{"about":"Lesson F3, gradients. Computed by tools/school/fill_gradients.mjs from system/school/gradients.mjs and the attention lab's model.json. Do not edit by hand.","modelJsonSha256":"67600098679443bf87c78f0f3ef1a1399ae51642b3e9608517105d7831219d5e","batch":16,"bowl":{"about":"f(v) = 1/2 (v - c)^T H (v - c), axes turned 30 degrees. Curvatures from a finite-difference Hessian at the minimum. predictedBound = 2 / largest curvature; measuredBound = largest step whose runs shrink, found by bisection on real runs. Runs: 60 steps from (-2, 2) at multiples of the predicted bound; perStepFactor is the measured shrink (<1) or growth (>1) per step of the distance to the minimum.","minimum":[1,0.5],"curvatures":[4,0.5],"conditionNumber":8,"predictedBound":0.5,"measuredBound":0.5,"relativeGap":1.11e-13,"runs":[{"multiple":0.5,"step":0.25,"steps":60,"outcome":"converges","startLoss":8.7894,"finalLoss":2.1524e-7,"perStepFactor":0.875,"path":[[-2,2,8.789],[-0.2246,2.621,1.5],[-0.07151,2.356,1.148],[0.06243,2.124,0.879],[0.1796,1.921,0.673],[0.2822,1.743,0.5153],[0.3719,1.588,0.3945],[0.4504,1.452,0.302],[0.5191,1.333,0.2313],[0.5792,1.229,0.1771],[0.6318,1.138,0.1356],[0.6778,1.058,0.1038],[0.7181,0.9882,0.07946],[0.7533,0.9272,0.06084],[0.7842,0.8738,0.04658],[0.8112,0.8271,0.03566],[0.8348,0.7862,0.0273],[0.8554,0.7504,0.0209],[0.8735,0.7191,0.016],[0.8893,0.6917,0.01225],[0.9031,0.6678,0.009382],[0.9152,0.6468,0.007183],[0.9258,0.6284,0.005499],[0.9351,0.6124,0.00421],[0.9432,0.5983,0.003224],[0.9503,0.586,0.002468],[0.9565,0.5753,0.00189],[0.962,0.5659,0.001447],[0.9667,0.5576,0.001108],[0.9709,0.5504,0.0008481],[0.9745,0.5441,0.0006493],[0.9777,0.5386,0.0004971],[0.9805,0.5338,0.0003806],[0.9829,0.5296,0.0002914],[0.9851,0.5259,0.0002231],[0.9869,0.5226,0.0001708],[0.9886,0.5198,0.0001308],[0.99,0.5173,0.0001001],[0.9912,0.5152,0.00007666],[0.9923,0.5133,0.00005869],[0.9933,0.5116,0.00004494],[0.9941,0.5102,0.0000344],[0.9949,0.5089,0.00002634],[0.9955,0.5078,0.00002017],[0.9961,0.5068,0.00001544],[0.9966,0.506,0.00001182],[0.997,0.5052,0.000009051],[0.9974,0.5046,0.00000693],[0.9977,0.504,0.000005306],[0.998,0.5035,0.000004062],[0.9982,0.5031,0.00000311],[0.9985,0.5027,0.000002381],[0.9986,0.5023,0.000001823],[0.9988,0.502,0.000001396],[0.999,0.5018,0.000001069],[0.9991,0.5016,8.182e-7],[0.9992,0.5014,6.264e-7],[0.9993,0.5012,4.796e-7],[0.9994,0.501,3.672e-7],[0.9995,0.5009,2.811e-7],[0.9995,0.5008,2.152e-7]]},{"multiple":0.99,"step":0.495,"steps":60,"outcome":"converges slowly, zigzagging","startLoss":8.7894,"finalLoss":0.60478,"perStepFactor":0.98,"path":[[-2,2,8.789],[1.515,3.23,7.669],[-1.33,0.9852,6.929],[1.91,2.403,6.407],[-0.925,0.425,6.013],[2.109,1.92,5.695],[-0.6719,0.1216,5.425],[2.198,1.633,5.185],[-0.5055,-0.03691,4.965],[2.226,1.458,4.76],[-0.3892,-0.1139,4.567],[2.22,1.346,4.383],[-0.3021,-0.1452,4.208],[2.196,1.271,4.041],[-0.2323,-0.1511,3.88],[2.162,1.217,3.726],[-0.1732,-0.1432,3.579],[2.124,1.175,3.437],[-0.1209,-0.1278,3.301],[2.084,1.14,3.17],[-0.07324,-0.1087,3.045],[2.044,1.111,2.924],[-0.02887,-0.08781,2.808],[2.004,1.084,2.697],[0.01293,-0.06637,2.59],[1.965,1.06,2.488],[0.05262,-0.04498,2.389],[1.927,1.037,2.294],[0.09048,-0.02399,2.204],[1.89,1.015,2.116],[0.1267,-0.00357,2.033],[1.855,0.9943,1.952],[0.1614,0.01618,1.875],[1.822,0.9746,1.8],[0.1946,0.03524,1.729],[1.789,0.9557,1.661],[0.2266,0.05358,1.595],[1.758,0.9376,1.532],[0.2572,0.07122,1.471],[1.728,0.9203,1.413],[0.2866,0.08818,1.357],[1.699,0.9036,1.303],[0.3149,0.1045,1.252],[1.671,0.8876,1.202],[0.342,0.1201,1.154],[1.645,0.8723,1.109],[0.3681,0.1352,1.065],[1.619,0.8575,1.023],[0.3931,0.1496,0.9821],[1.595,0.8434,0.9432],[0.4172,0.1635,0.9059],[1.571,0.8298,0.87],[0.4402,0.1768,0.8356],[1.549,0.8167,0.8025],[0.4624,0.1896,0.7707],[1.527,0.8042,0.7402],[0.4837,0.2019,0.7109],[1.506,0.7921,0.6827],[0.5041,0.2137,0.6557],[1.486,0.7806,0.6297],[0.5238,0.225,0.6048]]},{"multiple":1.01,"step":0.505,"steps":60,"outcome":"diverges, zigzagging","startLoss":8.7894,"finalLoss":73.534,"perStepFactor":1.02,"path":[[-2,2,8.789],[1.586,3.254,8.201],[-1.447,0.8931,8.005],[2.114,2.493,8.034],[-1.169,0.2566,8.194],[2.44,2.086,8.433],[-1.047,-0.1177,8.723],[2.656,1.878,9.046],[-1.012,-0.3464,9.396],[2.811,1.781,9.766],[-1.027,-0.4944,10.16],[2.933,1.748,10.56],[-1.072,-0.5981,10.99],[3.039,1.75,11.43],[-1.136,-0.678,11.89],[3.136,1.774,12.37],[-1.21,-0.7455,12.87],[3.231,1.811,13.39],[-1.293,-0.8069,13.93],[3.326,1.856,14.5],[-1.382,-0.8659,15.08],[3.423,1.906,15.69],[-1.477,-0.9245,16.33],[3.522,1.96,16.99],[-1.576,-0.984,17.67],[3.625,2.018,18.39],[-1.679,-1.045,19.13],[3.731,2.078,19.9],[-1.787,-1.108,20.71],[3.842,2.141,21.54],[-1.899,-1.173,22.41],[3.957,2.208,23.32],[-2.016,-1.241,24.26],[4.076,2.276,25.24],[-2.138,-1.312,26.26],[4.201,2.348,27.32],[-2.265,-1.385,28.42],[4.33,2.423,29.57],[-2.397,-1.461,30.77],[4.465,2.5,32.01],[-2.534,-1.54,33.3],[4.605,2.581,34.65],[-2.677,-1.623,36.05],[4.75,2.665,37.5],[-2.825,-1.708,39.02],[4.902,2.753,40.6],[-2.98,-1.798,42.24],[5.059,2.844,43.94],[-3.141,-1.891,45.72],[5.223,2.938,47.56],[-3.308,-1.987,49.49],[5.394,3.037,51.49],[-3.482,-2.088,53.57],[5.572,3.139,55.73],[-3.663,-2.192,57.98],[5.756,3.246,60.32],[-3.851,-2.301,62.76],[5.948,3.357,65.3],[-4.047,-2.414,67.93],[6.148,3.472,70.68],[-4.251,-2.532,73.53]]},{"multiple":2,"step":1,"steps":12,"outcome":"diverges, zigzagging","startLoss":8.7894,"finalLoss":1929200000000,"perStepFactor":3,"path":[[-2,2,8.789],[5.102,4.484,61.97],[-13.75,-7.21,553.4],[44.04,25.75,4980],[-128.7,-74.2,44820],[389.9,225.1,403400],[-1166,-673.1,3630000],[3501,2021,32670000],[-10500,-6062,294000000],[31500,18190,2646000000],[-94510,-54560,23820000000],[283500,163700,214400000000],[-850600,-491100,1929000000000]]},{"multiple":0.6,"step":0.3,"steps":60,"outcome":"converges","startLoss":8.7894,"finalLoss":6.6409e-9,"perStepFactor":0.85,"path":[[-2,2,8.789],[0.1305,2.745,1.688],[-0.07517,2.214,1.033],[0.1533,1.996,0.7391],[0.2669,1.764,0.5337],[0.3795,1.576,0.3856],[0.4721,1.414,0.2786],[0.5514