{
  "paper": {
    "title": "Gaussian Mean Field Variational Inference can Overestimate Predictive Variance",
    "openreview": "RG7maF4bGu"
  },
  "protocol": {
    "precision": "float64",
    "device": "CPU",
    "external_compute_cost": 0
  },
  "summary": {
    "problems": 140,
    "dimensions": [
      2,
      3,
      5,
      8,
      16,
      32,
      64
    ],
    "alpha_range": [
      0.0011005438914875921,
      946.4622246988179
    ],
    "noise_variance_range": [
      0.0011138089123204126,
      900.7295682224885
    ],
    "maximum_posterior_condition": 13850.875912934025,
    "gate_counts": {
      "posterior_trace_exceeds_mfvi": 140,
      "mfvi_overestimates_min_direction": 140,
      "max_direction_mutation_reverses": 140,
      "training_distribution_mfvi_exceeds_exact": 140,
      "training_identity": 140,
      "first_pc_is_min_posterior_direction": 140,
      "first_pc_overestimate": 140,
      "last_pc_mutation_reverses": 140,
      "nonspherical_prior_breaks_alignment": 140
    },
    "claim_1": {
      "minimum_trace_margin": 7.880246609540988e-07,
      "minimum_overestimate_margin": 4.3670042426917865e-09,
      "maximum_direction_mutation_failures": 140,
      "kl_optimizer_checks": 24,
      "kl_optimizer_worst_relative_error": 4.930412283060204e-07
    },
    "claim_2": {
      "largest_expected_exact_minus_mfvi": -1.6610865466911604e-12,
      "worst_identity_absolute_error": 1.2079226507921703e-13,
      "all_training_distribution_expectations_nonpositive": true
    },
    "claim_3": {
      "worst_first_pc_alignment_error": 1.3322676295501878e-15,
      "minimum_first_pc_overestimate": 4.3670042426897426e-09,
      "last_pc_mutation_failures": 140,
      "nonspherical_prior_alignment_breaks": 140
    },
    "general_derivation": {
      "mfvi_optimum": "S*=diag(1/diag(Sigma^-1))",
      "trace_proof": "For A=Sigma^-1, A_ii <= lambda_max(A), and Schur complements give Sigma_ii >= 1/A_ii; summing yields Tr(Sigma)>=Tr(S*).",
      "direction_proof": "min_i 1/A_ii >= 1/lambda_max(A)=lambda_min(Sigma), hence S* dominates Sigma along Sigma's minimum-eigenvalue direction.",
      "training_distribution_identity": "tr[(X'X/N)(Sigma-S*)]=-(sigma^2 alpha/N)[Tr(Sigma)-Tr(S*)] <= 0.",
      "first_pc_proof": "Sigma^-1=X'X/sigma^2+alpha I commutes with X'X; its largest data eigenvalue maps to Sigma's smallest eigenvalue."
    }
  },
  "records": [
    {
      "dimension": 2,
      "seed": 0,
      "samples": 160,
      "data_covariance_condition": 732.9601108772436,
      "alpha": 4.8900444006896375,
      "noise_variance": 492.35944808640306,
      "posterior_condition": 43.00102689066658,
      "trace_exact_posterior": 0.1961992965040288,
      "trace_mfvi": 0.021724005816323826,
      "trace_margin": 0.17447529068770495,
      "minimum_posterior_direction_margin": 0.0041540720216647195,
      "maximum_posterior_direction_control": -0.17862936270936972,
      "training_distribution_expected_exact_minus_mfvi": -2.6254818874945602,
      "training_distribution_identity_rhs": -2.625481887494549,
      "identity_absolute_error": 1.1102230246251565e-14,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.0041540720216647195,
      "last_pc_control_margin": -0.17862936270936972,
      "nonspherical_prior_first_pc_alignment_control": 0.8560765569242473,
      "kl_optimizer_relative_error": 1.1534025572957738e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 1,
      "samples": 160,
      "data_covariance_condition": 16.388903633800073,
      "alpha": 0.0020046339507912643,
      "noise_variance": 0.2605567105961478,
      "posterior_condition": 18.62029174620117,
      "trace_exact_posterior": 0.0018356362936134915,
      "trace_mfvi": 0.0012286313892055692,
      "trace_margin": 0.0006070049044079222,
      "minimum_posterior_direction_margin": 3.4449197161493595e-05,
      "maximum_posterior_direction_control": -0.000641454101569416,
      "training_distribution_expected_exact_minus_mfvi": -1.9815706524977103e-09,
      "training_distribution_identity_rhs": -1.9815706523256216e-09,
      "identity_absolute_error": 1.7208872258706326e-19,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 3.444919716149361e-05,
      "last_pc_control_margin": -0.000641454101569416,
      "nonspherical_prior_first_pc_alignment_control": 0.17482611024545475,
      "kl_optimizer_relative_error": 1.4427940340926375e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 2,
      "samples": 160,
      "data_covariance_condition": 219.54099652129267,
      "alpha": 0.030058538272440836,
      "noise_variance": 583.9058834548634,
      "posterior_condition": 165.21660299472143,
      "trace_exact_posterior": 3.6942129575795266,
      "trace_mfvi": 2.0869738837775045,
      "trace_margin": 1.6072390738020221,
      "minimum_posterior_direction_margin": 0.009787311663326055,
      "maximum_posterior_direction_control": -1.617026385465348,
      "training_distribution_expected_exact_minus_mfvi": -0.17630767077299123,
      "training_distribution_identity_rhs": -0.17630767077299217,
      "identity_absolute_error": 9.43689570931383e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.009787311663326055,
      "last_pc_control_margin": -1.617026385465348,
      "nonspherical_prior_first_pc_alignment_control": 0.06885315291022721,
      "kl_optimizer_relative_error": 7.188651780675932e-09,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 3,
      "samples": 160,
      "data_covariance_condition": 15.598570470842608,
      "alpha": 0.09915880228366157,
      "noise_variance": 93.59722314223231,
      "posterior_condition": 12.897374383681033,
      "trace_exact_posterior": 0.6067821217080616,
      "trace_mfvi": 0.16479221691910562,
      "trace_margin": 0.44198990478895595,
      "minimum_posterior_direction_margin": 0.03715020562816018,
      "maximum_posterior_direction_control": -0.4791401104171161,
      "training_distribution_expected_exact_minus_mfvi": -0.025638145267801452,
      "training_distribution_identity_rhs": -0.025638145267801466,
      "identity_absolute_error": 1.3877787807814457e-17,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.03715020562816019,
      "last_pc_control_margin": -0.4791401104171161,
      "nonspherical_prior_first_pc_alignment_control": 0.651972194117605,
      "kl_optimizer_relative_error": 2.432573696301355e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 4,
      "samples": 160,
      "data_covariance_condition": 510.5504050156486,
      "alpha": 76.64017655271832,
      "noise_variance": 84.78693171138329,
      "posterior_condition": 12.99869316292852,
      "trace_exact_posterior": 0.01375578221882449,
      "trace_mfvi": 0.012599406822424492,
      "trace_margin": 0.0011563753963999973,
      "minimum_posterior_direction_margin": 9.637511191408444e-05,
      "maximum_posterior_direction_control": -0.0012527505083140813,
      "training_distribution_expected_exact_minus_mfvi": -0.046963913115303166,
      "training_distribution_identity_rhs": -0.04696391311530325,
      "identity_absolute_error": 8.326672684688674e-17,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 9.637511191408444e-05,
      "last_pc_control_margin": -0.0012527505083140813,
      "nonspherical_prior_first_pc_alignment_control": 0.9958129867412844,
      "kl_optimizer_relative_error": 7.619967761044392e-09,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 5,
      "samples": 160,
      "data_covariance_condition": 8857.97877391801,
      "alpha": 111.30782496857502,
      "noise_variance": 86.75119847516237,
      "posterior_condition": 142.0805808222932,
      "trace_exact_posterior": 0.008888443958371198,
      "trace_mfvi": 0.003218992951597007,
      "trace_margin": 0.005669451006774191,
      "minimum_posterior_direction_margin": 4.018590633614912e-05,
      "maximum_posterior_direction_control": -0.00570963691311034,
      "training_distribution_expected_exact_minus_mfvi": -0.3421544586654926,
      "training_distribution_identity_rhs": -0.34215445866549254,
      "identity_absolute_error": 5.551115123125783e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 4.018590633614911e-05,
      "last_pc_control_margin": -0.00570963691311034,
      "nonspherical_prior_first_pc_alignment_control": 0.9936122812887618,
      "kl_optimizer_relative_error": 6.04190686213526e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 6,
      "samples": 160,
      "data_covariance_condition": 109.23296870533848,
      "alpha": 0.040621817280379044,
      "noise_variance": 0.05989195166181781,
      "posterior_condition": 102.81026620833217,
      "trace_exact_posterior": 0.00038099010175916435,
      "trace_mfvi": 1.9495352546936467e-05,
      "trace_margin": 0.00036149474921222787,
      "minimum_posterior_direction_margin": 3.5506708967100335e-06,
      "maximum_posterior_direction_control": -0.0003650454201089379,
      "training_distribution_expected_exact_minus_mfvi": -5.496798593539451e-09,
      "training_distribution_identity_rhs": -5.496798595244396e-09,
      "identity_absolute_error": 1.7049449739248981e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 3.5506708967100335e-06,
      "last_pc_control_margin": -0.0003650454201089379,
      "nonspherical_prior_first_pc_alignment_control": 0.8700945678812478,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 7,
      "samples": 160,
      "data_covariance_condition": 488.6337658337963,
      "alpha": 120.45444298383784,
      "noise_variance": 0.001593061663082062,
      "posterior_condition": 364.3929053248226,
      "trace_exact_posterior": 8.098747126154064e-06,
      "trace_mfvi": 8.883074563927814e-08,
      "trace_margin": 8.009916380514786e-06,
      "minimum_posterior_direction_margin": 2.204202741205118e-08,
      "maximum_posterior_direction_control": -8.031958407926836e-06,
      "training_distribution_expected_exact_minus_mfvi": -9.606460686500578e-09,
      "training_distribution_identity_rhs": -9.606460686374745e-09,
      "identity_absolute_error": 1.2583236914279168e-19,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 2.20420274120512e-08,
      "last_pc_control_margin": -8.031958407926836e-06,
      "nonspherical_prior_first_pc_alignment_control": 0.7310140362002593,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 8,
      "samples": 160,
      "data_covariance_condition": 172.3285654531328,
      "alpha": 309.4881293133708,
      "noise_variance": 286.5189665661739,
      "posterior_condition": 1.3019005218287865,
      "trace_exact_posterior": 0.0056999499464558505,
      "trace_mfvi": 0.005659107785424546,
      "trace_margin": 4.0842161031304745e-05,
      "minimum_posterior_direction_margin": 0.00013528350591744486,
      "maximum_posterior_direction_control": -0.00017612566694874914,
      "training_distribution_expected_exact_minus_mfvi": -0.022635292066981366,
      "training_distribution_identity_rhs": -0.022635292066981578,
      "identity_absolute_error": 2.1163626406917047e-16,
      "first_pc_min_posterior_alignment": 0.9999999999999999,
      "first_pc_mfvi_minus_exact_margin": 0.000135283505917445,
      "last_pc_control_margin": -0.00017612566694874928,
      "nonspherical_prior_first_pc_alignment_control": 0.9398352098750682,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 9,
      "samples": 160,
      "data_covariance_condition": 5.206109606068182,
      "alpha": 730.9545592159355,
      "noise_variance": 14.523283310030939,
      "posterior_condition": 1.059061363226191,
      "trace_exact_posterior": 0.0026265144448779313,
      "trace_mfvi": 0.002625726420216977,
      "trace_margin": 7.880246609540988e-07,
      "minimum_posterior_direction_margin": 1.3342473283870623e-05,
      "maximum_posterior_direction_control": -1.4130497944824939e-05,
      "training_distribution_expected_exact_minus_mfvi": -5.228474747276157e-05,
      "training_distribution_identity_rhs": -5.2284747472739475e-05,
      "identity_absolute_error": 2.2097395527970187e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 1.334247328387062e-05,
      "last_pc_control_margin": -1.4130497944824935e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.9479451298074838,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 10,
      "samples": 160,
      "data_covariance_condition": 17.96365926681665,
      "alpha": 0.029736915959865853,
      "noise_variance": 405.0713574570963,
      "posterior_condition": 13.639075410454279,
      "trace_exact_posterior": 2.1798748005557425,
      "trace_mfvi": 0.5712514673764055,
      "trace_margin": 1.608623333179337,
      "minimum_posterior_direction_margin": 0.12727381402035007,
      "maximum_posterior_direction_control": -1.735897147199687,
      "training_distribution_expected_exact_minus_mfvi": -0.12110493532311312,
      "training_distribution_identity_rhs": -0.12110493532311267,
      "identity_absolute_error": 4.440892098500626e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.1272738140203501,
      "last_pc_control_margin": -1.7358971471996871,
      "nonspherical_prior_first_pc_alignment_control": 0.7732059740213237,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 11,
      "samples": 160,
      "data_covariance_condition": 566.7166448466202,
      "alpha": 2.9526436076495637,
      "noise_variance": 91.97990505974481,
      "posterior_condition": 204.40132370735935,
      "trace_exact_posterior": 0.21935116175822758,
      "trace_mfvi": 0.1073814487073908,
      "trace_margin": 0.11196971305083678,
      "minimum_posterior_direction_margin": 0.0005504866488083062,
      "maximum_posterior_direction_control": -0.11252019969964507,
      "training_distribution_expected_exact_minus_mfvi": -0.19005730605025883,
      "training_distribution_identity_rhs": -0.19005730605025883,
      "identity_absolute_error": 0.0,
      "first_pc_min_posterior_alignment": 0.9999999999999999,
      "first_pc_mfvi_minus_exact_margin": 0.000550486648808306,
      "last_pc_control_margin": -0.11252019969964507,
      "nonspherical_prior_first_pc_alignment_control": 0.07196172659025962,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 12,
      "samples": 160,
      "data_covariance_condition": 5794.753962754924,
      "alpha": 0.0012287669416727336,
      "noise_variance": 145.62301434751205,
      "posterior_condition": 4582.528220305747,
      "trace_exact_posterior": 0.7865044811957704,
      "trace_mfvi": 0.001506688287064505,
      "trace_margin": 0.784997792908706,
      "minimum_posterior_direction_margin": 0.00017133972665053101,
      "maximum_posterior_direction_control": -0.7851691326353565,
      "training_distribution_expected_exact_minus_mfvi": -0.0008779059416296548,
      "training_distribution_identity_rhs": -0.0008779059416386064,
      "identity_absolute_error": 8.951606816909319e-15,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.00017133972665053814,
      "last_pc_control_margin": -0.7851691326353565,
      "nonspherical_prior_first_pc_alignment_control": 0.9322706672481442,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 13,
      "samples": 160,
      "data_covariance_condition": 3149.2796759438434,
      "alpha": 0.863110345183133,
      "noise_variance": 76.82450970465732,
      "posterior_condition": 2236.8512359405468,
      "trace_exact_posterior": 0.3631392734145114,
      "trace_mfvi": 0.000767303178946938,
      "trace_margin": 0.36237197023556444,
      "minimum_posterior_direction_margin": 0.00016207338145339246,
      "maximum_posterior_direction_control": -0.3625340436170179,
      "training_distribution_expected_exact_minus_mfvi": -0.15017606964797114,
      "training_distribution_identity_rhs": -0.15017606964797472,
      "identity_absolute_error": 3.58046925441613e-15,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.00016207338145339246,
      "last_pc_control_margin": -0.3625340436170179,
      "nonspherical_prior_first_pc_alignment_control": 0.8346705054286666,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 14,
      "samples": 160,
      "data_covariance_condition": 69.49863770009839,
      "alpha": 0.0011005438914875921,
      "noise_variance": 0.3045519207973873,
      "posterior_condition": 66.3354800582926,
      "trace_exact_posterior": 0.001822186839284399,
      "trace_mfvi": 0.00012609620064562527,
      "trace_margin": 0.0016960906386387737,
      "minimum_posterior_direction_margin": 2.595971801424762e-05,
      "maximum_posterior_direction_control": -0.0017220503566530217,
      "training_distribution_expected_exact_minus_mfvi": -3.553021085242555e-09,
      "training_distribution_identity_rhs": -3.553021086903181e-09,
      "identity_absolute_error": 1.6606258774752257e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 2.5959718014247607e-05,
      "last_pc_control_margin": -0.0017220503566530213,
      "nonspherical_prior_first_pc_alignment_control": 0.5455029412261702,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 15,
      "samples": 160,
      "data_covariance_condition": 281.5092114091122,
      "alpha": 0.0077898963308751035,
      "noise_variance": 0.2885515138142242,
      "posterior_condition": 281.7911813123749,
      "trace_exact_posterior": 0.0015522925684865474,
      "trace_mfvi": 0.00034641495760248604,
