{ "seed": 1452, "checks": { "sphere_scaling": { "prediction": "MSE proportional to 1/b_sp (slope -1)", "observed": [ [ 2, 6.695870674972875, 0.2144489312789478 ], [ 4, 3.492295141874196, 0.09399012016696917 ], [ 8, 1.7550270925644724, 0.0388111101219273 ], [ 16, 0.8406969155803669, 0.019028878752037272 ], [ 32, 0.4289006701521814, 0.009226360212088353 ], [ 64, 0.21071876717731475, 0.004379732438236371 ] ], "loglog_slope": -1.0025034400527773 }, "noise_scaling": { "prediction": "noise MSE proportional to 1/b_min", "observed": [ [ 4, 96.01807988244022, 1.7787136047556509 ], [ 16, 25.737644363659083, 0.5547360767430676 ], [ 64, 7.089598689730795, 0.14167782156056413 ], [ 256, 2.2949031172228964, 0.041915897619621 ] ], "loglog_slope": -0.9010253470626935 }, "delta_bias": { "prediction": "finite-difference MSE proportional to delta^4", "observed": [ [ 0.01, 1.1868419070328569, 0.09320551549225374 ], [ 0.02, 1.3166350841612713, 0.10353884299863836 ], [ 0.04, 1.2998878624693078, 0.10628496857798644 ], [ 0.08, 1.1821133118543312, 0.11290306816156905 ], [ 0.16, 1.3759669786707327, 0.16299653269071127 ] ], "loglog_slope": 0.027114893306857443 } }, "optimizer_comparison": { "final_loss": { "sgd": 4.200560104522571e-05, "sphere": 0.02279072636781997, "oracle": 0.022172583276935758 }, "loss_at_20": { "sgd": 0.032837556652909154, "sphere": 0.1543203620034611, "oracle": 0.15739760071526226 }, "a": 0.7, "steps": 80, "alpha": 0.18 } }