,1.277,0.2013],[0.6186,1.161,0.1454],[0.6758,1.061,0.1051],[0.7245,0.9772,0.07592],[0.7658,0.9056,0.05485],[0.8009,0.8448,0.03963],[0.8308,0.7931,0.02863],[0.8562,0.7491,0.02069],[0.8777,0.7117,0.01495],[0.8961,0.68,0.0108],[0.9117,0.653,0.007802],[0.9249,0.63,0.005637],[0.9362,0.6105,0.004073],[0.9458,0.594,0.002942],[0.9539,0.5799,0.002126],[0.9608,0.5679,0.001536],[0.9667,0.5577,0.00111],[0.9717,0.549,0.0008018],[0.9759,0.5417,0.0005793],[0.9795,0.5354,0.0004185],[0.9826,0.5301,0.0003024],[0.9852,0.5256,0.0002185],[0.9874,0.5218,0.0001579],[0.9893,0.5185,0.000114],[0.9909,0.5157,0.0000824],[0.9923,0.5134,0.00005953],[0.9934,0.5114,0.00004301],[0.9944,0.5097,0.00003108],[0.9953,0.5082,0.00002245],[0.996,0.507,0.00001622],[0.9966,0.5059,0.00001172],[0.9971,0.505,0.000008468],[0.9975,0.5043,0.000006118],[0.9979,0.5036,0.000004421],[0.9982,0.5031,0.000003194],[0.9985,0.5026,0.000002308],[0.9987,0.5022,0.000001667],[0.9989,0.5019,0.000001205],[0.9991,0.5016,8.703e-7],[0.9992,0.5014,6.288e-7],[0.9993,0.5012,4.543e-7],[0.9994,0.501,3.282e-7],[0.9995,0.5008,2.371e-7],[0.9996,0.5007,1.713e-7],[0.9996,0.5006,1.238e-7],[0.9997,0.5005,8.944e-8],[0.9997,0.5004,6.462e-8],[0.9998,0.5004,4.669e-8],[0.9998,0.5003,3.373e-8],[0.9998,0.5003,2.437e-8],[0.9999,0.5002,1.761e-8],[0.9999,0.5002,1.272e-8],[0.9999,0.5002,9.192e-9],[0.9999,0.5001,6.641e-9]]},{"multiple":1.2,"step":0.6,"steps":39,"outcome":"diverges, zigzagging","startLoss":8.7894,"finalLoss":1707900000000,"perStepFactor":1.4,"path":[[-2,2,8.789],[2.261,3.49,14.35],[-2.823,-0.1233,26.71],[4.912,3.867,51.66],[-5.484,-2.468,100.9],[9.373,5.877,197.6],[-11.22,-6.172,387.3],[17.76,10.44,759],[-22.7,-13,1488],[34.01,19.69,2916],[-45.33,-26.16,5715],[65.78,37.97,11200],[-89.76,-51.85,21960],[128,73.87,43030],[-176.9,-102.2,84340],[250,144.3,165300],[-347.6,-200.7,324000],[489,282.3,635100],[-682.2,-393.9,1245000],[957.5,552.7,2440000],[-1338,-772.6,4782000],[1876,1083,9372000],[-2624,-1515,18370000],[3675,2122,36000000],[-5143,-2970,70570000],[7203,4159,138300000],[-10080,-5821,271100000],[14120,8150,531400000],[-19760,-11410,1041000000],[27670,15970,2041000000],[-38730,-22360,4001000000],[54230,31310,7842000000],[-75920,-43830,15370000000],[106300,61360,30120000000],[-148800,-85910,59040000000],[208300,120300,115700000000],[-291600,-168400,226800000000],[408300,235700,444600000000],[-571600,-330000,871400000000],[800300,462000,1708000000000]]}],"grid":{"n":31,"range":[[-3,3],[-3,3]],"min":0.006875,"max":54.639,"values":[[54.64,51.14,47.77,44.52,41.4,38.4,35.52,32.78,30.15,27.65,25.28,23.03,20.91,18.91,17.04,15.29,13.67,12.17,10.79,9.545,8.422,7.423,6.55,5.802,5.178,4.68,4.307,4.058,3.935,3.936,4.063],[52.49,49.05,45.74,42.55,39.49,36.55,33.74,31.05,28.49,26.05,23.74,21.55,19.49,17.55,15.74,14.05,12.49,11.05,9.737,8.55,7.487,6.549,5.736,5.049,4.486,4.048,3.735,3.548,3.485,3.547,3.734],[50.4,47.02,43.77,40.64,37.64,34.76,32.01,29.38,26.88,24.51,22.25,20.13,18.12,16.25,14.49,12.87,11.37,9.988,8.736,7.609,6.607,5.73,4.978,4.35,3.848,3.471,3.219,3.092,3.09,3.213,3.46],[48.36,45.05,41.85,38.79,35.85,33.03,30.34,27.77,25.33,23.01,20.82,18.76,16.81,15,13.31,11.74,10.3,8.981,7.79,6.723,5.782,4.965,4.274,3.707,3.266,2.949,2.758,2.691,2.75,2.933,3.242],[46.38,43.12,39.99,36.99,34.11,31.35,28.72,26.21,23.83,21.58,19.45,17.44,15.56,13.8,12.17,10.67,9.285,8.03,6.899,5.893,5.012,4.256,3.625,3.119,2.738,2.482,2.352,2.346,2.465,2.709,3.078],[44.45,41.26,38.19,35.24,32.42,29.73,27.16,24.71,22.39,20.19,18.12,16.18,14.36,12.66,11.09,9.648,8.328,7.133,6.062,5.117,4.297,3.602,3.031,2.586,2.266,2.071,2,2.055,2.235,2.539,2.969],[42.58,39.45,36.44,33.55,30.79,28.16,25.65,23.26,21,18.87,16.86,14.97,13.21,11.58,10.07,8.685,7.425,6.291,5.281,4.397,3.637,3.002,2.493,2.108,1.848,1.714,1.704,1.819,2.06,2.425,2.915],[40.76,37.69,34.74,31.92,29.22,26.64,24.19,21.87,19.67,17.6,15.65,13.82,12.12,10.55,9.101,7.777,6.578,5.504,4.555,3.731,3.032,2.458,2.009,1.685,1.486,1.412,1.463,1.639,1.94,2.366,2.917],[39,35.99,33.1,30.33,27.7,25.18,22.79,20.53,18.39,16.38,14.49,12.73,11.09,9.576,8.187,6.924,5.786,4.772,3.884,3.12,2.482,1.968,1.58,1.317,1.178,1.165,1.276,1.513,1.875,2.361,2.973],[37.29,34.34,31.51,28.81,26.23,23.78,21.45,19.25,17.17,15.22,13.39,11.69,10.11,8.656,7.329,6.126,5.048,4.095,3.267,2.565,1.987,1.534,1.206,1.004,0.9257,0.9729,1.145,1.442,1.865,2.412,3.084],[35.64,32.75,29.98,27.34,24.82,22.43,20.16,18.02,16,14.11,12.34,10.7,9.184,7.792,6.525,5.383,4.366,3.473,2.706,2.064,1.547,1.155,0.8875,0.7454,0.7282,0.8361,1.069,1.427,1.91,2.517,3.25],[34.04,31.21,28.5,25.92,23.47,21.13,18.93,16.85,14.89,13.06,11.35,9.771,8.314,6.983,5.776,4.695,3.738,2.906,2.2,1.618,1.162,0.8303,0.6238,0.5423,0.5857,0.7542,1.048,1.466,2.01,2.678,3.471],[32.5,29.73,27.08,24.56,22.17,19.9,17.75,15.73,13.83,12.06,10.42,8.895,7.499,6.228,5.082,4.061,3.166,2.395,1.749,1.228,0.8319,0.561,0.415,0.3941,0.4982,0.7273,1.081,1.56,2.165,2.894,3.748],[31.01,28.3,25.72,23.26,20.92,18.71,16.63,14.67,12.83,11.12,9.535,8.075,6.739,5.529,4.444,3.483,2.648,1.938,1.352,0.8922,0.5569,0.3466,0.2613,0.301,0.4657,0.7554,1.17,1.71,2.374,3.164,4.079],[29.58,26.93,24.41,22.01,19.73,17.58,15.56,13.66,11.88,10.23,8.709,7.309,6.034,4.885,3.86,2.96,2.186,1.536,1.011,0.6116,0.3369,0.1872,0.1625,0.2628,0.4882,0.8385,1.314,1.914,2.639,3.49,4.465],[28.2,25.61,23.15,20.81,18.6,16.51,14.54,12.7,10.99,9.401,7.937,6.598,5.384,4.295,3.331,2.492,1.778,1.189,0.725,0.3859,0.1719,0.08282,0.1188,0.2797,0.5657,0.9766,1.513,2.173,2.959,3.87,4.906],[26.88,24.35,21.95,19.67,17.52,15.49,13.58,11.81,10.15,8.625,7.221,5.943,4.789,3.761,2.857,2.079,1.426,0.8972,0.4937,0.2153,0.06187,0.03344,0.13,0.3516,0.6981,1.17,1.766,2.488,3.334,4.306,5.403],[25.61,23.15,20.8,18.58,16.49,14.52,12.68,10.96,9.371,7.903,6.56,5.342,4.249,3.282,2.439,1.721,1.128,0.6603,0.3175,0.09969,0.006875,0.03906,0.1963,0.4784,0.8856,1.418,2.075,2.857,3.764,4.797,5.954],[24.4,21.99,19.71,17.55,15.52,13.61,11.83,10.18,8.643,7.236,5.954,4.797,3.764,2.857,2.075,1.418,0.8856,0.4784,0.1963,0.03906,0.006875,0.09969,0.3175,0.6603,1.128,1.721