      "trace_margin": 0.0012058776108840614,
      "minimum_posterior_direction_margin": 4.29457080969557e-06,
      "maximum_posterior_direction_control": -0.001210172181693757,
      "training_distribution_expected_exact_minus_mfvi": -1.6940970424448795e-08,
      "training_distribution_identity_rhs": -1.694097042600329e-08,
      "identity_absolute_error": 1.5544940553913032e-18,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 4.29457080969557e-06,
      "last_pc_control_margin": -0.001210172181693757,
      "nonspherical_prior_first_pc_alignment_control": 0.9936799912282173,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 16,
      "samples": 160,
      "data_covariance_condition": 13.561567554114518,
      "alpha": 4.628560927951618,
      "noise_variance": 0.008942931886209215,
      "posterior_condition": 12.636781385390783,
      "trace_exact_posterior": 5.6092611224186476e-05,
      "trace_mfvi": 3.4013290438589866e-05,
      "trace_margin": 2.207932078559661e-05,
      "minimum_posterior_direction_margin": 1.897373513720533e-06,
      "maximum_posterior_direction_control": -2.3976694299317148e-05,
      "training_distribution_expected_exact_minus_mfvi": -5.712045188553289e-09,
      "training_distribution_identity_rhs": -5.7120451885495775e-09,
      "identity_absolute_error": 3.711559408525435e-21,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 1.8973735137205324e-06,
      "last_pc_control_margin": -2.3976694299317148e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.25450459408002724,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 17,
      "samples": 160,
      "data_covariance_condition": 22.1863182871749,
      "alpha": 0.24351098974407076,
      "noise_variance": 0.0780595609982177,
      "posterior_condition": 19.676356785560863,
      "trace_exact_posterior": 0.00044901676416506743,
      "trace_mfvi": 0.0003042246333068002,
      "trace_margin": 0.00014479213085826723,
      "minimum_posterior_direction_margin": 7.752696766331292e-06,
      "maximum_posterior_direction_control": -0.00015254482762459853,
      "training_distribution_expected_exact_minus_mfvi": -1.7201631794828582e-08,
      "training_distribution_identity_rhs": -1.720163179489509e-08,
      "identity_absolute_error": 6.650862997171364e-20,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 7.752696766331292e-06,
      "last_pc_control_margin": -0.00015254482762459853,
      "nonspherical_prior_first_pc_alignment_control": 0.9860982636190845,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 18,
      "samples": 160,
      "data_covariance_condition": 8.067692989140253,
      "alpha": 4.474572512651684,
      "noise_variance": 103.16824824897391,
      "posterior_condition": 3.013490367385064,
      "trace_exact_posterior": 0.22823805710117928,
      "trace_mfvi": 0.1744726783038278,
      "trace_margin": 0.05376537879735149,
      "minimum_posterior_direction_margin": 0.026702575621048025,
      "maximum_posterior_direction_control": -0.08046795441839949,
      "training_distribution_expected_exact_minus_mfvi": -0.15512447838543525,
      "training_distribution_identity_rhs": -0.1551244783854354,
      "identity_absolute_error": 1.3877787807814457e-16,
      "first_pc_min_posterior_alignment": 0.9999999999999999,
      "first_pc_mfvi_minus_exact_margin": 0.026702575621048046,
      "last_pc_control_margin": -0.08046795441839952,
      "nonspherical_prior_first_pc_alignment_control": 0.8029401486061302,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 2,
      "seed": 19,
      "samples": 160,
      "data_covariance_condition": 371.86134306404324,
      "alpha": 503.955923110584,
      "noise_variance": 0.022336526428848782,
      "posterior_condition": 359.28526259153995,
      "trace_exact_posterior": 0.0001454225929647406,
      "trace_mfvi": 2.55157984463414e-06,
      "trace_margin": 0.00014287101312010646,
      "minimum_posterior_direction_margin": 3.9876329851441524e-07,
      "maximum_posterior_direction_control": -0.00014326977641862087,
      "training_distribution_expected_exact_minus_mfvi": -1.005153368031816e-05,
      "training_distribution_identity_rhs": -1.0051533680318234e-05,
      "identity_absolute_error": 7.453889935837843e-20,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 3.9876329851441524e-07,
      "last_pc_control_margin": -0.00014326977641862087,
      "nonspherical_prior_first_pc_alignment_control": 0.44110981762035073,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 0,
      "samples": 160,
      "data_covariance_condition": 534.9245997277525,
      "alpha": 104.08370611739791,
      "noise_variance": 298.65465178212554,
      "posterior_condition": 4.08003425442126,
      "trace_exact_posterior": 0.020463152401760637,
      "trace_mfvi": 0.018572275244898122,
      "trace_margin": 0.0018908771568625152,
      "minimum_posterior_direction_margin": 0.00062846050005351,
      "maximum_posterior_direction_control": -0.0021352961590019497,
      "training_distribution_expected_exact_minus_mfvi": -0.36736295860321827,
      "training_distribution_identity_rhs": -0.3673629586032187,
      "identity_absolute_error": 4.440892098500626e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 0.000628460500053511,
      "last_pc_control_margin": -0.002135296159001952,
      "nonspherical_prior_first_pc_alignment_control": 0.09954914185326867,
      "kl_optimizer_relative_error": 6.465223298632693e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 1,
      "samples": 160,
      "data_covariance_condition": 3756.032111312886,
      "alpha": 0.021528540944285208,
      "noise_variance": 0.009881362272628489,
      "posterior_condition": 3055.115360774002,
      "trace_exact_posterior": 6.430161711197089e-05,
      "trace_mfvi": 3.4926487026070867e-07,
      "trace_margin": 6.395235224171018e-05,
      "minimum_posterior_direction_margin": 3.853174780358147e-08,
      "maximum_posterior_direction_control": -6.31684893164158e-05,
      "training_distribution_expected_exact_minus_mfvi": -8.502917071447227e-11,
      "training_distribution_identity_rhs": -8.50291738452153e-11,
      "identity_absolute_error": 3.1307430384409335e-18,
      "first_pc_min_posterior_alignment": 0.9999999999999999,
      "first_pc_mfvi_minus_exact_margin": 3.853174780358072e-08,
      "last_pc_control_margin": -6.316848931641576e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.392819864460617,
      "kl_optimizer_relative_error": 9.790931374673059e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 2,
      "samples": 160,
      "data_covariance_condition": 3.842736199900424,
      "alpha": 0.024242110695146004,
      "noise_variance": 10.925283581963042,
      "posterior_condition": 3.872418857444885,
      "trace_exact_posterior": 0.11971354531856954,
      "trace_mfvi": 0.09650882551920399,
      "trace_margin": 0.023204719799365545,
      "minimum_posterior_direction_margin": 0.008188505584547937,
      "maximum_posterior_direction_control": -0.03106880916357787,
      "training_distribution_expected_exact_minus_mfvi": -3.841134322555809e-05,
      "training_distribution_identity_rhs": -3.841134322555931e-05,
      "identity_absolute_error": 1.2197274440461925e-18,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 0.008188505584547931,
      "last_pc_control_margin": -0.03106880916357787,
      "nonspherical_prior_first_pc_alignment_control": 0.602321562378626,
      "kl_optimizer_relative_error": 3.737619536747121e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 3,
      "samples": 160,
      "data_covariance_condition": 2422.6422713915754,
      "alpha": 0.048659414999661615,
      "noise_variance": 0.015945693146230757,
      "posterior_condition": 2326.377950921651,
      "trace_exact_posterior": 0.00010174090710924416,
      "trace_mfvi": 9.96732084468601e-07,
      "trace_margin": 0.00010074417502477557,
      "minimum_posterior_direction_margin": 7.834293497112105e-08,
      "maximum_posterior_direction_control": -9.900883906831172e-05,
      "training_distribution_expected_exact_minus_mfvi": -4.885513819916809e-10,
      "training_distribution_identity_rhs": -4.885513840981535e-10,
      "identity_absolute_error": 2.1064726087261277e-18,
      "first_pc_min_posterior_alignment": 0.9999999999999997,
      "first_pc_mfvi_minus_exact_margin": 7.83429349711196e-08,
      "last_pc_control_margin": -9.900883906831178e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.25883313155012655,
      "kl_optimizer_relative_error": 1.7068232263887833e-07,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 4,
      "samples": 160,
      "data_covariance_condition": 1244.0585100254968,
      "alpha": 0.05194695899903766,
      "noise_variance": 35.580275063581595,
      "posterior_condition": 1059.5358863494262,
      "trace_exact_posterior": 0.18560481713292287,
      "trace_mfvi": 0.0018874480844296164,
      "trace_margin": 0.18371736904849326,
      "minimum_posterior_direction_margin": 0.00031853623422034604,
      "maximum_posterior_direction_control": -0.1776883518260594,
      "training_distribution_expected_exact_minus_mfvi": -0.0021222652587595194,
      "training_distribution_identity_rhs": -0.0021222652587697287,
      "identity_absolute_error": 1.0209281336992504e-14,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.0003185362342203493,
      "last_pc_control_margin": -0.1776883518260595,
      "nonspherical_prior_first_pc_alignment_control": 0.4682115392505697,
      "kl_optimizer_relative_error": 9.069096143144115e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 5,
      "samples": 160,
      "data_covariance_condition": 8772.215407562,
      "alpha": 0.012841465859930712,
      "noise_variance": 0.3375876059926373,
      "posterior_condition": 9186.56677871417,
      "trace_exact_posterior": 0.0021268291426158404,
      "trace_mfvi": 7.180259177131068e-05,
      "trace_margin": 0.00205502655084453,
      "minimum_posterior_direction_margin": 2.2825238442964543e-07,
      "maximum_posterior_direction_control": -0.0020549040106760436,
      "training_distribution_expected_exact_minus_mfvi": -5.567991321672719e-08,
      "training_distribution_identity_rhs": -5.567991324818733e-08,
      "identity_absolute_error": 3.14601403848946e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 2.282523844296267e-07,
      "last_pc_control_margin": -0.0020549040106760427,
      "nonspherical_prior_first_pc_alignment_control": 0.14491269928545347,
      "kl_optimizer_relative_error": 1.0325809510955161e-07,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 6,
      "samples": 160,
      "data_covariance_condition": 9.360570447869113,
      "alpha": 0.06536952056383433,
      "noise_variance": 758.1217947252411,
      "posterior_condition": 8.72506395554095,
      "trace_exact_posterior": 6.048757276988704,
      "trace_mfvi": 2.9825685423728654,
      "trace_margin": 3.0661887346158387,
      "minimum_posterior_direction_margin": 0.4987958479952467,
      "maximum_posterior_direction_control": -3.025486468204856,
      "training_distribution_expected_exact_minus_mfvi": -0.9497147494759091,
      "training_distribution_identity_rhs": -0.9497147494759095,
      "identity_absolute_error": 4.440892098500626e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.49879584799524646,
      "last_pc_control_margin": -3.025486468204857,
      "nonspherical_prior_first_pc_alignment_control": 0.4366619172880963,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 7,
      "samples": 160,
      "data_covariance_condition": 163.55070493818758,
      "alpha": 0.0020173062716247418,
      "noise_variance": 0.004392377343128253,
      "posterior_condition": 205.17324549769165,
      "trace_exact_posterior": 3.202191050311289e-05,
      "trace_mfvi": 2.0274677120694324e-06,
      "trace_margin": 2.999444279104346e-05,
      "minimum_posterior_direction_margin": 2.099158424456432e-07,
      "maximum_posterior_direction_control": -2.915166884357165e-05,
      "training_distribution_expected_exact_minus_mfvi": -1.6610865466911604e-12,
      "training_distribution_identity_rhs": -1.6610866856039738e-12,
      "identity_absolute_error": 1.38912813458453e-19,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 2.099158424456433e-07,
      "last_pc_control_margin": -2.9151668843571652e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.7032798716513722,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 8,
      "samples": 160,
      "data_covariance_condition": 294.4932848518228,
      "alpha": 0.1485081652136893,
      "noise_variance": 0.044977010955868986,
      "posterior_condition": 291.3713738109211,
      "trace_exact_posterior": 0.0003031557353907895,
      "trace_mfvi": 5.053179133207072e-05,
      "trace_margin": 0.0002526239440587188,
      "minimum_posterior_direction_margin": 7.564862794514372e-07,
      "maximum_posterior_direction_control": -0.0002553929491913509,
      "training_distribution_expected_exact_minus_mfvi": -1.0546186596486023e-08,
      "training_distribution_identity_rhs": -1.0546186596617717e-08,
      "identity_absolute_error": 1.3169377096334243e-19,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 7.564862794514354e-07,
      "last_pc_control_margin": -0.00025539294919135096,
      "nonspherical_prior_first_pc_alignment_control": 0.18735227790083786,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 9,
      "samples": 160,
      "data_covariance_condition": 16.80099798706912,
      "alpha": 3.497588898678122,
      "noise_variance": 761.7394711416375,
      "posterior_condition": 1.827825822701063,
      "trace_exact_posterior": 0.6498330538393639,
      "trace_mfvi": 0.6302798959018139,
      "trace_margin": 0.01955315793754997,
      "minimum_posterior_direction_margin": 0.028015729459007117,
      "maximum_posterior_direction_control": -0.025229046105267806,
      "training_distribution_expected_exact_minus_mfvi": -0.32559081697395204,
      "training_distribution_identity_rhs": -0.32559081697395204,
      "identity_absolute_error": 0.0,
      "first_pc_min_posterior_alignment": 1.0000000000000007,
      "first_pc_mfvi_minus_exact_margin": 0.028015729459007096,
      "last_pc_control_margin": -0.025229046105267793,
      "nonspherical_prior_first_pc_alignment_control": 0.8878893113683882,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 10,
      "samples": 160,
      "data_covariance_condition": 119.72621131533309,
      "alpha": 0.00826821385082892,
      "noise_variance": 92.08323311366107,
      "posterior_condition": 133.50444659018328,
      "trace_exact_posterior": 0.641751751508051,
      "trace_mfvi": 0.12428642658762414,
      "trace_margin": 0.5174653249204269,
      "minimum_posterior_direction_margin": 0.005534664349993876,
      "maximum_posterior_direction_control": -0.49344908568989415,
      "training_distribution_expected_exact_minus_mfvi": -0.0024623712436746313,
      "training_distribution_identity_rhs": -0.002462371243673323,
      "identity_absolute_error": 1.3084151817555068e-15,
      "first_pc_min_posterior_alignment": 0.9999999999999999,
      "first_pc_mfvi_minus_exact_margin": 0.005534664349993872,
      "last_pc_control_margin": -0.4934490856898946,
      "nonspherical_prior_first_pc_alignment_control": 0.12460949324921446,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 11,
      "samples": 160,
      "data_covariance_condition": 11.488197531780244,
      "alpha": 7.263879891678658,
      "noise_variance": 11.528144658577322,
      "posterior_condition": 8.44737758312971,
      "trace_exact_posterior": 0.07217127960781079,
      "trace_mfvi": 0.046333953433986524,
      "trace_margin": 0.025837326173824268,
      "minimum_posterior_direction_margin": 0.0029407223082212725,
      "maximum_posterior_direction_control": -0.030900475916495574,
      "training_distribution_expected_exact_minus_mfvi": -0.013522458497033641,
      "training_distribution_identity_rhs": -0.013522458497033632,
      "identity_absolute_error": 8.673617379884035e-18,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 0.0029407223082212716,
      "last_pc_control_margin": -0.0309004759164956,
      "nonspherical_prior_first_pc_alignment_control": 0.2522244725231906,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 12,
      "samples": 160,
      "data_covariance_condition": 833.4407055838738,
      "alpha": 187.53844730819105,
      "noise_variance": 410.71549056597684,
      "posterior_condition": 2.8226194529790516,
      "trace_exact_posterior": 0.012243479121213638,
      "trace_mfvi": 0.010786172463054512,
      "trace_margin": 0.0014573066581591264,
      "minimum_posterior_direction_margin": 0.0008292902484064192,
      "maximum_posterior_direction_control": -0.0013127678020019556,
      "training_distribution_expected_exact_minus_mfvi": -0.7015560359725109,
      "training_distribution_identity_rhs": -0.701556035972511,
      "identity_absolute_error": 1.1102230246251565e-16,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 0.0008292902484064192,
      "last_pc_control_margin": -0.0013127678020019534,
      "nonspherical_prior_first_pc_alignment_control": 0.6025002253471543,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 13,
