rrm workspace: TRM/HRM/SRM code, Maze dataset, dynamical-analysis pipelineHEADmain

Curated export for clone-and-run Maze training (2x A6000) + diagnostics.
trm/hrm pretrain.py carry trajectory-augmentation code (backward-compatible).
Heavy artifacts (checkpoints/wandb/npz) gitignored; see PROVENANCE.md.

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

1 files changed, 4562 insertions, 0 deletions

diff --git a/research/flossing/step3_H_engelken_l2_26040.json b/research/flossing/step3_H_engelken_l2_26040.json
new file mode 100644
index 0000000..7f83dd1
--- /dev/null
+++ b/research/flossing/step3_H_engelken_l2_26040.json
@@ -0,0 +1,4562 @@
+{
+  "args": {
+    "ckpt_root": "/home/yurenh2/rrm/hrm/checkpoints/Sudoku-extreme-1k-aug-1000 ACT-torch/HierarchicalReasoningModel_ACTV1 righteous-python",
+    "ckpt_name": "step_26040",
+    "n_steps": 500,
+    "batch_size": 8,
+    "lr": 1e-05,
+    "alpha_rf": 10.0,
+    "lambda_star": -0.05,
+    "rf_mode": "engelken_l2",
+    "k_lyap": 4,
+    "lyap_act_steps": 4,
+    "seed": 42,
+    "eval_every": 100,
+    "eval_n": 512,
+    "eval_batch_size": 32,
+    "out": "step3_H_engelken_l2_26040.json"
+  },
+  "initial_acc": 0.517578125,
+  "initial_tok_acc": 0.8276668595679012,
+  "steps": [
+    {
+      "step": 0,
+      "sup_loss": 0.5685057694081904,
+      "rf_loss": 0.04733970761299133,
+      "total_loss": 1.0419028455381039,
+      "lyap1_mean": -0.17961826920509338,
+      "lyap1_max": -0.03562028706073761,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 1,
+      "sup_loss": 0.4037203596835466,
+      "rf_loss": 0.04868277162313461,
+      "total_loss": 0.8905480908160539,
+      "lyap1_mean": -0.1962278187274933,
+      "lyap1_max": -0.05477383732795715,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 2,
+      "sup_loss": 0.7260843704153586,
+      "rf_loss": 0.03834356367588043,
+      "total_loss": 1.1095200071741629,
+      "lyap1_mean": -0.179014652967453,
+      "lyap1_max": -0.08531452715396881,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 3,
+      "sup_loss": 0.5733422230332987,
+      "rf_loss": 0.03530708700418472,
+      "total_loss": 0.9264130781739848,
+      "lyap1_mean": -0.16334569454193115,
+      "lyap1_max": -0.08895331621170044,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 4,
+      "sup_loss": 0.5724905901822916,
+      "rf_loss": 0.022322028875350952,
+      "total_loss": 0.7957108789358012,
+      "lyap1_mean": -0.11591002345085144,
+      "lyap1_max": -0.03171190619468689,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 5,
+      "sup_loss": 1.090127790364056,
+      "rf_loss": 0.017973486334085464,
+      "total_loss": 1.26986264625433,
+      "lyap1_mean": -0.09209123998880386,
+      "lyap1_max": -0.013063598424196243,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 6,
+      "sup_loss": 0.5915127479597668,
+      "rf_loss": 0.02214599773287773,
+      "total_loss": 0.8129727327391247,
+      "lyap1_mean": -0.13739216327667236,
+      "lyap1_max": -0.07255011051893234,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 7,
+      "sup_loss": 0.6257641620826888,
+      "rf_loss": 0.016999084502458572,
+      "total_loss": 0.7957549996566939,
+      "lyap1_mean": -0.11748845130205154,
+      "lyap1_max": -0.07193292677402496,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 8,
+      "sup_loss": 0.808008071043134,
+      "rf_loss": 0.010237942449748516,
+      "total_loss": 0.9103874974032643,
+      "lyap1_mean": -0.07238984107971191,
+      "lyap1_max": 0.06215187534689903,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 9,
+      "sup_loss": 0.8027612794633473,
+      "rf_loss": 0.00995316356420517,
+      "total_loss": 0.902292915105399,
+      "lyap1_mean": -0.06326894462108612,
+      "lyap1_max": -0.013731321319937706,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 10,
+      "sup_loss": 0.5939262124702214,
+      "rf_loss": 0.01176164299249649,
+      "total_loss": 0.7115426423951863,
+      "lyap1_mean": -0.05144178494811058,
+      "lyap1_max": 0.07538376748561859,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 11,
+      "sup_loss": 0.7857643136142598,
+      "rf_loss": 0.014156627468764782,
+      "total_loss": 0.9273305901645528,
+      "lyap1_mean": -0.07053661346435547,
+      "lyap1_max": 0.01587703265249729,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 12,
+      "sup_loss": 0.42034114134631767,
+      "rf_loss": 0.004009572323411703,
+      "total_loss": 0.4604368655117573,
+      "lyap1_mean": -0.010957201011478901,
+      "lyap1_max": 0.06507517397403717,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 13,
+      "sup_loss": 0.7346591511356957,
+      "rf_loss": 0.006361983250826597,
+      "total_loss": 0.7982789808499939,
+      "lyap1_mean": -0.045017778873443604,
+      "lyap1_max": 0.0644940659403801,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 14,
+      "sup_loss": 0.6003631415970868,
+      "rf_loss": 0.006417217664420605,
+      "total_loss": 0.664535320103938,
+      "lyap1_mean": -0.02459695003926754,
+      "lyap1_max": 0.09718253463506699,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 15,
+      "sup_loss": 0.6666138558415055,
+      "rf_loss": 0.003170786425471306,
+      "total_loss": 0.6983217200962185,
+      "lyap1_mean": -0.015526402741670609,
+      "lyap1_max": 0.06174377724528313,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 16,
+      "sup_loss": 0.6264223578747624,
+      "rf_loss": 0.0035191080532968044,
+      "total_loss": 0.661613439339053,
+      "lyap1_mean": -0.03805670887231827,
+      "lyap1_max": 0.014193112961947918,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 17,
+      "sup_loss": 0.7883959278661291,
+      "rf_loss": 0.002783984411507845,
+      "total_loss": 0.816235771049885,
+      "lyap1_mean": -0.019641263410449028,
+      "lyap1_max": 0.06892091035842896,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 18,
+      "sup_loss": 0.630542506588173,
+      "rf_loss": 0.0018181016203016043,
+      "total_loss": 0.6487235232568503,
+      "lyap1_mean": -0.00036901235580444336,
+      "lyap1_max": 0.058217715471982956,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 19,
+      "sup_loss": 0.4510660575104757,
+      "rf_loss": 0.002530134515836835,
+      "total_loss": 0.47636740220318274,
+      "lyap1_mean": 0.04247730225324631,
+      "lyap1_max": 0.1444515883922577,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 20,
+      "sup_loss": 0.591171203205298,
+      "rf_loss": 0.002410288667306304,
+      "total_loss": 0.6152740903440224,
+      "lyap1_mean": 0.027764346450567245,
+      "lyap1_max": 0.1268729418516159,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 21,
+      "sup_loss": 0.7110254087879104,
+      "rf_loss": 0.00277963955886662,
+      "total_loss": 0.7388218039109153,
+      "lyap1_mean": 0.04433313012123108,
+      "lyap1_max": 0.180991530418396,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 22,
+      "sup_loss": 0.7429860286764757,
+      "rf_loss": 0.0024447953328490257,
+      "total_loss": 0.7674339820049659,
+      "lyap1_mean": 0.041937220841646194,
+      "lyap1_max": 0.11016540974378586,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 23,
+      "sup_loss": 0.7952349237507468,
+      "rf_loss": 0.0016880775801837444,
+      "total_loss": 0.8121157004839068,
+      "lyap1_mean": 0.040097083896398544,
+      "lyap1_max": 0.09598131477832794,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 24,
+      "sup_loss": 0.9802007689222377,
+      "rf_loss": 0.002183329313993454,
+      "total_loss": 1.0020340620621724,
+      "lyap1_mean": 0.045153796672821045,
+      "lyap1_max": 0.11071624606847763,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 25,
+      "sup_loss": 1.0263492223784836,
+      "rf_loss": 0.001687627867795527,
+      "total_loss": 1.0432255008236082,
+      "lyap1_mean": 0.039729706943035126,
+      "lyap1_max": 0.07604333758354187,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 26,
+      "sup_loss": 0.9724431080774142,
+      "rf_loss": 0.0019558616913855076,
+      "total_loss": 0.9920017240599467,
+      "lyap1_mean": 0.04495204985141754,
+      "lyap1_max": 0.10596223920583725,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 27,
+      "sup_loss": 0.9266472872971946,
+      "rf_loss": 0.0025822618044912815,
+      "total_loss": 0.9524699044107848,
+      "lyap1_mean": 0.049810200929641724,
+      "lyap1_max": 0.11686775088310242,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 28,
+      "sup_loss": 1.02238951078999,
+      "rf_loss": 0.001928186509758234,
+      "total_loss": 1.0416713749562498,
+      "lyap1_mean": 0.03899875283241272,
+      "lyap1_max": 0.07007154077291489,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 29,
+      "sup_loss": 1.022255369170766,
+      "rf_loss": 0.000942970858886838,
+      "total_loss": 1.0316850772939732,
+      "lyap1_mean": 0.030243759974837303,
+      "lyap1_max": 0.07064474374055862,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 30,
+      "sup_loss": 1.115455735429077,
+      "rf_loss": 0.0035400432534515858,
+      "total_loss": 1.1508561670322703,
+      "lyap1_mean": 0.06256316602230072,
+      "lyap1_max": 0.12286612391471863,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 31,
+      "sup_loss": 1.1081254239650644,
+      "rf_loss": 0.0009436927502974868,
+      "total_loss": 1.11756235170087,
+      "lyap1_mean": 0.025741783902049065,
+      "lyap1_max": 0.06098508834838867,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 32,
+      "sup_loss": 1.3330808317926912,
+      "rf_loss": 0.001529136672616005,
+      "total_loss": 1.3483721985188513,
+      "lyap1_mean": 0.009526968002319336,
+      "lyap1_max": 0.07304955273866653,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 33,
+      "sup_loss": 1.1160696579651308,
+      "rf_loss": 0.0014449862064793706,
+      "total_loss": 1.1305195197970939,
+      "lyap1_mean": 0.04755067080259323,
+      "lyap1_max": 0.08680564165115356,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 34,
+      "sup_loss": 1.3752232870355265,
+      "rf_loss": 0.0011022250400856137,
+      "total_loss": 1.386245537203552,
+      "lyap1_mean": 0.03920470178127289,
+      "lyap1_max": 0.07262717187404633,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 35,
+      "sup_loss": 1.0649683098537737,
+      "rf_loss": 0.0010181765537708998,
+      "total_loss": 1.075150075857144,
+      "lyap1_mean": 0.022791411727666855,
+      "lyap1_max": 0.07735683023929596,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 36,
+      "sup_loss": 1.2711832644219327,
+      "rf_loss": 0.001157189253717661,
+      "total_loss": 1.2827551569591094,
+      "lyap1_mean": 0.025203941389918327,
+      "lyap1_max": 0.07131651043891907,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 37,
+      "sup_loss": 1.045884820948804,
+      "rf_loss": 0.000637406250461936,
+      "total_loss": 1.0522588834534234,
+      "lyap1_mean": 0.0056057702749967575,
+      "lyap1_max": 0.06628408282995224,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 38,
+      "sup_loss": 0.9247773794306515,
+      "rf_loss": 0.0010192577028647065,
+      "total_loss": 0.934969956226468,
+      "lyap1_mean": 0.00907827913761139,
+      "lyap1_max": 0.056182872503995895,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 39,
+      "sup_loss": 0.9647666968012714,
+      "rf_loss": 0.0015987898223102093,
+      "total_loss": 0.980754595955696,
+      "lyap1_mean": -0.02172931656241417,
+      "lyap1_max": 0.0204969123005867,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 40,
+      "sup_loss": 1.0836263473553287,
+      "rf_loss": 0.0007719015702605247,
+      "total_loss": 1.091345363057934,
+      "lyap1_mean": 0.001784016378223896,
+      "lyap1_max": 0.04458495229482651,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 41,
+      "sup_loss": 0.8702809644760731,
+      "rf_loss": 0.0011745584197342396,
+      "total_loss": 0.8820265486734155,
+      "lyap1_mean": 0.00010476470924913883,
+      "lyap1_max": 0.06304346770048141,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 42,
+      "sup_loss": 1.0207136267592647,
+      "rf_loss": 0.0012569136451929808,
+      "total_loss": 1.0332827636768558,
+      "lyap1_mean": 0.010860885493457317,
+      "lyap1_max": 0.08084891736507416,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 43,
+      "sup_loss": 0.9606826421586823,
+      "rf_loss": 0.0009243196109309793,
+      "total_loss": 0.9699258380351614,
+      "lyap1_mean": 0.01678728125989437,
+      "lyap1_max": 0.06903886049985886,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 44,
+      "sup_loss": 1.0901127846272887,
+      "rf_loss": 0.0012237848713994026,
+      "total_loss": 1.1023506333412827,
+      "lyap1_mean": -0.015907209366559982,
+      "lyap1_max": 0.05972520634531975,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 45,
+      "sup_loss": 0.9793125943791718,
+      "rf_loss": 0.001833557616919279,
+      "total_loss": 0.9976481714796872,
+      "lyap1_mean": -0.007533593103289604,
+      "lyap1_max": 0.08245179802179337,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 46,
+      "sup_loss": 0.9388600364856128,
+      "rf_loss": 0.0006953688571229577,
+      "total_loss": 0.9458137248240117,
+      "lyap1_mean": -0.008189670741558075,
+      "lyap1_max": 0.02575668692588806,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 47,
+      "sup_loss": 0.8805779430660073,
+      "rf_loss": 0.0010967841371893883,
+      "total_loss": 0.8915457844379012,
+      "lyap1_mean": -0.006138445809483528,
+      "lyap1_max": 0.05779226869344711,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 48,
+      "sup_loss": 0.906661640539172,
+      "rf_loss": 0.0012606774689629674,
+      "total_loss": 0.919268414995971,
+      "lyap1_mean": 0.014625970274209976,
+      "lyap1_max": 0.04772620648145676,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 49,
+      "sup_loss": 0.9708721882765906,
+      "rf_loss": 0.0017687194049358368,
+      "total_loss": 0.988559382325949,
+      "lyap1_mean": 0.005887090228497982,
+      "lyap1_max": 0.06245606765151024,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 50,
+      "sup_loss": 0.948081890190455,
+      "rf_loss": 0.0013340074801817536,
+      "total_loss": 0.9614219647594419,
+      "lyap1_mean": -0.007961807772517204,
+      "lyap1_max": 0.07622306793928146,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 51,
+      "sup_loss": 0.937688244701925,
+      "rf_loss": 0.0010047812247648835,
+      "total_loss": 0.9477360567167432,
+      "lyap1_mean": 0.012427473440766335,
+      "lyap1_max": 0.09291605651378632,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 52,
+      "sup_loss": 0.8327632227239812,
+      "rf_loss": 0.0007577986107207835,
+      "total_loss": 0.8403412087147737,
+      "lyap1_mean": 0.023599660024046898,
+      "lyap1_max": 0.08097882568836212,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 53,
+      "sup_loss": 0.8893683336617775,
+      "rf_loss": 0.0006583798676729202,
+      "total_loss": 0.8959521323385067,
+      "lyap1_mean": 0.0042661018669605255,
+      "lyap1_max": 0.044909410178661346,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 54,
+      "sup_loss": 0.8669029851207197,
+      "rf_loss": 0.0008011930622160435,
+      "total_loss": 0.8749149157428802,
+      "lyap1_mean": 0.010470177046954632,
+      "lyap1_max": 0.07171719521284103,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 55,
+      "sup_loss": 0.9071669661054531,
+      "rf_loss": 0.000478514120914042,
+      "total_loss": 0.9119521070817629,
+      "lyap1_mean": -0.001809057779610157,
+      "lyap1_max": 0.023866182193160057,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 56,
+      "sup_loss": 0.7750197502494872,
+      "rf_loss": 0.0008240361930802464,
+      "total_loss": 0.783260111947459,
+      "lyap1_mean": -0.011191976256668568,
+      "lyap1_max": 0.026470284909009933,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 57,
+      "sup_loss": 1.0672955790312266,
+      "rf_loss": 0.0008987840265035629,
+      "total_loss": 1.0762834192962623,
+      "lyap1_mean": 0.015051664784550667,
+      "lyap1_max": 0.05193695053458214,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 58,
+      "sup_loss": 0.9934163731671343,
+      "rf_loss": 0.000589272822253406,
+      "total_loss": 0.999309101622499,
+      "lyap1_mean": -0.0008965558372437954,
+      "lyap1_max": 0.02534179762005806,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 59,
+      "sup_loss": 0.8509506245077478,