,2.439,3.282,4.249,5.342,6.56],[23.24,20.9,18.68,16.58,14.61,12.76,11.04,9.442,7.971,6.624,5.403,4.306,3.334,2.488,1.766,1.17,0.6981,0.3516,0.13,0.03344,0.06187,0.2153,0.4937,0.8972,1.426,2.079,2.857,3.761,4.789,5.943,7.221],[22.14,19.85,17.69,15.66,13.75,11.96,10.3,8.764,7.353,6.067,4.906,3.87,2.959,2.173,1.513,0.9766,0.5657,0.2797,0.1188,0.08282,0.1719,0.3859,0.725,1.189,1.778,2.492,3.331,4.295,5.384,6.598,7.937],[21.09,18.87,16.77,14.79,12.94,11.22,9.616,8.141,6.791,5.565,4.465,3.49,2.639,1.914,1.314,0.8385,0.4882,0.2628,0.1625,0.1872,0.3369,0.6116,1.011,1.536,2.186,2.96,3.86,4.885,6.034,7.309,8.709],[20.1,17.94,15.9,13.98,12.19,10.53,8.988,7.573,6.283,5.119,4.079,3.164,2.374,1.71,1.17,0.7554,0.4657,0.301,0.2613,0.3466,0.5569,0.8922,1.352,1.938,2.648,3.483,4.444,5.529,6.739,8.075,9.535],[19.16,17.06,15.08,13.23,11.5,9.893,8.414,7.06,5.831,4.727,3.748,2.894,2.165,1.56,1.081,0.7273,0.4982,0.3941,0.415,0.561,0.8319,1.228,1.749,2.395,3.166,4.061,5.082,6.228,7.499,8.895,10.42],[18.28,16.24,14.32,12.53,10.86,9.314,7.895,6.602,5.433,4.39,3.471,2.678,2.01,1.466,1.048,0.7542,0.5857,0.5423,0.6238,0.8303,1.162,1.618,2.2,2.906,3.738,4.695,5.776,6.983,8.314,9.771,11.35],[17.45,15.47,13.61,11.88,10.27,8.789,7.432,6.199,5.091,4.108,3.25,2.517,1.91,1.427,1.069,0.8361,0.7282,0.7454,0.8875,1.155,1.547,2.064,2.706,3.473,4.366,5.383,6.525,7.792,9.184,10.7,12.34],[16.68,14.76,12.96,11.29,9.742,8.32,7.023,5.851,4.803,3.881,3.084,2.412,1.865,1.442,1.145,0.9729,0.9257,1.004,1.206,1.534,1.987,2.565,3.267,4.095,5.048,6.126,7.329,8.656,10.11,11.69,13.39],[15.96,14.1,12.37,10.75,9.267,7.906,6.669,5.558,4.571,3.709,2.973,2.361,1.875,1.513,1.276,1.165,1.178,1.317,1.58,1.968,2.482,3.12,3.884,4.772,5.786,6.924,8.187,9.576,11.09,12.73,14.49],[15.3,13.5,11.82,10.27,8.847,7.546,6.37,5.32,4.394,3.593,2.917,2.366,1.94,1.639,1.463,1.412,1.486,1.685,2.009,2.458,3.032,3.731,4.555,5.504,6.578,7.777,9.101,10.55,12.12,13.82,15.65],[14.69,12.95,11.34,9.848,8.482,7.242,6.127,5.136,4.271,3.531,2.915,2.425,2.06,1.819,1.704,1.714,1.848,2.108,2.493,3.002,3.637,4.397,5.281,6.291,7.425,8.685,10.07,11.58,13.21,14.97,16.86],[14.14,12.46,10.91,9.477,8.173,6.993,5.938,5.008,4.204,3.524,2.969,2.539,2.235,2.055,2,2.071,2.266,2.586,3.031,3.602,4.297,5.117,6.062,7.133,8.328,9.648,11.09,12.66,14.36,16.18,18.12]]}},"rosenbrock":{"about":"f = (1 - x)^2 + 100 (y - x^2)^2 from (-1.2, 1), fixed step 0.001, 20000 steps; path thinned to 200 points. Curvatures from a finite-difference Hessian. The stable step at the minimum is 2 / largest curvature there.","step":0.001,"steps":20000,"end":[0.999861,0.999721],"finalLoss":1.9385e-8,"firstStepBelow":{"1e-1":1817,"1e-2":3925,"1e-4":9339,"1e-6":15068},"curvatures":{"atMinimum":[1001.6,0.39936],"atStart":[1506.4,23.633]},"conditionNumberAtMinimum":2508,"boundAtMinimum":0.0019968,"path":[[-1.2,1,24.2],[-0.94734,0.90549,3.7986],[-0.85707,0.74264,3.4552],[-0.7558,0.57931,3.0894],[-0.63959,0.41704,2.6946],[-0.50229,0.25982,2.2625],[-0.33507,0.1185,1.7863],[-0.13365,0.020871,1.2861],[0.070475,0.0038174,0.86415],[0.22704,0.048659,0.5983],[0.33654,0.11018,0.44112],[0.41654,0.17063,0.34126],[0.47827,0.22613,0.27289],[0.52795,0.27637,0.22339],[0.56918,0.32183,0.18606],[0.60419,0.3631,0.15704],[0.63444,0.40073,0.13395],[0.66093,0.4352,0.11523],[0.6844,0.46689,0.099833],[0.70536,0.49614,0.087005],[0.72424,0.52323,0.076211],[0.74134,0.54839,0.067049],[0.75692,0.57181,0.059213],[0.77118,0.59367,0.05247],[0.78427,0.61411,0.046633],[0.79635,0.63326,0.041556],[0.80753,0.65124,0.03712],[0.81789,0.66814,0.033229],[0.82753,0.68404,0.029804],[0.83651,0.69904,0.026779],[0.8449,0.71318,0.024101],[0.85275,0.72655,0.021723],[0.86011,0.73918,0.019606],[0.86702,0.75114,0.017718],[0.87351,0.76247,0.01603],[0.87962,0.77321,0.014519],[0.88537,0.78339,0.013163],[0.8908,0.79307,0.011946],[0.89593,0.80225,0.01085],[0.90078,0.81098,0.0098626],[0.90536,0.81928,0.008972],[0.90971,0.82718,0.0081677],[0.91382,0.8347,0.0074404],[0.91772,0.84186,0.0067821],[0.92142,0.84868,0.0061857],[0.92493,0.85519,0.0056449],[0.92827,0.86139,0.0051541],[0.93144,0.8673,0.0047082],[0.93446,0.87294,0.004303],[0.93733,0.87833,0.0039343],[0.94006,0.88347,0.0035987],[0.94266,0.88838,0.0032931],[0.94514,0.89307,0.0030145],[0.9475,0.89755,0.0027604],[0.94976,0.90183,0.0025287],[0.9519,0.90592,0.0023171],[0.95395,0.90984,0.0021238],[0.95591,0.91358,0.0019472],[0.95778,0.91716,0.0017858],[0.95956,0.92059,0.0016382],[0.96126,0.92386,0.0015032],[0.96289,0.927,0.0013796],[0.96444,0.93,0.0012665],[0.96593,0.93288,0.0011629],[0.96735,0.93563,0.0010679],[0.96871,0.93826,0.00098096],[0.97,0.94079,0.00090123],[0.97125,0.9432,0.00082812],[0.97244,0.94552,0.00076107],[0.97357,0.94774,0.00069956],[0.97466,0.94986,0.00064312],[0.9757,0.9519,0.00059132],[0.9767,0.95385,0.00054376],[0.97766,0.95572,0.0005001],[0.97857,0.95751,0.00046],[0.97945,0.95923,0.00042317],[0.98028,0.96088,0.00038933],[0.98109,0.96246,0.00035824],[0.98186,0.96397,0.00032966],[0.9826,0.96542,0.0003034],[0.9833,0.96682,0.00027925],[0.98398,0.96815,0.00025705],[0.98463,0.96943,0.00023664],[0.98525,0.97066,0.00021786],[0.98585,0.97184,0.0002006],[0.98642,0.97297,0.00018471],[0.98697,0.97405,0.0001701],[0.98749,0.97509,0.00015665],[0.988,0.97609,0.00014427],[0.98848,0.97705,0.00013289],[0.98895,0.97797,0.0001224],[0.98939,0.97885,0.00011276],[0.98982,0.9797,0.00010388],[0.99023,0.98051,0.000095698],[0.99062,0.98129,0.00008817],[0.99099,0.98203,0.000081238],[0.99136,0.98275,0.000074854],[0.9917,0.98344,0.000068976],[0.99203,0.9841,0.000063562],[0.99235,0.98473,0.000058575],[0.99266,0.98534,0.000053982],[0.99295,0.98593,0.000049751],[0.99323,0.98649,0.000045853],[0.9935,0.98702,0.000042262],[0.99376,0.98754,0.000038954],[0.99401,0.98804,0.000035906],[0.99425,0.98851,0.000033097],[0.99448,0.98897,0.000030509],[0.9947,0.98941,0.000028124],[0.99491,0.98983,0.000025927],[0.99512,0.99023,0.000023902],[0.99531,0.99062,0.000022035],[0.9955,0.991,0.000020315],[0.99568,0.99135,0.000018729],[0.99585,0.9917,0.000017268],[0.99601,0.99203,0.000015921],[0.99617,0.99234,0.00001