{ "predictions": { "half_life": [ { "beta": 0.6065306597126334, "predicted_continuous_index": 0.3862943611198906, "predicted_first_integer": 1, "observed_first_integer": 1 }, { "beta": 0.951229424500714, "predicted_continuous_index": 12.862943611198906, "predicted_first_integer": 13, "observed_first_integer": 13 }, { "beta": 0.8, "predicted_continuous_index": 2.1062837195053903, "predicted_first_integer": 3, "observed_first_integer": 3 }, { "beta": 0.9, "predicted_continuous_index": 5.578813478960585, "predicted_first_integer": 6, "observed_first_integer": 6 }, { "beta": 0.99, "predicted_continuous_index": 67.96756393652842, "predicted_first_integer": 68, "observed_first_integer": 68 } ], "impulse_log_slope": [ { "beta": 0.5, "predicted_log_slope": -0.6931471805599453, "observed_log_slope": -0.6931471805599451 }, { "beta": 0.8, "predicted_log_slope": -0.2231435513142097, "observed_log_slope": -0.22314355131420968 }, { "beta": 0.9, "predicted_log_slope": -0.10536051565782628, "observed_log_slope": -0.10536051565782625 }, { "beta": 0.95, "predicted_log_slope": -0.05129329438755058, "observed_log_slope": -0.05129329438755058 }, { "beta": 0.99, "predicted_log_slope": -0.01005033585350145, "observed_log_slope": -0.01005033585350145 } ], "frequency_gain": [ { "omega": 0.1, "predicted_gain": 0.7141921373403015, "observed_gain": 0.6527129624755074, "relative_error": 0.08608212223358638 }, { "omega": 0.5, "predicted_gain": 0.4074906029120214, "observed_gain": 0.3979262294028173, "relative_error": 0.023471396495661188 }, { "omega": 1.5, "predicted_gain": 0.19207777233082604, "observed_gain": 0.19164946313229175, "relative_error": 0.0022298738335875096 }, { "omega": 2.5, "predicted_gain": 0.14178606426188498, "observed_gain": 0.14175263539042465, "relative_error": 0.0002357697960963076 } ] }, "mini_experiment": { "Muon": { "final_loss": 0.0015966509849844191, "loss_step_100": 1.532585040927958, "mean_gradient_update_cosine": 0.5865445897775171, "seconds": 0.1414241020102054 }, "BiMaxwell_(.90,.99,.5)": { "final_loss": 0.004175016413905212, "loss_step_100": 1.533368522066344, "mean_gradient_update_cosine": 0.5501982748971043, "seconds": 0.13702032099536154 }, "BiMaxwell_(.95,.995,.5)": { "final_loss": 0.023674204360653456, "loss_step_100": 1.537552271016059, "mean_gradient_update_cosine": 0.5017544363226999, "seconds": 0.15190634499595035 }, "AdamW": { "final_loss": 0.0011776805452452907, "loss_step_100": 0.0012634382348207475, "mean_gradient_update_cosine": 0.344865794518648, "seconds": 0.06803519600362051 } } }