+      "rf_loss": 0.0012565349461510777,
+      "total_loss": 0.863515973736428,
+      "lyap1_mean": 0.016088515520095825,
+      "lyap1_max": 0.08727994561195374,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 60,
+      "sup_loss": 0.8560125275786259,
+      "rf_loss": 0.0009822192369028926,
+      "total_loss": 0.8658347201804855,
+      "lyap1_mean": 0.010940521955490112,
+      "lyap1_max": 0.06902682781219482,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 61,
+      "sup_loss": 0.7822388925952962,
+      "rf_loss": 0.0007923028315417469,
+      "total_loss": 0.790161921027129,
+      "lyap1_mean": 0.010721568949520588,
+      "lyap1_max": 0.046501096338033676,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 62,
+      "sup_loss": 0.7867431655911451,
+      "rf_loss": 0.0007841487531550229,
+      "total_loss": 0.79458465300628,
+      "lyap1_mean": 0.015161175280809402,
+      "lyap1_max": 0.06127696484327316,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 63,
+      "sup_loss": 0.9796870258901141,
+      "rf_loss": 0.0009735000785440207,
+      "total_loss": 0.9894220271412156,
+      "lyap1_mean": 0.030849896371364594,
+      "lyap1_max": 0.05115961283445358,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 64,
+      "sup_loss": 0.8667651121316741,
+      "rf_loss": 0.0007720908033661544,
+      "total_loss": 0.8744860202817509,
+      "lyap1_mean": 0.00514454348012805,
+      "lyap1_max": 0.03350814804434776,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 65,
+      "sup_loss": 0.9285918461139675,
+      "rf_loss": 0.0006139737088233232,
+      "total_loss": 0.9347315832022007,
+      "lyap1_mean": 0.02313666045665741,
+      "lyap1_max": 0.07489283382892609,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 66,
+      "sup_loss": 0.9292679695899022,
+      "rf_loss": 0.0007672343635931611,
+      "total_loss": 0.9369403129930032,
+      "lyap1_mean": 0.017080869525671005,
+      "lyap1_max": 0.05519671365618706,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 67,
+      "sup_loss": 0.8833299849364642,
+      "rf_loss": 0.0005487698363140225,
+      "total_loss": 0.8888176830667738,
+      "lyap1_mean": 0.015383392572402954,
+      "lyap1_max": 0.03457961231470108,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 68,
+      "sup_loss": 0.7192734614290887,
+      "rf_loss": 0.0009494900004938245,
+      "total_loss": 0.7287683612011963,
+      "lyap1_mean": 0.02931375801563263,
+      "lyap1_max": 0.06417189538478851,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 69,
+      "sup_loss": 0.9773822999437343,
+      "rf_loss": 0.00047331611858680844,
+      "total_loss": 0.982115461013187,
+      "lyap1_mean": 0.0006819623522460461,
+      "lyap1_max": 0.045399174094200134,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 70,
+      "sup_loss": 0.898837200120858,
+      "rf_loss": 0.0004178817616775632,
+      "total_loss": 0.903016017504803,
+      "lyap1_mean": 0.0021388689056038857,
+      "lyap1_max": 0.01755302958190441,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 71,
+      "sup_loss": 0.9310006558809163,
+      "rf_loss": 0.000795674161054194,
+      "total_loss": 0.9389573972586276,
+      "lyap1_mean": -0.00210399623028934,
+      "lyap1_max": 0.04350053891539574,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 72,
+      "sup_loss": 0.7472467435975779,
+      "rf_loss": 0.0005887816078029573,
+      "total_loss": 0.7531345597920228,
+      "lyap1_mean": 0.01201567705720663,
+      "lyap1_max": 0.054979175329208374,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 73,
+      "sup_loss": 0.9232985406126353,
+      "rf_loss": 0.0014685147907584906,
+      "total_loss": 0.9379836889858815,
+      "lyap1_mean": 0.01818285509943962,
+      "lyap1_max": 0.06256735324859619,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 74,
+      "sup_loss": 0.9751061908348712,
+      "rf_loss": 0.001035476801916957,
+      "total_loss": 0.985460959319702,
+      "lyap1_mean": -0.0048950654454529285,
+      "lyap1_max": 0.03788025677204132,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 75,
+      "sup_loss": 0.8937195082349892,
+      "rf_loss": 0.0006578811444342136,
+      "total_loss": 0.9002983196793314,
+      "lyap1_mean": 0.019708964973688126,
+      "lyap1_max": 0.09762965142726898,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 76,
+      "sup_loss": 0.8535985832459301,
+      "rf_loss": 0.0009039461147040129,
+      "total_loss": 0.8626380448586315,
+      "lyap1_mean": 0.03407550975680351,
+      "lyap1_max": 0.12100587785243988,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 77,
+      "sup_loss": 0.956974660124313,
+      "rf_loss": 0.00034145964309573174,
+      "total_loss": 0.9603892565552703,
+      "lyap1_mean": -0.002304722322151065,
+      "lyap1_max": 0.031193500384688377,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 78,
+      "sup_loss": 0.8709132723016859,
+      "rf_loss": 0.0007564492407254875,
+      "total_loss": 0.8784777648253561,
+      "lyap1_mean": -0.010317929089069366,
+      "lyap1_max": 0.014308694750070572,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 79,
+      "sup_loss": 0.8926876699052452,
+      "rf_loss": 0.000809231773018837,
+      "total_loss": 0.9007799876354335,
+      "lyap1_mean": 0.00890345685184002,
+      "lyap1_max": 0.07712709903717041,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 80,
+      "sup_loss": 0.9308004029025333,
+      "rf_loss": 0.000586956855840981,
+      "total_loss": 0.9366699712281125,
+      "lyap1_mean": 0.007967646233737469,
+      "lyap1_max": 0.034532975405454636,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 81,
+      "sup_loss": 0.9048253627408934,
+      "rf_loss": 0.0007890273700468242,
+      "total_loss": 0.912715636557777,
+      "lyap1_mean": 0.005160762462764978,
+      "lyap1_max": 0.06929047405719757,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 82,
+      "sup_loss": 1.0682013006485167,
+      "rf_loss": 0.0008669301168993115,
+      "total_loss": 1.0768706015846792,
+      "lyap1_mean": 0.01971331238746643,
+      "lyap1_max": 0.08884965628385544,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 83,
+      "sup_loss": 0.8773910718892765,
+      "rf_loss": 0.0009027048945426941,
+      "total_loss": 0.8864181208347034,
+      "lyap1_mean": 0.011390965431928635,
+      "lyap1_max": 0.10590040683746338,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 84,
+      "sup_loss": 1.0509876585209055,
+      "rf_loss": 0.0010455549927428365,
+      "total_loss": 1.0614432082155032,
+      "lyap1_mean": 0.027538806200027466,
+      "lyap1_max": 0.07328002899885178,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 85,
+      "sup_loss": 0.9374051712276997,
+      "rf_loss": 0.0005886475555598736,
+      "total_loss": 0.9432916467832985,
+      "lyap1_mean": 0.012019120156764984,
+      "lyap1_max": 0.03143277019262314,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 86,
+      "sup_loss": 1.024807690164325,
+      "rf_loss": 0.0006263715913519263,
+      "total_loss": 1.031071406310675,
+      "lyap1_mean": 0.019472159445285797,
+      "lyap1_max": 0.06757614016532898,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 87,
+      "sup_loss": 0.956803132676507,
+      "rf_loss": 0.0008426582789979875,
+      "total_loss": 0.9652297151172409,
+      "lyap1_mean": 0.033071599900722504,
+      "lyap1_max": 0.0748434066772461,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 88,
+      "sup_loss": 1.2538178616144413,
+      "rf_loss": 0.0007898804033175111,
+      "total_loss": 1.2617166654147858,
+      "lyap1_mean": 0.012752903625369072,
+      "lyap1_max": 0.04508042335510254,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 89,
+      "sup_loss": 1.2244843964809977,
+      "rf_loss": 0.0026937611401081085,
+      "total_loss": 1.2514220078820788,
+      "lyap1_mean": 0.06309334188699722,
+      "lyap1_max": 0.09706675261259079,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 90,
+      "sup_loss": 0.8729644475041664,
+      "rf_loss": 0.0018438478000462055,
+      "total_loss": 0.8914029245733058,
+      "lyap1_mean": 0.04707999527454376,
+      "lyap1_max": 0.13656100630760193,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 91,
+      "sup_loss": 1.1460387086893336,
+      "rf_loss": 0.001148674520663917,
+      "total_loss": 1.1575254541288034,
+      "lyap1_mean": 0.03688160702586174,
+      "lyap1_max": 0.08540346473455429,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 92,
+      "sup_loss": 1.0368121470141838,
+      "rf_loss": 0.0005813109455630183,
+      "total_loss": 1.0426252567026446,
+      "lyap1_mean": 0.030644692480564117,
+      "lyap1_max": 0.06765295565128326,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 93,
+      "sup_loss": 1.265380117299348,
+      "rf_loss": 0.0009110441897064447,
+      "total_loss": 1.2744905587307511,
+      "lyap1_mean": 0.01823984459042549,
+      "lyap1_max": 0.10411642491817474,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 94,
+      "sup_loss": 1.0463235274731653,
+      "rf_loss": 0.0011213610414415598,
+      "total_loss": 1.0575371374219196,
+      "lyap1_mean": 0.020743204280734062,
+      "lyap1_max": 0.08302636444568634,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 95,
+      "sup_loss": 0.9319028509875134,
+      "rf_loss": 0.0013563008978962898,
+      "total_loss": 0.9454658599664763,
+      "lyap1_mean": 0.0007464122027158737,
+      "lyap1_max": 0.06916027516126633,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 96,
+      "sup_loss": 1.06596370183561,
+      "rf_loss": 0.0008498276001773775,
+      "total_loss": 1.0744619774881379,
+      "lyap1_mean": 0.03118612803518772,
+      "lyap1_max": 0.09811311215162277,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 97,
+      "sup_loss": 1.072917703036636,
+      "rf_loss": 0.0015398014802485704,
+      "total_loss": 1.0883157173734603,
+      "lyap1_mean": 0.02613639086484909,
+      "lyap1_max": 0.09150408208370209,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 98,
+      "sup_loss": 1.1403091269937977,
+      "rf_loss": 0.00037640397204086185,
+      "total_loss": 1.1440731668306217,
+      "lyap1_mean": 0.00798884592950344,
+      "lyap1_max": 0.03982461988925934,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 99,
+      "sup_loss": 1.1678134895302203,
+      "rf_loss": 0.0008322176872752607,
+      "total_loss": 1.176135666053727,
+      "lyap1_mean": 0.02701447159051895,
+      "lyap1_max": 0.09839626401662827,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 100,
+      "sup_loss": 1.0825047804332586,
+      "rf_loss": 0.0009897247655317187,
+      "total_loss": 1.0924020283214064,
+      "lyap1_mean": 0.03514108061790466,
+      "lyap1_max": 0.08384718745946884,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 101,
+      "sup_loss": 1.0566211691090823,
+      "rf_loss": 0.000662648119032383,
+      "total_loss": 1.0632476502994062,
+      "lyap1_mean": 0.010695166885852814,
+      "lyap1_max": 0.044515423476696014,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 102,
+      "sup_loss": 0.9540854248320448,
+      "rf_loss": 0.0008922077831812203,
+      "total_loss": 0.9630075025474417,
+      "lyap1_mean": -0.001102598849684,
+      "lyap1_max": 0.059472303837537766,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 103,
+      "sup_loss": 1.2378926715896048,
+      "rf_loss": 0.0011251629330217838,
+      "total_loss": 1.2491443009198226,
+      "lyap1_mean": 0.025233585387468338,
+      "lyap1_max": 0.15528038144111633,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 104,
+      "sup_loss": 1.2206421905156746,
+      "rf_loss": 0.0011612236266955733,
+      "total_loss": 1.232254427015461,
+      "lyap1_mean": 0.01595454290509224,
+      "lyap1_max": 0.10135995596647263,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 105,
+      "sup_loss": 1.1160003799524831,
+      "rf_loss": 0.0008753755828365684,
+      "total_loss": 1.1247541360136795,
+      "lyap1_mean": -0.0015059742145240307,
+      "lyap1_max": 0.05327044054865837,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 106,
+      "sup_loss": 1.056875475730015,
+      "rf_loss": 0.001199170364998281,
+      "total_loss": 1.0688671796128284,
+      "lyap1_mean": 0.007520242128521204,
+      "lyap1_max": 0.1097741648554802,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 107,
+      "sup_loss": 1.0807725492239617,
+      "rf_loss": 0.0016184437554329634,
+      "total_loss": 1.0969569872439526,
+      "lyap1_mean": 0.01128618884831667,
+      "lyap1_max": 0.13724112510681152,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 108,
+      "sup_loss": 0.9868772662822702,
+      "rf_loss": 0.0008488181047141552,
+      "total_loss": 0.9953654473294118,
+      "lyap1_mean": -0.018499474972486496,
+      "lyap1_max": 0.003989826887845993,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 109,
+      "sup_loss": 1.1690339865109372,
+      "rf_loss": 0.0010800857562571764,
+      "total_loss": 1.1798348436078476,
+      "lyap1_mean": -0.006732122972607613,
+      "lyap1_max": 0.053807806223630905,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 110,
+      "sup_loss": 1.1322090776941094,
+      "rf_loss": 0.0010293642990291119,
+      "total_loss": 1.1425027206844005,
+      "lyap1_mean": 0.0171597208827734,
+      "lyap1_max": 0.07977798581123352,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 111,
+      "sup_loss": 1.094741669558202,
+      "rf_loss": 0.0008166237385012209,
+      "total_loss": 1.1029079072924601,
+      "lyap1_mean": -0.006677547469735146,
+      "lyap1_max": 0.024394815787672997,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 112,
+      "sup_loss": 1.2645858870416828,
+      "rf_loss": 0.0013192887417972088,
+      "total_loss": 1.277778774459655,
+      "lyap1_mean": 0.02593936026096344,
+      "lyap1_max": 0.08183470368385315,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 113,
+      "sup_loss": 1.1902706309393027,
+      "rf_loss": 0.001410051016137004,
+      "total_loss": 1.204371141566334,
+      "lyap1_mean": 0.006131772417575121,
+      "lyap1_max": 0.05749688670039177,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 114,
+      "sup_loss": 1.2074002124902719,
+      "rf_loss": 0.0003617902402766049,
+      "total_loss": 1.2110181147766226,
+      "lyap1_mean": 0.012099153362214565,
+      "lyap1_max": 0.032726533710956573,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 115,
+      "sup_loss": 1.0970542792486497,
+      "rf_loss": 0.0004731625085696578,
+      "total_loss": 1.101785904567177,
+      "lyap1_mean": 0.023841751739382744,
+      "lyap1_max": 0.0763063058257103,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 116,
+      "sup_loss": 0.960792728763117,
+      "rf_loss": 0.0007222419371828437,
+      "total_loss": 0.9680151483677761,
+      "lyap1_mean": 0.004050332121551037,
+      "lyap1_max": 0.053266432136297226,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 117,
+      "sup_loss": 1.1271560781156014,
+      "rf_loss": 0.0008394162287004292,
+      "total_loss": 1.1355502402861903,
+      "lyap1_mean": 0.006569029297679663,
+      "lyap1_max": 0.09283764660358429,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 118,
+      "sup_loss": 0.9776678578699395,
+      "rf_loss": 0.0008354542660526931,
+      "total_loss": 0.9860224006468817,
+      "lyap1_mean": 0.015399960801005363,
+      "lyap1_max": 0.05128543823957443,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 119,
+      "sup_loss": 1.2191235145671409,
+      "rf_loss": 0.0009178364416584373,
+      "total_loss": 1.2283018792165559,
+      "lyap1_mean": 0.017467226833105087,
+      "lyap1_max": 0.054577093571424484,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 120,
+      "sup_loss": 1.01672085777038,
+      "rf_loss": 0.0007249012123793364,
+      "total_loss": 1.0239698698941733,
+      "lyap1_mean": -0.01085918303579092,
+      "lyap1_max": 0.028561361134052277,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 121,
+      "sup_loss": 1.0686201601382077,
+      "rf_loss": 0.00035850302083417773,
+      "total_loss": 1.0722051904629648,
+      "lyap1_mean": 0.019602736458182335,
+      "lyap1_max": 0.05404075235128403,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 122,
+      "sup_loss": 1.405205714402767,
+      "rf_loss": 0.0008368202252313495,
+      "total_loss": 1.4135739168879111,
+      "lyap1_mean": 0.013442832976579666,
+      "lyap1_max": 0.0517943911254406,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 123,