468],[0.99632,0.99265,0.000013535],[0.99647,0.99294,0.00001248],[0.99661,0.99322,0.000011507],[0.99675,0.99349,0.000010611],[0.99687,0.99375,0.0000097843],[0.997,0.99399,0.0000090222],[0.99712,0.99423,0.0000083197],[0.99723,0.99446,0.000007672],[0.99734,0.99468,0.0000070748],[0.99745,0.99489,0.0000065241],[0.99755,0.99509,0.0000060165],[0.99765,0.99529,0.0000055484],[0.99774,0.99548,0.0000051167],[0.99783,0.99565,0.0000047187],[0.99792,0.99583,0.0000043518],[0.998,0.99599,0.0000040134],[0.99808,0.99615,0.0000037013],[0.99815,0.9963,0.0000034136],[0.99823,0.99645,0.0000031482],[0.9983,0.99659,0.0000029035],[0.99836,0.99673,0.0000026779],[0.99843,0.99686,0.0000024698],[0.99849,0.99698,0.0000022779],[0.99855,0.9971,0.0000021009],[0.99861,0.99721,0.0000019377],[0.99866,0.99732,0.0000017872],[0.99872,0.99743,0.0000016484],[0.99877,0.99753,0.0000015203],[0.99882,0.99763,0.0000014023],[0.99886,0.99772,0.0000012934],[0.99891,0.99781,0.0000011929],[0.99895,0.9979,0.0000011003],[0.99899,0.99798,0.0000010149],[0.99903,0.99806,9.3609e-7],[0.99907,0.99814,8.6342e-7],[0.99911,0.99821,7.964e-7],[0.99914,0.99828,7.3458e-7],[0.99918,0.99835,6.7756e-7],[0.99921,0.99842,6.2498e-7],[0.99924,0.99848,5.7647e-7],[0.99927,0.99854,5.3173e-7],[0.9993,0.9986,4.9047e-7],[0.99933,0.99865,4.5241e-7],[0.99935,0.99871,4.173e-7],[0.99938,0.99876,3.8492e-7],[0.9994,0.99881,3.5506e-7],[0.99943,0.99885,3.2751e-7],[0.99945,0.9989,3.021e-7],[0.99947,0.99894,2.7866e-7],[0.99949,0.99899,2.5705e-7],[0.99951,0.99903,2.371e-7],[0.99953,0.99906,2.1871e-7],[0.99955,0.9991,2.0175e-7],[0.99957,0.99914,1.861e-7],[0.99959,0.99917,1.7166e-7],[0.9996,0.9992,1.5835e-7],[0.99962,0.99923,1.4606e-7],[0.99963,0.99927,1.3473e-7],[0.99965,0.99929,1.2428e-7],[0.99966,0.99932,1.1465e-7],[0.99968,0.99935,1.0575e-7],[0.99969,0.99937,9.7552e-8],[0.9997,0.9994,8.9986e-8],[0.99971,0.99942,8.3008e-8],[0.99972,0.99945,7.657e-8],[0.99973,0.99947,7.0632e-8],[0.99974,0.99949,6.5155e-8],[0.99976,0.99951,6.0102e-8],[0.99976,0.99953,5.5442e-8],[0.99977,0.99955,5.1142e-8],[0.99978,0.99957,4.7177e-8],[0.99979,0.99958,4.3518e-8],[0.9998,0.9996,4.0144e-8],[0.99981,0.99961,3.7031e-8],[0.99982,0.99963,3.416e-8],[0.99982,0.99964,3.1511e-8],[0.99983,0.99966,2.9068e-8],[0.99984,0.99967,2.6814e-8],[0.99984,0.99969,2.4735e-8],[0.99985,0.9997,2.2817e-8],[0.99986,0.99971,2.1048e-8],[0.99986,0.99972,1.9416e-8],[0.99986,0.99972,1.9385e-8]],"grid":{"n":31,"range":[[-2,2],[-1,3]],"min":0.0064198,"max":2509,"values":[[2509,2019,1611,1274,999,777,600.2,461.3,353.8,272.2,211.4,167.3,136.5,116.3,104.9,101,104.3,115.3,134.9,165.2,208.8,269,350.1,457,595.4,771.7,993.2,1268,1604,2012,2501],[2377,1901,1506,1181,916.8,704.8,536.9,406.1,305.7,230.2,174.7,134.9,107.4,89.55,79.51,76.11,78.98,88.48,105.8,132.7,172,227,302,401.8,532.1,699.4,910.9,1175,1499,1894,2369],[2249,1787,1405,1091,838.1,636,477.2,354.4,261.2,191.8,141.5,105.9,81.76,66.32,57.7,54.78,57.17,65.25,80.16,103.8,138.8,188.6,257.4,350.1,472.4,630.7,832.2,1085,1398,1780,2241],[2125,1676,1307,1005,762.9,570.8,421,306.3,220.2,157,111.9,80.58,59.72,46.64,39.45,37,38.92,45.58,58.12,78.44,109.2,153.8,216.4,302,416.2,565.5,757.1,998.9,1300,1669,2117],[2004,1569,1212,922.8,691.4,509.2,368.4,261.7,182.7,125.7,85.79,58.77,41.23,30.52,24.75,22.78,24.22,29.46,39.63,56.63,83.12,122.5,179,257.4,363.6,503.9,685.5,916.4,1205,1562,1996],[1887,1466,1122,843.9,623.3,451.1,319.3,220.7,148.8,97.98,63.27,40.52,26.3,17.96,13.61,12.11,13.08,16.9,24.7,38.38,60.6,94.78,145.1,216.4,314.5,445.8,617.5,837.5,1115,1458,1879],[1773,1366,1034,768.5,558.9,396.6,273.8,183.2,118.5,73.8,44.31,25.82,14.92,8.955,6.027,5,5.494,7.888,13.32,23.69,41.64,70.6,114.7,179,269,391.3,553,762.1,1027,1358,1765],[1663,1269,950.6,696.7,497.9,345.6,231.8,149.3,91.68,53.18,28.9,14.68,7.098,3.503,1.998,1.444,1.464,2.436,5.498,12.55,26.23,49.98,87.95,145.1,227,340.3,492.1,690.3,943.7,1262,1655],[1556,1176,870.5,628.4,440.6,298.2,193.4,119,68.45,36.11,17.05,7.094,2.831,1.606,1.523,1.444,0.9901,0.5398,1.231,4.96,14.38,32.91,64.72,114.7,188.6,292.9,434.7,622,863.6,1169,1548],[1453,1087,794,563.7,386.8,254.4,158.6,92.21,48.78,22.6,8.753,3.064,2.12,3.266,4.605,5,4.072,2.199,0.52,0.9309,6.086,19.4,45.04,87.95,153.8,249,380.9,557.3,787,1080,1445],[1353,1001,721,502.6,336.5,214.1,127.3,68.98,32.66,12.64,4.012,2.59,4.964,8.48,11.24,12.11,10.71,7.414,3.364,0.4568,1.346,9.444,28.92,64.72,122.5,208.8,330.6,496.2,714,993.7,1345],[1257,918.9,651.5,445,289.8,177.3,99.58,49.31,20.1,6.244,2.827,5.672,11.36,17.25,21.43,22.78,20.9,16.18,9.764,3.538,0.1605,3.044,16.36,45.04,94.78,172,284,438.6,644.6,911.4,1249],[1165,840.2,585.6,390.9,246.7,144.2,75.4,33.19,11.09,3.4,5.198,12.31,21.32,29.58,35.18,37,34.65,28.51,19.72,10.18,2.531,0.2,7.355,28.92,70.6,138.8,240.8,384.5,578.7,832.8,1157],[1076,765.1,523.3,340.4,207.1,114.5,54.78,20.63,5.636,4.111,11.12,22.5,34.83,45.46,52.49,54.78,51.95,44.39,33.23,20.37,8.457,0.9111,1.903,16.36,49.98,109.2,201.2,334,516.3,757.6,1068],[990.8,693.5,464.5,293.5,171.1,88.46,37.71,11.62,3.74,8.378,20.6,36.25,51.9,64.9,73.35,76.11,72.81,63.83,50.3,34.12,17.94,5.178,0.00642,7.355,32.91,83.12,165.2,287.1,457.5,686,982.8],[909,625.5,409.3,250.1,138.6,65.94,24.2,6.169,5.399,16.2,33.64,53.55,72.52,87.89,97.76,101,97.23,86.82,70.92,51.42,30.98,13,1.666,1.903,19.4,60.6,132.7,243.7,402.3,618,901],[830.8,561,357.6,210.3,109.7,46.98,14.24,4.273,10.61,27.58,50.23,74.41,96.7,114.4,125.7,129.4,125.2,113.4,95.1,72.28,47.57,24.38,6.88,0.00642,9.444,41.64,103.8,203.9,350.6,553.5,822.8],[756.1,500.1,309.5,174,84.31,31.57,7.844,5.932,19.38,42.51,70.38,98.83,124.4,144.5,157.3,161.4,156.7,143.5,122.8,96.69,67.72,39.31,15.65,1.666,3.044,26.23,78.44,167.6,302.5,492.6,748.1],[685,442.7,264.9,141.3,62.5,19.72,5,11.15,31.71,61,94.09,126.8,155.7,178.2,192.3,197,191.8,177.1,154.1,124.7,91.42,57.8,27.98,6.88,0.2,14.38,56.63,134.9,258,435.2,677],[617.4,388.9,223.9,112.2,44.25,11.42,5.711,19.92,47.59,83.04,121.3,158.3,190.6,215.4,231,236.1,230.4,214.3,189,156.2,118.7,79.84,43.86,15.65,0.9111,6.086,38.38,105.8,217,381.4,609.4],[553.4,338.6,186.4,86