      "samples": 160,
      "data_covariance_condition": 20.124295213998156,
      "alpha": 23.30770784952581,
      "noise_variance": 0.01329816191396093,
      "posterior_condition": 19.36140028265522,
      "trace_exact_posterior": 0.00010316094066412748,
      "trace_mfvi": 4.45353058990216e-05,
      "trace_margin": 5.862563476510588e-05,
      "minimum_posterior_direction_margin": 3.581379265434221e-06,
      "maximum_posterior_direction_control": -6.02360989602568e-05,
      "training_distribution_expected_exact_minus_mfvi": -1.1356872696675802e-07,
      "training_distribution_identity_rhs": -1.1356872696673922e-07,
      "identity_absolute_error": 1.8806778407005637e-20,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 3.5813792654342185e-06,
      "last_pc_control_margin": -6.023609896025678e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.1486330830417792,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 14,
      "samples": 160,
      "data_covariance_condition": 3455.2720938412917,
      "alpha": 19.36953732381745,
      "noise_variance": 1.9250351181522232,
      "posterior_condition": 3156.8492880050662,
      "trace_exact_posterior": 0.010365049139725212,
      "trace_mfvi": 4.784970705621971e-05,
      "trace_margin": 0.010317199432668992,
      "minimum_posterior_direction_margin": 6.151492428464586e-06,
      "maximum_posterior_direction_control": -0.0101383481741055,
      "training_distribution_expected_exact_minus_mfvi": -0.002404361396904299,
      "training_distribution_identity_rhs": -0.0024043613969051457,
      "identity_absolute_error": 8.465450562766819e-16,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 6.1514924284646335e-06,
      "last_pc_control_margin": -0.010138348174105506,
      "nonspherical_prior_first_pc_alignment_control": 0.37859216279913244,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 15,
      "samples": 160,
      "data_covariance_condition": 349.5926704751836,
      "alpha": 0.1975832288009577,
      "noise_variance": 801.579540940025,
      "posterior_condition": 209.49020011143682,
      "trace_exact_posterior": 2.9329056771538062,
      "trace_mfvi": 0.5361831923546198,
      "trace_margin": 2.3967224847991866,
      "minimum_posterior_direction_margin": 0.009780366378695195,
      "maximum_posterior_direction_control": -2.4388299156714224,
      "training_distribution_expected_exact_minus_mfvi": -2.3724358044020804,
      "training_distribution_identity_rhs": -2.372435804402079,
      "identity_absolute_error": 1.3322676295501878e-15,
      "first_pc_min_posterior_alignment": 0.9999999999999997,
      "first_pc_mfvi_minus_exact_margin": 0.00978036637869523,
      "last_pc_control_margin": -2.4388299156714246,
      "nonspherical_prior_first_pc_alignment_control": 0.9812514773926944,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 16,
      "samples": 160,
      "data_covariance_condition": 402.6723903039224,
      "alpha": 0.9246650563317729,
      "noise_variance": 18.511533607817842,
      "posterior_condition": 348.9233937097746,
      "trace_exact_posterior": 0.10747658476390679,
      "trace_mfvi": 0.054149768711488765,
      "trace_margin": 0.05332681605241802,
      "minimum_posterior_direction_margin": 0.00029684840453308455,
      "maximum_posterior_direction_control": -0.05069069511164344,
      "training_distribution_expected_exact_minus_mfvi": -0.005704958863187073,
      "training_distribution_identity_rhs": -0.005704958863187153,
      "identity_absolute_error": 8.066464163292153e-17,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.0002968484045330846,
      "last_pc_control_margin": -0.05069069511164342,
      "nonspherical_prior_first_pc_alignment_control": 0.6319977736996649,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 17,
      "samples": 160,
      "data_covariance_condition": 411.3076341722807,
      "alpha": 0.11353273596791319,
      "noise_variance": 673.5862591652786,
      "posterior_condition": 361.68151078482157,
      "trace_exact_posterior": 3.7319493678027067,
      "trace_mfvi": 0.25547121556242036,
      "trace_margin": 3.4764781522402863,
      "minimum_posterior_direction_margin": 0.010079933710482304,
      "maximum_posterior_direction_control": -3.4769061290927343,
      "training_distribution_expected_exact_minus_mfvi": -1.6616281642060864,
      "training_distribution_identity_rhs": -1.6616281642060164,
      "identity_absolute_error": 6.994405055138486e-14,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.010079933710482372,
      "last_pc_control_margin": -3.4769061290927312,
      "nonspherical_prior_first_pc_alignment_control": 0.7862900766707825,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 18,
      "samples": 160,
      "data_covariance_condition": 3637.5502208643925,
      "alpha": 4.334897141689805,
      "noise_variance": 0.00899824105899039,
      "posterior_condition": 3466.992718063827,
      "trace_exact_posterior": 5.821482796914733e-05,
      "trace_mfvi": 7.216764411233105e-07,
      "trace_margin": 5.7493151528024015e-05,
      "minimum_posterior_direction_margin": 2.9008236770019795e-08,
      "maximum_posterior_direction_control": -5.669018732143201e-05,
      "training_distribution_expected_exact_minus_mfvi": -1.4016273177882419e-08,
      "training_distribution_identity_rhs": -1.4016273178863402e-08,
      "identity_absolute_error": 9.809832669286874e-19,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 2.900823677001938e-08,
      "last_pc_control_margin": -5.669018732143198e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.7812658833881654,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 3,
      "seed": 19,
      "samples": 160,
      "data_covariance_condition": 191.94544816020897,
      "alpha": 0.10935367596239341,
      "noise_variance": 40.23028929703526,
      "posterior_condition": 203.51620303325396,
      "trace_exact_posterior": 0.31931019831872337,
      "trace_mfvi": 0.018635615492838285,
      "trace_margin": 0.3006745828258851,
      "minimum_posterior_direction_margin": 0.002189921236242515,
      "maximum_posterior_direction_control": -0.294101059548941,
      "training_distribution_expected_exact_minus_mfvi": -0.00826729198984013,
      "training_distribution_identity_rhs": -0.008267291989844161,
      "identity_absolute_error": 4.0314973581701e-15,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.0021899212362425143,
      "last_pc_control_margin": -0.2941010595489411,
      "nonspherical_prior_first_pc_alignment_control": 0.3173952258201518,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 0,
      "samples": 160,
      "data_covariance_condition": 75.70543757211529,
      "alpha": 0.6619108845020281,
      "noise_variance": 0.019795283937526963,
      "posterior_condition": 65.30886798701155,
      "trace_exact_posterior": 0.00019881817606721188,
      "trace_mfvi": 3.670232297896168e-05,
      "trace_margin": 0.00016211585308825022,
      "minimum_posterior_direction_margin": 3.792312991989093e-06,
      "maximum_posterior_direction_control": -0.00011983692126647574,
      "training_distribution_expected_exact_minus_mfvi": -1.3275985260441015e-08,
      "training_distribution_identity_rhs": -1.3275985260494105e-08,
      "identity_absolute_error": 5.309010607487842e-20,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 3.792312991989101e-06,
      "last_pc_control_margin": -0.0001198369212664758,
      "nonspherical_prior_first_pc_alignment_control": 0.4322282984075899,
      "kl_optimizer_relative_error": 4.773545169356927e-07,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 1,
      "samples": 160,
      "data_covariance_condition": 8382.91437242635,
      "alpha": 0.005397694575954482,
      "noise_variance": 0.014255298845130389,
      "posterior_condition": 8271.122212731756,
      "trace_exact_posterior": 0.00011794587155905877,
      "trace_mfvi": 7.527707270135621e-07,
      "trace_margin": 0.0001171931008320452,
      "minimum_posterior_direction_margin": 3.348804604179345e-08,
      "maximum_posterior_direction_control": -0.00010768842644423378,
      "training_distribution_expected_exact_minus_mfvi": -5.635944349366268e-11,
      "training_distribution_identity_rhs": -5.6359443443968903e-11,
      "identity_absolute_error": 4.969377356556958e-20,
      "first_pc_min_posterior_alignment": 0.9999999999999999,
      "first_pc_mfvi_minus_exact_margin": 3.348804604178992e-08,
      "last_pc_control_margin": -0.00010768842644423376,
      "nonspherical_prior_first_pc_alignment_control": 0.13928535825756208,
      "kl_optimizer_relative_error": 5.600328755439499e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 2,
      "samples": 160,
      "data_covariance_condition": 484.82794996552457,
      "alpha": 2.2227952532956543,
      "noise_variance": 3.1594377924815613,
      "posterior_condition": 555.4141726330744,
      "trace_exact_posterior": 0.02364522024356308,
      "trace_mfvi": 0.0020848861314290636,
      "trace_margin": 0.021560334112134018,
      "minimum_posterior_direction_margin": 6.089026195392705e-05,
      "maximum_posterior_direction_control": -0.017935446126863732,
      "training_distribution_expected_exact_minus_mfvi": -0.000946334718458567,
      "training_distribution_identity_rhs": -0.0009463347184584492,
      "identity_absolute_error": 1.1785277614917433e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 6.08902619539269e-05,
      "last_pc_control_margin": -0.017935446126863725,
      "nonspherical_prior_first_pc_alignment_control": 0.08576414950688127,
      "kl_optimizer_relative_error": 1.5052768987749974e-07,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 3,
      "samples": 160,
      "data_covariance_condition": 77.42454958600868,
      "alpha": 0.18382092670818534,
      "noise_variance": 34.75672400605314,
      "posterior_condition": 72.99353666417989,
      "trace_exact_posterior": 0.33958560473570565,
      "trace_mfvi": 0.06467850819554295,
      "trace_margin": 0.2749070965401627,
      "minimum_posterior_direction_margin": 0.0067743769437326835,
      "maximum_posterior_direction_control": -0.22069694255623568,
      "training_distribution_expected_exact_minus_mfvi": -0.010977406706275025,
      "training_distribution_identity_rhs": -0.010977406706274614,
      "identity_absolute_error": 4.111294638065033e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 0.0067743769437326705,
      "last_pc_control_margin": -0.22069694255623543,
      "nonspherical_prior_first_pc_alignment_control": 0.5485450787101617,
      "kl_optimizer_relative_error": 9.469399396115717e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 4,
      "samples": 160,
      "data_covariance_condition": 18.277442048314,
      "alpha": 0.04863335805090449,
      "noise_variance": 47.13477504653103,
      "posterior_condition": 17.847699281747612,
      "trace_exact_posterior": 0.536438780572624,
      "trace_mfvi": 0.2548705950664846,
      "trace_margin": 0.2815681855061394,
      "minimum_posterior_direction_margin": 0.018323745185811063,
      "maximum_posterior_direction_control": -0.23730872894927035,
      "training_distribution_expected_exact_minus_mfvi": -0.004034031602287612,
      "training_distribution_identity_rhs": -0.004034031602287671,
      "identity_absolute_error": 5.898059818321144e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.01832374518581107,
      "last_pc_control_margin": -0.23730872894927033,
      "nonspherical_prior_first_pc_alignment_control": 0.49230089655311254,
      "kl_optimizer_relative_error": 7.26095693824551e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 5,
      "samples": 160,
      "data_covariance_condition": 310.11360202418945,
      "alpha": 1.4437019890029317,
      "noise_variance": 1.487536633728112,
      "posterior_condition": 381.5248819345836,
      "trace_exact_posterior": 0.014419159214072243,
      "trace_mfvi": 0.0009184236019063654,
      "trace_margin": 0.013500735612165879,
      "minimum_posterior_direction_margin": 6.745292435471207e-05,
      "maximum_posterior_direction_control": -0.010752491040610282,
      "training_distribution_expected_exact_minus_mfvi": -0.00018121021455097297,
      "training_distribution_identity_rhs": -0.00018121021455090242,
      "identity_absolute_error": 7.05544563744942e-17,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 6.745292435471193e-05,
      "last_pc_control_margin": -0.01075249104061028,
      "nonspherical_prior_first_pc_alignment_control": 0.5107254297794676,
      "kl_optimizer_relative_error": 6.088320426035153e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 6,
      "samples": 160,
      "data_covariance_condition": 565.3340739579569,
      "alpha": 0.6488204039680902,
      "noise_variance": 7.237800499592825,
      "posterior_condition": 522.867084520839,
      "trace_exact_posterior": 0.050768631654374397,
      "trace_mfvi": 0.00626535310741804,
      "trace_margin": 0.044503278546956355,
      "minimum_posterior_direction_margin": 0.00020439036969960214,
      "maximum_posterior_direction_control": -0.03611529931499759,
      "training_distribution_expected_exact_minus_mfvi": -0.001306180305130394,
      "training_distribution_identity_rhs": -0.0013061803051307532,
      "identity_absolute_error": 3.5930459996169617e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.00020439036969960135,
      "last_pc_control_margin": -0.03611529931499757,
      "nonspherical_prior_first_pc_alignment_control": 0.08720253755711994,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 7,
      "samples": 160,
      "data_covariance_condition": 733.7049261427181,
      "alpha": 59.11265286577181,
      "noise_variance": 0.271965873193486,
      "posterior_condition": 1028.143537379711,
      "trace_exact_posterior": 0.0022871973433323156,
      "trace_mfvi": 0.00011227236309507272,
      "trace_margin": 0.002174924980237243,
      "minimum_posterior_direction_margin": 3.464881749974378e-06,
      "maximum_posterior_direction_control": -0.0018314234372687503,
      "training_distribution_expected_exact_minus_mfvi": -0.00021853407304160964,
      "training_distribution_identity_rhs": -0.0002185340730416107,
      "identity_absolute_error": 1.0570971181733668e-18,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 3.4648817499745676e-06,
      "last_pc_control_margin": -0.0018314234372687516,
      "nonspherical_prior_first_pc_alignment_control": 0.6929460069171187,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 8,
      "samples": 160,
      "data_covariance_condition": 4.6526994519937475,
      "alpha": 0.067882748300136,
      "noise_variance": 26.742672497953752,
      "posterior_condition": 5.832256095342073,
      "trace_exact_posterior": 0.4816285918294172,
      "trace_mfvi": 0.3609433387747181,
      "trace_margin": 0.12068525305469907,
      "minimum_posterior_direction_margin": 0.02562880056167845,
      "maximum_posterior_direction_control": -0.12030961534639512,
      "training_distribution_expected_exact_minus_mfvi": -0.0013692994868485199,
      "training_distribution_identity_rhs": -0.0013692994868484793,
      "identity_absolute_error": 4.0549161250957866e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.025628800561678447,
      "last_pc_control_margin": -0.12030961534639512,
      "nonspherical_prior_first_pc_alignment_control": 0.13800406112294133,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 9,
      "samples": 160,
      "data_covariance_condition": 83.20703944349656,
      "alpha": 304.1592566644892,
      "noise_variance": 364.3243268393196,
      "posterior_condition": 1.0940290658197007,
      "trace_exact_posterior": 0.015960153384917172,
      "trace_mfvi": 0.015945504450390995,
      "trace_margin": 1.4648934526177715e-05,
      "minimum_posterior_direction_margin": 0.00014942002715293264,
      "maximum_posterior_direction_control": -1.298760300888083e-05,
      "training_distribution_expected_exact_minus_mfvi": -0.010145542267806335,
      "training_distribution_identity_rhs": -0.01014554226780558,
      "identity_absolute_error": 7.546047120499111e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.00014942002715293283,
      "last_pc_control_margin": -1.2987603008880841e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.4415953663177956,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 10,
      "samples": 160,
      "data_covariance_condition": 9.913795526858864,
      "alpha": 0.0582326245174233,
      "noise_variance": 0.41706451117551435,
      "posterior_condition": 12.348120322713527,
      "trace_exact_posterior": 0.005793037151859305,
      "trace_mfvi": 0.003935095625088508,
      "trace_margin": 0.0018579415267707964,
      "minimum_posterior_direction_margin": 0.0001646895912637002,
      "maximum_posterior_direction_control": -0.0018553401443040802,
      "training_distribution_expected_exact_minus_mfvi": -2.820211372432929e-07,
      "training_distribution_identity_rhs": -2.82021137244452e-07,
      "identity_absolute_error": 1.1591116487583066e-18,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.00016468959126370042,
      "last_pc_control_margin": -0.00185534014430408,