+      "sup_loss": 1.1518605582938883,
+      "rf_loss": 0.0005323010263964534,
+      "total_loss": 1.1571835687906835,
+      "lyap1_mean": 0.012687107548117638,
+      "lyap1_max": 0.04220093786716461,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 124,
+      "sup_loss": 1.1970887058146416,
+      "rf_loss": 0.0005115274107083678,
+      "total_loss": 1.2022039801545559,
+      "lyap1_mean": 0.01099344901740551,
+      "lyap1_max": 0.05866736173629761,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 125,
+      "sup_loss": 1.1011430113990868,
+      "rf_loss": 0.0014086717274039984,
+      "total_loss": 1.115229729138788,
+      "lyap1_mean": 0.027196090668439865,
+      "lyap1_max": 0.066633440554142,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 126,
+      "sup_loss": 1.1699132299651405,
+      "rf_loss": 0.0004765711782965809,
+      "total_loss": 1.1746789416898986,
+      "lyap1_mean": 0.012494692578911781,
+      "lyap1_max": 0.0659983903169632,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 127,
+      "sup_loss": 1.1501944627067169,
+      "rf_loss": 0.0007082691881805658,
+      "total_loss": 1.1572771545885225,
+      "lyap1_mean": 0.01921798475086689,
+      "lyap1_max": 0.0494837686419487,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 128,
+      "sup_loss": 1.1801312745080337,
+      "rf_loss": 0.0005792698357254267,
+      "total_loss": 1.185923972865288,
+      "lyap1_mean": 0.006444226019084454,
+      "lyap1_max": 0.0724438801407814,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 129,
+      "sup_loss": 1.0836304972172945,
+      "rf_loss": 0.0006729363230988383,
+      "total_loss": 1.0903598606811136,
+      "lyap1_mean": 0.006663222331553698,
+      "lyap1_max": 0.08426569402217865,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 130,
+      "sup_loss": 1.180659495124045,
+      "rf_loss": 0.0007275000098161399,
+      "total_loss": 1.1879344953386217,
+      "lyap1_mean": -0.005528916604816914,
+      "lyap1_max": 0.01743876188993454,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 131,
+      "sup_loss": 1.169137834311079,
+      "rf_loss": 0.0014068072196096182,
+      "total_loss": 1.1832059069728365,
+      "lyap1_mean": -0.012744858860969543,
+      "lyap1_max": 0.0484539195895195,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 132,
+      "sup_loss": 1.042590925006699,
+      "rf_loss": 0.001247535226866603,
+      "total_loss": 1.0550662777410262,
+      "lyap1_mean": -0.007364945486187935,
+      "lyap1_max": 0.09321796149015427,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 133,
+      "sup_loss": 1.1904447090543167,
+      "rf_loss": 0.001985467504709959,
+      "total_loss": 1.2102993850327388,
+      "lyap1_mean": -0.02280796505510807,
+      "lyap1_max": 0.04867285490036011,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 134,
+      "sup_loss": 1.129249584345467,
+      "rf_loss": 0.0008814185857772827,
+      "total_loss": 1.13806377020324,
+      "lyap1_mean": 0.014115991070866585,
+      "lyap1_max": 0.051282741129398346,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 135,
+      "sup_loss": 0.9870567964672554,
+      "rf_loss": 0.0021919149439781904,
+      "total_loss": 1.0089759463726986,
+      "lyap1_mean": -0.017625734210014343,
+      "lyap1_max": 0.06481499969959259,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 136,
+      "sup_loss": 1.000722678870133,
+      "rf_loss": 0.0012177110183984041,
+      "total_loss": 1.0128997885884559,
+      "lyap1_mean": -0.014045312069356441,
+      "lyap1_max": 0.037885114550590515,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 137,
+      "sup_loss": 1.3689126065297847,
+      "rf_loss": 0.0007626177975907922,
+      "total_loss": 1.376538784272862,
+      "lyap1_mean": 0.008834890089929104,
+      "lyap1_max": 0.06582190841436386,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 138,
+      "sup_loss": 1.3437230888120943,
+      "rf_loss": 0.0009394993539899588,
+      "total_loss": 1.3531180828176552,
+      "lyap1_mean": 0.011946289800107479,
+      "lyap1_max": 0.09125296771526337,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 139,
+      "sup_loss": 1.2766020547538643,
+      "rf_loss": 0.001409234362654388,
+      "total_loss": 1.2906943986132389,
+      "lyap1_mean": 0.0232047438621521,
+      "lyap1_max": 0.11831438541412354,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 140,
+      "sup_loss": 1.3302581152794197,
+      "rf_loss": 0.00076719606295228,
+      "total_loss": 1.3379300759089425,
+      "lyap1_mean": 0.019289076328277588,
+      "lyap1_max": 0.08421679586172104,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 141,
+      "sup_loss": 1.397082939666813,
+      "rf_loss": 0.0007698746048845351,
+      "total_loss": 1.404781685599243,
+      "lyap1_mean": 0.023189324885606766,
+      "lyap1_max": 0.0919947549700737,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 142,
+      "sup_loss": 1.4534181425775328,
+      "rf_loss": 0.000721208518370986,
+      "total_loss": 1.4606302277612426,
+      "lyap1_mean": 0.015056228265166283,
+      "lyap1_max": 0.07089594751596451,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 143,
+      "sup_loss": 1.2864042887271914,
+      "rf_loss": 0.0004899534396827221,
+      "total_loss": 1.2913038231240186,
+      "lyap1_mean": 0.012849303893744946,
+      "lyap1_max": 0.03634604811668396,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 144,
+      "sup_loss": 1.3581954879073255,
+      "rf_loss": 0.0012775929644703865,
+      "total_loss": 1.3709714175520293,
+      "lyap1_mean": 0.005843585357069969,
+      "lyap1_max": 0.05753130838274956,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 145,
+      "sup_loss": 1.4048740496069372,
+      "rf_loss": 0.0007381130708381534,
+      "total_loss": 1.4122551805481494,
+      "lyap1_mean": 0.02068162150681019,
+      "lyap1_max": 0.0496211051940918,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 146,
+      "sup_loss": 1.3849838606672278,
+      "rf_loss": 0.0006646994152106345,
+      "total_loss": 1.3916308547029188,
+      "lyap1_mean": 0.011234735138714314,
+      "lyap1_max": 0.10357298702001572,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 147,
+      "sup_loss": 1.4254397012949278,
+      "rf_loss": 0.0013342644087970257,
+      "total_loss": 1.438782345382898,
+      "lyap1_mean": 0.024530548602342606,
+      "lyap1_max": 0.08816304057836533,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 148,
+      "sup_loss": 1.157072117197474,
+      "rf_loss": 0.0016489962581545115,
+      "total_loss": 1.1735620793133579,
+      "lyap1_mean": 0.04004575312137604,
+      "lyap1_max": 0.1303563266992569,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 149,
+      "sup_loss": 1.1390629206487566,
+      "rf_loss": 0.0004111626767553389,
+      "total_loss": 1.1431745472998947,
+      "lyap1_mean": 0.010188091546297073,
+      "lyap1_max": 0.034788090735673904,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 150,
+      "sup_loss": 1.2075074229352807,
+      "rf_loss": 0.0007685477612540126,
+      "total_loss": 1.2151929007806515,
+      "lyap1_mean": -0.01246840599924326,
+      "lyap1_max": 0.03272509574890137,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 151,
+      "sup_loss": 1.2131103756070076,
+      "rf_loss": 0.0006261632079258561,
+      "total_loss": 1.2193720074534355,
+      "lyap1_mean": -0.006888964679092169,
+      "lyap1_max": 0.04138804227113724,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 152,
+      "sup_loss": 1.3232039983268296,
+      "rf_loss": 0.0006777630187571049,
+      "total_loss": 1.3299816285144006,
+      "lyap1_mean": 0.0013273009099066257,
+      "lyap1_max": 0.038768164813518524,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 153,
+      "sup_loss": 1.0612979438799472,
+      "rf_loss": 0.0004672252689488232,
+      "total_loss": 1.0659701964530202,
+      "lyap1_mean": 0.0007033562287688255,
+      "lyap1_max": 0.03725506365299225,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 154,
+      "sup_loss": 1.2373004218512245,
+      "rf_loss": 0.00043797693797387183,
+      "total_loss": 1.2416801911727555,
+      "lyap1_mean": 0.007727539166808128,
+      "lyap1_max": 0.05859715864062309,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 155,
+      "sup_loss": 0.9835219086102821,
+      "rf_loss": 0.0006558194290846586,
+      "total_loss": 0.9900801029011287,
+      "lyap1_mean": -0.011583348736166954,
+      "lyap1_max": 0.026512738317251205,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 156,
+      "sup_loss": 1.321538352648178,
+      "rf_loss": 0.0003542369813658297,
+      "total_loss": 1.325080722345421,
+      "lyap1_mean": -0.00776063883677125,
+      "lyap1_max": 0.030904680490493774,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 157,
+      "sup_loss": 1.2355240322887828,
+      "rf_loss": 0.0004204224096611142,
+      "total_loss": 1.2397282561525633,
+      "lyap1_mean": 0.00013014720752835274,
+      "lyap1_max": 0.03947022929787636,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 158,
+      "sup_loss": 1.1643700458193411,
+      "rf_loss": 0.00028564780950546265,
+      "total_loss": 1.1672265239143957,
+      "lyap1_mean": 0.0025940013583749533,
+      "lyap1_max": 0.031320761889219284,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 159,
+      "sup_loss": 1.338438711594032,
+      "rf_loss": 0.0004457629402168095,
+      "total_loss": 1.3428963408797847,
+      "lyap1_mean": 0.009651683270931244,
+      "lyap1_max": 0.03257076442241669,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 160,
+      "sup_loss": 1.295166485067568,
+      "rf_loss": 0.00048577316920273006,
+      "total_loss": 1.3000242165849722,
+      "lyap1_mean": 0.016009461134672165,
+      "lyap1_max": 0.07643973082304001,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 161,
+      "sup_loss": 1.0787318236146906,
+      "rf_loss": 0.0007973226602189243,
+      "total_loss": 1.0867050503332951,
+      "lyap1_mean": 0.021038297563791275,
+      "lyap1_max": 0.050172071903944016,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 162,
+      "sup_loss": 1.0800695104417937,
+      "rf_loss": 0.0015056091360747814,
+      "total_loss": 1.0951256018025415,
+      "lyap1_mean": 0.0422448106110096,
+      "lyap1_max": 0.09603795409202576,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 163,
+      "sup_loss": 1.2182780709534375,
+      "rf_loss": 0.0005032537737861276,
+      "total_loss": 1.2233106084584682,
+      "lyap1_mean": 0.017071589827537537,
+      "lyap1_max": 0.05678673833608627,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 164,
+      "sup_loss": 1.1618102379865136,
+      "rf_loss": 0.0006260440568439662,
+      "total_loss": 1.1680706786713686,
+      "lyap1_mean": 0.0260627418756485,
+      "lyap1_max": 0.08463140577077866,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 165,
+      "sup_loss": 1.2340237209880758,
+      "rf_loss": 0.000659830286167562,
+      "total_loss": 1.240622024082582,
+      "lyap1_mean": 0.018701354041695595,
+      "lyap1_max": 0.09716101735830307,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 166,
+      "sup_loss": 1.2275805466677059,
+      "rf_loss": 0.0003920367162209004,
+      "total_loss": 1.231500913655292,
+      "lyap1_mean": 0.014187945984303951,
+      "lyap1_max": 0.05689648911356926,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 167,
+      "sup_loss": 1.1492321000341374,
+      "rf_loss": 0.0007031067507341504,
+      "total_loss": 1.1562631673086483,
+      "lyap1_mean": 0.026898283511400223,
+      "lyap1_max": 0.08793625235557556,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 168,
+      "sup_loss": 1.2224533641436952,
+      "rf_loss": 0.0003716197970788926,
+      "total_loss": 1.2261695621726918,
+      "lyap1_mean": 0.002054463606327772,
+      "lyap1_max": 0.0322721004486084,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 169,
+      "sup_loss": 1.3356163681433137,
+      "rf_loss": 0.001087899669073522,
+      "total_loss": 1.3464953650668796,
+      "lyap1_mean": 0.00022093812003731728,
+      "lyap1_max": 0.04549761861562729,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 170,
+      "sup_loss": 1.1192015626954752,
+      "rf_loss": 0.00045205201604403555,
+      "total_loss": 1.123722082797708,
+      "lyap1_mean": 0.017767632380127907,
+      "lyap1_max": 0.04133617505431175,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 171,
+      "sup_loss": 1.1842432150986653,
+      "rf_loss": 0.0007166333962231874,
+      "total_loss": 1.1914095490608971,
+      "lyap1_mean": -0.005882376804947853,
+      "lyap1_max": 0.030085457488894463,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 172,
+      "sup_loss": 1.249599681204317,
+      "rf_loss": 0.0004344423650763929,
+      "total_loss": 1.2539441049714963,
+      "lyap1_mean": -0.004513539839535952,
+      "lyap1_max": 0.019238971173763275,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 173,
+      "sup_loss": 1.2251422100806628,
+      "rf_loss": 0.0004886339302174747,
+      "total_loss": 1.2300285494992529,
+      "lyap1_mean": 0.009230803698301315,
+      "lyap1_max": 0.04357466101646423,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 174,
+      "sup_loss": 1.1141196391973376,
+      "rf_loss": 0.0006923482287675142,
+      "total_loss": 1.1210431214850127,
+      "lyap1_mean": 0.0039965370669960976,
+      "lyap1_max": 0.06606049090623856,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 175,
+      "sup_loss": 1.0185929264463214,
+      "rf_loss": 0.0008066887967288494,
+      "total_loss": 1.0266598144136099,
+      "lyap1_mean": -0.0027522509917616844,
+      "lyap1_max": 0.07425520569086075,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 176,
+      "sup_loss": 1.1600996339975558,
+      "rf_loss": 0.0007484590169042349,
+      "total_loss": 1.1675842241665981,
+      "lyap1_mean": 0.024981245398521423,
+      "lyap1_max": 0.0686129480600357,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 177,
+      "sup_loss": 1.3823677258452194,
+      "rf_loss": 0.00034431106178089976,
+      "total_loss": 1.3858108365794437,
+      "lyap1_mean": 0.00446769455447793,
+      "lyap1_max": 0.04835920035839081,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 178,
+      "sup_loss": 1.3308781064182935,
+      "rf_loss": 0.0007816175930202007,
+      "total_loss": 1.3386942823484955,
+      "lyap1_mean": 0.02307233214378357,
+      "lyap1_max": 0.10534416139125824,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 179,
+      "sup_loss": 1.2166868508253854,
+      "rf_loss": 0.0004185791767667979,
+      "total_loss": 1.2208726424184304,
+      "lyap1_mean": 0.0047370693646371365,
+      "lyap1_max": 0.022703660652041435,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 180,
+      "sup_loss": 1.2239921656670125,
+      "rf_loss": 0.0005176485283300281,
+      "total_loss": 1.2291686511831434,
+      "lyap1_mean": 0.0022171023301780224,
+      "lyap1_max": 0.04419127106666565,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 181,
+      "sup_loss": 1.243462219820423,
+      "rf_loss": 0.0012785675935447216,
+      "total_loss": 1.2562478957558703,
+      "lyap1_mean": 0.021596524864435196,
+      "lyap1_max": 0.058567821979522705,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 182,
+      "sup_loss": 1.464607456603025,
+      "rf_loss": 0.0006567127420566976,
+      "total_loss": 1.4711745841400072,
+      "lyap1_mean": 0.009746843948960304,
+      "lyap1_max": 0.04620875418186188,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 183,
+      "sup_loss": 1.2401887675130292,
+      "rf_loss": 0.000524076574947685,
+      "total_loss": 1.2454295333789214,
+      "lyap1_mean": -0.004803978838026524,
+      "lyap1_max": 0.035470593720674515,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 184,
+      "sup_loss": 1.3737399515392372,
+      "rf_loss": 0.0005270419642329216,
+      "total_loss": 1.3790103711815664,
+      "lyap1_mean": 0.016861990094184875,
+      "lyap1_max": 0.062393344938755035,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 185,
+      "sup_loss": 1.298909792440156,
+      "rf_loss": 0.0007151907193474472,
+      "total_loss": 1.3060616997500458,
+      "lyap1_mean": 0.000977073796093464,
+      "lyap1_max": 0.06407023966312408,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 186,
+      "sup_loss": 1.4027343553648122,
+      "rf_loss": 0.0006197948241606355,
+      "total_loss": 1.4089323033735879,
+      "lyap1_mean": 0.009357218630611897,
