
+      "fa_directional_drift_s": -0.03279969120450552,
+      "bp_directional_drift_s": -0.05215199954950663
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100001,
+      "target_steps": 50,
+      "early_steps": 2,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.6761942818704343,
+      "empirical_gap": 0.10572625641375888,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.686715285479813,
+      "fixed_gap": 0.13809514422034352,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.2869459097168434,
+      "directional_gap": -0.5788912430086022,
+      "kfa_fro_drift": 0.012153573967221653,
+      "kbp_fro_drift": 0.008699609326803939,
+      "fa_bp_overlap_0": 0.9793427016451279,
+      "fa_bp_overlap_s": 0.9797325684797786,
+      "fa_bp_overlap_slope": 0.0001949334173253492,
+      "fa_directional_gain_s": 1978.896136276908,
+      "bp_directional_gain_s": 2592.6428733031407,
+      "fa_directional_drift_s": -0.06562585266663484,
+      "bp_directional_drift_s": -0.10107009171436698
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100001,
+      "target_steps": 50,
+      "early_steps": 5,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.6761942818704343,
+      "empirical_gap": 0.10572625641375888,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.686715285479813,
+      "fixed_gap": 0.13809514422034352,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.254444649138838,
+      "directional_gap": -0.6113925035866075,
+      "kfa_fro_drift": 0.020756394173052927,
+      "kbp_fro_drift": 0.018494600675005555,
+      "fa_bp_overlap_0": 0.9793427016451279,
+      "fa_bp_overlap_s": 0.9801603686588448,
+      "fa_bp_overlap_slope": 0.00016353340274337657,
+      "fa_directional_gain_s": 1775.6058888550517,
+      "bp_directional_gain_s": 2208.8212378124035,
+      "fa_directional_drift_s": -0.16161328127082417,
+      "bp_directional_drift_s": -0.23415002769110577
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100002,
+      "target_steps": 50,
+      "early_steps": 1,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.665831997258412,
+      "empirical_gap": 0.09536397180173672,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.6570973933324966,
+      "fixed_gap": 0.10847725207302705,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.8658371527254456,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.0059185583886561645,
+      "kbp_fro_drift": 0.006585346078790702,
+      "fa_bp_overlap_0": 0.9805923675370241,
+      "fa_bp_overlap_s": 0.9806074823235712,
+      "fa_bp_overlap_slope": 1.5114786547143488e-05,
+      "fa_directional_gain_s": 2215.901012008652,
+      "bp_directional_gain_s": 2733.7296720154964,
+      "fa_directional_drift_s": -0.042220850924819996,
+      "bp_directional_drift_s": -0.05215199954950663
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100002,
+      "target_steps": 50,
+      "early_steps": 2,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.665831997258412,
+      "empirical_gap": 0.09536397180173672,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.6570973933324966,
+      "fixed_gap": 0.10847725207302705,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.8658371527254456,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.008730339488493308,
+      "kbp_fro_drift": 0.008699609326803939,
+      "fa_bp_overlap_0": 0.9805923675370241,
+      "fa_bp_overlap_s": 0.9806190733718962,
+      "fa_bp_overlap_slope": 1.335291743609357e-05,
+      "fa_directional_gain_s": 2123.8438979838074,
+      "bp_directional_gain_s": 2592.6428733031407,
+      "fa_directional_drift_s": -0.08201070789912063,
+      "bp_directional_drift_s": -0.10107009171436698
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100002,
+      "target_steps": 50,
+      "early_steps": 5,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.665831997258412,
+      "empirical_gap": 0.09536397180173672,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.6570973933324966,
+      "fixed_gap": 0.10847725207302705,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.7228115256666987,
+      "directional_gap": -0.14302562705874688,
+      "kfa_fro_drift": 0.019503100852995645,
+      "kbp_fro_drift": 0.018494600675005555,
+      "fa_bp_overlap_0": 0.9805923675370241,
+      "fa_bp_overlap_s": 0.98059528222392,
+      "fa_bp_overlap_slope": 5.829373791899072e-07,