      "nonspherical_prior_first_pc_alignment_control": 0.012890558449813362,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 11,
      "samples": 160,
      "data_covariance_condition": 3.5258246789675227,
      "alpha": 0.01942542724765166,
      "noise_variance": 900.7295682224885,
      "posterior_condition": 3.030873789901256,
      "trace_exact_posterior": 15.76562621510055,
      "trace_mfvi": 13.537620869710082,
      "trace_margin": 2.228005345390468,
      "minimum_posterior_direction_margin": 0.8178082225764932,
      "maximum_posterior_direction_control": -1.8176769155155135,
      "training_distribution_expected_exact_minus_mfvi": -0.24364709906385673,
      "training_distribution_identity_rhs": -0.24364709906385693,
      "identity_absolute_error": 1.942890293094024e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.817808222576494,
      "last_pc_control_margin": -1.817676915515513,
      "nonspherical_prior_first_pc_alignment_control": 0.3246677291906054,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 12,
      "samples": 160,
      "data_covariance_condition": 66.64302553573972,
      "alpha": 0.8928949790073456,
      "noise_variance": 7.772228376585567,
      "posterior_condition": 71.35913627568812,
      "trace_exact_posterior": 0.06927178309729078,
      "trace_mfvi": 0.012774580025889229,
      "trace_margin": 0.05649720307140155,
      "minimum_posterior_direction_margin": 0.0013306601434622473,
      "maximum_posterior_direction_control": -0.043110884067533564,
      "training_distribution_expected_exact_minus_mfvi": -0.0024504898036473138,
      "training_distribution_identity_rhs": -0.002450489803647442,
      "identity_absolute_error": 1.2836953722228372e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 0.001330660143462251,
      "last_pc_control_margin": -0.04311088406753358,
      "nonspherical_prior_first_pc_alignment_control": 0.22271215154611831,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 13,
      "samples": 160,
      "data_covariance_condition": 10.358565381381247,
      "alpha": 0.03428160110878292,
      "noise_variance": 1.216030176259615,
      "posterior_condition": 11.18186432928886,
      "trace_exact_posterior": 0.017773612291065694,
      "trace_mfvi": 0.010682710960475284,
      "trace_margin": 0.007090901330590409,
      "minimum_posterior_direction_margin": 0.0008695594896003986,
      "maximum_posterior_direction_control": -0.005049260529764961,
      "training_distribution_expected_exact_minus_mfvi": -1.8475104736579552e-06,
      "training_distribution_identity_rhs": -1.8475104736571678e-06,
      "identity_absolute_error": 7.873171244728722e-19,
      "first_pc_min_posterior_alignment": 0.9999999999999993,
      "first_pc_mfvi_minus_exact_margin": 0.0008695594896003982,
      "last_pc_control_margin": -0.005049260529764965,
      "nonspherical_prior_first_pc_alignment_control": 0.34802313688794795,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 14,
      "samples": 160,
      "data_covariance_condition": 182.9220523317841,
      "alpha": 0.619680916547843,
      "noise_variance": 451.8930993519372,
      "posterior_condition": 75.37700572189587,
      "trace_exact_posterior": 1.8775274550754992,
      "trace_mfvi": 0.4041540239771809,
      "trace_margin": 1.4733734310983184,
      "minimum_posterior_direction_margin": 0.030050226326809478,
      "maximum_posterior_direction_control": -0.9522530257683579,
      "training_distribution_expected_exact_minus_mfvi": -2.5786754337959277,
      "training_distribution_identity_rhs": -2.5786754337959277,
      "identity_absolute_error": 0.0,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 0.030050226326809506,
      "last_pc_control_margin": -0.9522530257683581,
      "nonspherical_prior_first_pc_alignment_control": 0.34813128523871756,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 15,
      "samples": 160,
      "data_covariance_condition": 7267.5155207925945,
      "alpha": 4.300676548916851,
      "noise_variance": 0.3954889708897702,
      "posterior_condition": 6766.163789297683,
      "trace_exact_posterior": 0.0026491860218698874,
      "trace_mfvi": 3.3375011173542355e-05,
      "trace_margin": 0.002615811010696345,
      "minimum_posterior_direction_margin": 8.072541952800181e-07,
      "maximum_posterior_direction_control": -0.002373139526496578,
      "training_distribution_expected_exact_minus_mfvi": -2.780721779005165e-05,
      "training_distribution_identity_rhs": -2.7807217790086668e-05,
      "identity_absolute_error": 3.5019730171281793e-17,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 8.072541952799422e-07,
      "last_pc_control_margin": -0.0023731395264965753,
      "nonspherical_prior_first_pc_alignment_control": 0.3744743733203975,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 16,
      "samples": 160,
      "data_covariance_condition": 26.19167797624815,
      "alpha": 4.670303058683787,
      "noise_variance": 3.347816024468093,
      "posterior_condition": 23.749535283129955,
      "trace_exact_posterior": 0.035522365305062045,
      "trace_mfvi": 0.012345167023806378,
      "trace_margin": 0.023177198281255668,
      "minimum_posterior_direction_margin": 0.0013189746664725769,
      "maximum_posterior_direction_control": -0.01693224464631847,
      "training_distribution_expected_exact_minus_mfvi": -0.002264892535348503,
      "training_distribution_identity_rhs": -0.0022648925353485286,
      "identity_absolute_error": 2.5587171270657905e-17,
      "first_pc_min_posterior_alignment": 0.9999999999999999,
      "first_pc_mfvi_minus_exact_margin": 0.0013189746664725782,
      "last_pc_control_margin": -0.016932244646318474,
      "nonspherical_prior_first_pc_alignment_control": 0.30788709089985894,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 17,
      "samples": 160,
      "data_covariance_condition": 2561.917710790773,
      "alpha": 45.40309670597287,
      "noise_variance": 92.99998815110845,
      "posterior_condition": 94.0896359450432,
      "trace_exact_posterior": 0.0482731778887862,
      "trace_mfvi": 0.016241230970477746,
      "trace_margin": 0.03203194691830845,
      "minimum_posterior_direction_margin": 0.00029216726083046104,
      "maximum_posterior_direction_control": -0.018947419877954536,
      "training_distribution_expected_exact_minus_mfvi": -0.8453405877721057,
      "training_distribution_identity_rhs": -0.8453405877721031,
      "identity_absolute_error": 2.6645352591003757e-15,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 0.00029216726083046115,
      "last_pc_control_margin": -0.018947419877954515,
      "nonspherical_prior_first_pc_alignment_control": 0.03358700236727062,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 18,
      "samples": 160,
      "data_covariance_condition": 106.38952149219764,
      "alpha": 1.1467508396164903,
      "noise_variance": 0.132375186264676,
      "posterior_condition": 77.28957695685492,
      "trace_exact_posterior": 0.0012141836651809344,
      "trace_mfvi": 0.00022598663028422283,
      "trace_margin": 0.0009881970348967115,
      "minimum_posterior_direction_margin": 1.9564641924547085e-05,
      "maximum_posterior_direction_control": -0.0007661783603865014,
      "training_distribution_expected_exact_minus_mfvi": -9.375603117883294e-07,
      "training_distribution_identity_rhs": -9.375603117874027e-07,
      "identity_absolute_error": 9.266540442962046e-19,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 1.9564641924547017e-05,
      "last_pc_control_margin": -0.0007661783603865012,
      "nonspherical_prior_first_pc_alignment_control": 0.4084839485121669,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 5,
      "seed": 19,
      "samples": 160,
      "data_covariance_condition": 4102.799985064572,
      "alpha": 334.2068787657359,
      "noise_variance": 2.785757525914974,
      "posterior_condition": 611.6714872343568,
      "trace_exact_posterior": 0.004038319861962339,
      "trace_mfvi": 0.00012587564705112038,
      "trace_margin": 0.003912444214911218,
      "minimum_posterior_direction_margin": 1.2508661807012768e-05,
      "maximum_posterior_direction_control": -0.0024922512826275585,
      "training_distribution_expected_exact_minus_mfvi": -0.022766007392275772,
      "training_distribution_identity_rhs": -0.022766007392276313,
      "identity_absolute_error": 5.412337245047638e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 1.250866180701279e-05,
      "last_pc_control_margin": -0.002492251282627561,
      "nonspherical_prior_first_pc_alignment_control": 0.3301085317899482,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 0,
      "samples": 160,
      "data_covariance_condition": 7126.464930031552,
      "alpha": 4.055577573711629,
      "noise_variance": 14.174600090805026,
      "posterior_condition": 7495.585133767806,
      "trace_exact_posterior": 0.10949130735822335,
      "trace_mfvi": 0.0011672200171478852,
      "trace_margin": 0.10832408734107546,
      "minimum_posterior_direction_margin": 2.713881744410988e-05,
      "maximum_posterior_direction_control": -0.07395526236048144,
      "training_distribution_expected_exact_minus_mfvi": -0.03891961933101529,
      "training_distribution_identity_rhs": -0.038919619331010596,
      "identity_absolute_error": 4.690692279041286e-15,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 2.713881744411001e-05,
      "last_pc_control_margin": -0.07395526236048142,
      "nonspherical_prior_first_pc_alignment_control": 0.7221309475893551,
      "kl_optimizer_relative_error": 2.013229849452663e-07,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 1,
      "samples": 160,
      "data_covariance_condition": 1908.8879932123584,
      "alpha": 1.4729505631630286,
      "noise_variance": 0.00765860041818504,
      "posterior_condition": 1255.6985508903663,
      "trace_exact_posterior": 7.255339186917488e-05,
      "trace_mfvi": 3.3947993233751406e-06,
      "trace_margin": 6.915859254579974e-05,
      "minimum_posterior_direction_margin": 7.274087960390942e-08,
      "maximum_posterior_direction_control": -4.3858050811129934e-05,
      "training_distribution_expected_exact_minus_mfvi": -4.876000543976335e-09,
      "training_distribution_identity_rhs": -4.876000546091631e-09,
      "identity_absolute_error": 2.1152960409226543e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 7.274087960390634e-08,
      "last_pc_control_margin": -4.385805081112999e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.2100785943762739,
      "kl_optimizer_relative_error": 4.930412283060204e-07,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 2,
      "samples": 160,
      "data_covariance_condition": 18.276509153815883,
      "alpha": 527.0924689181961,
      "noise_variance": 112.6848032507173,
      "posterior_condition": 1.0516653906259574,
      "trace_exact_posterior": 0.01490719533890433,
      "trace_mfvi": 0.014903450251350108,
      "trace_margin": 3.745087554221996e-06,
      "minimum_posterior_direction_margin": 5.540761641253015e-05,
      "maximum_posterior_direction_control": -3.7944430512796244e-05,
      "training_distribution_expected_exact_minus_mfvi": -0.0013902540036614132,
      "training_distribution_identity_rhs": -0.0013902540036604062,
      "identity_absolute_error": 1.0070069778045365e-15,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 5.540761641253017e-05,
      "last_pc_control_margin": -3.7944430512795424e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.19408886705843112,
      "kl_optimizer_relative_error": 5.379259412743215e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 3,
      "samples": 160,
      "data_covariance_condition": 11.940240261898163,
      "alpha": 22.819670741085275,
      "noise_variance": 13.18330084849798,
      "posterior_condition": 4.813236270177838,
      "trace_exact_posterior": 0.13162203021954447,
      "trace_mfvi": 0.1022221831233768,
      "trace_margin": 0.029399847096167664,
      "minimum_posterior_direction_margin": 0.005947317630962868,
      "maximum_posterior_direction_control": -0.015210672373544565,
      "training_distribution_expected_exact_minus_mfvi": -0.05527880243214547,
      "training_distribution_identity_rhs": -0.05527880243214549,
      "identity_absolute_error": 2.0816681711721685e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000007,
      "first_pc_mfvi_minus_exact_margin": 0.005947317630962863,
      "last_pc_control_margin": -0.015210672373544568,
      "nonspherical_prior_first_pc_alignment_control": 0.48493861769058355,
      "kl_optimizer_relative_error": 1.4376535229137563e-07,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 4,
      "samples": 160,
      "data_covariance_condition": 44.1241677056085,
      "alpha": 0.6393362124887932,
      "noise_variance": 140.68631391873535,
      "posterior_condition": 32.671138928584504,
      "trace_exact_posterior": 1.5635137888273232,
      "trace_mfvi": 0.647863783499759,
      "trace_margin": 0.9156500053275641,
      "minimum_posterior_direction_margin": 0.029678796555043938,
      "maximum_posterior_direction_control": -0.45759226772914496,
      "training_distribution_expected_exact_minus_mfvi": -0.5147432668261266,
      "training_distribution_identity_rhs": -0.5147432668261261,
      "identity_absolute_error": 4.440892098500626e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000007,
      "first_pc_mfvi_minus_exact_margin": 0.029678796555043893,
      "last_pc_control_margin": -0.4575922677291445,
      "nonspherical_prior_first_pc_alignment_control": 0.6964758417329948,
      "kl_optimizer_relative_error": 6.840641254031142e-08,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 5,
      "samples": 160,
      "data_covariance_condition": 162.29988713661822,
      "alpha": 0.03665845370142817,
      "noise_variance": 0.0016788018305766658,
      "posterior_condition": 222.87998726281413,
      "trace_exact_posterior": 2.3113395515165907e-05,
      "trace_mfvi": 4.207573172884228e-06,
      "trace_margin": 1.890582234228168e-05,
      "minimum_posterior_direction_margin": 1.0169145802866423e-07,
      "maximum_posterior_direction_control": -1.2194106092463349e-05,
      "training_distribution_expected_exact_minus_mfvi": -7.2719213209247084e-12,
      "training_distribution_identity_rhs": -7.271921229484112e-12,
      "identity_absolute_error": 9.144059680414348e-20,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 1.016914580286646e-07,
      "last_pc_control_margin": -1.2194106092463359e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.18176662977004185,
      "kl_optimizer_relative_error": 1.1492471407205961e-07,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 6,
      "samples": 160,
      "data_covariance_condition": 6845.952383054639,
      "alpha": 0.04269478924630776,
      "noise_variance": 0.0017065103183289117,
      "posterior_condition": 7489.580260750744,
      "trace_exact_posterior": 1.601935896297613e-05,
      "trace_mfvi": 2.3201611035840993e-07,
      "trace_margin": 1.5787342852617722e-05,
      "minimum_posterior_direction_margin": 4.3670042426917865e-09,
      "maximum_posterior_direction_control": -1.1606445574881135e-05,
      "training_distribution_expected_exact_minus_mfvi": -7.189068852481335e-12,
      "training_distribution_identity_rhs": -7.1890722886204116e-12,
      "identity_absolute_error": 3.436139076215301e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 4.3670042426897426e-09,
      "last_pc_control_margin": -1.1606445574881134e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.3099745061692832,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 7,
      "samples": 160,
      "data_covariance_condition": 49.42381540384701,
      "alpha": 84.80736893288491,
      "noise_variance": 0.04463673736420327,
      "posterior_condition": 50.191811951928436,
      "trace_exact_posterior": 0.0006177420553214013,
      "trace_mfvi": 0.00020862750288804053,
      "trace_margin": 0.0004091145524333608,
      "minimum_posterior_direction_margin": 1.0180476510501902e-05,
      "maximum_posterior_direction_control": -0.00020861340929802875,
      "training_distribution_expected_exact_minus_mfvi": -9.679456629623917e-06,
      "training_distribution_identity_rhs": -9.67945662962352e-06,
      "identity_absolute_error": 3.9641141931501256e-19,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 1.0180476510501895e-05,
      "last_pc_control_margin": -0.000208613409298029,
      "nonspherical_prior_first_pc_alignment_control": 0.17256724004717794,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 8,
      "samples": 160,
      "data_covariance_condition": 3060.5026785810787,
      "alpha": 0.07587528523801955,
      "noise_variance": 0.5141001911940596,
      "posterior_condition": 3584.130931162399,
      "trace_exact_posterior": 0.00511096574274552,
      "trace_mfvi": 6.307668603631387e-05,
      "trace_margin": 0.005047889056709206,
      "minimum_posterior_direction_margin": 3.1688938627297873e-06,
      "maximum_posterior_direction_control": -0.003514198120565552,
      "training_distribution_expected_exact_minus_mfvi": -1.2306595345637494e-06,
      "training_distribution_identity_rhs": -1.2306595347104725e-06,