+      "lyap1_max": 0.046438902616500854,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 187,
+      "sup_loss": 1.3746727890210235,
+      "rf_loss": 0.0005517613026313484,
+      "total_loss": 1.3801904021637523,
+      "lyap1_mean": 0.0011497186496853828,
+      "lyap1_max": 0.03101596049964428,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 188,
+      "sup_loss": 1.2671637498913604,
+      "rf_loss": 0.0009581827325746417,
+      "total_loss": 1.2767455774499374,
+      "lyap1_mean": 0.0035438840277493,
+      "lyap1_max": 0.08548040688037872,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 189,
+      "sup_loss": 1.267287969164693,
+      "rf_loss": 0.000703421188518405,
+      "total_loss": 1.274322181049877,
+      "lyap1_mean": -0.0027904859744012356,
+      "lyap1_max": 0.053053103387355804,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 190,
+      "sup_loss": 1.3526585106357838,
+      "rf_loss": 0.000571909942664206,
+      "total_loss": 1.3583776098295952,
+      "lyap1_mean": 0.004709537141025066,
+      "lyap1_max": 0.041502099484205246,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 191,
+      "sup_loss": 1.262131002176932,
+      "rf_loss": 0.0004053425509482622,
+      "total_loss": 1.2661844276864147,
+      "lyap1_mean": 0.002271033823490143,
+      "lyap1_max": 0.026568349450826645,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 192,
+      "sup_loss": 1.2339496388867068,
+      "rf_loss": 0.0007855149451643229,
+      "total_loss": 1.2418047878726888,
+      "lyap1_mean": -0.019017376005649567,
+      "lyap1_max": 0.014895807020366192,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 193,
+      "sup_loss": 0.986318587217345,
+      "rf_loss": 0.0005758744664490223,
+      "total_loss": 0.9920773318818352,
+      "lyap1_mean": -0.001333925873041153,
+      "lyap1_max": 0.043975960463285446,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 194,
+      "sup_loss": 1.3757298494802117,
+      "rf_loss": 0.00045753869926556945,
+      "total_loss": 1.3803052365892827,
+      "lyap1_mean": 0.008196542970836163,
+      "lyap1_max": 0.04362962767481804,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 195,
+      "sup_loss": 1.2166308928754366,
+      "rf_loss": 0.0010206587612628937,
+      "total_loss": 1.2268374804880655,
+      "lyap1_mean": 0.025556430220603943,
+      "lyap1_max": 0.07464911043643951,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 196,
+      "sup_loss": 1.1521582948471485,
+      "rf_loss": 0.00032926135463640094,
+      "total_loss": 1.1554509085099278,
+      "lyap1_mean": 0.008313937112689018,
+      "lyap1_max": 0.032452717423439026,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 197,
+      "sup_loss": 1.1842540256314478,
+      "rf_loss": 0.0004416440206114203,
+      "total_loss": 1.1886704657793543,
+      "lyap1_mean": 0.013774862512946129,
+      "lyap1_max": 0.03887798637151718,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 198,
+      "sup_loss": 1.136558088571916,
+      "rf_loss": 0.0003095163556281477,
+      "total_loss": 1.1396532520699898,
+      "lyap1_mean": 0.009820901788771152,
+      "lyap1_max": 0.05576726049184799,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 199,
+      "sup_loss": 1.230491817675596,
+      "rf_loss": 0.0013962533557787538,
+      "total_loss": 1.2444543510005528,
+      "lyap1_mean": 0.03611571714282036,
+      "lyap1_max": 0.10857196897268295,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 200,
+      "sup_loss": 1.294392276041867,
+      "rf_loss": 0.0005306578241288662,
+      "total_loss": 1.2996988542831556,
+      "lyap1_mean": 0.008881606161594391,
+      "lyap1_max": 0.04738537594676018,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 201,
+      "sup_loss": 1.4131060151344987,
+      "rf_loss": 0.00042551400838419795,
+      "total_loss": 1.417361155334756,
+      "lyap1_mean": -0.0009504088084213436,
+      "lyap1_max": 0.0489705465734005,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 202,
+      "sup_loss": 1.2561133590978775,
+      "rf_loss": 0.0007632037741132081,
+      "total_loss": 1.2637453967225942,
+      "lyap1_mean": 0.0074675679206848145,
+      "lyap1_max": 0.03931625187397003,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 203,
+      "sup_loss": 1.2744359893442954,
+      "rf_loss": 0.0011068428866565228,
+      "total_loss": 1.2855044182108606,
+      "lyap1_mean": 0.0010042442008852959,
+      "lyap1_max": 0.1272994577884674,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 204,
+      "sup_loss": 1.2493466025835431,
+      "rf_loss": 0.00040510576218366623,
+      "total_loss": 1.2533976602053798,
+      "lyap1_mean": -0.013290760107338428,
+      "lyap1_max": 0.0059391106478869915,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 205,
+      "sup_loss": 1.2114527509740418,
+      "rf_loss": 0.0005638866568915546,
+      "total_loss": 1.2170916176593727,
+      "lyap1_mean": -0.009376316331326962,
+      "lyap1_max": 0.013558893464505672,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 206,
+      "sup_loss": 1.0918119352819824,
+      "rf_loss": 0.0004608319140970707,
+      "total_loss": 1.096420254422953,
+      "lyap1_mean": 0.0008914151694625616,
+      "lyap1_max": 0.03911463916301727,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 207,
+      "sup_loss": 1.2070632985064553,
+      "rf_loss": 0.0005100212292745709,
+      "total_loss": 1.2121635105663704,
+      "lyap1_mean": 0.0017476906068623066,
+      "lyap1_max": 0.04372255504131317,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 208,
+      "sup_loss": 1.1910730250609989,
+      "rf_loss": 0.00015481235459446907,
+      "total_loss": 1.1926211486069436,
+      "lyap1_mean": 0.0007014029542915523,
+      "lyap1_max": 0.012952337972819805,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 209,
+      "sup_loss": 1.1533989948752763,
+      "rf_loss": 0.0005860110395587981,
+      "total_loss": 1.159259105154449,
+      "lyap1_mean": -0.002168317325413227,
+      "lyap1_max": 0.03926722705364227,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 210,
+      "sup_loss": 1.385314392369675,
+      "rf_loss": 0.0002945143496617675,
+      "total_loss": 1.3882595358662926,
+      "lyap1_mean": 0.01028104405850172,
+      "lyap1_max": 0.034069303423166275,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 211,
+      "sup_loss": 1.1804826487354414,
+      "rf_loss": 0.0005935410736128688,
+      "total_loss": 1.1864180597044007,
+      "lyap1_mean": 0.029001785442233086,
+      "lyap1_max": 0.04907079041004181,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 212,
+      "sup_loss": 1.247616589515704,
+      "rf_loss": 0.0001637705572647974,
+      "total_loss": 1.249254295117456,
+      "lyap1_mean": 0.008447797037661076,
+      "lyap1_max": 0.03724531829357147,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 213,
+      "sup_loss": 1.1759229338675325,
+      "rf_loss": 0.00032233004458248615,
+      "total_loss": 1.1791462343133574,
+      "lyap1_mean": 0.006149024702608585,
+      "lyap1_max": 0.03448253870010376,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 214,
+      "sup_loss": 1.1496963115436682,
+      "rf_loss": 0.00044808158418163657,
+      "total_loss": 1.1541771275019,
+      "lyap1_mean": 0.016512496396899223,
+      "lyap1_max": 0.05415614694356918,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 215,
+      "sup_loss": 1.0997539379154067,
+      "rf_loss": 0.00022520520724356174,
+      "total_loss": 1.1020059899878423,
+      "lyap1_mean": 0.01093449629843235,
+      "lyap1_max": 0.03161671757698059,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 216,
+      "sup_loss": 1.1160387284479103,
+      "rf_loss": 0.0005825181142427027,
+      "total_loss": 1.121863909473922,
+      "lyap1_mean": 0.011543605476617813,
+      "lyap1_max": 0.07355349510908127,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 217,
+      "sup_loss": 1.0719854428832767,
+      "rf_loss": 0.000717509537935257,
+      "total_loss": 1.0791605382626293,
+      "lyap1_mean": 0.0025165430270135403,
+      "lyap1_max": 0.04004869982600212,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 218,
+      "sup_loss": 0.9572228153682136,
+      "rf_loss": 0.00021778937662020326,
+      "total_loss": 0.9594007090180003,
+      "lyap1_mean": 0.006354915909469128,
+      "lyap1_max": 0.02549804374575615,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 219,
+      "sup_loss": 1.085927781587558,
+      "rf_loss": 0.0006267091957852244,
+      "total_loss": 1.092194873778241,
+      "lyap1_mean": 0.01769602857530117,
+      "lyap1_max": 0.06930018961429596,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 220,
+      "sup_loss": 1.1667901144872748,
+      "rf_loss": 0.0002687779488041997,
+      "total_loss": 1.1694778939753168,
+      "lyap1_mean": -0.007445859257131815,
+      "lyap1_max": 0.011619901284575462,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 221,
+      "sup_loss": 1.125804921582883,
+      "rf_loss": 0.0003253528557252139,
+      "total_loss": 1.1290584501983427,
+      "lyap1_mean": 0.005712142214179039,
+      "lyap1_max": 0.03973882645368576,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 222,
+      "sup_loss": 1.109624641833186,
+      "rf_loss": 0.0006590286502614617,
+      "total_loss": 1.11621492810297,
+      "lyap1_mean": 0.0010898327454924583,
+      "lyap1_max": 0.05502500757575035,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 223,
+      "sup_loss": 1.1076962469006297,
+      "rf_loss": 0.00028322695288807154,
+      "total_loss": 1.1105285164295104,
+      "lyap1_mean": 0.008485198952257633,
+      "lyap1_max": 0.031716566532850266,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 224,
+      "sup_loss": 1.1403941053124687,
+      "rf_loss": 0.0004460351192392409,
+      "total_loss": 1.1448544563884457,
+      "lyap1_mean": 0.022015493363142014,
+      "lyap1_max": 0.04843788966536522,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 225,
+      "sup_loss": 1.0407381234528184,
+      "rf_loss": 0.00021437948453240097,
+      "total_loss": 1.04288191835635,
+      "lyap1_mean": -0.009396563284099102,
+      "lyap1_max": 0.005776097532361746,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 226,
+      "sup_loss": 0.9020646379965113,
+      "rf_loss": 0.0005184628535062075,
+      "total_loss": 0.9072492665315733,
+      "lyap1_mean": 0.005507745314389467,
+      "lyap1_max": 0.04297318309545517,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 227,
+      "sup_loss": 1.155286250266666,
+      "rf_loss": 0.0003320233372505754,
+      "total_loss": 1.1586064836973795,
+      "lyap1_mean": 0.009740143083035946,
+      "lyap1_max": 0.043023452162742615,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 228,
+      "sup_loss": 1.3090920042215646,
+      "rf_loss": 0.00043732966878451407,
+      "total_loss": 1.313465300851202,
+      "lyap1_mean": 0.010155659168958664,
+      "lyap1_max": 0.05580703541636467,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 229,
+      "sup_loss": 0.9454736266791252,
+      "rf_loss": 0.00071377691347152,
+      "total_loss": 0.9526113955810097,
+      "lyap1_mean": 0.031232386827468872,
+      "lyap1_max": 0.08235272765159607,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 230,
+      "sup_loss": 0.9688143573320436,
+      "rf_loss": 0.0003939494490623474,
+      "total_loss": 0.972753851822667,
+      "lyap1_mean": 0.012347599491477013,
+      "lyap1_max": 0.038280703127384186,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 231,
+      "sup_loss": 1.080645326817523,
+      "rf_loss": 0.00023701178724877536,
+      "total_loss": 1.0830154447482183,
+      "lyap1_mean": 0.0036642877385020256,
+      "lyap1_max": 0.019626928493380547,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 232,
+      "sup_loss": 1.0170740507959164,
+      "rf_loss": 0.00040199956856667995,
+      "total_loss": 1.0210940464815832,
+      "lyap1_mean": 0.02249947376549244,
+      "lyap1_max": 0.045361779630184174,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 233,
+      "sup_loss": 1.0718197468864585,
+      "rf_loss": 0.00035527104046195745,
+      "total_loss": 1.075372457291078,
+      "lyap1_mean": -0.012889394536614418,
+      "lyap1_max": 0.0024765280541032553,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 234,
+      "sup_loss": 1.0740169652597882,
+      "rf_loss": 0.00042519468115642667,
+      "total_loss": 1.0782689119549371,
+      "lyap1_mean": -0.005139858461916447,
+      "lyap1_max": 0.032853372395038605,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 235,
+      "sup_loss": 1.053878335804642,
+      "rf_loss": 0.0006923668552190065,
+      "total_loss": 1.060802004356832,
+      "lyap1_mean": -0.01437373273074627,
+      "lyap1_max": -0.0005521836574189365,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 236,
+      "sup_loss": 1.101505580617774,
+      "rf_loss": 0.00023306632647290826,
+      "total_loss": 1.1038362437660878,
+      "lyap1_mean": -0.0031446577049791813,
+      "lyap1_max": 0.02078188955783844,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 237,
+      "sup_loss": 1.0860282060424908,
+      "rf_loss": 0.0002825594274327159,
+      "total_loss": 1.088853800316818,
+      "lyap1_mean": 0.0017375325551256537,
+      "lyap1_max": 0.04200796037912369,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 238,
+      "sup_loss": 1.116761413247498,
+      "rf_loss": 0.00037331029307097197,
+      "total_loss": 1.1204945161782076,
+      "lyap1_mean": -0.003956994041800499,
+      "lyap1_max": 0.015233258716762066,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 239,
+      "sup_loss": 1.0827392053705738,
+      "rf_loss": 0.00041603719000704587,
+      "total_loss": 1.0868995774452672,
+      "lyap1_mean": 0.00977347418665886,
+      "lyap1_max": 0.04908054322004318,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 240,
+      "sup_loss": 1.167193739139784,
+      "rf_loss": 0.0007127605495043099,
+      "total_loss": 1.1743213445184117,
+      "lyap1_mean": 0.01351904310286045,
+      "lyap1_max": 0.055083077400922775,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 241,
+      "sup_loss": 1.1502273373417393,
+      "rf_loss": 0.0002528834156692028,
+      "total_loss": 1.1527561714984313,
+      "lyap1_mean": 0.007275504991412163,
+      "lyap1_max": 0.03570827469229698,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 242,
+      "sup_loss": 0.9769047248006257,
+      "rf_loss": 0.0006347870221361518,
+      "total_loss": 0.9832525952548179,
+      "lyap1_mean": 0.0059813037514686584,
+      "lyap1_max": 0.03335800766944885,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 243,
+      "sup_loss": 1.0778287535676085,
+      "rf_loss": 0.0002963563601952046,
+      "total_loss": 1.0807923172277683,
+      "lyap1_mean": 0.0033149709925055504,
+      "lyap1_max": 0.04205486178398132,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 244,
+      "sup_loss": 1.1436510434196558,
+      "rf_loss": 0.00021027745970059186,
+      "total_loss": 1.145753817987558,
+      "lyap1_mean": 0.005397175904363394,
+      "lyap1_max": 0.03145812079310417,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 245,
+      "sup_loss": 0.9964591785188841,
+      "rf_loss": 0.00041549449088051915,
+      "total_loss": 1.000614123311274,
+      "lyap1_mean": 0.01421111449599266,
+      "lyap1_max": 0.04318409413099289,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 246,
+      "sup_loss": 1.1503912009585322,
+      "rf_loss": 0.00032140599796548486,
+      "total_loss": 1.1536052608217717,
+      "lyap1_mean": -0.007486388087272644,
+      "lyap1_max": 0.002759923692792654,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 247,
+      "sup_loss": 0.985158399673448,
+      "rf_loss": 0.0003355597727932036,
+      "total_loss": 0.9885139972849647,
+      "lyap1_mean": -0.005212470423430204,
+      "lyap1_max": 0.029510242864489555,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 248,
+      "sup_loss": 0.9873357452134826,
+      "rf_loss": 0.00027210061671212316,
+      "total_loss": 0.9900567512641885,
+      "lyap1_mean": 0.0038145226426422596,
+      "lyap1_max": 0.02737104520201683,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 249,
+      "sup_loss": 0.8394017795071298,
+      "rf_loss": 0.0002795498294290155,
+      "total_loss": 0.8421972778596276,
+      "lyap1_mean": 0.0018518627621233463,
+      "lyap1_max": 0.03751225396990776,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 250,