+      "fa_directional_gain_s": 1861.1186010308454,
+      "bp_directional_gain_s": 2208.8212378124035,
+      "fa_directional_drift_s": -0.19556849319388608,
+      "bp_directional_drift_s": -0.23415002769110577
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100003,
+      "target_steps": 50,
+      "early_steps": 1,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.665868768518039,
+      "empirical_gap": 0.0954007430613637,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.6694883149629254,
+      "fixed_gap": 0.12086817370345582,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.8658371527254456,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.007221673320200367,
+      "kbp_fro_drift": 0.006585346078790702,
+      "fa_bp_overlap_0": 0.9773423620210906,
+      "fa_bp_overlap_s": 0.9774137712707848,
+      "fa_bp_overlap_slope": 7.14092496941765e-05,
+      "fa_directional_gain_s": 2313.194200327081,
+      "bp_directional_gain_s": 2733.7296720154964,
+      "fa_directional_drift_s": -0.042705235300988985,
+      "bp_directional_drift_s": -0.05215199954950663
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100003,
+      "target_steps": 50,
+      "early_steps": 2,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.665868768518039,
+      "empirical_gap": 0.0954007430613637,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.6694883149629254,
+      "fixed_gap": 0.12086817370345582,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.8658371527254456,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.010905745405402506,
+      "kbp_fro_drift": 0.008699609326803939,
+      "fa_bp_overlap_0": 0.9773423620210906,
+      "fa_bp_overlap_s": 0.9774462865458688,
+      "fa_bp_overlap_slope": 5.1962262389126934e-05,
+      "fa_directional_gain_s": 2213.9016326765113,
+      "bp_directional_gain_s": 2592.6428733031407,
+      "fa_directional_drift_s": -0.0837965778142862,
+      "bp_directional_drift_s": -0.10107009171436698
+    },
+    {
+      "init_seed": 10000,
+      "feedback_seed": 100003,
+      "target_steps": 50,
+      "early_steps": 5,
+      "empirical_bp_loss": 2.5704680254566754,
+      "empirical_fa_loss": 2.665868768518039,
+      "empirical_gap": 0.0954007430613637,
+      "fixed_bp_loss": 2.5486201412594696,
+      "fixed_fa_loss": 2.6694883149629254,
+      "fixed_gap": 0.12086817370345582,
+      "directional_bp_loss": 3.8658371527254456,
+      "directional_fa_loss": 3.7750787437205657,
+      "directional_gap": -0.09075840900487986,
+      "kfa_fro_drift": 0.01593493947748635,
+      "kbp_fro_drift": 0.018494600675005555,
+      "fa_bp_overlap_0": 0.9773423620210906,
+      "fa_bp_overlap_s": 0.9774743013922653,
+      "fa_bp_overlap_slope": 2.6387874234945487e-05,
+      "fa_directional_gain_s": 1935.6582715355592,
+      "bp_directional_gain_s": 2208.8212378124035,
+      "fa_directional_drift_s": -0.19894510831588735,
+      "bp_directional_drift_s": -0.23415002769110577
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101000,
+      "target_steps": 50,
+      "early_steps": 1,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.697143412487514,
+      "empirical_gap": 0.1268088386664301,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6946737310587165,
+      "fixed_gap": 0.14360608621061388,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.006484177311394147,
+      "kbp_fro_drift": 0.006384612514262938,
+      "fa_bp_overlap_0": 0.976951289661455,
+      "fa_bp_overlap_s": 0.9770480161704411,
+      "fa_bp_overlap_slope": 9.672650898617796e-05,
+      "fa_directional_gain_s": 2558.0484494675547,
+      "bp_directional_gain_s": 3642.853516902313,
+      "fa_directional_drift_s": -0.04312301540828878,
+      "bp_directional_drift_s": -0.06369219976030034
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101000,
+      "target_steps": 50,
+      "early_steps": 2,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.697143412487514,
+      "empirical_gap": 0.1268088386664301,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6946737310587165,
+      "fixed_gap": 0.14360608621061388,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.009943291504341702,
+      "kbp_fro_drift": 0.009896827277091172,
+      "fa_bp_overlap_0": 0.976951289661455,
+      "fa_bp_overlap_s": 0.9770564468965752,