.56,29.55,6.679,9.978,32.24,67.03,108.6,152.2,193.4,229,256.2,273.2,278.8,272.6,255.1,227.4,191.3,149.5,105.4,63.3,27.98,5.178,1.346,23.69,80.16,179.5,331.2,545.4],[493,292,152.5,64.52,18.41,5.494,17.8,48.12,90.02,137.8,186.5,232,270.9,300.5,318.9,325,318.4,299.4,269.3,229.9,183.9,134.6,86.29,43.86,13,0.1605,12.55,58.12,145.6,284.5,485],[436.1,248.8,122.2,46.03,10.83,7.864,29.18,67.56,116.6,170.5,224.5,274.2,316.4,348.4,368.2,374.8,367.7,347.3,314.8,272.1,221.8,167.3,112.8,63.3,24.38,2.531,4.96,39.63,115.3,241.3,428.1],[382.8,209.2,95.41,31.1,6.798,13.79,44.11,90.55,146.7,206.8,265.9,320,365.5,399.8,421.1,428.1,420.5,398.8,363.9,317.8,263.3,203.6,142.9,86.29,39.31,8.457,0.9309,24.7,88.48,201.8,374.8],[333,173.2,72.18,19.72,6.323,23.27,62.6,117.1,180.3,246.6,311,369.3,418.1,454.8,477.5,485,477,453.8,416.5,367.2,308.3,243.4,176.6,112.8,57.8,17.94,0.4568,13.32,65.25,165.7,325],[286.8,140.7,52.51,11.9,9.405,36.31,84.64,147.2,217.5,290,359.6,422.1,474.3,513.4,537.5,545.4,536.9,512.3,472.7,420,356.9,286.8,213.8,142.9,79.84,30.98,3.538,5.498,45.58,133.3,278.8],[244.1,111.8,36.39,7.631,16.04,52.9,110.2,180.9,258.3,336.9,411.7,478.6,534,575.5,601,609.4,600.5,574.4,532.4,476.4,409,333.7,254.6,176.6,105.4,47.57,10.18,1.231,29.46,104.3,236.1],[205,86.44,23.83,6.92,26.23,73.05,139.4,218.1,302.6,387.4,467.4,538.5,597.3,641.1,668.1,677,667.5,640.1,595.7,536.4,464.8,384.2,298.9,213.8,134.6,67.72,20.37,0.52,16.9,78.98,197],[169.4,64.63,14.82,9.764,39.98,96.75,172.1,258.9,350.5,441.4,526.7,602.1,664.2,710.3,738.7,748.1,738.2,709.3,662.6,599.9,524,438.2,346.8,254.6,167.3,91.42,34.12,3.364,7.888,57.17,161.4],[137.4,46.38,9.369,16.16,57.29,124,208.4,303.2,402,499,589.5,669.1,734.6,783.1,812.9,822.8,812.4,782.1,733,667,586.8,495.8,398.2,298.9,203.6,118.7,51.42,9.764,2.436,38.92,129.4],[109,31.69,7.473,26.12,78.15,154.8,248.2,351.1,457,560.2,655.9,739.8,808.5,859.4,890.6,901,890.1,858.4,806.9,737.6,653.2,557,453.2,346.8,243.4,149.5,72.28,19.72,0.5398,24.22,101]]}},"twoValleys":{"about":"f = (x^2 - 1)^2 + 1.5 (y - 0.4 x)^2 + 0.2 x. Step 0.05 until |grad| < 1e-9. basin[j][i] is -1 when descent from that grid point ends in the left valley, +1 for the right; grid spans [-2, 2]^2, rows are y.","leftValley":{"at":[-1.0241,-0.40965],"f":-0.20244},"rightValley":{"at":[0.97399,0.3896],"f":0.19743},"runs":[{"start":[-1.5,1],"end":[-1.0241,-0.40965],"f":-0.20244,"steps":148,"valley":"left","path":[[-1.5,1,5.103],[-0.9153,0.3169,0.5431],[-0.9383,-0.01047,0.0263],[-0.9762,-0.1882,-0.1316],[-0.9988,-0.2869,-0.1807],[-1.011,-0.3418,-0.1958],[-1.017,-0.3722,-0.2004],[-1.02,-0.389,-0.2018],[-1.022,-0.3983,-0.2023],[-1.023,-0.4034,-0.2024],[-1.023,-0.4062,-0.2024],[-1.024,-0.4077,-0.2024],[-1.024,-0.4086,-0.2024],[-1.024,-0.4091,-0.2024],[-1.024,-0.4093,-0.2024],[-1.024,-0.4095,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024]]},{"start":[1.5,-1],"end":[0.97399,0.3896],"f":0.19743,"steps":151,"valley":"right","path":[[1.5,-1,5.703],[0.8681,-0.3218,0.9057],[0.8754,-0.002715,0.4165],[0.9142,0.1692,0.2677],[0.9416,0.2656,0.2197],[0.9566,0.32,0.2044],[0.9646,0.3507,0.1996],[0.9688,0.3679,0.1981],[0.9711,0.3775,0.1976],[0.9724,0.3828,0.1975],[0.9731,0.3858,0.1975],[0.9735,0.3875,0.1974],[0.9737,0.3884,0.1974],[0.9738,0.3889,0.1974],[0.9739,0.3892,0.1974],[0.9739,0.3894,0.1974],[0.974,0.3895,0.1974],[0.974,0.3895,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974]]},{"start":[0.1,1.5],"end":[0.97399,0.3896],"f":0.19743,"steps":144,"valley":"right","path":[[0.1,1.5,4.197],[0.5054,0.8345,1.255],[0.8561,0.5639,0.3162],[0.9701,0.4705,0.2077],[0.9811,0.4325,0.2],[0.9791,0.4132,0.1982],[0.977,0.4027,0.1977],[0.9757,0.3969,0.1975],[0.9749,0.3937,0.1975],[0.9745,0.3919,0.1974],[0.9743,0.3909,0.1974],[0.9742,0.3903,0.1974],[0.9741,0.39,0.1974],[0.974,0.3898,0.1974],[0.974,0.3897,0.1974],[0.974,0.3897,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974]]},{"start":[-0.05,-1.5],"end":[-1.0241,-0.40965],"f":-0.20244,"steps":141,"valley":"left","path":[[-0.05,-1.5,4.271],[-0.5161,-0.8292,1.017],[-0.9237,-0.569,-0.1035],[-1.026,-0.4854,-0.194],[-1.031,-0.4503,-0.2001],[-1.028,-0.432,-0.2017],[-1.026,-0.4219,-0.2022],[-1.025,-0.4164,-0.2024],[-1.025,-0.4134,-0.2024],[-1.025,-0.4117,-0.2024],[-1.024,-0.4108,-0.2024],[-1.024,-0.4103,-0.2024],[-1.024,-0.41,-0.2024],[-1.024,-0.4098,-0.2024],[-1.024,-0.4098,-0.2024],[-1.024,-0.4097,-0.2024],[-1.024,-0.4097,-0.2024],[-1.024,-0.4097,-0.2024],[-1.024,-0.4097,-0.2024],[-1.024,-0.4097,-0.2024],[-1.024,-0.4097,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024]]},{"start":[0.3,0],"end":[0.97399,0.3896],"f":0.19743,"steps":150,"valley":"right","path":[[0.3,0,0.9097],[0.4811,0.07076,0.7091],[0.7123,0.1477,0.4134],[0.8773,0.2286,0.251],[0.9399,0.2933,0.2118],[0.9591,0.3347,0.2018],[0.9664,0.3588,0.1988],[0.9699,0.3724,0.1979],[0.9717,0.38,0.1976],[0.9727,0.3842,0.1975],[0.9733,0.3866,0.1974],[0.9736,0.3879,0.1974],[0.9738,0.3887,0.1974],[0.9739,0.3891,0.1974],[0.9739,0.3893,0.1974],[0.974,0.3894,0.1974],[0.974,0.3895,0.1974],[0.974,0.3895,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974],[0.974,0.3896,0.1974]]},{"start":[-0.3,0],"end":[-1.0241,-0.40965],"f":-0.20244,"steps":146,"valley":"left","path":[[-0.3,0,0.7897],[-0.5699,-0.07771,0.3757],[-0.8514,-0.1741,-0.05304],[-0.9757,-0.2663,-0.1698],[-1.006,-0.3287,-0.1929],[-1.015,-0.3648,-0.1995],[-1.019,-0.3849,-0.2016],[-1.021,-0.396,-0.2022],[-1.023,-0.4021,-0.2024],[-1.023,-0.4055,-0.2024],[-1.024,-0.4074,-0.2024],[-1.024,-0.4084,-0.2024],[-1.024,-0.409,-0.2024],[-1.024,-0.4093,-0.2024],[-1.024,-0.4094,-0.2024],[-1.024,-0.4095,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024],[-1.024,-0.4096,-0.2024]]}],"basin":[[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1]],"grid":{"n":31,"range":[[-2,2],[-2,2]],"min":-0.19328,"max":21.16,"values":[[10.76,8.155,6.232,4.888,4.028,3.565,3.419,3.519,3.799,4.203,4.682,5.194,5.704,6.187,6.622,7,7.316,7.573,7.784,7.967,8.149,8.363,8.652,9.065,9.659,10.5,11.65,13.21,15.25,17.86,21.16],[10.31,7.681,5.736,4.371,3.489,3.005,2.838