+      "sup_loss": 1.0826316864671404,
+      "rf_loss": 0.00018370128236711025,
+      "total_loss": 1.0844686992908115,
+      "lyap1_mean": -0.007914356887340546,
+      "lyap1_max": 0.009681856259703636,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 251,
+      "sup_loss": 1.0697681142807347,
+      "rf_loss": 0.0002460549585521221,
+      "total_loss": 1.072228663866256,
+      "lyap1_mean": 0.00865616463124752,
+      "lyap1_max": 0.031496502459049225,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 252,
+      "sup_loss": 1.0095570532086138,
+      "rf_loss": 0.0004136253264732659,
+      "total_loss": 1.0136933063569311,
+      "lyap1_mean": 0.016592049971222878,
+      "lyap1_max": 0.03929860517382622,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 253,
+      "sup_loss": 1.1306624840589414,
+      "rf_loss": 0.000277303799521178,
+      "total_loss": 1.1334355221705685,
+      "lyap1_mean": -0.0006996877491474152,
+      "lyap1_max": 0.030703939497470856,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 254,
+      "sup_loss": 0.9361403511721619,
+      "rf_loss": 0.0003395423118490726,
+      "total_loss": 0.9395357742324449,
+      "lyap1_mean": 0.006946917623281479,
+      "lyap1_max": 0.04426782578229904,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 255,
+      "sup_loss": 1.0568800828858607,
+      "rf_loss": 0.000265790440607816,
+      "total_loss": 1.0595379871755235,
+      "lyap1_mean": 0.004944342188537121,
+      "lyap1_max": 0.025493085384368896,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 256,
+      "sup_loss": 1.152634748032339,
+      "rf_loss": 0.0006374926306307316,
+      "total_loss": 1.1590096743386462,
+      "lyap1_mean": 0.009020336903631687,
+      "lyap1_max": 0.06816211342811584,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 257,
+      "sup_loss": 0.9337560609408517,
+      "rf_loss": 0.00020099418179597706,
+      "total_loss": 0.9357660026715,
+      "lyap1_mean": 0.0007302706362679601,
+      "lyap1_max": 0.02342945896089077,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 258,
+      "sup_loss": 0.7755347639619564,
+      "rf_loss": 0.00023449858417734504,
+      "total_loss": 0.7778797499201452,
+      "lyap1_mean": -0.008167944848537445,
+      "lyap1_max": 0.01886557601392269,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 259,
+      "sup_loss": 1.0462627193765661,
+      "rf_loss": 0.00022802397143095732,
+      "total_loss": 1.0485429590908757,
+      "lyap1_mean": 0.005292356945574284,
+      "lyap1_max": 0.031203866004943848,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 260,
+      "sup_loss": 0.9636214970669021,
+      "rf_loss": 0.00036613750853575766,
+      "total_loss": 0.9672828720940521,
+      "lyap1_mean": 0.0028775986284017563,
+      "lyap1_max": 0.04055153578519821,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 261,
+      "sup_loss": 1.09045030947145,
+      "rf_loss": 0.00012848466576542705,
+      "total_loss": 1.091735156158208,
+      "lyap1_mean": 0.002666915999725461,
+      "lyap1_max": 0.025670250877738,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 262,
+      "sup_loss": 0.9290085646416469,
+      "rf_loss": 0.000533412559889257,
+      "total_loss": 0.9343426904733702,
+      "lyap1_mean": 0.016918715089559555,
+      "lyap1_max": 0.06419993191957474,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 263,
+      "sup_loss": 0.8995996638583751,
+      "rf_loss": 0.0005999940913170576,
+      "total_loss": 0.9055996047715457,
+      "lyap1_mean": 0.003375892760232091,
+      "lyap1_max": 0.02885797992348671,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 264,
+      "sup_loss": 0.9075340813577323,
+      "rf_loss": 0.00022225840075407177,
+      "total_loss": 0.9097566654525845,
+      "lyap1_mean": 0.003982872236520052,
+      "lyap1_max": 0.03640617057681084,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 265,
+      "sup_loss": 0.9095910432690519,
+      "rf_loss": 0.0002434904599795118,
+      "total_loss": 0.9120259479561585,
+      "lyap1_mean": 0.0037932260893285275,
+      "lyap1_max": 0.02825883775949478,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 266,
+      "sup_loss": 0.9307230435206396,
+      "rf_loss": 0.0003125971124973148,
+      "total_loss": 0.9338490147038204,
+      "lyap1_mean": 0.012463826686143875,
+      "lyap1_max": 0.02807118557393551,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 267,
+      "sup_loss": 0.9679079180349621,
+      "rf_loss": 0.00042212975677102804,
+      "total_loss": 0.972129215835503,
+      "lyap1_mean": 0.004506136290729046,
+      "lyap1_max": 0.03190257400274277,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 268,
+      "sup_loss": 1.032026557281363,
+      "rf_loss": 9.76300798356533e-05,
+      "total_loss": 1.0330028580797195,
+      "lyap1_mean": -0.0015024453168734908,
+      "lyap1_max": 0.019064662978053093,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 269,
+      "sup_loss": 0.9936065461241476,
+      "rf_loss": 0.00016726287140045315,
+      "total_loss": 0.9952791748090483,
+      "lyap1_mean": -0.0004863522481173277,
+      "lyap1_max": 0.022353988140821457,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 270,
+      "sup_loss": 0.8846222783946869,
+      "rf_loss": 0.0001271489600185305,
+      "total_loss": 0.8858937679366645,
+      "lyap1_mean": 8.248933590948582e-05,
+      "lyap1_max": 0.0207429900765419,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 271,
+      "sup_loss": 0.9104863714221458,
+      "rf_loss": 0.00031472009140998125,
+      "total_loss": 0.9136335723362456,
+      "lyap1_mean": -0.0010477022733539343,
+      "lyap1_max": 0.024186182767152786,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 272,
+      "sup_loss": 0.8969777711297647,
+      "rf_loss": 0.0003343627613503486,
+      "total_loss": 0.9003213986850606,
+      "lyap1_mean": 0.00872502475976944,
+      "lyap1_max": 0.059548329561948776,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 273,
+      "sup_loss": 1.0619163686683395,
+      "rf_loss": 0.000128305095131509,
+      "total_loss": 1.0631994196487584,
+      "lyap1_mean": 0.0013924074592068791,
+      "lyap1_max": 0.015342898666858673,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 274,
+      "sup_loss": 1.0778763103731173,
+      "rf_loss": 0.0004181234980933368,
+      "total_loss": 1.082057545470466,
+      "lyap1_mean": 0.025709977373480797,
+      "lyap1_max": 0.05004364252090454,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 275,
+      "sup_loss": 0.9578726684826656,
+      "rf_loss": 0.0005437140353024006,
+      "total_loss": 0.9633098088356896,
+      "lyap1_mean": 0.017253587022423744,
+      "lyap1_max": 0.08519332110881805,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 276,
+      "sup_loss": 0.9502594399997197,
+      "rf_loss": 0.0003478818107396364,
+      "total_loss": 0.9537382581071161,
+      "lyap1_mean": -0.013250810094177723,
+      "lyap1_max": 0.010615438222885132,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 277,
+      "sup_loss": 0.752728295509749,
+      "rf_loss": 0.0002720009651966393,
+      "total_loss": 0.7554483050453,
+      "lyap1_mean": 0.00645105168223381,
+      "lyap1_max": 0.027726655825972557,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 278,
+      "sup_loss": 1.0048978646998155,
+      "rf_loss": 0.00014452889445237815,
+      "total_loss": 1.006343153702547,
+      "lyap1_mean": 0.009242580272257328,
+      "lyap1_max": 0.03247532248497009,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 279,
+      "sup_loss": 1.052675516526254,
+      "rf_loss": 0.0004716835683211684,
+      "total_loss": 1.0573923524422963,
+      "lyap1_mean": 0.010205498896539211,
+      "lyap1_max": 0.03905957192182541,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 280,
+      "sup_loss": 1.1853878162427376,
+      "rf_loss": 0.00026345349033363163,
+      "total_loss": 1.1880223510878662,
+      "lyap1_mean": -0.009569738991558552,
+      "lyap1_max": 0.022395437583327293,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 281,
+      "sup_loss": 1.0773678932015534,
+      "rf_loss": 0.0001731758238747716,
+      "total_loss": 1.079099651440301,
+      "lyap1_mean": 0.005271016154438257,
+      "lyap1_max": 0.047857534140348434,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 282,
+      "sup_loss": 0.8603285052668211,
+      "rf_loss": 0.0002051343908533454,
+      "total_loss": 0.8623798491753546,
+      "lyap1_mean": -0.010942870751023293,
+      "lyap1_max": 0.003561045043170452,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 283,
+      "sup_loss": 0.9356869716598931,
+      "rf_loss": 0.00015103902842383832,
+      "total_loss": 0.9371973619732353,
+      "lyap1_mean": 0.004985013045370579,
+      "lyap1_max": 0.019862765446305275,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 284,
+      "sup_loss": 1.0969564626200619,
+      "rf_loss": 0.00021522499446291476,
+      "total_loss": 1.0991087125355872,
+      "lyap1_mean": 0.008212023414671421,
+      "lyap1_max": 0.03142416849732399,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 285,
+      "sup_loss": 1.2414483768607538,
+      "rf_loss": 0.00033073569647967815,
+      "total_loss": 1.2447557338255506,
+      "lyap1_mean": 0.0009542866609990597,
+      "lyap1_max": 0.03164326772093773,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 286,
+      "sup_loss": 0.7350290430421691,
+      "rf_loss": 0.00016585885896347463,
+      "total_loss": 0.7366876316900115,
+      "lyap1_mean": 0.0024000774137675762,
+      "lyap1_max": 0.022374724969267845,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 287,
+      "sup_loss": 1.1125125474280058,
+      "rf_loss": 0.00018027512123808265,
+      "total_loss": 1.1143152986403866,
+      "lyap1_mean": 0.0015682949451729655,
+      "lyap1_max": 0.011832288466393948,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 288,
+      "sup_loss": 0.9463507155053692,
+      "rf_loss": 0.00047821339103393257,
+      "total_loss": 0.9511328492410855,
+      "lyap1_mean": 0.006277003325521946,
+      "lyap1_max": 0.025196120142936707,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 289,
+      "sup_loss": 1.0818276311332948,
+      "rf_loss": 0.00030152907129377127,
+      "total_loss": 1.0848429218462325,
+      "lyap1_mean": 0.0023460621014237404,
+      "lyap1_max": 0.03763557970523834,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 290,
+      "sup_loss": 0.8731882458972361,
+      "rf_loss": 0.00032431521685793996,
+      "total_loss": 0.8764313979494002,
+      "lyap1_mean": 0.008599772118031979,
+      "lyap1_max": 0.03761935606598854,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 291,
+      "sup_loss": 0.9303160506045864,
+      "rf_loss": 0.000312640389893204,
+      "total_loss": 0.9334424543871032,
+      "lyap1_mean": -0.0007641860283911228,
+      "lyap1_max": 0.023944174870848656,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 292,
+      "sup_loss": 1.0779463318718576,
+      "rf_loss": 0.0002663324121385813,
+      "total_loss": 1.0806096559932434,
+      "lyap1_mean": 0.007997788488864899,
+      "lyap1_max": 0.04130307957530022,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 293,
+      "sup_loss": 0.8991983009940983,
+      "rf_loss": 0.0003481362364254892,
+      "total_loss": 0.9026796634747685,
+      "lyap1_mean": -0.007921327836811543,
+      "lyap1_max": 0.016246706247329712,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 294,
+      "sup_loss": 1.0019606907725125,
+      "rf_loss": 0.0002422334800940007,
+      "total_loss": 1.0043830256316602,
+      "lyap1_mean": -0.0028915423899888992,
+      "lyap1_max": 0.032470908015966415,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 295,
+      "sup_loss": 0.9582906459784285,
+      "rf_loss": 0.00011773454025387764,
+      "total_loss": 0.9594679913809673,
+      "lyap1_mean": 0.003170010168105364,
+      "lyap1_max": 0.015841446816921234,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 296,
+      "sup_loss": 1.0455321694078172,
+      "rf_loss": 0.00033107755007222295,
+      "total_loss": 1.0488429447921241,
+      "lyap1_mean": 0.010387985967099667,
+      "lyap1_max": 0.04452218860387802,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 297,
+      "sup_loss": 0.9115776640496467,
+      "rf_loss": 0.0003586995881050825,
+      "total_loss": 0.9151646599306975,
+      "lyap1_mean": -0.0005546128377318382,
+      "lyap1_max": 0.03546595200896263,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 298,
+      "sup_loss": 1.0530128818441955,
+      "rf_loss": 0.00011512800847413018,
+      "total_loss": 1.0541641619725926,
+      "lyap1_mean": -0.0008801508229225874,
+      "lyap1_max": 0.021047208458185196,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 299,
+      "sup_loss": 0.8539388545424843,
+      "rf_loss": 0.0003565078368410468,
+      "total_loss": 0.8575039329108948,
+      "lyap1_mean": 0.005254128947854042,
+      "lyap1_max": 0.034091074019670486,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 300,
+      "sup_loss": 1.2149988076841272,
+      "rf_loss": 0.00037528740358538926,
+      "total_loss": 1.2187516816617734,
+      "lyap1_mean": 0.011013287119567394,
+      "lyap1_max": 0.06026303395628929,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 301,
+      "sup_loss": 1.121959851667055,
+      "rf_loss": 0.0001968175347428769,
+      "total_loss": 1.1239280270726915,
+      "lyap1_mean": 0.003824469167739153,
+      "lyap1_max": 0.03919287398457527,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 302,
+      "sup_loss": 1.0335725128580189,
+      "rf_loss": 0.00027469033375382423,
+      "total_loss": 1.0363194161955571,
+      "lyap1_mean": 0.004753062501549721,
+      "lyap1_max": 0.05190999433398247,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 303,
+      "sup_loss": 1.1671561262474426,
+      "rf_loss": 0.00014054658822715282,
+      "total_loss": 1.168561592129714,
+      "lyap1_mean": 0.003499295562505722,
+      "lyap1_max": 0.01662776619195938,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 304,
+      "sup_loss": 0.8764641285969416,
+      "rf_loss": 0.00026471633464097977,
+      "total_loss": 0.8791112919433514,
+      "lyap1_mean": 0.004877040162682533,
+      "lyap1_max": 0.05040377378463745,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 305,
+      "sup_loss": 0.9300421700476202,
+      "rf_loss": 0.00015813770005479455,
+      "total_loss": 0.9316235470481682,
+      "lyap1_mean": 0.001994555117562413,
+      "lyap1_max": 0.0252141784876585,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 306,
+      "sup_loss": 0.9600932718866542,
+      "rf_loss": 0.000249681732384488,
+      "total_loss": 0.9625900892687067,
+      "lyap1_mean": -0.004738993011415005,
+      "lyap1_max": 0.01970631815493107,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 307,
+      "sup_loss": 1.3647865308918647,
+      "rf_loss": 0.00033346336567774415,
+      "total_loss": 1.3681211644322269,
+      "lyap1_mean": 0.009092768654227257,
+      "lyap1_max": 0.04349925369024277,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 308,
+      "sup_loss": 1.3679451076234057,
+      "rf_loss": 0.00022543178056366742,
+      "total_loss": 1.3701994253708347,
+      "lyap1_mean": 0.0007522033993154764,
+      "lyap1_max": 0.016748148947954178,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 309,
+      "sup_loss": 1.154708427701464,
+      "rf_loss": 0.00013611925533041358,
+      "total_loss": 1.1560696202547682,
+      "lyap1_mean": 0.00034841825254261494,
+      "lyap1_max": 0.01709853485226631,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 310,
+      "sup_loss": 1.081087706283893,
+      "rf_loss": 0.000587626826018095,
+      "total_loss": 1.086963974544074,
+      "lyap1_mean": 0.009529756382107735,
+      "lyap1_max": 0.044675882905721664,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 311,
+      "sup_loss": 1.0974215949162969,
+      "rf_loss": 0.000362647813744843,
+      "total_loss": 1.1010480730537453,
+      "lyap1_mean": 0.013234236277639866,
+      "lyap1_max": 0.04778950661420822,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 312,
+      "sup_loss": 0.8987146357428573,
+      "rf_loss": 0.000414027163060382,
+      "total_loss": 0.9028549075480841,
+      "lyap1_mean": 0.006011820398271084,
+      "lyap1_max": 0.03268713504076004,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 313,
+      "sup_loss": 1.0830792861980718,
+      "rf_loss": 0.0003822727594524622,
+      "total_loss": 1.0869020137925964,