      "identity_absolute_error": 1.467230471233899e-16,
      "first_pc_min_posterior_alignment": 0.9999999999999999,
      "first_pc_mfvi_minus_exact_margin": 3.1688938627300105e-06,
      "last_pc_control_margin": -0.0035141981205655494,
      "nonspherical_prior_first_pc_alignment_control": 0.2600736575007361,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 9,
      "samples": 160,
      "data_covariance_condition": 327.13507765784203,
      "alpha": 0.1671377373723072,
      "noise_variance": 4.2179501973434474,
      "posterior_condition": 375.3085321542909,
      "trace_exact_posterior": 0.05552548174222936,
      "trace_mfvi": 0.005617437057491402,
      "trace_margin": 0.04990804468473796,
      "minimum_posterior_direction_margin": 0.00024966096021765806,
      "maximum_posterior_direction_control": -0.03281420636515586,
      "training_distribution_expected_exact_minus_mfvi": -0.0002199006630156375,
      "training_distribution_identity_rhs": -0.00021990066301515456,
      "identity_absolute_error": 4.829307526793558e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.0002496609602176583,
      "last_pc_control_margin": -0.03281420636515582,
      "nonspherical_prior_first_pc_alignment_control": 0.12327777438736676,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 10,
      "samples": 160,
      "data_covariance_condition": 1097.0301569145283,
      "alpha": 454.60349023430297,
      "noise_variance": 0.0017689794645535622,
      "posterior_condition": 1443.2069922202706,
      "trace_exact_posterior": 1.8589350625773147e-05,
      "trace_mfvi": 9.734464753285097e-07,
      "trace_margin": 1.7615904150444638e-05,
      "minimum_posterior_direction_margin": 2.9511860311610575e-08,
      "maximum_posterior_direction_control": -1.145429373795481e-05,
      "training_distribution_expected_exact_minus_mfvi": -8.854020293053855e-08,
      "training_distribution_identity_rhs": -8.854020293076255e-08,
      "identity_absolute_error": 2.240005098793599e-19,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 2.9511860311610827e-08,
      "last_pc_control_margin": -1.1454293737954801e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.23110571399222174,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 11,
      "samples": 160,
      "data_covariance_condition": 197.11181322000417,
      "alpha": 87.17473241951228,
      "noise_variance": 0.004906302734576798,
      "posterior_condition": 193.4395035939136,
      "trace_exact_posterior": 5.834047429941845e-05,
      "trace_mfvi": 6.557944706746557e-06,
      "trace_margin": 5.1782529592671894e-05,
      "minimum_posterior_direction_margin": 3.3250960195426127e-07,
      "maximum_posterior_direction_control": -2.9398412701202e-05,
      "training_distribution_expected_exact_minus_mfvi": -1.3842299588594893e-07,
      "training_distribution_identity_rhs": -1.3842299588596603e-07,
      "identity_absolute_error": 1.7099477622696188e-20,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 3.325096019542617e-07,
      "last_pc_control_margin": -2.9398412701202028e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.1964380413537797,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 12,
      "samples": 160,
      "data_covariance_condition": 413.3881404070319,
      "alpha": 1.0968650604135737,
      "noise_variance": 0.10617640641446835,
      "posterior_condition": 344.99037658871794,
      "trace_exact_posterior": 0.0010914372889427116,
      "trace_mfvi": 8.592129425285925e-05,
      "trace_margin": 0.0010055159946898524,
      "minimum_posterior_direction_margin": 5.843087663864703e-06,
      "maximum_posterior_direction_control": -0.0006210813329533412,
      "training_distribution_expected_exact_minus_mfvi": -7.318974358988051e-07,
      "training_distribution_identity_rhs": -7.318974359020156e-07,
      "identity_absolute_error": 3.210466628330612e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 5.8430876638647205e-06,
      "last_pc_control_margin": -0.0006210813329533406,
      "nonspherical_prior_first_pc_alignment_control": 0.20770753645095416,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 13,
      "samples": 160,
      "data_covariance_condition": 8.975081927715737,
      "alpha": 0.008811575792141323,
      "noise_variance": 0.8483701752887572,
      "posterior_condition": 10.280798596641189,
      "trace_exact_posterior": 0.01897993411414436,
      "trace_mfvi": 0.011931641929642248,
      "trace_margin": 0.007048292184502113,
      "minimum_posterior_direction_margin": 0.0006804013473029868,
      "maximum_posterior_direction_control": -0.003934947558405924,
      "training_distribution_expected_exact_minus_mfvi": -3.2930846164064623e-07,
      "training_distribution_identity_rhs": -3.2930846164411874e-07,
      "identity_absolute_error": 3.472517446387411e-18,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 0.0006804013473029879,
      "last_pc_control_margin": -0.0039349475584059285,
      "nonspherical_prior_first_pc_alignment_control": 0.2684625635322962,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 14,
      "samples": 160,
      "data_covariance_condition": 46.650523682790904,
      "alpha": 358.31858175948514,
      "noise_variance": 0.0019706280539489736,
      "posterior_condition": 42.291354122053974,
      "trace_exact_posterior": 2.90456347302776e-05,
      "trace_mfvi": 1.0042950652749483e-05,
      "trace_margin": 1.9002684077528116e-05,
      "minimum_posterior_direction_margin": 3.72478394143584e-07,
      "maximum_posterior_direction_control": -1.0613544381718528e-05,
      "training_distribution_expected_exact_minus_mfvi": -8.386272250599507e-08,
      "training_distribution_identity_rhs": -8.386272250598318e-08,
      "identity_absolute_error": 1.189816593096275e-20,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 3.724783941435841e-07,
      "last_pc_control_margin": -1.0613544381718535e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.1424381600942309,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 15,
      "samples": 160,
      "data_covariance_condition": 5.899468013728873,
      "alpha": 141.68105176749745,
      "noise_variance": 3.5964261128227504,
      "posterior_condition": 2.5911340990158997,
      "trace_exact_posterior": 0.03184608763690157,
      "trace_mfvi": 0.029376902986144638,
      "trace_margin": 0.0024691846507569302,
      "minimum_posterior_direction_margin": 0.001366623733789059,
      "maximum_posterior_direction_control": -0.002052448734814553,
      "training_distribution_expected_exact_minus_mfvi": -0.007863511032249009,
      "training_distribution_identity_rhs": -0.007863511032249025,
      "identity_absolute_error": 1.5612511283791264e-17,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 0.0013666237337890573,
      "last_pc_control_margin": -0.002052448734814551,
      "nonspherical_prior_first_pc_alignment_control": 0.19851199196376423,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 16,
      "samples": 160,
      "data_covariance_condition": 54.18601180884217,
      "alpha": 16.637985234496753,
      "noise_variance": 0.8550711376881254,
      "posterior_condition": 52.115091621921316,
      "trace_exact_posterior": 0.011939744688679208,
      "trace_mfvi": 0.003791256391111551,
      "trace_margin": 0.008148488297567657,
      "minimum_posterior_direction_margin": 0.00015395068766566386,
      "maximum_posterior_direction_control": -0.0040564263787018565,
      "training_distribution_expected_exact_minus_mfvi": -0.0007245361273306682,
      "training_distribution_identity_rhs": -0.000724536127330672,
      "identity_absolute_error": 3.7947076036992655e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.0001539506876656643,
      "last_pc_control_margin": -0.004056426378701856,
      "nonspherical_prior_first_pc_alignment_control": 0.1837358953632954,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 17,
      "samples": 160,
      "data_covariance_condition": 73.54577722548251,
      "alpha": 237.73328599788573,
      "noise_variance": 17.388226160800272,
      "posterior_condition": 3.7689273897732884,
      "trace_exact_posterior": 0.023101742729677226,
      "trace_mfvi": 0.019692623321425854,
      "trace_margin": 0.0034091194082513723,
      "minimum_posterior_direction_margin": 0.0010017251334049331,
      "maximum_posterior_direction_control": -0.0013976475846620392,
      "training_distribution_expected_exact_minus_mfvi": -0.08807801207595692,
      "training_distribution_identity_rhs": -0.08807801207595697,
      "identity_absolute_error": 5.551115123125783e-17,
      "first_pc_min_posterior_alignment": 0.9999999999999987,
      "first_pc_mfvi_minus_exact_margin": 0.001001725133404934,
      "last_pc_control_margin": -0.0013976475846620353,
      "nonspherical_prior_first_pc_alignment_control": 0.664200640268557,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 18,
      "samples": 160,
      "data_covariance_condition": 11.082387706963624,
      "alpha": 0.007138301592904321,
      "noise_variance": 214.74003001721465,
      "posterior_condition": 12.509545344729856,
      "trace_exact_posterior": 4.467542199202225,
      "trace_mfvi": 2.829286301271172,
      "trace_margin": 1.638255897931053,
      "minimum_posterior_direction_margin": 0.11900962973543931,
      "maximum_posterior_direction_control": -1.1241868979834502,
      "training_distribution_expected_exact_minus_mfvi": -0.015695301397862946,
      "training_distribution_identity_rhs": -0.015695301397862307,
      "identity_absolute_error": 6.38378239159465e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.11900962973543934,
      "last_pc_control_margin": -1.1241868979834497,
      "nonspherical_prior_first_pc_alignment_control": 0.33158449430396914,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 8,
      "seed": 19,
      "samples": 160,
      "data_covariance_condition": 719.5169636259177,
      "alpha": 0.02607868967343373,
      "noise_variance": 3.2630362148158545,
      "posterior_condition": 605.048705253887,
      "trace_exact_posterior": 0.031348548557074654,
      "trace_mfvi": 0.002169048392522443,
      "trace_margin": 0.02917950016455221,
      "minimum_posterior_direction_margin": 6.13925350600344e-05,
      "maximum_posterior_direction_control": -0.01821723820798407,
      "training_distribution_expected_exact_minus_mfvi": -1.5519064062857746e-05,
      "training_distribution_identity_rhs": -1.5519064063004682e-05,
      "identity_absolute_error": 1.46936499426098e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 6.139253506003447e-05,
      "last_pc_control_margin": -0.018217238207984043,
      "nonspherical_prior_first_pc_alignment_control": 0.2143472256449183,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 0,
      "samples": 160,
      "data_covariance_condition": 29.08873572191224,
      "alpha": 0.026298224333264873,
      "noise_variance": 0.10089355083841346,
      "posterior_condition": 38.93955449453808,
      "trace_exact_posterior": 0.0035584015022302154,
      "trace_mfvi": 0.001208667311806051,
      "trace_margin": 0.0023497341904241643,
      "minimum_posterior_direction_margin": 4.54150069692327e-05,
      "maximum_posterior_direction_control": -0.0008063224256568591,
      "training_distribution_expected_exact_minus_mfvi": -3.896624762925097e-08,
      "training_distribution_identity_rhs": -3.8966247631685755e-08,
      "identity_absolute_error": 2.4347829719926855e-18,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 4.5415006969232664e-05,
      "last_pc_control_margin": -0.0008063224256568591,
      "nonspherical_prior_first_pc_alignment_control": 0.36480392378944726,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 1,
      "samples": 160,
      "data_covariance_condition": 8.766856522136123,
      "alpha": 22.990211849048972,
      "noise_variance": 0.008532889351028219,
      "posterior_condition": 11.043156932356089,
      "trace_exact_posterior": 0.00041269512878983744,
      "trace_mfvi": 0.0002492955484383544,
      "trace_margin": 0.00016339958035148307,
      "minimum_posterior_direction_margin": 7.631095607518246e-06,
      "maximum_posterior_direction_control": -4.7965432624054066e-05,
      "training_distribution_expected_exact_minus_mfvi": -2.003410941862572e-07,
      "training_distribution_identity_rhs": -2.0034109418625146e-07,
      "identity_absolute_error": 5.743942173568224e-21,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 7.63109560751826e-06,
      "last_pc_control_margin": -4.79654326240541e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.32852652045383757,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 2,
      "samples": 160,
      "data_covariance_condition": 16.807018907428503,
      "alpha": 0.6856505200975936,
      "noise_variance": 21.64036786437631,
      "posterior_condition": 19.633036376669757,
      "trace_exact_posterior": 0.7763463598260796,
      "trace_mfvi": 0.4014982225844318,
      "trace_margin": 0.3748481372416478,
      "minimum_posterior_direction_margin": 0.01162196688239307,
      "maximum_posterior_direction_control": -0.13414121624254102,
      "training_distribution_expected_exact_minus_mfvi": -0.03476184535603516,
      "training_distribution_identity_rhs": -0.03476184535603506,
      "identity_absolute_error": 9.71445146547012e-17,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 0.01162196688239307,
      "last_pc_control_margin": -0.13414121624254088,
      "nonspherical_prior_first_pc_alignment_control": 0.14885807469082113,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 3,
      "samples": 160,
      "data_covariance_condition": 385.08501794043144,
      "alpha": 278.9999611117594,
      "noise_variance": 7.721990651047371,
      "posterior_condition": 29.29838900685908,
      "trace_exact_posterior": 0.025955947545257693,
      "trace_mfvi": 0.010727912173024289,
      "trace_margin": 0.015228035372233405,
      "minimum_posterior_direction_margin": 0.0003112092354090105,
      "maximum_posterior_direction_control": -0.00265626291955549,
      "training_distribution_expected_exact_minus_mfvi": -0.20504883611388705,
      "training_distribution_identity_rhs": -0.20504883611388716,
      "identity_absolute_error": 1.1102230246251565e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.00031120923540900995,
      "last_pc_control_margin": -0.0026562629195554985,
      "nonspherical_prior_first_pc_alignment_control": 0.49341624805444984,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 4,
      "samples": 160,
      "data_covariance_condition": 39.88096549049742,
      "alpha": 12.547919354429466,
      "noise_variance": 673.2690259818216,
      "posterior_condition": 1.8653708274222616,
      "trace_exact_posterior": 1.0728120461716408,
      "trace_mfvi": 1.0424932547529802,
      "trace_margin": 0.030318791418660673,
      "minimum_posterior_direction_margin": 0.019327247256994494,
      "maximum_posterior_direction_control": -0.009919983030941465,
      "training_distribution_expected_exact_minus_mfvi": -1.600855957189298,
      "training_distribution_identity_rhs": -1.6008559571892973,
      "identity_absolute_error": 6.661338147750939e-16,
      "first_pc_min_posterior_alignment": 0.9999999999999999,
      "first_pc_mfvi_minus_exact_margin": 0.01932724725699448,
      "last_pc_control_margin": -0.009919983030941434,
      "nonspherical_prior_first_pc_alignment_control": 0.02284463185480677,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 5,
      "samples": 160,
      "data_covariance_condition": 2566.0106545713206,
      "alpha": 2.776985061340526,
      "noise_variance": 0.031614819047035975,
      "posterior_condition": 2271.4977243836634,
      "trace_exact_posterior": 0.0004942115772827891,
      "trace_mfvi": 1.0673777446251305e-05,
      "trace_margin": 0.0004835377998365378,
      "minimum_posterior_direction_margin": 3.1719395312680135e-07,
      "maximum_posterior_direction_control": -0.00018213654138054462,
      "training_distribution_expected_exact_minus_mfvi": -2.6532287297002693e-07,
      "training_distribution_identity_rhs": -2.653228729759215e-07,
      "identity_absolute_error": 5.8945552195018795e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 3.1719395312679664e-07,
      "last_pc_control_margin": -0.00018213654138054465,
      "nonspherical_prior_first_pc_alignment_control": 0.0006360977228899159,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 6,
      "samples": 160,
      "data_covariance_condition": 30.022198664711805,
      "alpha": 0.011608677525417265,
      "noise_variance": 3.753222133017077,
      "posterior_condition": 28.640411756001956,
      "trace_exact_posterior": 0.11536211357127868,
      "trace_mfvi": 0.053063217203752885,
      "trace_margin": 0.062298896367525794,
      "minimum_posterior_direction_margin": 0.0012449968445294524,
      "maximum_posterior_direction_control": -0.01931954523162236,
      "training_distribution_expected_exact_minus_mfvi": -1.696474696675046e-05,
      "training_distribution_identity_rhs": -1.6964746966715717e-05,
      "identity_absolute_error": 3.474190336458238e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.0012449968445294515,
