{ "seed": 2688, "orthogonality": { "dimension": 8, "sigma_min_feature_matrix": 1.0000000001981044e-07, "mgs_rank": 8, "max_abs_QtQ_minus_I": 2.826667372390901e-10, "min_mgs_residual": 1.1054034901468194e-06 }, "stability_sweep": { "predicted_boundary_alpha": 2.0, "rows": [ { "alpha": 0.25, "predicted_norm_after_30": 0.00017858209017001473, "observed_norm_after_30": 0.0001785820901700147, "observed_stable": true }, { "alpha": 0.75, "predicted_norm_after_30": 8.673617379884035e-19, "observed_norm_after_30": 8.6736173798840345e-19, "observed_stable": true }, { "alpha": 1.0, "predicted_norm_after_30": 0.0, "observed_norm_after_30": 0.0, "observed_stable": true }, { "alpha": 1.25, "predicted_norm_after_30": 8.673617379884035e-19, "observed_norm_after_30": 8.6736173798840345e-19, "observed_stable": true }, { "alpha": 1.75, "predicted_norm_after_30": 0.00017858209017001473, "observed_norm_after_30": 0.0001785820901700147, "observed_stable": true }, { "alpha": 1.99, "predicted_norm_after_30": 0.7397003733882802, "observed_norm_after_30": 0.73970037338828, "observed_stable": true }, { "alpha": 2.01, "predicted_norm_after_30": 1.3478489153328972, "observed_norm_after_30": 1.3478489153328967, "observed_stable": false }, { "alpha": 2.5, "predicted_norm_after_30": 191751.0592328841, "observed_norm_after_30": 191751.059232884, "observed_stable": false } ] }, "excitation_transition": { "predicted_transition_k": 8, "rows": [ { "independent_directions": 0, "norm_at_start": 0.9999999999999999, "norm_at_step_15": 0.9999999999999999, "predicted_norm_at_step_15": 1.0, "all_direction_contraction": false }, { "independent_directions": 1, "norm_at_start": 0.9999999999999999, "norm_at_step_15": 0.9354143466934853, "predicted_norm_at_step_15": 0.9354143466934853, "all_direction_contraction": false }, { "independent_directions": 2, "norm_at_start": 0.9999999999999999, "norm_at_step_15": 0.8660254037844386, "predicted_norm_at_step_15": 0.8660254037844386, "all_direction_contraction": false }, { "independent_directions": 3, "norm_at_start": 0.9999999999999999, "norm_at_step_15": 0.7905694150420948, "predicted_norm_at_step_15": 0.7905694150420949, "all_direction_contraction": false }, { "independent_directions": 4, "norm_at_start": 0.9999999999999999, "norm_at_step_15": 0.7071067811865475, "predicted_norm_at_step_15": 0.7071067811865476, "all_direction_contraction": false }, { "independent_directions": 5, "norm_at_start": 0.9999999999999999, "norm_at_step_15": 0.6123724356957945, "predicted_norm_at_step_15": 0.6123724356957945, "all_direction_contraction": false }, { "independent_directions": 6, "norm_at_start": 0.9999999999999999, "norm_at_step_15": 0.49999999999999994, "predicted_norm_at_step_15": 0.5, "all_direction_contraction": false }, { "independent_directions": 7, "norm_at_start": 0.9999999999999999, "norm_at_step_15": 0.35355339059327373, "predicted_norm_at_step_15": 0.3535533905932738, "all_direction_contraction": false }, { "independent_directions": 8, "norm_at_start": 0.9999999999999999, "norm_at_step_15": 3.276799999999992e-11, "predicted_norm_at_step_15": 3.2767999999999886e-11, "all_direction_contraction": true } ] }, "replay_comparison": { "predicted_mgs_slope": -1.6094379124341005, "rows": [ { "case": "well_conditioned", "sigma_min": 1.0, "raw_norm_step_10": 1.0239999999999852e-07, "mgs_norm_step_10": 1.0239999999999913e-07, "raw_log_slope_late": -1.6094379124341012, "mgs_log_slope_late": -1.6094379124341007 }, { "case": "ill_conditioned", "sigma_min": 0.001, "raw_norm_step_10": 696342.7809960718, "mgs_norm_step_10": 1.0239999999999984e-07, "raw_log_slope_late": 1.5064575950364518, "mgs_log_slope_late": -1.6094379124341003 } ] } }