,2.916,3.175,3.558,4.015,4.506,4.995,5.456,5.87,6.227,6.521,6.757,6.947,7.108,7.269,7.462,7.73,8.121,8.694,9.512,10.65,12.18,14.19,16.79,20.07],[9.907,7.259,5.294,3.907,3.004,2.498,2.31,2.367,2.604,2.966,3.402,3.871,4.339,4.779,5.172,5.507,5.78,5.995,6.163,6.303,6.442,6.614,6.86,7.231,7.782,8.578,9.692,11.2,13.2,15.77,19.03],[9.56,6.891,4.904,3.496,2.572,2.045,1.835,1.871,2.087,2.427,2.842,3.29,3.736,4.155,4.526,4.84,5.092,5.285,5.432,5.551,5.669,5.819,6.044,6.393,6.923,7.698,8.791,10.28,12.25,14.81,18.04],[9.267,6.577,4.568,3.139,2.193,1.645,1.414,1.428,1.623,1.942,2.335,2.762,3.187,3.584,3.934,4.227,4.457,4.629,4.755,4.852,4.949,5.078,5.282,5.609,6.118,6.872,7.943,9.411,11.36,13.89,17.11],[9.027,6.315,4.286,2.835,1.868,1.298,1.046,1.039,1.212,1.51,1.882,2.287,2.691,3.067,3.396,3.667,3.876,4.027,4.131,4.207,4.282,4.39,4.572,4.879,5.366,6.098,7.148,8.595,10.53,13.04,16.23],[8.84,6.107,4.056,2.584,1.596,1.005,0.7312,0.7027,0.855,1.131,1.482,1.866,2.248,2.603,2.91,3.16,3.348,3.477,3.56,3.615,3.669,3.755,3.916,4.201,4.667,5.378,6.407,7.832,9.742,12.23,15.4],[8.707,5.953,3.88,2.387,1.377,0.7649,0.4699,0.42,0.551,0.8059,1.135,1.498,1.859,2.192,2.478,2.707,2.873,2.981,3.043,3.076,3.109,3.174,3.314,3.577,4.022,4.712,5.719,7.123,9.011,11.48,14.63],[8.627,5.851,3.758,2.243,1.212,0.5783,0.2619,0.1907,0.3003,0.5339,0.842,1.183,1.523,1.835,2.1,2.307,2.452,2.539,2.579,2.591,2.602,2.646,2.764,3.007,3.43,4.098,5.084,6.467,8.334,10.78,13.91],[8.6,5.803,3.688,2.152,1.1,0.4449,0.1072,0.01472,0.103,0.3152,0.602,0.9216,1.24,1.531,1.774,1.96,2.084,2.149,2.168,2.159,2.149,2.171,2.268,2.489,2.891,3.538,4.503,5.864,7.71,10.13,13.24],[8.627,5.809,3.672,2.115,1.041,0.3649,0.005867,-0.108,-0.04099,0.1499,0.4153,0.7136,1.011,1.28,1.502,1.667,1.769,1.813,1.811,1.78,1.749,1.75,1.826,2.025,2.406,3.032,3.975,5.315,7.139,9.542,12.63],[8.707,5.867,3.71,2.131,1.036,0.3383,-0.04213,-0.1773,-0.1317,0.03787,0.282,0.559,0.8347,1.083,1.284,1.427,1.508,1.531,1.507,1.455,1.402,1.382,1.436,1.615,1.974,2.578,3.5,4.819,6.622,9.003,12.07],[8.84,5.979,3.8,2.2,1.084,0.3649,-0.0368,-0.1933,-0.169,-0.0208,0.202,0.4576,0.712,0.9386,1.118,1.24,1.3,1.301,1.256,1.183,1.109,1.067,1.1,1.257,1.595,2.178,3.079,4.376,6.158,8.518,11.56],[9.027,6.145,3.944,2.323,1.185,0.4449,0.02187,-0.156,-0.153,-0.02613,0.1753,0.4096,0.6427,0.8479,1.006,1.107,1.145,1.125,1.059,0.9643,0.8686,0.8059,0.8177,0.9534,1.27,1.832,2.711,3.987,5.747,8.086,11.11],[9.267,6.363,4.142,2.499,1.34,0.5783,0.1339,-0.06528,-0.08365,0.02187,0.202,0.415,0.6267,0.8106,0.9477,1.027,1.044,1.003,0.9147,0.799,0.682,0.5979,0.5883,0.7027,0.9979,1.538,2.396,3.651,5.39,7.707,10.71],[9.56,6.635,4.392,2.728,1.548,0.7649,0.2992,0.07872,0.03901,0.1232,0.282,0.4736,0.664,0.8266,0.9424,1,0.9957,0.9332,0.824,0.687,0.5486,0.4432,0.4123,0.5054,0.7792,1.298,2.135,3.368,5.086,7.382,10.36],[9.907,6.961,4.696,3.011,1.809,1.005,0.5179,0.276,0.215,0.2779,0.4153,0.5856,0.7547,0.8959,0.9904,1.027,1.001,0.9172,0.7867,0.6283,0.4686,0.3419,0.2897,0.3614,0.6139,1.112,1.927,3.139,4.835,7.11,10.07],[10.31,7.339,5.054,3.347,2.124,1.298,0.7899,0.5267,0.4443,0.4859,0.602,0.751,0.8987,1.019,1.092,1.107,1.06,0.9546,0.8027,0.623,0.442,0.2939,0.2203,0.2707,0.5019,0.9783,1.772,2.963,4.638,6.891,9.827],[10.76,7.771,5.464,3.736,2.492,1.645,1.115,0.8307,0.727,0.7472,0.842,0.9696,1.096,1.195,1.246,1.24,1.172,1.045,0.872,0.671,0.4686,0.2992,0.2043,0.2334,0.4432,0.8983,1.671,2.84,4.494,6.726,9.64],[11.27,8.257,5.928,4.179,2.913,2.045,1.494,1.188,1.063,1.062,1.135,1.242,1.347,1.424,1.454,1.427,1.337,1.189,0.9947,0.7723,0.5486,0.3579,0.2417,0.2494,0.4379,0.8716,1.623,2.771,4.403,6.614,9.507],[11.83,8.795,6.446,4.675,3.388,2.498,1.926,1.599,1.452,1.43,1.482,1.567,1.651,1.707,1.716,1.667,1.556,1.387,1.171,0.927,0.682,0.4699,0.3323,0.3187,0.4859,0.8983,1.628,2.755,4.366,6.555,9.427],[12.44,9.387,7.016,5.224,3.916,3.005,2.411,2.063,1.895,1.851,1.882,1.946,2.008,2.043,2.03,1.96,1.828,1.637,1.4,1.135,0.8686,0.6352,0.4763,0.4414,0.5872,0.9783,1.687,2.792,4.382,6.55,9.4],[13.11,10.03,7.64,5.827,4.497,3.565,2.95,2.58,2.391,2.326,2.335,2.378,2.419,2.432,2.398,2.307,2.153,1.941,1.683,1.396,1.109,0.8539,0.6737,0.6174,0.7419,1.112,1.799,2.883,4.451,6.598,9.427],[13.83,10.73,8.318,6.483,5.132,4.178,3.542,3.151,2.94,2.854,2.842,2.863,2.883,2.875,2.82,2.707,2.532,2.299,2.019,1.711,1.402,1.126,0.9243,0.8467,0.9499,1.298,1.964,3.027,4.574,6.699,9.507],[14.6,11.48,9.048,7.192,5.82,4.845,4.187,3.775,3.543,3.435,3.402,3.402,3.4,3.371,3.294,3.16,2.964,2.709,2.408,2.079,1.749,1.451,1.228,1.129,1.211,1.538,2.183,3.224,4.75,6.854,9.64],[15.43,12.29,9.832,7.955,6.561,5.565,4.886,4.452,4.199,4.07,4.015,3.994,3.971,3.92,3.822,3.667,3.449,3.173,2.851,2.5,2.149,1.83,1.586,1.465,1.526,1.832,2.455,3.475,4.979,7.062,9.827],[16.31,13.15,10.67,8.771,7.356,6.338,5.638,5.183,4.908,4.758,4.682,4.639,4.595,4.523,4.404,4.227,3.988,3.691,3.347,2.975,2.602,2.262,1.996,1.855,1.894,2.178,2.78,3.779,5.262,7.323,10.07],[17.24,14.06,11.56,9.64,8.204,7.165,6.443,5.967,5.671,5.499,5.402,5.338,5.272,5.179,5.038,4.84,4.58,4.261,3.896,3.503,3.109,2.747,2.46,2.297,2.315,2.578,3.159,4.136,5.598,7.638,10.36],[18.23,15.02,12.5,10.56,9.105,8.045,7.302,6.804,6.487,6.294,6.175,6.09,6.003,5.888,5.726,5.507,5.225,4.885,4.499,4.084,3.669,3.286,2.978,2.793,2.79,3.032,3.591,4.547,5.987,8.006,10.71],[19.27,16.04,13.5,11.54,10.06,8.978,8.214,7.695,7.356,7.142,7.002,6.895,6.787,6.651,6.468,6.227,5.924,5.563,5.155,4.719,4.282,3.878,3.548,3.343,3.318,3.538,4.076,5.011,6.43,8.427,11.11],[20.36,17.12,14.55,12.57,11.07,9.965,9.179,8.639,8.279,8.043,7.882,7.754,7.624,7.467,7.262,7,6.676,6.293,5.864,5.407,4.949,4.523,4.172,3.945,3.899,4.098,4.615,5.528,6.926,8.902,11.56]]}},"gradientCheck":{"about":"Worst relative error |exact - numeric| / (|exact| + |numeric|) of each surface's gradient against central differences (h = 1e-5) at four points; the controls flip the gradient's sign or swap its two components and must