      "last_pc_control_margin": -0.01931954523162235,
      "nonspherical_prior_first_pc_alignment_control": 0.2655341365859409,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 7,
      "samples": 160,
      "data_covariance_condition": 45.94351201545618,
      "alpha": 946.4622246988179,
      "noise_variance": 0.18404864484649555,
      "posterior_condition": 26.780456702014384,
      "trace_exact_posterior": 0.0034695867857910804,
      "trace_mfvi": 0.001492119101402541,
      "trace_margin": 0.0019774676843885394,
      "minimum_posterior_direction_margin": 5.07959392264982e-05,
      "maximum_posterior_direction_control": -0.0005324594791431897,
      "training_distribution_expected_exact_minus_mfvi": -0.0021529072560366983,
      "training_distribution_identity_rhs": -0.002152907256036698,
      "identity_absolute_error": 4.336808689942018e-19,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 5.079593922649816e-05,
      "last_pc_control_margin": -0.0005324594791431905,
      "nonspherical_prior_first_pc_alignment_control": 0.3334601767452344,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 8,
      "samples": 160,
      "data_covariance_condition": 13.744413333902113,
      "alpha": 0.12508041159773242,
      "noise_variance": 3.722374852201114,
      "posterior_condition": 18.561148034040034,
      "trace_exact_posterior": 0.1487193577632016,
      "trace_mfvi": 0.07703637393420129,
      "trace_margin": 0.07168298382900032,
      "minimum_posterior_direction_margin": 0.0019408198615906203,
      "maximum_posterior_direction_control": -0.023074091884084352,
      "training_distribution_expected_exact_minus_mfvi": -0.0002085957708993065,
      "training_distribution_identity_rhs": -0.00020859577089932146,
      "identity_absolute_error": 1.496198998029996e-17,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 0.0019408198615906216,
      "last_pc_control_margin": -0.02307409188408436,
      "nonspherical_prior_first_pc_alignment_control": 0.3373195221900558,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 9,
      "samples": 160,
      "data_covariance_condition": 3.328481222287846,
      "alpha": 0.35357561315057806,
      "noise_variance": 0.0810901098706331,
      "posterior_condition": 4.667579678013622,
      "trace_exact_posterior": 0.005324109265627868,
      "trace_mfvi": 0.00426475132984189,
      "trace_margin": 0.0010593579357859786,
      "minimum_posterior_direction_margin": 0.0001245145388875943,
      "maximum_posterior_direction_control": -0.0003384494910473729,
      "training_distribution_expected_exact_minus_mfvi": -1.8983353438941613e-07,
      "training_distribution_identity_rhs": -1.898335343896797e-07,
      "identity_absolute_error": 2.635860652736976e-19,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 0.00012451453888759416,
      "last_pc_control_margin": -0.000338449491047373,
      "nonspherical_prior_first_pc_alignment_control": 0.2642865263318588,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 10,
      "samples": 160,
      "data_covariance_condition": 2519.1466996212803,
      "alpha": 0.2615911399534498,
      "noise_variance": 0.012701066965734236,
      "posterior_condition": 2685.3296051170623,
      "trace_exact_posterior": 0.00020897825153880537,
      "trace_mfvi": 4.8278886994436544e-06,
      "trace_margin": 0.00020415036283936172,
      "minimum_posterior_direction_margin": 1.491414756123581e-07,
      "maximum_posterior_direction_control": -8.325218975867189e-05,
      "training_distribution_expected_exact_minus_mfvi": -4.239292771666844e-09,
      "training_distribution_identity_rhs": -4.239292763124447e-09,
      "identity_absolute_error": 8.542396756231073e-18,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 1.4914147561236446e-07,
      "last_pc_control_margin": -8.32521897586719e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.05352501666996189,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 11,
      "samples": 160,
      "data_covariance_condition": 397.4165642145123,
      "alpha": 0.9543412019642304,
      "noise_variance": 126.93456547428123,
      "posterior_condition": 233.18902346908652,
      "trace_exact_posterior": 1.887254836233709,
      "trace_mfvi": 0.1987067711270079,
      "trace_margin": 1.688548065106701,
      "minimum_posterior_direction_margin": 0.007694855938857931,
      "maximum_posterior_direction_control": -0.5024344779299873,
      "training_distribution_expected_exact_minus_mfvi": -1.2784301950146313,
      "training_distribution_identity_rhs": -1.2784301950146446,
      "identity_absolute_error": 1.3322676295501878e-14,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 0.007694855938857928,
      "last_pc_control_margin": -0.5024344779299876,
      "nonspherical_prior_first_pc_alignment_control": 0.32827372750816985,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 12,
      "samples": 160,
      "data_covariance_condition": 6.6821535401643475,
      "alpha": 39.40309790156926,
      "noise_variance": 0.0012718751423592665,
      "posterior_condition": 9.172957727084377,
      "trace_exact_posterior": 6.161558917852487e-05,
      "trace_mfvi": 4.093238196455991e-05,
      "trace_margin": 2.068320721396496e-05,
      "minimum_posterior_direction_margin": 1.440561055050469e-06,
      "maximum_posterior_direction_control": -7.040036062629139e-06,
      "training_distribution_expected_exact_minus_mfvi": -6.4784744083135465e-09,
      "training_distribution_identity_rhs": -6.478474408320523e-09,
      "identity_absolute_error": 6.976441286272235e-21,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 1.4405610550504695e-06,
      "last_pc_control_margin": -7.040036062629135e-06,
      "nonspherical_prior_first_pc_alignment_control": 0.001947972008672518,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 13,
      "samples": 160,
      "data_covariance_condition": 4311.748276350884,
      "alpha": 0.9539087896939477,
      "noise_variance": 5.029534038970279,
      "posterior_condition": 4497.433381580117,
      "trace_exact_posterior": 0.07886598028171725,
      "trace_mfvi": 0.0019177209923778998,
      "trace_margin": 0.07694825928933935,
      "minimum_posterior_direction_margin": 3.3278546225525195e-05,
      "maximum_posterior_direction_control": -0.031243334913270512,
      "training_distribution_expected_exact_minus_mfvi": -0.0023073496923147582,
      "training_distribution_identity_rhs": -0.002307349692315808,
      "identity_absolute_error": 1.0499413838349625e-15,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 3.327854622553422e-05,
      "last_pc_control_margin": -0.031243334913270485,
      "nonspherical_prior_first_pc_alignment_control": 0.15576729468839617,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 14,
      "samples": 160,
      "data_covariance_condition": 1074.2728400193807,
      "alpha": 0.15653538896744504,
      "noise_variance": 0.022527736439252405,
      "posterior_condition": 1255.033851877361,
      "trace_exact_posterior": 0.000421328857203639,
      "trace_mfvi": 1.7750714939373478e-05,
      "trace_margin": 0.00040357814226426556,
      "minimum_posterior_direction_margin": 4.689170732609625e-07,
      "maximum_posterior_direction_control": -0.00015581101409160712,
      "training_distribution_expected_exact_minus_mfvi": -8.894831952814786e-09,
      "training_distribution_identity_rhs": -8.894831952018473e-09,
      "identity_absolute_error": 7.963135408149989e-19,
      "first_pc_min_posterior_alignment": 1.0000000000000009,
      "first_pc_mfvi_minus_exact_margin": 4.689170732609974e-07,
      "last_pc_control_margin": -0.00015581101409160722,
      "nonspherical_prior_first_pc_alignment_control": 0.5050574688237509,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 15,
      "samples": 160,
      "data_covariance_condition": 19.216585841543484,
      "alpha": 4.409124508908385,
      "noise_variance": 142.6473868301211,
      "posterior_condition": 4.65544904438894,
      "trace_exact_posterior": 1.7980615079854332,
      "trace_mfvi": 1.4356759693230026,
      "trace_margin": 0.3623855386624306,
      "minimum_posterior_direction_margin": 0.04077586777356953,
      "maximum_posterior_direction_control": -0.10254591661231904,
      "training_distribution_expected_exact_minus_mfvi": -1.4245151058787837,
      "training_distribution_identity_rhs": -1.4245151058787837,
      "identity_absolute_error": 0.0,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 0.04077586777356956,
      "last_pc_control_margin": -0.10254591661231913,
      "nonspherical_prior_first_pc_alignment_control": 0.28009955309463325,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 16,
      "samples": 160,
      "data_covariance_condition": 30.318565014157503,
      "alpha": 0.03286853747585588,
      "noise_variance": 0.002674148141046675,
      "posterior_condition": 48.68827180036395,
      "trace_exact_posterior": 9.10851343574694e-05,
      "trace_mfvi": 3.196790265047522e-05,
      "trace_margin": 5.9117231706994185e-05,
      "minimum_posterior_direction_margin": 1.2974805883979091e-06,
      "maximum_posterior_direction_control": -2.02154053788732e-05,
      "training_distribution_expected_exact_minus_mfvi": -3.247580679775544e-11,
      "training_distribution_identity_rhs": -3.247580678478303e-11,
      "identity_absolute_error": 1.297241505272771e-20,
      "first_pc_min_posterior_alignment": 1.0000000000000009,
      "first_pc_mfvi_minus_exact_margin": 1.2974805883979117e-06,
      "last_pc_control_margin": -2.0215405378873206e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.27625735782255767,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 17,
      "samples": 160,
      "data_covariance_condition": 3828.7752395293755,
      "alpha": 49.34607298430189,
      "noise_variance": 9.5734412611236,
      "posterior_condition": 957.7529376867358,
      "trace_exact_posterior": 0.05931135145076341,
      "trace_mfvi": 0.0026059794088822467,
      "trace_margin": 0.05670537204188116,
      "minimum_posterior_direction_margin": 6.272969413040566e-05,
      "maximum_posterior_direction_control": -0.014288967017141243,
      "training_distribution_expected_exact_minus_mfvi": -0.1674267685852731,
      "training_distribution_identity_rhs": -0.16742676858527064,
      "identity_absolute_error": 2.4702462297909733e-15,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 6.272969413040282e-05,
      "last_pc_control_margin": -0.014288967017141243,
      "nonspherical_prior_first_pc_alignment_control": 0.1505412460573801,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 18,
      "samples": 160,
      "data_covariance_condition": 3132.894316084197,
      "alpha": 0.012091988381034613,
      "noise_variance": 0.550745577907065,
      "posterior_condition": 3561.55351739153,
      "trace_exact_posterior": 0.009043634078949973,
      "trace_mfvi": 0.00015946098096430745,
      "trace_margin": 0.008884173097985665,
      "minimum_posterior_direction_margin": 5.168776437318164e-06,
      "maximum_posterior_direction_control": -0.0039121049860181166,
      "training_distribution_expected_exact_minus_mfvi": -3.697820016286853e-07,
      "training_distribution_identity_rhs": -3.697820016662011e-07,
      "identity_absolute_error": 3.7515777448162606e-17,
      "first_pc_min_posterior_alignment": 0.9999999999999998,
      "first_pc_mfvi_minus_exact_margin": 5.1687764373244606e-06,
      "last_pc_control_margin": -0.003912104986018116,
      "nonspherical_prior_first_pc_alignment_control": 0.24522193066580347,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 16,
      "seed": 19,
      "samples": 160,
      "data_covariance_condition": 1337.6775197642178,
      "alpha": 149.94025844613543,
      "noise_variance": 26.30787874587107,
      "posterior_condition": 56.40001161324224,
      "trace_exact_posterior": 0.049471199441497735,
      "trace_mfvi": 0.015214533920475424,
      "trace_margin": 0.034256665521022314,
      "minimum_posterior_direction_margin": 0.0004031572615201105,
      "maximum_posterior_direction_control": -0.005132879881503348,
      "training_distribution_expected_exact_minus_mfvi": -0.8445574382465648,
      "training_distribution_identity_rhs": -0.8445574382465642,
      "identity_absolute_error": 6.661338147750939e-16,
      "first_pc_min_posterior_alignment": 0.9999999999999993,
      "first_pc_mfvi_minus_exact_margin": 0.0004031572615201109,
      "last_pc_control_margin": -0.005132879881503323,
      "nonspherical_prior_first_pc_alignment_control": 0.05476698780666158,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 0,
      "samples": 256,
      "data_covariance_condition": 11.86342926986681,
      "alpha": 0.013572245377247933,
      "noise_variance": 3.0709224626614824,
      "posterior_condition": 18.208039939511394,
      "trace_exact_posterior": 0.16635860306411288,
      "trace_mfvi": 0.08995193585713276,
      "trace_margin": 0.07640666720698011,
      "minimum_posterior_direction_margin": 0.001564444113540294,
      "maximum_posterior_direction_control": -0.013207358117032128,
      "training_distribution_expected_exact_minus_mfvi": -1.243975551923147e-05,
      "training_distribution_identity_rhs": -1.2439755519201292e-05,
      "identity_absolute_error": 3.017808984477621e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 0.0015644441135403047,
      "last_pc_control_margin": -0.013207358117032131,
      "nonspherical_prior_first_pc_alignment_control": 0.0044939542119087905,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 1,
      "samples": 256,
      "data_covariance_condition": 627.7892928693296,
      "alpha": 30.48653181867791,
      "noise_variance": 36.17627568565246,
      "posterior_condition": 119.60516350745702,
      "trace_exact_posterior": 0.28940533674436825,
      "trace_mfvi": 0.04715698636270625,
      "trace_margin": 0.24224835038166198,
      "minimum_posterior_direction_margin": 0.0009586150485466677,
      "maximum_posterior_direction_control": -0.025931862325810056,
      "training_distribution_expected_exact_minus_mfvi": -1.0436448611465967,
      "training_distribution_identity_rhs": -1.0436448611465974,
      "identity_absolute_error": 6.661338147750939e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.0009586150485466677,
      "last_pc_control_margin": -0.02593186232581003,
      "nonspherical_prior_first_pc_alignment_control": 0.012963419840640603,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 2,
      "samples": 256,
      "data_covariance_condition": 5.056630403349046,
      "alpha": 1.011364562029277,
      "noise_variance": 26.447050168060954,
      "posterior_condition": 8.069866239055031,
      "trace_exact_posterior": 1.7433131818976282,
      "trace_mfvi": 1.2846245657368631,
      "trace_margin": 0.45868861616076506,
      "minimum_posterior_direction_margin": 0.020981838215838256,
      "maximum_posterior_direction_control": -0.09349566017810082,
      "training_distribution_expected_exact_minus_mfvi": -0.047925093359760154,
      "training_distribution_identity_rhs": -0.04792509335976016,
      "identity_absolute_error": 6.938893903907228e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.02098183821583826,
      "last_pc_control_margin": -0.0934956601781008,
      "nonspherical_prior_first_pc_alignment_control": 0.011620261098715964,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 3,
      "samples": 256,
      "data_covariance_condition": 2622.9517200252085,
      "alpha": 0.15542139330143862,
      "noise_variance": 890.1736799546835,
      "posterior_condition": 2034.3928657249478,
      "trace_exact_posterior": 13.599684459806522,
      "trace_mfvi": 0.34097835907122076,
      "trace_margin": 13.258706100735301,
      "minimum_posterior_direction_margin": 0.007913829950121808,
      "maximum_posterior_direction_control": -2.625009514442892,
      "training_distribution_expected_exact_minus_mfvi": -7.165503719496453,
      "training_distribution_identity_rhs": -7.165503719496332,
      "identity_absolute_error": 1.2079226507921703e-13,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.007913829950123064,
      "last_pc_control_margin": -2.6250095144428904,
      "nonspherical_prior_first_pc_alignment_control": 0.054400151206153824,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 4,
      "samples": 256,
      "data_covariance_condition": 421.97045379854313,
      "alpha": 0.0015375468682990905,
      "noise_variance": 0.014123360553246095,
      "posterior_condition": 540.9079321831622,
      "trace_exact_posterior": 0.000346988000186869,
      "trace_mfvi": 2.885782573629357e-05,
      "trace_margin": 0.0003181301744505755,
      "minimum_posterior_direction_margin": 5.184239682701193e-07,
      "maximum_posterior_direction_control": -6.532480050313973e-05,
      "training_distribution_expected_exact_minus_mfvi": -2.6985553851348278e-11,
      "training_distribution_identity_rhs": -2.698555209272612e-11,
      "identity_absolute_error": 1.758622158514839e-18,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 5.184239682701206e-07,
