{ "seed": 2104, "predictions": { "gramian": "lambda_min=min(1,q), with positivity iff q>0", "noise_scaling": "small-posterior covariance eigenvalue approximately sigma^2", "diffusion": "consensus disagreement ratio is bounded by rho^t" }, "gramian": [ { "q": 0.0, "observed": 0.0, "predicted": 0.0, "abs_error": 0.0 }, { "q": 0.05, "observed": 0.05, "predicted": 0.05, "abs_error": 0.0 }, { "q": 0.1, "observed": 0.1, "predicted": 0.1, "abs_error": 0.0 }, { "q": 0.25, "observed": 0.25, "predicted": 0.25, "abs_error": 0.0 }, { "q": 0.5, "observed": 0.5, "predicted": 0.5, "abs_error": 0.0 }, { "q": 1.0, "observed": 1.0, "predicted": 1.0, "abs_error": 0.0 }, { "q": 2.0, "observed": 1.0, "predicted": 1.0, "abs_error": 0.0 } ], "noise_scaling": [ { "sigma": 0.1, "observed": 0.009999999900000002, "predicted": 0.010000000000000002, "ratio": 0.9999999900000001 }, { "sigma": 0.2, "observed": 0.03999999840000007, "predicted": 0.04000000000000001, "ratio": 0.9999999600000016 }, { "sigma": 0.5, "observed": 0.24999993750001562, "predicted": 0.25, "ratio": 0.9999997500000625 }, { "sigma": 1.0, "observed": 0.9999990000010001, "predicted": 1.0, "ratio": 0.9999990000010001 }, { "sigma": 2.0, "observed": 3.9999840000640003, "predicted": 4.0, "ratio": 0.9999960000160001 }, { "sigma": 4.0, "observed": 15.999744004095934, "predicted": 16.0, "ratio": 0.9999840002559959 } ], "diffusion": { "rho": 0.5000000000000001, "rows": [ { "rounds": 1, "observed_ratio": 0.15811388300841897, "predicted_bound": 0.5000000000000001, "ratio_to_bound": 0.3162277660168379 }, { "rounds": 2, "observed_ratio": 0.07905694150420949, "predicted_bound": 0.2500000000000001, "ratio_to_bound": 0.3162277660168378 }, { "rounds": 3, "observed_ratio": 0.03952847075210474, "predicted_bound": 0.12500000000000008, "ratio_to_bound": 0.3162277660168377 }, { "rounds": 5, "observed_ratio": 0.009882117688026186, "predicted_bound": 0.031250000000000035, "ratio_to_bound": 0.3162277660168376 }, { "rounds": 8, "observed_ratio": 0.0012352647110032732, "predicted_bound": 0.003906250000000007, "ratio_to_bound": 0.3162277660168374 }, { "rounds": 12, "observed_ratio": 7.720404443770458e-05, "predicted_bound": 0.00024414062500000065, "ratio_to_bound": 0.3162277660168371 }, { "rounds": 20, "observed_ratio": 3.015782985847835e-07, "predicted_bound": 9.536743164062542e-07, "ratio_to_bound": 0.31622776601683655 } ] }, "fusion_mse": { "information_diffusion": 0.19808281555717885, "arithmetic_mean": 0.19743105589453624 } }