fail.","points":[[0.3,-0.7],[-1.2,1],[1.5,0.2],[-0.4,-1.1]],"bowl":{"exact":5.4663e-12,"signFlippedControl":1,"swappedAxesControl":0.46468},"rosenbrock":{"exact":1.0552e-10,"signFlippedControl":1,"swappedAxesControl":0.96854},"two-valleys":{"exact":4.5656e-11,"signFlippedControl":1,"swappedAxesControl":0.99964}},"landscape":{"about":"Held-out loss (first 64 rows of the corpus's held-out set) on a 21 x 21 grid of theta + a d1 + b d2, a and b in [-1, 1], for the trained model and for the same model at its initialisation (seed 7). d1, d2 are seeded Gaussian directions with filter-wise normalisation (Li et al. 2018); values[j][i] has b = alphas[j], a = alphas[i]. slopeBackward is grad . d from the backward pass; slopeFiniteDiff is the same slope by central differences (h = 0.01).","note":"A 2D slice shows the loss on one flat sheet through a space with thousands of dimensions. It can show whether the trained point sits in a basin along these two directions, how wide that basin is relative to the weights' own size, and how the trained point differs from the starting point. It cannot show the loss along any other direction, so a slice that looks like a bowl does not prove the point is a minimum, and a smooth slice does not rule out sharp directions elsewhere. Two random directions in high dimension are nearly at right angles to each other and to the gradient, so the slice usually misses the steepest way down.","rows":64,"trained":{"n":21,"span":1,"alphas":[-1,-0.9,-0.8,-0.7,-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1],"values":[[13.99,12.7,11.39,10.15,9.061,8.161,7.461,6.952,6.574,6.38,6.363,6.47,6.722,7.125,7.606,8.226,9.044,9.939,10.86,11.83,12.86],[12.71,11.36,10.04,8.804,7.706,6.845,6.25,5.803,5.465,5.27,5.25,5.355,5.592,5.971,6.461,7.06,7.896,8.839,9.822,10.88,11.98],[11.47,10.06,8.737,7.492,6.412,5.623,5.065,4.653,4.368,4.185,4.144,4.227,4.479,4.854,5.352,5.965,6.73,7.675,8.707,9.824,10.98],[10.3,8.887,7.544,6.331,5.295,4.494,3.93,3.556,3.326,3.165,3.129,3.197,3.426,3.814,4.321,4.944,5.66,6.517,7.546,8.687,9.885],[9.337,7.879,6.52,5.33,4.33,3.504,2.948,2.577,2.367,2.275,2.268,2.361,2.585,2.956,3.447,4.023,4.736,5.542,6.486,7.595,8.788],[8.569,7.09,5.722,4.522,3.526,2.732,2.196,1.856,1.669,1.57,1.56,1.67,1.935,2.315,2.797,3.347,4.015,4.794,5.697,6.728,7.846],[7.953,6.472,5.126,3.935,2.927,2.199,1.694,1.377,1.202,1.126,1.115,1.185,1.379,1.742,2.239,2.812,3.429,4.171,5.066,6.045,7.088],[7.469,6.041,4.705,3.522,2.543,1.847,1.376,1.07,0.9106,0.8446,0.8617,0.9342,1.057,1.314,1.769,2.335,2.959,3.651,4.496,5.453,6.478],[7.137,5.753,4.415,3.249,2.3,1.66,1.191,0.9196,0.7795,0.7337,0.729,0.759,0.8379,1.031,1.429,1.982,2.568,3.26,4.079,5.009,6.02],[6.964,5.554,4.239,3.109,2.183,1.55,1.103,0.8655,0.7549,0.7103,0.6998,0.7124,0.764,0.9022,1.216,1.722,2.321,2.99,3.799,4.729,5.731],[6.917,5.529,4.219,3.118,2.188,1.538,1.093,0.8552,0.762,0.7237,0.7,0.7096,0.7547,0.8685,1.134,1.586,2.164,2.853,3.654,4.597,5.595],[7.075,5.72,4.382,3.258,2.331,1.641,1.156,0.8911,0.7853,0.739,0.7132,0.7221,0.7737,0.8939,1.152,1.598,2.144,2.883,3.712,4.617,5.585],[7.435,6.109,4.759,3.563,2.611,1.881,1.348,0.9961,0.8407,0.7751,0.7487,0.7596,0.8195,0.962,1.244,1.721,2.299,3.064,3.915,4.802,5.742],[7.898,6.62,5.312,4.086,3.07,2.27,1.667,1.229,0.9851,0.8708,0.8279,0.8364,0.9222,1.107,1.458,1.977,2.593,3.362,4.217,5.113,6.007],[8.365,7.173,5.949,4.756,3.698,2.838,2.132,1.62,1.279,1.109,1.025,1.045,1.175,1.418,1.798,2.339,3.001,3.774,4.623,5.496,6.34],[8.906,7.77,6.603,5.488,4.425,3.529,2.8,2.245,1.811,1.554,1.452,1.471,1.598,1.842,2.229,2.79,3.486,4.263,5.078,5.907,6.704],[9.601,8.537,7.42,6.338,5.32,4.428,3.661,3.034,2.561,2.202,2.031,2.02,2.143,2.384,2.777,3.331,4.026,4.795,5.573,6.346,7.106],[10.28,9.352,8.336,7.306,6.322,5.459,4.668,3.994,3.453,3.022,2.763,2.689,2.786,3.023,3.38,3.891,4.557,5.304,6.056,6.813,7.573],[10.98,10.15,9.22,8.248,7.314,6.476,5.722,5.034,4.433,3.96,3.62,3.463,3.497,3.692,4.015,4.469,5.086,5.799,6.546,7.303,8.059],[11.7,10.94,10.09,9.194,8.276,7.459,6.75,6.078,5.445,4.92,4.543,4.317,4.255,4.375,4.668,5.091,5.655,6.313,7.037,7.796,8.569],[12.44,11.72,10.91,10.08,9.233,8.435,7.724,7.075,6.451,5.895,5.445,5.163,5.035,5.083,5.331,5.738,6.256,6.86,7.544,8.272,9.043]],"min":0.6998,"max":13.986,"center":0.69996,"argmin":[0,-0.1],"slopeBackward":[-0.018323,0.061209],"slopeFiniteDiff":[-0.018189,0.061333],"directionCosine":-0.00531,"gradientCosines":[-0.00238,0.00794],"directionNorms":[46.108,46.108],"weightNorm":48.273},"init":{"n":21,"span":1,"alphas":[-1,-0.9,-0.8,-0.7,-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1],"values":[[3.852,3.85,3.848,3.846,3.844,3.842,3.84,3.838,3.837,3.836,3.836,3.835,3.835,3.835,3.835,3.836,3.836,3.837,3.837,3.838,3.838],[3.852,3.85,3.848,3.846,3.844,3.842,3.84,3.838,3.837,3.836,3.835,3.835,3.835,3.834,3.835,3.835,3.835,3.835,3.835,3.835,3.835],[3.852,3.85,3.848,3.846,3.844,3.842,3.84,3.838,3.837,3.836,3.835,3.834,3.834,3.834,3.834,3.833,3.833,3.833,3.833,3.833,3.833],[3.851,3.85,3.848,3.846,3.844,3.842,3.84,3.839,3.837,3.836,3.835,3.834,3.834,3.833,3.833,3.832,3.832,3.831,3.831,3.83,3.83],[3.851,3.85,3.848,3.846,3.845,3.843,3.841,3.839,3.838,3.836,3.835,3.834,3.833,3.832,3.832,3.831,3.83,3.829,3.829,3.828,3.827],[3.851,3.85,3.849,3.847,3.845,3.844,3.842,3.84,3.838,3.837,3.836,3.834,3.833,3.832,3.831,3.83,3.829,3.828,3.827,3.825,3.825],[3.851,3.85,3.849,3.848,3.846,3.844,3.843,3.841,3.839,3.838,3.836,3.835,3.833,3.832,3.83,3.829,3.827,3.826,3.824,3.823,3.822],[3.852,3.851,3.85,3.848,3.847,3.846,3.844,3.842,3.84,3.839,3.837,3.835,3.833,3.831,3.829,3.828,3.826,3.824,3.823,3.821,3.82],[3.852,3.851,3.85,3.849,3.848,3.847,3.845,3.844,3.842,3.84,3.838,3.836,3.834,3.831,3.829,3.827,3.825,3.823,3.821,3.82,3.818],[3.852,3.851,3.851,3.85,3.849,3.848,3.846,3.845,3.843,3.841,3.839,3.837,3.834,3.832,3.829,3.827,3.824,3.822,3.82,3.819,3.817],[3.852,3.851,3.851,3.851,3.85,3.849,3.848,3.846,3.845,3.843,3.841,3.838,3.835,3.832,3.829,3.827,3.824,3.822,3.82,3.818,3.817],[3.852,3.852,3.852,3.851,3.851,3.85,3.849,3.848,3.846,3.845,3.842,3.839,3.836,3.833,3.83,3.827,3.825,3.822,3.82,3.818,3.817],[3.852,3.852,3.852,3.852,3.852,3.851,3.851,3.85,3.848,3.846,3.844,