      "last_pc_control_margin": -6.532480050313965e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.029704508747485932,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 5,
      "samples": 256,
      "data_covariance_condition": 348.5696978610018,
      "alpha": 873.6634973231223,
      "noise_variance": 15.228508437138947,
      "posterior_condition": 8.316704808437395,
      "trace_exact_posterior": 0.023935129961719523,
      "trace_mfvi": 0.01645424091058955,
      "trace_margin": 0.007480889051129973,
      "minimum_posterior_direction_margin": 0.00032398176921114095,
      "maximum_posterior_direction_control": -0.0005945442525734495,
      "training_distribution_expected_exact_minus_mfvi": -0.3887897506845126,
      "training_distribution_identity_rhs": -0.38878975068451294,
      "identity_absolute_error": 3.3306690738754696e-16,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 0.0003239817692111408,
      "last_pc_control_margin": -0.0005945442525734518,
      "nonspherical_prior_first_pc_alignment_control": 0.2436819924868162,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 6,
      "samples": 256,
      "data_covariance_condition": 67.23495762896212,
      "alpha": 201.6399799493579,
      "noise_variance": 6.659284304130903,
      "posterior_condition": 12.39061637721678,
      "trace_exact_posterior": 0.06880789473780452,
      "trace_mfvi": 0.04107667794920039,
      "trace_margin": 0.02773121678860413,
      "minimum_posterior_direction_margin": 0.0008075943614331092,
      "maximum_posterior_direction_control": -0.0029538773909463228,
      "training_distribution_expected_exact_minus_mfvi": -0.145456509879636,
      "training_distribution_identity_rhs": -0.14545650987963607,
      "identity_absolute_error": 8.326672684688674e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.00080759436143311,
      "last_pc_control_margin": -0.0029538773909463262,
      "nonspherical_prior_first_pc_alignment_control": 0.22495425275194675,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 7,
      "samples": 256,
      "data_covariance_condition": 9864.76757765071,
      "alpha": 0.2857805868494454,
      "noise_variance": 18.67695472094031,
      "posterior_condition": 13850.875912934025,
      "trace_exact_posterior": 0.3251155218362508,
      "trace_mfvi": 0.002279226685868735,
      "trace_margin": 0.3228362951503821,
      "minimum_posterior_direction_margin": 4.567838297491554e-05,
      "maximum_posterior_direction_control": -0.0870629195043415,
      "training_distribution_expected_exact_minus_mfvi": -0.006731024619586598,
      "training_distribution_identity_rhs": -0.006731024619612501,
      "identity_absolute_error": 2.5902890943285684e-14,
      "first_pc_min_posterior_alignment": 0.9999999999999993,
      "first_pc_mfvi_minus_exact_margin": 4.567838297485129e-05,
      "last_pc_control_margin": -0.08706291950434149,
      "nonspherical_prior_first_pc_alignment_control": 0.07892408426911254,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 8,
      "samples": 256,
      "data_covariance_condition": 103.72697698514689,
      "alpha": 1.0861696543073793,
      "noise_variance": 18.943736316438706,
      "posterior_condition": 123.75109982500669,
      "trace_exact_posterior": 0.5656595303520489,
      "trace_mfvi": 0.10798570707321214,
      "trace_margin": 0.4576738232788367,
      "minimum_posterior_direction_margin": 0.0022394419767293484,
      "maximum_posterior_direction_control": -0.07812591890799064,
      "training_distribution_expected_exact_minus_mfvi": -0.03678573293112929,
      "training_distribution_identity_rhs": -0.036785732931130556,
      "identity_absolute_error": 1.2628786905111156e-15,
      "first_pc_min_posterior_alignment": 0.9999999999999994,
      "first_pc_mfvi_minus_exact_margin": 0.0022394419767293493,
      "last_pc_control_margin": -0.07812591890799063,
      "nonspherical_prior_first_pc_alignment_control": 0.020226795105392086,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 9,
      "samples": 256,
      "data_covariance_condition": 1986.1224590989755,
      "alpha": 0.26724883029237095,
      "noise_variance": 163.6432361065473,
      "posterior_condition": 2022.0628354853527,
      "trace_exact_posterior": 2.9886082707712918,
      "trace_mfvi": 0.0842999500936556,
      "trace_margin": 2.9043083206776363,
      "minimum_posterior_direction_margin": 0.0016769413645909659,
      "maximum_posterior_direction_control": -0.6131154399033762,
      "training_distribution_expected_exact_minus_mfvi": -0.49615414744353903,
      "training_distribution_identity_rhs": -0.4961541474435405,
      "identity_absolute_error": 1.4988010832439613e-15,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 0.0016769413645900582,
      "last_pc_control_margin": -0.6131154399033768,
      "nonspherical_prior_first_pc_alignment_control": 0.15247991197134425,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 10,
      "samples": 256,
      "data_covariance_condition": 8.907928015711567,
      "alpha": 0.004611302486665287,
      "noise_variance": 0.03270087540973514,
      "posterior_condition": 14.220151197912017,
      "trace_exact_posterior": 0.0018842602362069524,
      "trace_mfvi": 0.0011416478591134106,
      "trace_margin": 0.0007426123770935419,
      "minimum_posterior_direction_margin": 2.0505383683690757e-05,
      "maximum_posterior_direction_control": -0.0001256777658865229,
      "training_distribution_expected_exact_minus_mfvi": -4.374266196661348e-10,
      "training_distribution_identity_rhs": -4.3742661956536895e-10,
      "identity_absolute_error": 1.0076584975150272e-19,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 2.0505383683690743e-05,
      "last_pc_control_margin": -0.00012567776588652302,
      "nonspherical_prior_first_pc_alignment_control": 0.03610549618785747,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 11,
      "samples": 256,
      "data_covariance_condition": 364.06129993142594,
      "alpha": 0.19650286819371962,
      "noise_variance": 0.013208520202308898,
      "posterior_condition": 434.8643276751281,
      "trace_exact_posterior": 0.00032947543847936883,
      "trace_mfvi": 2.7884960444683724e-05,
      "trace_margin": 0.0003015904780346851,
      "minimum_posterior_direction_margin": 5.918343835693936e-07,
      "maximum_posterior_direction_control": -6.368878716390995e-05,
      "training_distribution_expected_exact_minus_mfvi": -3.0577411561861118e-09,
      "training_distribution_identity_rhs": -3.0577411574032886e-09,
      "identity_absolute_error": 1.2171768326273852e-18,
      "first_pc_min_posterior_alignment": 0.9999999999999993,
      "first_pc_mfvi_minus_exact_margin": 5.918343835694176e-07,
      "last_pc_control_margin": -6.368878716390985e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.08448238025594619,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 12,
      "samples": 256,
      "data_covariance_condition": 44.70110584029732,
      "alpha": 23.267997962534345,
      "noise_variance": 728.3386736419186,
      "posterior_condition": 1.654430139298015,
      "trace_exact_posterior": 1.1920398712269704,
      "trace_mfvi": 1.1669062882375536,
      "trace_margin": 0.025133582989416814,
      "minimum_posterior_direction_margin": 0.010008805978096788,
      "maximum_posterior_direction_control": -0.004356294929426571,
      "training_distribution_expected_exact_minus_mfvi": -1.66382186710535,
      "training_distribution_identity_rhs": -1.6638218671053484,
      "identity_absolute_error": 1.5543122344752192e-15,
      "first_pc_min_posterior_alignment": 1.0000000000000007,
      "first_pc_mfvi_minus_exact_margin": 0.010008805978096802,
      "last_pc_control_margin": -0.004356294929426455,
      "nonspherical_prior_first_pc_alignment_control": 0.2754587841587338,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 13,
      "samples": 256,
      "data_covariance_condition": 6830.414996332373,
      "alpha": 0.021270501550535243,
      "noise_variance": 0.12214275185021158,
      "posterior_condition": 9809.655504177514,
      "trace_exact_posterior": 0.0023167785008316693,
      "trace_mfvi": 2.1476896864289163e-05,
      "trace_margin": 0.00229530160396738,
      "minimum_posterior_direction_margin": 3.777009094520256e-07,
      "maximum_posterior_direction_control": -0.0006231840559493931,
      "training_distribution_expected_exact_minus_mfvi": -2.3294061966538476e-08,
      "training_distribution_identity_rhs": -2.3294061927735765e-08,
      "identity_absolute_error": 3.880271166261751e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 3.7770090945197923e-07,
      "last_pc_control_margin": -0.0006231840559493925,
      "nonspherical_prior_first_pc_alignment_control": 0.08685963739808095,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 14,
      "samples": 256,
      "data_covariance_condition": 49.38040464935112,
      "alpha": 162.50659784964787,
      "noise_variance": 0.009828577437580784,
      "posterior_condition": 66.53908477208712,
      "trace_exact_posterior": 0.0003750866708499867,
      "trace_mfvi": 0.00010631099156503101,
      "trace_margin": 0.00026877567928495566,
      "minimum_posterior_direction_margin": 2.0221936225751064e-06,
      "maximum_posterior_direction_control": -4.6615431337822387e-05,
      "training_distribution_expected_exact_minus_mfvi": -1.6769173758513118e-06,
      "training_distribution_identity_rhs": -1.6769173758512827e-06,
      "identity_absolute_error": 2.9010878443459787e-20,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 2.022193622575115e-06,
      "last_pc_control_margin": -4.661543133782241e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.15039088538633383,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 15,
      "samples": 256,
      "data_covariance_condition": 101.31440451958888,
      "alpha": 0.3925392341251262,
      "noise_variance": 0.035306446846282175,
      "posterior_condition": 135.28496752976062,
      "trace_exact_posterior": 0.0011263974739875661,
      "trace_mfvi": 0.0002220531952395644,
      "trace_margin": 0.0009043442787480017,
      "minimum_posterior_direction_margin": 3.5421163393112317e-06,
      "maximum_posterior_direction_control": -0.0001533048128753845,
      "training_distribution_expected_exact_minus_mfvi": -4.895881688696473e-08,
      "training_distribution_identity_rhs": -4.895881688612809e-08,
      "identity_absolute_error": 8.366369413157339e-19,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 3.5421163393112342e-06,
      "last_pc_control_margin": -0.00015330481287538454,
      "nonspherical_prior_first_pc_alignment_control": 0.08177934920679038,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 16,
      "samples": 256,
      "data_covariance_condition": 122.79967053044898,
      "alpha": 0.0913506964179551,
      "noise_variance": 0.002891152950052672,
      "posterior_condition": 166.77987911854353,
      "trace_exact_posterior": 8.7999976079375e-05,
      "trace_mfvi": 1.568314599764233e-05,
      "trace_margin": 7.231683008173267e-05,
      "minimum_posterior_direction_margin": 2.669727911441066e-07,
      "maximum_posterior_direction_control": -1.410024230728231e-05,
      "training_distribution_expected_exact_minus_mfvi": -7.460747576518731e-11,
      "training_distribution_identity_rhs": -7.460747568540643e-11,
      "identity_absolute_error": 7.978088507179475e-20,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 2.669727911441083e-07,
      "last_pc_control_margin": -1.410024230728228e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.237738389230372,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 17,
      "samples": 256,
      "data_covariance_condition": 17.265236935831098,
      "alpha": 0.07271952680478522,
      "noise_variance": 0.008525237661916351,
      "posterior_condition": 24.78589041407085,
      "trace_exact_posterior": 0.0004059914959927289,
      "trace_mfvi": 0.00019459963409339958,
      "trace_margin": 0.00021139186189932931,
      "minimum_posterior_direction_margin": 3.5241455485666226e-06,
      "maximum_posterior_direction_control": -3.58018863118559e-05,
      "training_distribution_expected_exact_minus_mfvi": -5.11924409281211e-10,
      "training_distribution_identity_rhs": -5.119244091553768e-10,
      "identity_absolute_error": 1.2583423029916992e-19,
      "first_pc_min_posterior_alignment": 0.9999999999999993,
      "first_pc_mfvi_minus_exact_margin": 3.5241455485666315e-06,
      "last_pc_control_margin": -3.5801886311855985e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.14574222528243092,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 18,
      "samples": 256,
      "data_covariance_condition": 12.19243240987419,
      "alpha": 164.56354288371696,
      "noise_variance": 27.609545823399543,
      "posterior_condition": 1.7165778869062427,
      "trace_exact_posterior": 0.1582303580115309,
      "trace_mfvi": 0.15467587162743224,
      "trace_margin": 0.003554486384098665,
      "minimum_posterior_direction_margin": 0.0014309031239809976,
      "maximum_posterior_direction_control": -0.0009764406200701661,
      "training_distribution_expected_exact_minus_mfvi": -0.06308553360997862,
      "training_distribution_identity_rhs": -0.06308553360997878,
      "identity_absolute_error": 1.5265566588595902e-16,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 0.0014309031239809946,
      "last_pc_control_margin": -0.0009764406200701711,
      "nonspherical_prior_first_pc_alignment_control": 0.005426825627365298,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 32,
      "seed": 19,
      "samples": 256,
      "data_covariance_condition": 147.9692074843396,
      "alpha": 449.44493565532315,
      "noise_variance": 2.356127681722535,
      "posterior_condition": 33.05646229899546,
      "trace_exact_posterior": 0.024173684625430965,
      "trace_mfvi": 0.008732920486203968,
      "trace_margin": 0.015440764139226997,
      "minimum_posterior_direction_margin": 0.00018709972947353798,
      "maximum_posterior_direction_control": -0.0016074133949335562,
      "training_distribution_expected_exact_minus_mfvi": -0.0638710619042119,
      "training_distribution_identity_rhs": -0.06387106190421185,
      "identity_absolute_error": 5.551115123125783e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000009,
      "first_pc_mfvi_minus_exact_margin": 0.0001870997294735379,
      "last_pc_control_margin": -0.0016074133949335577,
      "nonspherical_prior_first_pc_alignment_control": 0.06945898552554496,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 0,
      "samples": 512,
      "data_covariance_condition": 1322.1486853231356,
      "alpha": 0.012488473940775534,
      "noise_variance": 28.866485970086856,
      "posterior_condition": 1836.4416457086147,
      "trace_exact_posterior": 0.6060295709071608,
      "trace_mfvi": 0.020970927363745145,
      "trace_margin": 0.5850586435434156,
      "minimum_posterior_direction_margin": 0.00023389231957405692,
      "maximum_posterior_direction_control": -0.07394194182408104,
      "training_distribution_expected_exact_minus_mfvi": -0.00041193882853980234,
      "training_distribution_identity_rhs": -0.000411938828542235,
      "identity_absolute_error": 2.4326786245143506e-15,
      "first_pc_min_posterior_alignment": 1.0000000000000009,
      "first_pc_mfvi_minus_exact_margin": 0.0002338923195740346,
      "last_pc_control_margin": -0.07394194182408104,
      "nonspherical_prior_first_pc_alignment_control": 0.2566078773244549,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 1,
      "samples": 512,
      "data_covariance_condition": 153.8376148338685,
      "alpha": 0.0049812350145130415,
      "noise_variance": 93.20302256769399,
      "posterior_condition": 205.70834295826631,
      "trace_exact_posterior": 2.6859820651042066,
      "trace_mfvi": 0.3903173669934504,
      "trace_margin": 2.2956646981107562,
      "minimum_posterior_direction_margin": 0.003891412875483622,
      "maximum_posterior_direction_control": -0.2077835157531398,
      "training_distribution_expected_exact_minus_mfvi": -0.0020816395172550918,
      "training_distribution_identity_rhs": -0.0020816395172437757,
      "identity_absolute_error": 1.1316034914665707e-14,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 0.0038914128754836256,
      "last_pc_control_margin": -0.2077835157531395,
      "nonspherical_prior_first_pc_alignment_control": 0.07165969188015528,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 2,
      "samples": 512,
      "data_covariance_condition": 689.60685111222,
      "alpha": 24.6525779865795,
      "noise_variance": 0.006574132648439933,
      "posterior_condition": 926.3332463609843,
      "trace_exact_posterior": 0.00015290358690854997,
      "trace_mfvi": 8.145918684837326e-06,
      "trace_margin": 0.00014475766822371263,
      "minimum_posterior_direction_margin": 9.174197540314312e-08,
      "maximum_posterior_direction_control": -1.6542538752530867e-05,
      "training_distribution_expected_exact_minus_mfvi": -4.5821829174156764e-08,
      "training_distribution_identity_rhs": -4.5821829173344016e-08,
      "identity_absolute_error": 8.127479652252024e-19,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 9.174197540313095e-08,