+      "lyap1_mean": 0.018470890820026398,
+      "lyap1_max": 0.041744910180568695,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 314,
+      "sup_loss": 0.9824957111070218,
+      "rf_loss": 0.00024591354303993285,
+      "total_loss": 0.9849548464792135,
+      "lyap1_mean": 0.007922054268419743,
+      "lyap1_max": 0.03414861112833023,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 315,
+      "sup_loss": 1.3771233966104526,
+      "rf_loss": 0.00018958121654577553,
+      "total_loss": 1.3790192087177027,
+      "lyap1_mean": -0.0024757785722613335,
+      "lyap1_max": 0.036494672298431396,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 316,
+      "sup_loss": 0.8298621679544479,
+      "rf_loss": 0.00034772552317008376,
+      "total_loss": 0.833339423302564,
+      "lyap1_mean": -0.009493287652730942,
+      "lyap1_max": 0.018481489270925522,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 317,
+      "sup_loss": 0.9916976124029607,
+      "rf_loss": 0.00033965439070016146,
+      "total_loss": 0.9950941563099623,
+      "lyap1_mean": -0.006734323687851429,
+      "lyap1_max": 0.01448076218366623,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 318,
+      "sup_loss": 1.0002303839113837,
+      "rf_loss": 0.00011411843297537416,
+      "total_loss": 1.0013715682702413,
+      "lyap1_mean": -0.0029810962732881308,
+      "lyap1_max": 0.021305210888385773,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 319,
+      "sup_loss": 0.9520741027765507,
+      "rf_loss": 0.0003433647216297686,
+      "total_loss": 0.955507749876433,
+      "lyap1_mean": -0.004488220438361168,
+      "lyap1_max": 0.025625810027122498,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 320,
+      "sup_loss": 1.095055594305719,
+      "rf_loss": 0.000555111444555223,
+      "total_loss": 1.1006067089841018,
+      "lyap1_mean": 0.01818501017987728,
+      "lyap1_max": 0.1161310076713562,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 321,
+      "sup_loss": 0.7785177416517539,
+      "rf_loss": 0.00016802485333755612,
+      "total_loss": 0.7801979901851295,
+      "lyap1_mean": -0.0003561568446457386,
+      "lyap1_max": 0.020113863050937653,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 322,
+      "sup_loss": 0.8681229262003415,
+      "rf_loss": 0.00025662750704213977,
+      "total_loss": 0.8706892013871782,
+      "lyap1_mean": 0.005512955132871866,
+      "lyap1_max": 0.02251434326171875,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 323,
+      "sup_loss": 1.1058117233974782,
+      "rf_loss": 0.00011394551256671548,
+      "total_loss": 1.1069511785231454,
+      "lyap1_mean": 0.002059966092929244,
+      "lyap1_max": 0.028853219002485275,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 324,
+      "sup_loss": 0.913058392500713,
+      "rf_loss": 0.00011414177424740046,
+      "total_loss": 0.9141998102722908,
+      "lyap1_mean": 0.0024744197726249695,
+      "lyap1_max": 0.021056532859802246,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 325,
+      "sup_loss": 0.6799539199901409,
+      "rf_loss": 0.0003233517927583307,
+      "total_loss": 0.6831874379759318,
+      "lyap1_mean": 0.014051083475351334,
+      "lyap1_max": 0.04080867022275925,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 326,
+      "sup_loss": 0.8787945503300514,
+      "rf_loss": 0.00038063351530581713,
+      "total_loss": 0.8826008854831096,
+      "lyap1_mean": 0.010538322851061821,
+      "lyap1_max": 0.04964001104235649,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 327,
+      "sup_loss": 0.784834753632421,
+      "rf_loss": 0.0002655179123394191,
+      "total_loss": 0.7874899328722305,
+      "lyap1_mean": 0.011951249092817307,
+      "lyap1_max": 0.03370867297053337,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 328,
+      "sup_loss": 0.9751250767304056,
+      "rf_loss": 0.00047681419528089464,
+      "total_loss": 0.9798932187414222,
+      "lyap1_mean": 0.017605604603886604,
+      "lyap1_max": 0.04515125975012779,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 329,
+      "sup_loss": 0.9551126333728452,
+      "rf_loss": 0.00046763865975663066,
+      "total_loss": 0.9597890200868269,
+      "lyap1_mean": 0.012959316372871399,
+      "lyap1_max": 0.04129626974463463,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 330,
+      "sup_loss": 0.7221610902522556,
+      "rf_loss": 0.0002590991207398474,
+      "total_loss": 0.7247520813432388,
+      "lyap1_mean": 0.0033387893345206976,
+      "lyap1_max": 0.03531496226787567,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 331,
+      "sup_loss": 0.9316095899033161,
+      "rf_loss": 0.0005407368298619986,
+      "total_loss": 0.9370169582019361,
+      "lyap1_mean": 0.022625930607318878,
+      "lyap1_max": 0.08623620122671127,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 332,
+      "sup_loss": 1.0218263871531235,
+      "rf_loss": 0.0002166982740163803,
+      "total_loss": 1.0239933698932873,
+      "lyap1_mean": 0.0017000704538077116,
+      "lyap1_max": 0.029081394895911217,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 333,
+      "sup_loss": 1.206305903929167,
+      "rf_loss": 0.0005635605775751173,
+      "total_loss": 1.2119415095885029,
+      "lyap1_mean": 0.021087098866701126,
+      "lyap1_max": 0.08236978948116302,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 334,
+      "sup_loss": 0.9154593871842517,
+      "rf_loss": 0.0003040444862563163,
+      "total_loss": 0.9184998319886072,
+      "lyap1_mean": -0.009128250181674957,
+      "lyap1_max": 0.027163676917552948,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 335,
+      "sup_loss": 1.187291337967421,
+      "rf_loss": 0.00014994812954682857,
+      "total_loss": 1.1887908192337855,
+      "lyap1_mean": -0.007902855053544044,
+      "lyap1_max": 0.007139233406633139,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 336,
+      "sup_loss": 0.8527293912644349,
+      "rf_loss": 0.00033549655927345157,
+      "total_loss": 0.8560843569735848,
+      "lyap1_mean": -0.01018538512289524,
+      "lyap1_max": 0.01911241188645363,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 337,
+      "sup_loss": 1.0692330057746473,
+      "rf_loss": 0.0006673415191471577,
+      "total_loss": 1.0759064209661189,
+      "lyap1_mean": 0.013967202976346016,
+      "lyap1_max": 0.061089955270290375,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 338,
+      "sup_loss": 0.7319838444641105,
+      "rf_loss": 0.0004384373314678669,
+      "total_loss": 0.7363682177787891,
+      "lyap1_mean": -0.009291533380746841,
+      "lyap1_max": 0.021181872114539146,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 339,
+      "sup_loss": 1.0514821827977556,
+      "rf_loss": 0.000675171846523881,
+      "total_loss": 1.0582339012629944,
+      "lyap1_mean": 0.007509840186685324,
+      "lyap1_max": 0.07740071415901184,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 340,
+      "sup_loss": 0.7359326649005272,
+      "rf_loss": 0.00021511359955184162,
+      "total_loss": 0.7380838009542533,
+      "lyap1_mean": -0.0008759938646107912,
+      "lyap1_max": 0.008030189201235771,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 341,
+      "sup_loss": 0.9383540545505274,
+      "rf_loss": 0.00013673621288035065,
+      "total_loss": 0.9397214166502271,
+      "lyap1_mean": -0.0021684225648641586,
+      "lyap1_max": 0.021709468215703964,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 342,
+      "sup_loss": 0.7884947513366823,
+      "rf_loss": 0.000276244682027027,
+      "total_loss": 0.7912571982151603,
+      "lyap1_mean": 0.008152669295668602,
+      "lyap1_max": 0.03177519887685776,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 343,
+      "sup_loss": 1.064940362598969,
+      "rf_loss": 0.00034162806696258485,
+      "total_loss": 1.0683566433268026,
+      "lyap1_mean": 0.017071254551410675,
+      "lyap1_max": 0.03842056542634964,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 344,
+      "sup_loss": 0.8594845748655144,
+      "rf_loss": 0.0003790432238020003,
+      "total_loss": 0.8632750069871191,
+      "lyap1_mean": 0.008613400161266327,
+      "lyap1_max": 0.028519321233034134,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 345,
+      "sup_loss": 1.1814298734555604,
+      "rf_loss": 0.0001696634280961007,
+      "total_loss": 1.183126507794729,
+      "lyap1_mean": 0.010345511138439178,
+      "lyap1_max": 0.031803689897060394,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 346,
+      "sup_loss": 1.1159766688680965,
+      "rf_loss": 0.00021276919869706035,
+      "total_loss": 1.1181043609714825,
+      "lyap1_mean": 0.005540401674807072,
+      "lyap1_max": 0.01586437039077282,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 347,
+      "sup_loss": 1.0340430264418272,
+      "rf_loss": 0.0005294992588460445,
+      "total_loss": 1.0393380190302877,
+      "lyap1_mean": 0.013183236122131348,
+      "lyap1_max": 0.08564373105764389,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 348,
+      "sup_loss": 0.9994264558318292,
+      "rf_loss": 0.00017756785382516682,
+      "total_loss": 1.0012021343118733,
+      "lyap1_mean": -0.004585119895637035,
+      "lyap1_max": 0.010038898326456547,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 349,
+      "sup_loss": 1.2263221955383785,
+      "rf_loss": 0.0002763431693892926,
+      "total_loss": 1.229085627290479,
+      "lyap1_mean": 0.004654465243220329,
+      "lyap1_max": 0.03776645287871361,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 350,
+      "sup_loss": 1.3941747207106043,
+      "rf_loss": 0.00018406054005026817,
+      "total_loss": 1.396015326111107,
+      "lyap1_mean": 0.008423686027526855,
+      "lyap1_max": 0.03181745111942291,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 351,
+      "sup_loss": 1.22534088217917,
+      "rf_loss": 0.00030218384927138686,
+      "total_loss": 1.2283627207882992,
+      "lyap1_mean": 0.013569017872214317,
+      "lyap1_max": 0.044622913002967834,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 352,
+      "sup_loss": 1.080304407799997,
+      "rf_loss": 0.0003007336053997278,
+      "total_loss": 1.0833117438539943,
+      "lyap1_mean": 0.003958737477660179,
+      "lyap1_max": 0.043574340641498566,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 353,
+      "sup_loss": 1.3349123020710418,
+      "rf_loss": 0.0001876549213193357,
+      "total_loss": 1.3367888512842352,
+      "lyap1_mean": -0.003518640762194991,
+      "lyap1_max": 0.007055350579321384,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 354,
+      "sup_loss": 1.251232564480947,
+      "rf_loss": 0.00010363863839302212,
+      "total_loss": 1.2522689508357734,
+      "lyap1_mean": 0.0026369807310402393,
+      "lyap1_max": 0.026991665363311768,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 355,
+      "sup_loss": 1.3254964298715095,
+      "rf_loss": 0.00013097483315505087,
+      "total_loss": 1.3268061781448524,
+      "lyap1_mean": -0.0071022589690983295,
+      "lyap1_max": 0.009562360122799873,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 356,
+      "sup_loss": 1.263909702370704,
+      "rf_loss": 0.00018640977214090526,
+      "total_loss": 1.2657738001503207,
+      "lyap1_mean": 0.0013969263527542353,
+      "lyap1_max": 0.01885506883263588,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 357,
+      "sup_loss": 1.4420388968988382,
+      "rf_loss": 0.00023822789080440998,
+      "total_loss": 1.4444211758068823,
+      "lyap1_mean": 0.0038868095725774765,
+      "lyap1_max": 0.03816128149628639,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 358,
+      "sup_loss": 1.3221954301116337,
+      "rf_loss": 0.0003648524871096015,
+      "total_loss": 1.3258439549827297,
+      "lyap1_mean": -0.011446245014667511,
+      "lyap1_max": 0.014203188940882683,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 359,
+      "sup_loss": 1.4600006713493237,
+      "rf_loss": 0.00017445784760639071,
+      "total_loss": 1.4617452498253876,
+      "lyap1_mean": -0.010806001722812653,
+      "lyap1_max": -0.0021142694167792797,
+      "frac_above_star": 0.0
+    },
+    {
+      "step": 360,
+      "sup_loss": 1.2617126488618142,
+      "rf_loss": 0.00021674513118341565,
+      "total_loss": 1.263880100057233,
+      "lyap1_mean": -0.011703467927873135,
+      "lyap1_max": 0.00175301858689636,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 361,
+      "sup_loss": 1.2391684995705499,
+      "rf_loss": 0.00019129246356897056,
+      "total_loss": 1.2410814242644472,
+      "lyap1_mean": 0.011774942278862,
+      "lyap1_max": 0.042920924723148346,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 362,
+      "sup_loss": 1.287907683007912,
+      "rf_loss": 0.00022531817376147956,
+      "total_loss": 1.2901608647746305,
+      "lyap1_mean": -0.0023370557464659214,
+      "lyap1_max": 0.023363759741187096,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 363,
+      "sup_loss": 1.3065271054793488,
+      "rf_loss": 0.00012793790665455163,
+      "total_loss": 1.3078064844876867,
+      "lyap1_mean": 0.005582902114838362,
+      "lyap1_max": 0.009831767529249191,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 364,
+      "sup_loss": 1.0501869938656234,
+      "rf_loss": 0.0003034636320080608,
+      "total_loss": 1.0532216302439117,
+      "lyap1_mean": 0.0053802551701664925,
+      "lyap1_max": 0.027310606092214584,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 365,
+      "sup_loss": 1.1877936187014533,
+      "rf_loss": 0.00023500762472394854,
+      "total_loss": 1.1901436950360043,
+      "lyap1_mean": 0.003823372069746256,
+      "lyap1_max": 0.01880890689790249,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 366,
+      "sup_loss": 1.1845974759481885,
+      "rf_loss": 0.00019285958842374384,
+      "total_loss": 1.1865260717742183,
+      "lyap1_mean": -0.0016128437127918005,
+      "lyap1_max": 0.013367373496294022,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 367,
+      "sup_loss": 1.3801175412127895,
+      "rf_loss": 0.0003086091601289809,
+      "total_loss": 1.383203632697664,
+      "lyap1_mean": 0.004702698439359665,
+      "lyap1_max": 0.021957289427518845,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 368,
+      "sup_loss": 1.233350966419207,
+      "rf_loss": 0.00018309426377527416,
+      "total_loss": 1.2351819091151675,
+      "lyap1_mean": -0.00373384403064847,
+      "lyap1_max": 0.009887619875371456,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 369,
+      "sup_loss": 1.079629306382429,
+      "rf_loss": 0.00027894650702364743,
+      "total_loss": 1.0824187713944577,
+      "lyap1_mean": 0.004969208035618067,
+      "lyap1_max": 0.045279085636138916,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 370,
+      "sup_loss": 1.1612044408391462,
+      "rf_loss": 0.0001589454332133755,
+      "total_loss": 1.1627938952003838,
+      "lyap1_mean": 0.010250097140669823,
+      "lyap1_max": 0.022960161790251732,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 371,
+      "sup_loss": 1.1105263064356259,
+      "rf_loss": 0.00013328655040822923,
+      "total_loss": 1.1118591719979158,
+      "lyap1_mean": 0.0071141645312309265,
+      "lyap1_max": 0.02374442294239998,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 372,
+      "sup_loss": 1.2505591797072981,
+      "rf_loss": 0.000143919896800071,
+      "total_loss": 1.2519983786752988,
+      "lyap1_mean": -0.0012452811934053898,
+      "lyap1_max": 0.015960771590471268,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 373,
+      "sup_loss": 1.1139564943390932,
+      "rf_loss": 0.00017745689547155052,
+      "total_loss": 1.1157310632647048,
+      "lyap1_mean": 0.003988704644143581,
+      "lyap1_max": 0.03651796281337738,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 374,
+      "sup_loss": 1.2237324369407012,
+      "rf_loss": 0.00019839250307995826,
+      "total_loss": 1.225716361942397,
+      "lyap1_mean": 0.010357335209846497,
+      "lyap1_max": 0.035272255539894104,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 375,
+      "sup_loss": 1.0899787760067448,
+      "rf_loss": 0.00022452775738202035,
+      "total_loss": 1.0922240536387726,
+      "lyap1_mean": -8.107325993478298e-05,
+      "lyap1_max": 0.022107919678092003,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 376,
+      "sup_loss": 1.123450384027865,
+      "rf_loss": 0.00015028085908852518,
+      "total_loss": 1.1249531926769578,
+      "lyap1_mean": 0.001973537728190422,