+      "fa_bp_overlap_slope": 5.2578617560139485e-05,
+      "fa_directional_gain_s": 2447.8190839515664,
+      "bp_directional_gain_s": 3410.877842279085,
+      "fa_directional_drift_s": -0.08435598850164468,
+      "bp_directional_drift_s": -0.12331596245287509
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101000,
+      "target_steps": 50,
+      "early_steps": 5,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.697143412487514,
+      "empirical_gap": 0.1268088386664301,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6946737310587165,
+      "fixed_gap": 0.14360608621061388,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 3.990204808513375,
+      "directional_gap": -0.07589685857591189,
+      "kfa_fro_drift": 0.016559323111176562,
+      "kbp_fro_drift": 0.017483644584136898,
+      "fa_bp_overlap_0": 0.976951289661455,
+      "fa_bp_overlap_s": 0.977089676811308,
+      "fa_bp_overlap_slope": 2.7677429970607292e-05,
+      "fa_directional_gain_s": 2137.5969318534508,
+      "bp_directional_gain_s": 2782.9928969587368,
+      "fa_directional_drift_s": -0.20039930953998655,
+      "bp_directional_drift_s": -0.284698672251328
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101001,
+      "target_steps": 50,
+      "early_steps": 1,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.678819805545933,
+      "empirical_gap": 0.10848523172484903,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6851718899206034,
+      "fixed_gap": 0.13410424507250074,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.007918613299755812,
+      "kbp_fro_drift": 0.006384612514262938,
+      "fa_bp_overlap_0": 0.9828127818056384,
+      "fa_bp_overlap_s": 0.982929851452701,
+      "fa_bp_overlap_slope": 0.00011706964706259537,
+      "fa_directional_gain_s": 2764.8865641420475,
+      "bp_directional_gain_s": 3642.853516902313,
+      "fa_directional_drift_s": -0.04339146607993533,
+      "bp_directional_drift_s": -0.06369219976030034
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101001,
+      "target_steps": 50,
+      "early_steps": 2,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.678819805545933,
+      "empirical_gap": 0.10848523172484903,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6851718899206034,
+      "fixed_gap": 0.13410424507250074,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.010209082104582094,
+      "kbp_fro_drift": 0.009896827277091172,
+      "fa_bp_overlap_0": 0.9828127818056384,
+      "fa_bp_overlap_s": 0.9829953623325879,
+      "fa_bp_overlap_slope": 9.129026347476366e-05,
+      "fa_directional_gain_s": 2640.0805951102316,
+      "bp_directional_gain_s": 3410.877842279085,
+      "fa_directional_drift_s": -0.08657242569266566,
+      "bp_directional_drift_s": -0.12331596245287509
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101001,
+      "target_steps": 50,
+      "early_steps": 5,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.678819805545933,
+      "empirical_gap": 0.10848523172484903,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6851718899206034,
+      "fixed_gap": 0.13410424507250074,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.01545339741556104,
+      "kbp_fro_drift": 0.017483644584136898,
+      "fa_bp_overlap_0": 0.9828127818056384,
+      "fa_bp_overlap_s": 0.9831641204628632,
+      "fa_bp_overlap_slope": 7.026773144496179e-05,
+      "fa_directional_gain_s": 2287.162854386855,
+      "bp_directional_gain_s": 2782.9928969587368,
+      "fa_directional_drift_s": -0.20867657525387207,
+      "bp_directional_drift_s": -0.284698672251328
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101002,
+      "target_steps": 50,
+      "early_steps": 1,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.684839622758295,
+      "empirical_gap": 0.11450504893721103,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6900721075509733,
+      "fixed_gap": 0.1390044627028706,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.004696247795133425,
+      "kbp_fro_drift": 0.006384612514262938,
+      "fa_bp_overlap_0": 0.9828061326343368,
+      "fa_bp_overlap_s": 0.9828344264937947,
+      "fa_bp_overlap_slope": 2.82938594579063e-05,
+      "fa_directional_gain_s": 2817.025852575887,
+      "bp_directional_gain_s": 3642.853516902313,
+      "fa_directional_drift_s": -0.047765096434622456,