      "last_pc_control_margin": -1.6542538752530867e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.018810192408479105,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 3,
      "samples": 512,
      "data_covariance_condition": 7.2447715394342005,
      "alpha": 475.1230682778277,
      "noise_variance": 0.2948990834222178,
      "posterior_condition": 9.017812854370282,
      "trace_exact_posterior": 0.015579211249190029,
      "trace_mfvi": 0.01088459860678851,
      "trace_margin": 0.004694612642401518,
      "minimum_posterior_direction_margin": 0.00010212825210600038,
      "maximum_posterior_direction_control": -0.0004033970812846218,
      "training_distribution_expected_exact_minus_mfvi": -0.0012847225366693256,
      "training_distribution_identity_rhs": -0.0012847225366693245,
      "identity_absolute_error": 1.0842021724855044e-18,
      "first_pc_min_posterior_alignment": 0.999999999999999,
      "first_pc_mfvi_minus_exact_margin": 0.00010212825210600043,
      "last_pc_control_margin": -0.0004033970812846219,
      "nonspherical_prior_first_pc_alignment_control": 0.11777964510773113,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 4,
      "samples": 512,
      "data_covariance_condition": 795.0205965049446,
      "alpha": 0.022267548761081866,
      "noise_variance": 0.01573367018735412,
      "posterior_condition": 1015.457195801383,
      "trace_exact_posterior": 0.00035137168568440434,
      "trace_mfvi": 1.6942401757181554e-05,
      "trace_margin": 0.0003344292839272228,
      "minimum_posterior_direction_margin": 1.9718601975532754e-07,
      "maximum_posterior_direction_control": -3.838123629626946e-05,
      "training_distribution_expected_exact_minus_mfvi": -2.2884255416276895e-10,
      "training_distribution_identity_rhs": -2.2884255718803907e-10,
      "identity_absolute_error": 3.0252701174136978e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 1.9718601975529774e-07,
      "last_pc_control_margin": -3.8381236296269414e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.12843067262682822,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 5,
      "samples": 512,
      "data_covariance_condition": 3226.894252771978,
      "alpha": 535.1040595062624,
      "noise_variance": 2.72835394624302,
      "posterior_condition": 1033.9845200324828,
      "trace_exact_posterior": 0.021404789808982312,
      "trace_mfvi": 0.0008962094376600653,
      "trace_margin": 0.020508580371322246,
      "minimum_posterior_direction_margin": 9.265950841504169e-06,
      "maximum_posterior_direction_control": -0.0014416544956306588,
      "training_distribution_expected_exact_minus_mfvi": -0.058479627002898146,
      "training_distribution_identity_rhs": -0.05847962700289856,
      "identity_absolute_error": 4.163336342344337e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 9.26595084150462e-06,
      "last_pc_control_margin": -0.0014416544956306586,
      "nonspherical_prior_first_pc_alignment_control": 0.1478923114397801,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 6,
      "samples": 512,
      "data_covariance_condition": 115.6635330189114,
      "alpha": 3.7440768563556226,
      "noise_variance": 0.023069900854324994,
      "posterior_condition": 149.9772242712996,
      "trace_exact_posterior": 0.000699550307548831,
      "trace_mfvi": 0.00012398054544396884,
      "trace_margin": 0.0005755697621048621,
      "minimum_posterior_direction_margin": 1.433242198980212e-06,
      "maximum_posterior_direction_control": -5.1122178936260445e-05,
      "training_distribution_expected_exact_minus_mfvi": -9.709983505959753e-08,
      "training_distribution_identity_rhs": -9.709983505847238e-08,
      "identity_absolute_error": 1.1251509215293295e-18,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 1.4332421989802002e-06,
      "last_pc_control_margin": -5.1122178936260485e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.013482615711278727,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 7,
      "samples": 512,
      "data_covariance_condition": 2482.172284497143,
      "alpha": 0.0037302869768726403,
      "noise_variance": 0.16564481086817806,
      "posterior_condition": 3328.1032005929906,
      "trace_exact_posterior": 0.0031784842211503694,
      "trace_mfvi": 6.599621054578859e-05,
      "trace_margin": 0.0031124880106045806,
      "minimum_posterior_direction_margin": 8.227021341735784e-07,
      "maximum_posterior_direction_control": -0.0003953956237753415,
      "training_distribution_expected_exact_minus_mfvi": -3.756278683160606e-09,
      "training_distribution_identity_rhs": -3.7562786828342364e-09,
      "identity_absolute_error": 3.2636990094708494e-19,
      "first_pc_min_posterior_alignment": 0.9999999999999997,
      "first_pc_mfvi_minus_exact_margin": 8.227021341737523e-07,
      "last_pc_control_margin": -0.00039539562377534105,
      "nonspherical_prior_first_pc_alignment_control": 0.08259005806404454,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 8,
      "samples": 512,
      "data_covariance_condition": 4571.331377320934,
      "alpha": 1.6333840211818842,
      "noise_variance": 0.2905870823458283,
      "posterior_condition": 5652.413370550646,
      "trace_exact_posterior": 0.0051657254643038795,
      "trace_mfvi": 7.237612828719274e-05,
      "trace_margin": 0.005093349336016687,
      "minimum_posterior_direction_margin": 7.977976285834685e-07,
      "maximum_posterior_direction_control": -0.0006891305426618617,
      "training_distribution_expected_exact_minus_mfvi": -4.721696956858177e-06,
      "training_distribution_identity_rhs": -4.7216969568467445e-06,
      "identity_absolute_error": 1.1432403689091292e-17,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 7.977976285814082e-07,
      "last_pc_control_margin": -0.0006891305426618619,
      "nonspherical_prior_first_pc_alignment_control": 0.14217610803879416,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 9,
      "samples": 512,
      "data_covariance_condition": 19.241429070923477,
      "alpha": 128.1097953036171,
      "noise_variance": 0.03339783516615497,
      "posterior_condition": 29.796734989115986,
      "trace_exact_posterior": 0.0015530762698673394,
      "trace_mfvi": 0.0006884952286334743,
      "trace_margin": 0.0008645810412338652,
      "minimum_posterior_direction_margin": 7.044491938723024e-06,
      "maximum_posterior_direction_control": -7.681431191949883e-05,
      "training_distribution_expected_exact_minus_mfvi": -7.224975873825317e-06,
      "training_distribution_identity_rhs": -7.224975873824708e-06,
      "identity_absolute_error": 6.090166890758419e-19,
      "first_pc_min_posterior_alignment": 0.9999999999999994,
      "first_pc_mfvi_minus_exact_margin": 7.044491938723032e-06,
      "last_pc_control_margin": -7.681431191949877e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.23539022965129622,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 10,
      "samples": 512,
      "data_covariance_condition": 155.09528328337927,
      "alpha": 0.002733172659572637,
      "noise_variance": 104.61604385839385,
      "posterior_condition": 194.3725660233688,
      "trace_exact_posterior": 3.050447450156701,
      "trace_mfvi": 0.45340683783132973,
      "trace_margin": 2.597040612325371,
      "minimum_posterior_direction_margin": 0.004875869148252766,
      "maximum_posterior_direction_control": -0.2313158637283632,
      "training_distribution_expected_exact_minus_mfvi": -0.0014503544129865517,
      "training_distribution_identity_rhs": -0.001450354412986515,
      "identity_absolute_error": 3.664603343001005e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.004875869148252784,
      "last_pc_control_margin": -0.23131586372836344,
      "nonspherical_prior_first_pc_alignment_control": 0.0769405143831327,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 11,
      "samples": 512,
      "data_covariance_condition": 4.401896739833469,
      "alpha": 2.43322868644144,
      "noise_variance": 5.756920290269759,
      "posterior_condition": 7.61841748479173,
      "trace_exact_posterior": 0.41982167017330446,
      "trace_mfvi": 0.3106691431041983,
      "trace_margin": 0.10915252706910616,
      "minimum_posterior_direction_margin": 0.002604719797491498,
      "maximum_posterior_direction_control": -0.010912137613014454,
      "training_distribution_expected_exact_minus_mfvi": -0.0029863243680205527,
      "training_distribution_identity_rhs": -0.002986324368020472,
      "identity_absolute_error": 8.066464163292153e-17,
      "first_pc_min_posterior_alignment": 0.999999999999999,
      "first_pc_mfvi_minus_exact_margin": 0.0026047197974915005,
      "last_pc_control_margin": -0.010912137613014423,
      "nonspherical_prior_first_pc_alignment_control": 0.0684745108515095,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 12,
      "samples": 512,
      "data_covariance_condition": 245.07135582839095,
      "alpha": 0.128098037566907,
      "noise_variance": 0.002066648519337045,
      "posterior_condition": 356.6103992803637,
      "trace_exact_posterior": 5.4850633928632595e-05,
      "trace_mfvi": 6.026933498015237e-06,
      "trace_margin": 4.882370043061736e-05,
      "minimum_posterior_direction_margin": 6.939893128111402e-08,
      "maximum_posterior_direction_control": -5.082210470204744e-06,
      "training_distribution_expected_exact_minus_mfvi": -2.5244677530790568e-11,
      "training_distribution_identity_rhs": -2.5244677618291668e-11,
      "identity_absolute_error": 8.750110066924567e-20,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 6.93989312811134e-08,
      "last_pc_control_margin": -5.0822104702047426e-06,
      "nonspherical_prior_first_pc_alignment_control": 0.16602301305011785,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 13,
      "samples": 512,
      "data_covariance_condition": 615.7429618211618,
      "alpha": 2.6633644041753928,
      "noise_variance": 289.7288834236791,
      "posterior_condition": 280.7733089337887,
      "trace_exact_posterior": 3.773994813195049,
      "trace_mfvi": 0.382185078520338,
      "trace_margin": 3.391809734674711,
      "minimum_posterior_direction_margin": 0.004471544373893724,
      "maximum_posterior_direction_control": -0.23578328653256841,
      "training_distribution_expected_exact_minus_mfvi": -5.111918310982677,
      "training_distribution_identity_rhs": -5.111918310982688,
      "identity_absolute_error": 1.0658141036401503e-14,
      "first_pc_min_posterior_alignment": 0.9999999999999993,
      "first_pc_mfvi_minus_exact_margin": 0.004471544373893741,
      "last_pc_control_margin": -0.23578328653256828,
      "nonspherical_prior_first_pc_alignment_control": 0.16834457441904271,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 14,
      "samples": 512,
      "data_covariance_condition": 91.73294645206741,
      "alpha": 103.71409860843391,
      "noise_variance": 0.004316850226288719,
      "posterior_condition": 135.46100959621523,
      "trace_exact_posterior": 0.00013813613140304602,
      "trace_mfvi": 2.8094596321500672e-05,
      "trace_margin": 0.00011004153508154534,
      "minimum_posterior_direction_margin": 3.199574447810929e-07,
      "maximum_posterior_direction_control": -1.0579418253354563e-05,
      "training_distribution_expected_exact_minus_mfvi": -9.622578382507355e-08,
      "training_distribution_identity_rhs": -9.622578382496227e-08,
      "identity_absolute_error": 1.112789534455337e-19,
      "first_pc_min_posterior_alignment": 0.9999999999999991,
      "first_pc_mfvi_minus_exact_margin": 3.199574447810927e-07,
      "last_pc_control_margin": -1.0579418253354576e-05,
      "nonspherical_prior_first_pc_alignment_control": 0.08329648570505263,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 15,
      "samples": 512,
      "data_covariance_condition": 4.125598914664759,
      "alpha": 0.014964382248846943,
      "noise_variance": 4.487242669594271,
      "posterior_condition": 8.576750323752641,
      "trace_exact_posterior": 0.3472597943870874,
      "trace_mfvi": 0.2589454143197426,
      "trace_margin": 0.08831438006734477,
      "minimum_posterior_direction_margin": 0.002155952140750086,
      "maximum_posterior_direction_control": -0.009668341435240016,
      "training_distribution_expected_exact_minus_mfvi": -1.1582433455731432e-05,
      "training_distribution_identity_rhs": -1.1582433455745072e-05,
      "identity_absolute_error": 1.3640618582583253e-17,
      "first_pc_min_posterior_alignment": 1.0000000000000002,
      "first_pc_mfvi_minus_exact_margin": 0.0021559521407500852,
      "last_pc_control_margin": -0.009668341435240011,
      "nonspherical_prior_first_pc_alignment_control": 0.08348820646405812,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 16,
      "samples": 512,
      "data_covariance_condition": 139.70797066247738,
      "alpha": 2.096311896770444,
      "noise_variance": 0.0011138089123204126,
      "posterior_condition": 182.44295894022005,
      "trace_exact_posterior": 3.2690081227624e-05,
      "trace_mfvi": 5.113981525574697e-06,
      "trace_margin": 2.75760997020493e-05,
      "minimum_posterior_direction_margin": 6.102065485594378e-08,
      "maximum_posterior_direction_control": -2.545365283682027e-06,
      "training_distribution_expected_exact_minus_mfvi": -1.257562178339515e-10,
      "training_distribution_identity_rhs": -1.2575621782133185e-10,
      "identity_absolute_error": 1.2619648370867986e-20,
      "first_pc_min_posterior_alignment": 0.9999999999999996,
      "first_pc_mfvi_minus_exact_margin": 6.102065485594388e-08,
      "last_pc_control_margin": -2.5453652836820273e-06,
      "nonspherical_prior_first_pc_alignment_control": 0.14247617396838574,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 17,
      "samples": 512,
      "data_covariance_condition": 9980.862978340154,
      "alpha": 509.8099230737761,
      "noise_variance": 55.54817325551418,
      "posterior_condition": 173.31562825138013,
      "trace_exact_posterior": 0.055847342266311675,
      "trace_mfvi": 0.006465360048689218,
      "trace_margin": 0.04938198221762246,
      "minimum_posterior_direction_margin": 7.503154680251549e-05,
      "maximum_posterior_direction_control": -0.0018253760342633548,
      "training_distribution_expected_exact_minus_mfvi": -2.7313454003816555,
      "training_distribution_identity_rhs": -2.7313454003816613,
      "identity_absolute_error": 5.773159728050814e-15,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 7.50315468025153e-05,
      "last_pc_control_margin": -0.0018253760342633474,
      "nonspherical_prior_first_pc_alignment_control": 0.07146241818809679,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 18,
      "samples": 512,
      "data_covariance_condition": 1517.9001153867518,
      "alpha": 201.5460851974505,
      "noise_variance": 1.040016771224085,
      "posterior_condition": 1155.685569241368,
      "trace_exact_posterior": 0.01681103131759982,
      "trace_mfvi": 0.0006732639110206895,
      "trace_margin": 0.01613776740657913,
      "minimum_posterior_direction_margin": 6.572236662627584e-06,
      "maximum_posterior_direction_control": -0.001616319918772593,
      "training_distribution_expected_exact_minus_mfvi": -0.006606754974372484,
      "training_distribution_identity_rhs": -0.0066067549743726054,
      "identity_absolute_error": 1.214306433183765e-16,
      "first_pc_min_posterior_alignment": 1.0,
      "first_pc_mfvi_minus_exact_margin": 6.572236662626615e-06,
      "last_pc_control_margin": -0.0016163199187725933,
      "nonspherical_prior_first_pc_alignment_control": 0.08203672120881549,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    },
    {
      "dimension": 64,
      "seed": 19,
      "samples": 512,
      "data_covariance_condition": 298.71849232652863,
      "alpha": 0.024566343341017313,
      "noise_variance": 0.0038343963836765986,
      "posterior_condition": 382.46338748772763,
      "trace_exact_posterior": 9.981220152486885e-05,
      "trace_mfvi": 9.521434345260522e-06,
      "trace_margin": 9.029076717960834e-05,
      "minimum_posterior_direction_margin": 1.0509095604227528e-07,
      "maximum_posterior_direction_control": -8.688096121343243e-06,
      "training_distribution_expected_exact_minus_mfvi": -1.661157856233434e-11,
      "training_distribution_identity_rhs": -1.661157861437133e-11,
      "identity_absolute_error": 5.2036992063999046e-20,
      "first_pc_min_posterior_alignment": 1.0000000000000004,
      "first_pc_mfvi_minus_exact_margin": 1.0509095604227398e-07,
      "last_pc_control_margin": -8.688096121343234e-06,
      "nonspherical_prior_first_pc_alignment_control": 0.01645391203041379,
      "kl_optimizer_relative_error": null,
      "gates": {
        "posterior_trace_exceeds_mfvi": true,
        "mfvi_overestimates_min_direction": true,
        "max_direction_mutation_reverses": true,
        "training_distribution_mfvi_exceeds_exact": true,
        "training_identity": true,
        "first_pc_is_min_posterior_direction": true,
        "first_pc_overestimate": true,
        "last_pc_mutation_reverses": true,
        "nonspherical_prior_breaks_alignment": true
      }
    }
  ]
}