3.841,3.838,3.835,3.831,3.828,3.825,3.823,3.821,3.819,3.817],[3.852,3.853,3.853,3.853,3.853,3.852,3.852,3.851,3.85,3.848,3.846,3.843,3.84,3.836,3.833,3.83,3.827,3.824,3.822,3.82,3.818],[3.853,3.853,3.853,3.854,3.854,3.853,3.853,3.852,3.851,3.85,3.848,3.845,3.842,3.838,3.835,3.831,3.828,3.826,3.823,3.821,3.819],[3.853,3.854,3.854,3.854,3.854,3.854,3.854,3.854,3.853,3.851,3.849,3.847,3.843,3.84,3.837,3.833,3.83,3.828,3.825,3.823,3.821],[3.854,3.855,3.855,3.855,3.855,3.855,3.855,3.855,3.854,3.853,3.851,3.848,3.845,3.842,3.839,3.835,3.832,3.83,3.827,3.825,3.823],[3.855,3.855,3.856,3.856,3.856,3.856,3.856,3.856,3.855,3.854,3.852,3.85,3.847,3.844,3.841,3.838,3.835,3.832,3.829,3.827,3.825],[3.856,3.856,3.857,3.857,3.857,3.857,3.857,3.857,3.856,3.855,3.853,3.851,3.849,3.846,3.843,3.84,3.837,3.834,3.832,3.83,3.828],[3.857,3.857,3.858,3.858,3.858,3.858,3.858,3.857,3.857,3.856,3.855,3.853,3.851,3.848,3.845,3.842,3.84,3.837,3.835,3.833,3.831],[3.858,3.859,3.859,3.859,3.859,3.859,3.859,3.858,3.858,3.857,3.856,3.854,3.852,3.85,3.847,3.845,3.842,3.84,3.837,3.835,3.834]],"min":3.8166,"max":3.8588,"center":3.8406,"argmin":[1,0.1],"slopeBackward":[-0.024484,0.01546],"slopeFiniteDiff":[-0.024483,0.015459],"directionCosine":-0.0118,"gradientCosines":[-0.00517,0.00326],"directionNorms":[2.52,2.52],"weightNorm":12.898}},"gradientNorm":{"about":"Global L2 norm of the gradient of the mean held-out loss over all parameters, from the model's own backward pass (lossAndGrad), on 64 and 256 held-out rows. Training clips the gradient at norm 1.0.","trained":{"rows64":{"loss":0.69996,"norm":0.16728},"rows256":{"loss":0.68741,"norm":0.12434}},"init":{"rows64":{"loss":3.8406,"norm":1.8796},"rows256":{"loss":3.8414,"norm":1.8679}},"nParams":20864},"oneNumber":{"about":"Every weight fixed except s, which multiplies the readout matrix wout (s = 1 is the trained model). dL/ds comes from the real backward pass by the chain rule. sStar is where dL/ds = 0 (bisection); curvature is d2L/ds2 by central differences of dL/ds. Descents start at s = 0.05 with 40 steps each; the control follows +dL/ds and climbs.","curve":[[0,3.8286,-12.892],[0.1,2.6276,-10.924],[0.2,1.7007,-7.361],[0.3,1.1587,-3.6989],[0.4,0.90362,-1.6598],[0.5,0.78939,-0.74931],[0.6,0.7372,-0.34712],[0.7,0.71298,-0.15965],[0.8,0.70229,-0.063862],[0.9,0.69889,-0.0085601],[1,0.69996,0.027907],[1.1,0.70416,0.054926],[1.2,0.71078,0.076687],[1.3,0.71939,0.095124],[1.4,0.72972,0.11118],[1.5,0.74156,0.12533],[1.6,0.75474,0.13789],[1.7,0.76909,0.14906],[1.8,0.78451,0.15899],[1.9,0.80085,0.16782],[2,0.81804,0.17568],[2.1,0.83596,0.18268],[2.2,0.85455,0.18893],[2.3,0.87373,0.19451],[2.4,0.89343,0.19951],[2.5,0.91361,0.204],[2.6,0.93422,0.20804],[2.7,0.95521,0.21168],[2.8,0.97654,0.21498],[2.9,0.99819,0.21798],[3,1.0201,0.22071]],"sStar":0.920431,"lossAtStar":0.6988,"lossAtOne":0.69996,"curvatureAtStar":0.40237,"boundAtStar":4.9706,"curvatureAtStart":19.113,"boundAtStart":0.10464,"descents":[{"step":0.02,"end":0.70688,"loss":0.71191,"path":[[0.05,3.204,-12.06],[0.2912,1.192,-3.958],[0.3704,0.9591,-2.108],[0.4126,0.8838,-1.5],[0.4426,0.8438,-1.179],[0.4661,0.8184,-0.9778],[0.4857,0.8007,-0.8381],[0.5025,0.7876,-0.735],[0.5172,0.7773,-0.6556],[0.5303,0.7692,-0.5923],[0.5421,0.7625,-0.5405],[0.5529,0.7569,-0.4974],[0.5629,0.7521,-0.4609],[0.5721,0.748,-0.4295],[0.5807,0.7444,-0.4022],[0.5887,0.7413,-0.3783],[0.5963,0.7385,-0.3571],[0.6034,0.736,-0.3381],[0.6102,0.7338,-0.3211],[0.6166,0.7318,-0.3058],[0.6227,0.73,-0.2918],[0.6286,0.7283,-0.2791],[0.6342,0.7268,-0.2674],[0.6395,0.7254,-0.2566],[0.6446,0.7241,-0.2467],[0.6496,0.7229,-0.2375],[0.6543,0.7218,-0.2289],[0.6589,0.7207,-0.2209],[0.6633,0.7198,-0.2135],[0.6676,0.7189,-0.2065],[0.6717,0.718,-0.1999],[0.6757,0.7173,-0.1937],[0.6796,0.7165,-0.1879],[0.6834,0.7158,-0.1824],[0.687,0.7152,-0.1772],[0.6905,0.7146,-0.1723],[0.694,0.714,-0.1676],[0.6973,0.7134,-0.1631],[0.7006,0.7129,-0.1589],[0.7038,0.7124,-0.1548],[0.7069,0.7119,-0.151]]},{"step":0.05,"end":0.83775,"loss":0.70035,"path":[[0.05,3.204,-12.06],[0.6531,0.7221,-0.2311],[0.6646,0.7195,-0.2113],[0.6752,0.7174,-0.1945],[0.6849,0.7155,-0.1801],[0.6939,0.714,-0.1676],[0.7023,0.7126,-0.1567],[0.7102,0.7114,-0.147],[0.7175,0.7104,-0.1383],[0.7244,0.7094,-0.1305],[0.7309,0.7086,-0.1235],[0.7371,0.7079,-0.1171],[0.743,0.7072,-0.1112],[0.7485,0.7066,-0.1059],[0.7538,0.7061,-0.101],[0.7589,0.7056,-0.0964],[0.7637,0.7051,-0.09217],[0.7683,0.7047,-0.08824],[0.7727,0.7043,-0.08458],[0.7769,0.704,-0.08115],[0.781,0.7036,-0.07794],[0.7849,0.7033,-0.07493],[0.7886,0.7031,-0.0721],[0.7923,0.7028,-0.06943],[0.7957,0.7026,-0.0669],[0.7991,0.7024,-0.06452],[0.8023,0.7021,-0.06226],[0.8054,0.702,-0.06011],[0.8084,0.7018,-0.05808],[0.8113,0.7016,-0.05614],[0.8141,0.7015,-0.0543],[0.8168,0.7013,-0.05254],[0.8195,0.7012,-0.05086],[0.822,0.701,-0.04926],[0.8245,0.7009,-0.04773],[0.8269,0.7008,-0.04626],[0.8292,0.7007,-0.04486],[0.8314,0.7006,-0.04351],[0.8336,0.7005,-0.04222],[0.8357,0.7004,-0.04098],[0.8378,0.7003,-0.03979]]},{"step":0.2,"end":1.2694,"loss":0.71656,"path":[[0.05,3.204,-12.06],[2.462,0.906,0.2024],[2.422,0.8978,0.2005],[2.382,0.8898,0.1986],[2.342,0.882,0.1967],[2.303,0.8743,0.1947],[2.264,0.8667,0.1926],[2.225,0.8593,0.1904],[2.187,0.8521,0.1882],[2.15,0.8451,0.1859],[2.112,0.8382,0.1835],[2.076,0.8315,0.1811],[2.039,0.825,0.1785],[2.004,0.8187,0.176],[1.969,0.8126,0.1733],[1.934,0.8066,0.1706],[1.9,0.8008,0.1678],[1.866,0.7952,0.165],[1.833,0.7898,0.162],[1.801,0.7846,0.1591],[1.769,0.7796,0.156],[1.738,0.7748,0.1529],[1.707,0.7702,0.1498],[1.677,0.7657,0.1466],[1.648,0.7615,0.1434],[1.619,0.7574,0.1401],[1.591,0.7535,0.1369],[1.564,0.7498,0.1335],[1.537,0.7463,0.1302],[1.511,0.743,0.1268],[1.486,0.7398,0.1234],[1.461,0.7368,0.12],[1.437,0.7339,0.1166],[1.414,0.7313,0.1132],[1.391,0.7287,0.1098],[1.369,0.7264,0.1064],[1.348,0.7241,0.1031],[1.327,0.722,0.0997],[1.307,0.7201,0.09637],[1.288,0.7183,0.09305],[1.269,0.7166,0.08977]]}],"climbControl":{"step":0.02,"end":-16.904,"loss":69.078,"startLoss":3.2039}},"seconds":37}