+      "lyap1_max": 0.015876080840826035,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 377,
+      "sup_loss": 1.2591855021939329,
+      "rf_loss": 0.00016787178174126893,
+      "total_loss": 1.2608642199822417,
+      "lyap1_mean": 0.008563505485653877,
+      "lyap1_max": 0.029847566038370132,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 378,
+      "sup_loss": 1.0804782365519032,
+      "rf_loss": 0.0004546337586361915,
+      "total_loss": 1.0850245743128881,
+      "lyap1_mean": 0.009113127365708351,
+      "lyap1_max": 0.03771106153726578,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 379,
+      "sup_loss": 1.0381991516009477,
+      "rf_loss": 0.00026458263164386153,
+      "total_loss": 1.0408449780338016,
+      "lyap1_mean": 0.006091234739869833,
+      "lyap1_max": 0.032480351626873016,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 380,
+      "sup_loss": 1.1916563063312913,
+      "rf_loss": 0.00017718999879434705,
+      "total_loss": 1.1934282063192347,
+      "lyap1_mean": -0.0030681448988616467,
+      "lyap1_max": 0.022553831338882446,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 381,
+      "sup_loss": 1.0032797915874823,
+      "rf_loss": 0.0003842143341898918,
+      "total_loss": 1.0071219349293812,
+      "lyap1_mean": 0.009876305237412453,
+      "lyap1_max": 0.03628404811024666,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 382,
+      "sup_loss": 1.142826239037314,
+      "rf_loss": 0.00013090905849821866,
+      "total_loss": 1.1441353295640886,
+      "lyap1_mean": 0.006887707859277725,
+      "lyap1_max": 0.03194943815469742,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 383,
+      "sup_loss": 0.9310589259073424,
+      "rf_loss": 0.00010744499013526365,
+      "total_loss": 0.9321333757650393,
+      "lyap1_mean": 0.0011878975201398134,
+      "lyap1_max": 0.012140262871980667,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 384,
+      "sup_loss": 1.028501722570121,
+      "rf_loss": 0.00026126779266633093,
+      "total_loss": 1.0311144004385766,
+      "lyap1_mean": 0.0030875822994858027,
+      "lyap1_max": 0.03217481076717377,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 385,
+      "sup_loss": 1.1138046220552908,
+      "rf_loss": 0.00012794131180271506,
+      "total_loss": 1.115084035173318,
+      "lyap1_mean": -0.00037476280704140663,
+      "lyap1_max": 0.0138908876106143,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 386,
+      "sup_loss": 1.050057915070511,
+      "rf_loss": 0.0002033141499850899,
+      "total_loss": 1.0520910565121542,
+      "lyap1_mean": 0.0027106227353215218,
+      "lyap1_max": 0.01858283393085003,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 387,
+      "sup_loss": 1.1507119303481743,
+      "rf_loss": 9.296108328271657e-05,
+      "total_loss": 1.1516415411518977,
+      "lyap1_mean": -0.0007836036384105682,
+      "lyap1_max": 0.013314811512827873,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 388,
+      "sup_loss": 1.151770404189694,
+      "rf_loss": 0.00019207912555430084,
+      "total_loss": 1.153691195416133,
+      "lyap1_mean": 0.006048441864550114,
+      "lyap1_max": 0.028743743896484375,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 389,
+      "sup_loss": 1.0694503021407835,
+      "rf_loss": 0.00013765548646915704,
+      "total_loss": 1.0708268569763713,
+      "lyap1_mean": -0.00048176327254623175,
+      "lyap1_max": 0.014707330614328384,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 390,
+      "sup_loss": 1.1375670169240482,
+      "rf_loss": 0.0002287014212924987,
+      "total_loss": 1.1398540310787655,
+      "lyap1_mean": 0.010357031598687172,
+      "lyap1_max": 0.07017502188682556,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 391,
+      "sup_loss": 0.9701064315410858,
+      "rf_loss": 0.00016050078556872904,
+      "total_loss": 0.9717114393385654,
+      "lyap1_mean": 0.009876640513539314,
+      "lyap1_max": 0.026254726573824883,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 392,
+      "sup_loss": 1.2244743657589006,
+      "rf_loss": 0.0002681146143004298,
+      "total_loss": 1.2271555119019049,
+      "lyap1_mean": 0.010869324207305908,
+      "lyap1_max": 0.03623178228735924,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 393,
+      "sup_loss": 1.1343000051198502,
+      "rf_loss": 0.0001446238165954128,
+      "total_loss": 1.1357462432567005,
+      "lyap1_mean": 0.003527736756950617,
+      "lyap1_max": 0.0220952145755291,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 394,
+      "sup_loss": 1.196085572436803,
+      "rf_loss": 0.00022083143994677812,
+      "total_loss": 1.1982938868071669,
+      "lyap1_mean": 0.012472571805119514,
+      "lyap1_max": 0.053791191428899765,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 395,
+      "sup_loss": 1.2199425143337148,
+      "rf_loss": 0.00017626742192078382,
+      "total_loss": 1.2217051885238188,
+      "lyap1_mean": -0.0004278027918189764,
+      "lyap1_max": 0.013471233658492565,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 396,
+      "sup_loss": 0.7947830341409854,
+      "rf_loss": 0.00010621130786603317,
+      "total_loss": 0.7958451472341976,
+      "lyap1_mean": 0.0041083539836108685,
+      "lyap1_max": 0.021584980189800262,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 397,
+      "sup_loss": 0.7343786382171311,
+      "rf_loss": 0.0002065861044684425,
+      "total_loss": 0.736444499349127,
+      "lyap1_mean": -0.0014899743255227804,
+      "lyap1_max": 0.015170207247138023,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 398,
+      "sup_loss": 0.9782658763861378,
+      "rf_loss": 0.0002796636545099318,
+      "total_loss": 0.9810625128148218,
+      "lyap1_mean": -0.012767158448696136,
+      "lyap1_max": 0.006639161612838507,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 399,
+      "sup_loss": 1.0500324255566102,
+      "rf_loss": 0.00022400807938538492,
+      "total_loss": 1.0522725064086718,
+      "lyap1_mean": -0.0003042339812964201,
+      "lyap1_max": 0.025292297825217247,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 400,
+      "sup_loss": 0.8180437137914074,
+      "rf_loss": 9.09142690943554e-05,
+      "total_loss": 0.8189528564532471,
+      "lyap1_mean": -0.006622130982577801,
+      "lyap1_max": 0.00855043064802885,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 401,
+      "sup_loss": 1.0000554325032618,
+      "rf_loss": 0.0001435068843420595,
+      "total_loss": 1.00149050140489,
+      "lyap1_mean": 0.005912610329687595,
+      "lyap1_max": 0.028700508177280426,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 402,
+      "sup_loss": 0.9591471450484552,
+      "rf_loss": 7.653752254555002e-05,
+      "total_loss": 0.9599125202593588,
+      "lyap1_mean": 0.008854338899254799,
+      "lyap1_max": 0.02040625736117363,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 403,
+      "sup_loss": 1.0009591496883465,
+      "rf_loss": 0.0002892955089919269,
+      "total_loss": 1.0038521048946811,
+      "lyap1_mean": 0.011423304677009583,
+      "lyap1_max": 0.03423696756362915,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 404,
+      "sup_loss": 0.8706963161947822,
+      "rf_loss": 0.0007900966447778046,
+      "total_loss": 0.8785972825261449,
+      "lyap1_mean": 0.02581450529396534,
+      "lyap1_max": 0.11038391292095184,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 405,
+      "sup_loss": 1.1305101409916338,
+      "rf_loss": 0.00029067861032672226,
+      "total_loss": 1.1334169270366934,
+      "lyap1_mean": 0.006183884106576443,
+      "lyap1_max": 0.01798461377620697,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 406,
+      "sup_loss": 1.0155706046126656,
+      "rf_loss": 0.00021247894619591534,
+      "total_loss": 1.017695394016417,
+      "lyap1_mean": -0.00032917968928813934,
+      "lyap1_max": 0.021476786583662033,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 407,
+      "sup_loss": 1.1746004913638923,
+      "rf_loss": 0.0004217844398226589,
+      "total_loss": 1.1788183358203266,
+      "lyap1_mean": 0.017555832862854004,
+      "lyap1_max": 0.04392223060131073,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 408,
+      "sup_loss": 0.9592317995741283,
+      "rf_loss": 0.0001943783281603828,
+      "total_loss": 0.9611755828266283,
+      "lyap1_mean": 0.005125498399138451,
+      "lyap1_max": 0.024367816746234894,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 409,
+      "sup_loss": 1.2447842966859104,
+      "rf_loss": 9.965807112166658e-05,
+      "total_loss": 1.2457808773825751,
+      "lyap1_mean": -0.003721399698406458,
+      "lyap1_max": 0.011587707325816154,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 410,
+      "sup_loss": 0.8120858097181543,
+      "rf_loss": 0.00012850650819018483,
+      "total_loss": 0.8133708748000561,
+      "lyap1_mean": -0.007047614548355341,
+      "lyap1_max": 0.0034825631882995367,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 411,
+      "sup_loss": 1.1551669657357988,
+      "rf_loss": 0.00013326901535037905,
+      "total_loss": 1.1564996558601988,
+      "lyap1_mean": 0.006064196117222309,
+      "lyap1_max": 0.026074018329381943,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 412,
+      "sup_loss": 0.9344849563434076,
+      "rf_loss": 0.00036407820880413055,
+      "total_loss": 0.9381257384314489,
+      "lyap1_mean": 0.006213470362126827,
+      "lyap1_max": 0.029989294707775116,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 413,
+      "sup_loss": 0.8140205679587659,
+      "rf_loss": 0.00013286796456668526,
+      "total_loss": 0.8153492475753289,
+      "lyap1_mean": -0.0055029625073075294,
+      "lyap1_max": 0.014025242999196053,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 414,
+      "sup_loss": 1.1731134135091337,
+      "rf_loss": 0.0002689448301680386,
+      "total_loss": 1.1758028616943987,
+      "lyap1_mean": -0.0004047991242259741,
+      "lyap1_max": 0.022194989025592804,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 415,
+      "sup_loss": 0.8704159763288593,
+      "rf_loss": 0.00012396840611472726,
+      "total_loss": 0.8716556603900065,
+      "lyap1_mean": -0.0011062358971685171,
+      "lyap1_max": 0.02740764617919922,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 416,
+      "sup_loss": 1.0897742532859753,
+      "rf_loss": 0.00025049594114534557,
+      "total_loss": 1.0922792127556364,
+      "lyap1_mean": 0.011989302933216095,
+      "lyap1_max": 0.030461367219686508,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 417,
+      "sup_loss": 1.0620598632865086,
+      "rf_loss": 0.00016979017527773976,
+      "total_loss": 1.063757765039286,
+      "lyap1_mean": 0.006981579586863518,
+      "lyap1_max": 0.02535887621343136,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 418,
+      "sup_loss": 0.808273106911827,
+      "rf_loss": 0.0001408795069437474,
+      "total_loss": 0.8096819020394721,
+      "lyap1_mean": 0.00596007052809,
+      "lyap1_max": 0.031172018498182297,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 419,
+      "sup_loss": 0.9142171330219943,
+      "rf_loss": 0.0003380377893336117,
+      "total_loss": 0.917597510798915,
+      "lyap1_mean": 0.01705130934715271,
+      "lyap1_max": 0.06398850679397583,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 420,
+      "sup_loss": 0.9617330447913179,
+      "rf_loss": 0.0002496945089660585,
+      "total_loss": 0.9642299899973938,
+      "lyap1_mean": -0.003841282334178686,
+      "lyap1_max": 0.015298145823180676,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 421,
+      "sup_loss": 0.8119553811207507,
+      "rf_loss": 0.0002456233778502792,
+      "total_loss": 0.8144116149574612,
+      "lyap1_mean": -0.005337407812476158,
+      "lyap1_max": 0.007728729397058487,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 422,
+      "sup_loss": 0.9304124530647581,
+      "rf_loss": 0.00028812268283218145,
+      "total_loss": 0.9332936798930799,
+      "lyap1_mean": 0.006114087533205748,
+      "lyap1_max": 0.050455134361982346,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 423,
+      "sup_loss": 0.761070092981577,
+      "rf_loss": 0.00022577632626052946,
+      "total_loss": 0.7633278561568708,
+      "lyap1_mean": -0.00252908025868237,
+      "lyap1_max": 0.024110784754157066,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 424,
+      "sup_loss": 1.049634882633962,
+      "rf_loss": 0.0001996136415982619,
+      "total_loss": 1.0516310191372562,
+      "lyap1_mean": 0.003937261179089546,
+      "lyap1_max": 0.03633200749754906,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 425,
+      "sup_loss": 0.7018263924053469,
+      "rf_loss": 0.00022678286768496037,
+      "total_loss": 0.7040942210821965,
+      "lyap1_mean": 0.00972006842494011,
+      "lyap1_max": 0.02682158350944519,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 426,
+      "sup_loss": 0.8947472050078208,
+      "rf_loss": 0.00018042004376184195,
+      "total_loss": 0.896551405474543,
+      "lyap1_mean": -0.007722445763647556,
+      "lyap1_max": 0.020267000421881676,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 427,
+      "sup_loss": 0.9828809867898235,
+      "rf_loss": 0.0002937359968200326,
+      "total_loss": 0.9858183467580238,
+      "lyap1_mean": 0.002162827178835869,
+      "lyap1_max": 0.022141367197036743,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 428,
+      "sup_loss": 0.9004100952293768,
+      "rf_loss": 0.00030195596627891064,
+      "total_loss": 0.9034296548921659,
+      "lyap1_mean": 0.012259379029273987,
+      "lyap1_max": 0.05270169675350189,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 429,
+      "sup_loss": 1.0260231446036565,
+      "rf_loss": 0.00012353371130302548,
+      "total_loss": 1.0272584817166868,
+      "lyap1_mean": 0.0014991620555520058,
+      "lyap1_max": 0.02733161859214306,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 430,
+      "sup_loss": 0.8128634623409424,
+      "rf_loss": 8.170215005520731e-05,
+      "total_loss": 0.8136804838123907,
+      "lyap1_mean": 0.0008925471920520067,
+      "lyap1_max": 0.01210947334766388,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 431,
+      "sup_loss": 1.1953809196863263,
+      "rf_loss": 0.0005463545676320791,
+      "total_loss": 1.200844465362647,
+      "lyap1_mean": 0.0165341105312109,
+      "lyap1_max": 0.05025937408208847,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 432,
+      "sup_loss": 0.7045512101297443,
+      "rf_loss": 0.0001785964414011687,
+      "total_loss": 0.7063371746019637,
+      "lyap1_mean": -0.0025741667486727238,
+      "lyap1_max": 0.01912851072847843,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 433,
+      "sup_loss": 0.7724261176272502,
+      "rf_loss": 0.0001685835886746645,
+      "total_loss": 0.7741119535139969,
+      "lyap1_mean": 0.0009917537681758404,
+      "lyap1_max": 0.01728457398712635,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 434,
+      "sup_loss": 0.8163505202093894,
+      "rf_loss": 0.000297651335131377,
+      "total_loss": 0.8193270336771185,
+      "lyap1_mean": -0.004546039737761021,
+      "lyap1_max": 0.03893832862377167,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 435,
+      "sup_loss": 0.6661284781844596,
+      "rf_loss": 0.00021682720398530364,
+      "total_loss": 0.668296750340728,
+      "lyap1_mean": 0.004550142213702202,
+      "lyap1_max": 0.03740696236491203,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 436,
+      "sup_loss": 0.7093524203025413,
+      "rf_loss": 0.00019765947945415974,
+      "total_loss": 0.7113290150970829,
+      "lyap1_mean": 0.006915641017258167,
+      "lyap1_max": 0.04001639038324356,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 437,
+      "sup_loss": 0.8130339399726121,
+      "rf_loss": 0.00020619196584448218,
+      "total_loss": 0.8150958597474722,
+      "lyap1_mean": 0.003460107371211052,
+      "lyap1_max": 0.03118758462369442,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 438,
+      "sup_loss": 0.80236313015619,
+      "rf_loss": 0.0003736149810720235,
+      "total_loss": 0.8060992799087026,
+      "lyap1_mean": 0.011024948209524155,
+      "lyap1_max": 0.0461135171353817,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 439,
+      "sup_loss": 0.7831381790968617,
+      "rf_loss": 0.0002050996117759496,
+      "total_loss": 0.7851891751564135,
+      "lyap1_mean": 0.008586326614022255,
+      "lyap1_max": 0.03315954655408859,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 440,