+      "bp_directional_drift_s": -0.06369219976030034
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101002,
+      "target_steps": 50,
+      "early_steps": 2,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.684839622758295,
+      "empirical_gap": 0.11450504893721103,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6900721075509733,
+      "fixed_gap": 0.1390044627028706,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.011615547485972856,
+      "kbp_fro_drift": 0.009896827277091172,
+      "fa_bp_overlap_0": 0.9828061326343368,
+      "fa_bp_overlap_s": 0.9828370787349955,
+      "fa_bp_overlap_slope": 1.5473050329339877e-05,
+      "fa_directional_gain_s": 2681.6012528700435,
+      "bp_directional_gain_s": 3410.877842279085,
+      "fa_directional_drift_s": -0.09354246497504826,
+      "bp_directional_drift_s": -0.12331596245287509
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101002,
+      "target_steps": 50,
+      "early_steps": 5,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.684839622758295,
+      "empirical_gap": 0.11450504893721103,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6900721075509733,
+      "fixed_gap": 0.1390044627028706,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.016755592275579465,
+      "kbp_fro_drift": 0.017483644584136898,
+      "fa_bp_overlap_0": 0.9828061326343368,
+      "fa_bp_overlap_s": 0.98286698124195,
+      "fa_bp_overlap_slope": 1.2169721522647947e-05,
+      "fa_directional_gain_s": 2302.9660340708997,
+      "bp_directional_gain_s": 2782.9928969587368,
+      "fa_directional_drift_s": -0.22153194392497408,
+      "bp_directional_drift_s": -0.284698672251328
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101003,
+      "target_steps": 50,
+      "early_steps": 1,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.681052714285519,
+      "empirical_gap": 0.11071814046443507,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6833566536237186,
+      "fixed_gap": 0.1322890087756159,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.004897653710957696,
+      "kbp_fro_drift": 0.006384612514262938,
+      "fa_bp_overlap_0": 0.9792574873433338,
+      "fa_bp_overlap_s": 0.9793685321860623,
+      "fa_bp_overlap_slope": 0.00011104484272850268,
+      "fa_directional_gain_s": 2642.014618440444,
+      "bp_directional_gain_s": 3642.853516902313,
+      "fa_directional_drift_s": -0.04286501182071257,
+      "bp_directional_drift_s": -0.06369219976030034
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101003,
+      "target_steps": 50,
+      "early_steps": 2,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.681052714285519,
+      "empirical_gap": 0.11071814046443507,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6833566536237186,
+      "fixed_gap": 0.1322890087756159,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.066101667089287,
+      "directional_gap": 0.0,
+      "kfa_fro_drift": 0.00887689134694127,
+      "kbp_fro_drift": 0.009896827277091172,
+      "fa_bp_overlap_0": 0.9792574873433338,
+      "fa_bp_overlap_s": 0.9794836801266967,
+      "fa_bp_overlap_slope": 0.00011309639168144425,
+      "fa_directional_gain_s": 2527.264099032341,
+      "bp_directional_gain_s": 3410.877842279085,
+      "fa_directional_drift_s": -0.08443621898612716,
+      "bp_directional_drift_s": -0.12331596245287509
+    },
+    {
+      "init_seed": 10001,
+      "feedback_seed": 101003,
+      "target_steps": 50,
+      "early_steps": 5,
+      "empirical_bp_loss": 2.570334573821084,
+      "empirical_fa_loss": 2.681052714285519,
+      "empirical_gap": 0.11071814046443507,
+      "fixed_bp_loss": 2.5510676448481027,
+      "fixed_fa_loss": 2.6833566536237186,
+      "fixed_gap": 0.1322890087756159,
+      "directional_bp_loss": 4.066101667089287,
+      "directional_fa_loss": 4.003389756543286,
+      "directional_gap": -0.06271191054600056,
+      "kfa_fro_drift": 0.015809691563003,
+      "kbp_fro_drift": 0.017483644584136898,
+      "fa_bp_overlap_0": 0.9792574873433338,
+      "fa_bp_overlap_s": 0.9798000976433185,
+      "fa_bp_overlap_slope": 0.00010852205999694054,
+      "fa_directional_gain_s": 2205.1230693187536,
+      "bp_directional_gain_s": 2782.9928969587368,
+      "fa_directional_drift_s": -0.20113975594421707,
+      "bp_directional_drift_s": -0.284698672251328
+    }
+  ]
+}