+      "sup_loss": 0.9917460121817269,
+      "rf_loss": 0.00016440813487861305,
+      "total_loss": 0.9933900935014092,
+      "lyap1_mean": 0.01062854379415512,
+      "lyap1_max": 0.024557411670684814,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 441,
+      "sup_loss": 0.7904166921792043,
+      "rf_loss": 0.0003805853775702417,
+      "total_loss": 0.794222546071322,
+      "lyap1_mean": 0.011500408872961998,
+      "lyap1_max": 0.05230266973376274,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 442,
+      "sup_loss": 0.8901183328387173,
+      "rf_loss": 0.0003032599634025246,
+      "total_loss": 0.8931509324145349,
+      "lyap1_mean": -0.0037205442786216736,
+      "lyap1_max": 0.024389095604419708,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 443,
+      "sup_loss": 1.0916506432580422,
+      "rf_loss": 0.00038087263237684965,
+      "total_loss": 1.0954593695818107,
+      "lyap1_mean": 0.004950481932610273,
+      "lyap1_max": 0.02659011445939541,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 444,
+      "sup_loss": 1.0132904142750943,
+      "rf_loss": 0.0002029124734690413,
+      "total_loss": 1.0153195389224732,
+      "lyap1_mean": -0.006262922193855047,
+      "lyap1_max": 0.023304184898734093,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 445,
+      "sup_loss": 0.8127069376189624,
+      "rf_loss": 0.00035192479845136404,
+      "total_loss": 0.816226185603476,
+      "lyap1_mean": -0.002635346259921789,
+      "lyap1_max": 0.011630894616246223,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 446,
+      "sup_loss": 1.038486163416464,
+      "rf_loss": 0.00015108796651475132,
+      "total_loss": 1.039997043139819,
+      "lyap1_mean": -0.0032633549999445677,
+      "lyap1_max": 0.014789674431085587,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 447,
+      "sup_loss": 0.7831251728938405,
+      "rf_loss": 0.00015550723765045404,
+      "total_loss": 0.7846802452703451,
+      "lyap1_mean": 0.0017000468214973807,
+      "lyap1_max": 0.016134917736053467,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 448,
+      "sup_loss": 1.0991620175902141,
+      "rf_loss": 0.00019220502872485667,
+      "total_loss": 1.1010840678483589,
+      "lyap1_mean": -0.00019003788474947214,
+      "lyap1_max": 0.03460751846432686,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 449,
+      "sup_loss": 0.9027748921038574,
+      "rf_loss": 0.00015335682837758213,
+      "total_loss": 0.9043084603585294,
+      "lyap1_mean": 0.005817316472530365,
+      "lyap1_max": 0.026541180908679962,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 450,
+      "sup_loss": 0.879878890644814,
+      "rf_loss": 0.0001899571652757004,
+      "total_loss": 0.8817784622684671,
+      "lyap1_mean": 0.004961543716490269,
+      "lyap1_max": 0.035123832523822784,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 451,
+      "sup_loss": 0.8195991862582063,
+      "rf_loss": 0.00017697250586934388,
+      "total_loss": 0.821368911258692,
+      "lyap1_mean": 0.009609140455722809,
+      "lyap1_max": 0.04792419821023941,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 452,
+      "sup_loss": 0.7434841318700814,
+      "rf_loss": 0.00028706894954666495,
+      "total_loss": 0.7463548214819634,
+      "lyap1_mean": -0.004553697071969509,
+      "lyap1_max": 0.03293677419424057,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 453,
+      "sup_loss": 0.7687443513036182,
+      "rf_loss": 0.00040055406861938536,
+      "total_loss": 0.7727498919316044,
+      "lyap1_mean": -0.0037581524811685085,
+      "lyap1_max": 0.018606944009661674,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 454,
+      "sup_loss": 0.783732918978408,
+      "rf_loss": 0.00013063426013104618,
+      "total_loss": 0.7850392616379261,
+      "lyap1_mean": 0.007669462822377682,
+      "lyap1_max": 0.017591215670108795,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 455,
+      "sup_loss": 0.9891923215250988,
+      "rf_loss": 0.0001631182967685163,
+      "total_loss": 0.990823504492784,
+      "lyap1_mean": -0.00887141190469265,
+      "lyap1_max": 0.0006580482004210353,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 456,
+      "sup_loss": 0.7137246155109548,
+      "rf_loss": 0.00031039788154885173,
+      "total_loss": 0.7168285944428586,
+      "lyap1_mean": 0.0035253644455224276,
+      "lyap1_max": 0.026791658252477646,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 457,
+      "sup_loss": 0.95654672712592,
+      "rf_loss": 0.00023773466818965971,
+      "total_loss": 0.958924073749609,
+      "lyap1_mean": 0.008907515555620193,
+      "lyap1_max": 0.023876488208770752,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 458,
+      "sup_loss": 0.7696645401700993,
+      "rf_loss": 0.00010521988588152453,
+      "total_loss": 0.7707167389852588,
+      "lyap1_mean": 0.003364754840731621,
+      "lyap1_max": 0.0209212563931942,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 459,
+      "sup_loss": 0.8935957309189685,
+      "rf_loss": 0.0002011849283007905,
+      "total_loss": 0.8956075802310802,
+      "lyap1_mean": 0.00449997978284955,
+      "lyap1_max": 0.022802961990237236,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 460,
+      "sup_loss": 0.9149104181049157,
+      "rf_loss": 0.00012357189552858472,
+      "total_loss": 0.9161461370602015,
+      "lyap1_mean": -2.2445747163146734e-05,
+      "lyap1_max": 0.01583683118224144,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 461,
+      "sup_loss": 0.8372265705793426,
+      "rf_loss": 0.00029270100640133023,
+      "total_loss": 0.8401535805269406,
+      "lyap1_mean": 0.0004579296801239252,
+      "lyap1_max": 0.03357531130313873,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 462,
+      "sup_loss": 0.7221520624936802,
+      "rf_loss": 0.0005827448912896216,
+      "total_loss": 0.7279795112901611,
+      "lyap1_mean": 0.00817757286131382,
+      "lyap1_max": 0.0904807299375534,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 463,
+      "sup_loss": 1.1397522089984224,
+      "rf_loss": 9.979658352676779e-05,
+      "total_loss": 1.1407501748045863,
+      "lyap1_mean": -0.0028882347978651524,
+      "lyap1_max": 0.0036767697893083096,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 464,
+      "sup_loss": 0.8244374136539226,
+      "rf_loss": 0.00021412112982943654,
+      "total_loss": 0.8265786248358017,
+      "lyap1_mean": 0.0026068217121064663,
+      "lyap1_max": 0.034244105219841,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 465,
+      "sup_loss": 0.8548496595292202,
+      "rf_loss": 0.00020204123575240374,
+      "total_loss": 0.8568700718867442,
+      "lyap1_mean": 0.004719071555882692,
+      "lyap1_max": 0.023445677012205124,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 466,
+      "sup_loss": 0.793412877995073,
+      "rf_loss": 0.0003364844887983054,
+      "total_loss": 0.7967777229412637,
+      "lyap1_mean": 0.014630552381277084,
+      "lyap1_max": 0.08415313810110092,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 467,
+      "sup_loss": 1.0101640708537587,
+      "rf_loss": 0.00037870698724873364,
+      "total_loss": 1.0139511406680384,
+      "lyap1_mean": 0.003153675701469183,
+      "lyap1_max": 0.02459203265607357,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 468,
+      "sup_loss": 0.9609871072096323,
+      "rf_loss": 0.00015309994341805577,
+      "total_loss": 0.9625181066438129,
+      "lyap1_mean": -0.002050811890512705,
+      "lyap1_max": 0.012179492972791195,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 469,
+      "sup_loss": 0.8342378414303732,
+      "rf_loss": 0.0002989508502651006,
+      "total_loss": 0.8372273498748165,
+      "lyap1_mean": 0.0012196569005027413,
+      "lyap1_max": 0.027616962790489197,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 470,
+      "sup_loss": 0.8970713537749709,
+      "rf_loss": 0.00022131259902380407,
+      "total_loss": 0.8992844798234166,
+      "lyap1_mean": 0.004970638081431389,
+      "lyap1_max": 0.03616394102573395,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 471,
+      "sup_loss": 1.091819400032706,
+      "rf_loss": 0.0002916678786277771,
+      "total_loss": 1.0947360788189837,
+      "lyap1_mean": 0.0044304197654128075,
+      "lyap1_max": 0.03935844823718071,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 472,
+      "sup_loss": 0.8795000460771062,
+      "rf_loss": 0.00026558764511719346,
+      "total_loss": 0.8821559224118628,
+      "lyap1_mean": 0.009968604892492294,
+      "lyap1_max": 0.028528472408652306,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 473,
+      "sup_loss": 0.851652783911088,
+      "rf_loss": 0.0004928096896037459,
+      "total_loss": 0.8565808810399561,
+      "lyap1_mean": 0.008000164292752743,
+      "lyap1_max": 0.042568475008010864,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 474,
+      "sup_loss": 0.7530638174373433,
+      "rf_loss": 0.0005161025328561664,
+      "total_loss": 0.7582248429987356,
+      "lyap1_mean": 0.003302076831459999,
+      "lyap1_max": 0.03553623706102371,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 475,
+      "sup_loss": 1.1689185693555317,
+      "rf_loss": 0.00020331505220383406,
+      "total_loss": 1.17095171987757,
+      "lyap1_mean": 0.004208677913993597,
+      "lyap1_max": 0.04931088909506798,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 476,
+      "sup_loss": 0.8597965269865548,
+      "rf_loss": 0.00023150441120378673,
+      "total_loss": 0.8621115711568004,
+      "lyap1_mean": 0.008306534960865974,
+      "lyap1_max": 0.04106663912534714,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 477,
+      "sup_loss": 0.9472331928562051,
+      "rf_loss": 0.0002491585328243673,
+      "total_loss": 0.9497247783008641,
+      "lyap1_mean": -0.0016983848763629794,
+      "lyap1_max": 0.014881202951073647,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 478,
+      "sup_loss": 0.860688777676741,
+      "rf_loss": 0.0001270508801098913,
+      "total_loss": 0.8619592865360476,
+      "lyap1_mean": -0.0009393058717250824,
+      "lyap1_max": 0.009995116852223873,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 479,
+      "sup_loss": 1.0486947804247986,
+      "rf_loss": 0.0002609976218082011,
+      "total_loss": 1.0513047565264653,
+      "lyap1_mean": 0.006258043460547924,
+      "lyap1_max": 0.02720521204173565,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 480,
+      "sup_loss": 1.121525591574981,
+      "rf_loss": 0.00016641525144223124,
+      "total_loss": 1.1231897440602996,
+      "lyap1_mean": 0.006540575996041298,
+      "lyap1_max": 0.0355600044131279,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 481,
+      "sup_loss": 1.057449530267506,
+      "rf_loss": 0.00018754623306449503,
+      "total_loss": 1.0593249926272548,
+      "lyap1_mean": 0.011100571602582932,
+      "lyap1_max": 0.039724864065647125,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 482,
+      "sup_loss": 1.312692209137756,
+      "rf_loss": 0.0002564340829849243,
+      "total_loss": 1.3152565499676052,
+      "lyap1_mean": 0.0017195316031575203,
+      "lyap1_max": 0.03209944814443588,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 483,
+      "sup_loss": 1.0750270822114105,
+      "rf_loss": 0.00017695879796519876,
+      "total_loss": 1.0767966701910625,
+      "lyap1_mean": -0.004613772034645081,
+      "lyap1_max": 0.019841820001602173,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 484,
+      "sup_loss": 1.0972600785189857,
+      "rf_loss": 0.000256759871263057,
+      "total_loss": 1.099827677115201,
+      "lyap1_mean": 0.0002938124816864729,
+      "lyap1_max": 0.028758954256772995,
+      "frac_above_star": 0.375
+    },
+    {
+      "step": 485,
+      "sup_loss": 1.5717814204347351,
+      "rf_loss": 0.00022034277208149433,
+      "total_loss": 1.57398484815555,
+      "lyap1_mean": 0.005202624946832657,
+      "lyap1_max": 0.047223374247550964,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 486,
+      "sup_loss": 1.038547689716165,
+      "rf_loss": 0.00022077056928537786,
+      "total_loss": 1.0407553954672264,
+      "lyap1_mean": 0.009502502158284187,
+      "lyap1_max": 0.031245078891515732,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 487,
+      "sup_loss": 1.1550944493534074,
+      "rf_loss": 0.00023151186178438365,
+      "total_loss": 1.157409568029459,
+      "lyap1_mean": 0.006009435281157494,
+      "lyap1_max": 0.04078226909041405,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 488,
+      "sup_loss": 1.0139076440501222,
+      "rf_loss": 0.0002623593609314412,
+      "total_loss": 1.0165312377176443,
+      "lyap1_mean": 0.014781896956264973,
+      "lyap1_max": 0.03157062828540802,
+      "frac_above_star": 1.0
+    },
+    {
+      "step": 489,
+      "sup_loss": 0.9591013920003194,
+      "rf_loss": 0.00012372503988444805,
+      "total_loss": 0.9603386423991639,
+      "lyap1_mean": 0.00815177895128727,
+      "lyap1_max": 0.020150594413280487,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 490,
+      "sup_loss": 1.2424928080642028,
+      "rf_loss": 0.0002221881877630949,
+      "total_loss": 1.2447146899418338,
+      "lyap1_mean": 0.0021297757048159838,
+      "lyap1_max": 0.028949718922376633,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 491,
+      "sup_loss": 1.1861002699570833,
+      "rf_loss": 9.679965296527371e-05,
+      "total_loss": 1.187068266501288,
+      "lyap1_mean": 0.004792722873389721,
+      "lyap1_max": 0.02008082903921604,
+      "frac_above_star": 0.75
+    },
+    {
+      "step": 492,
+      "sup_loss": 1.2069549940063546,
+      "rf_loss": 0.00016075800522230566,
+      "total_loss": 1.2085625741167854,
+      "lyap1_mean": 0.003924306482076645,
+      "lyap1_max": 0.019428851082921028,
+      "frac_above_star": 0.625
+    },
+    {
+      "step": 493,
+      "sup_loss": 1.131112771234349,
+      "rf_loss": 0.000112085064756684,
+      "total_loss": 1.1322336219110196,
+      "lyap1_mean": -0.0010163253173232079,
+      "lyap1_max": 0.020121874287724495,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 494,
+      "sup_loss": 1.326610120116431,
+      "rf_loss": 0.00014339442714117467,
+      "total_loss": 1.3280440644460505,
+      "lyap1_mean": 0.002897917293012142,
+      "lyap1_max": 0.022942185401916504,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 495,
+      "sup_loss": 1.3089637153470557,
+      "rf_loss": 9.300897363573313e-05,
+      "total_loss": 1.309893805083413,
+      "lyap1_mean": 0.011070841923356056,
+      "lyap1_max": 0.028349142521619797,
+      "frac_above_star": 0.875
+    },
+    {
+      "step": 496,
+      "sup_loss": 1.5416355307412466,
+      "rf_loss": 0.00016635050997138023,
+      "total_loss": 1.5432990358409604,
+      "lyap1_mean": 0.0004833017010241747,
+      "lyap1_max": 0.02827632799744606,
+      "frac_above_star": 0.5
+    },
+    {
+      "step": 497,
+      "sup_loss": 1.1065002836121525,
+      "rf_loss": 0.00013254478108137846,
+      "total_loss": 1.1078257314229663,
+      "lyap1_mean": -0.007725749164819717,
+      "lyap1_max": 0.0018641886999830604,
+      "frac_above_star": 0.125
+    },
+    {
+      "step": 498,
+      "sup_loss": 1.1091756086763251,
+      "rf_loss": 0.00023272285761777312,
+      "total_loss": 1.1115028373398144,
+      "lyap1_mean": -0.011215301230549812,
+      "lyap1_max": 0.0024032695218920708,
+      "frac_above_star": 0.25
+    },
+    {
+      "step": 499,
+      "sup_loss": 1.1626121224058652,
+      "rf_loss": 0.00014814006863161922,
+      "total_loss": 1.1640935230921814,
+      "lyap1_mean": 0.007189540192484856,
+      "lyap1_max": 0.026899944990873337,
+      "frac_above_star": 0.75
+    }
+  ],
+  "evals": [
+    {
+      "step": 0,
+      "acc": 0.517578125,
+      "tok_acc": 0.8276668595679012
+    },
+    {
+      "step": 100,
+      "acc": 0.185546875,
+      "tok_acc": 0.7311680169753086
+    },
+    {
+      "step": 200,
+      "acc": 0.0859375,
+      "tok_acc": 0.6451822916666666
+    },
+    {
+      "step": 300,
+      "acc": 0.298828125,
+      "tok_acc": 0.7502652391975309
+    },
+    {
+      "step": 400,
+      "acc": 0.3515625,
+      "tok_acc": 0.7707851080246914
+    },
+    {
+      "step": 500,
+      "acc": 0.296875,
+      "tok_acc": 0.7286120756172839
+    },
+    {
+      "step": 500,
+      "acc": 0.296875,
+      "tok_acc": 0.7286120756172839
+    }
+  ],
+  "final_acc": 0.296875,
+  "final_tok_acc": 0.7286120756172839
+}
\ No newline at end of file