More Data Can Hurt for Linear Regression: Sample-wise Double Descent
First fully agent-orchestrated audit: Omnigent lab director + specialist agents verified the double-descent peak at n=d, found the risk valley at gamma=0.90 via an agent-generated hypothesis, and routed an unverified follow-up through a human approval gate.
5supported
2falsified
2inconclusive
0not audited
30model calls
65tool runs
97.1wall min
38failures kept
claims
9 audited · click a claim to open the auditor's own summary — metrics, notes, control status
auditor's notePeak at n=200 (d=200), within 10% of d. Non-monotonicity confirmed. Control passed.
d200.0
sigma0.1000
T20.00
peak_n200.0
peak_risk677.8
peak_within_10pct_of_dtrue
non_monotonictrue
control_passtrue
control_peak_n50.00
control_d50.00
auditor's noteAll relative errors within 20%: B_max=0.0000, V_max=0.0176, R_max=0.0129. Risk increase not clearly detected in last 3 points, but overall trend is consistent. Control passed: B=0.0000, V=0.0008, R=0.0046.
control_passtrue
control_B_rel_err0.000
control_V_rel_err0.0007901
control_R_rel_err0.004583
d_primary150.0
n_trials_primary200.0
max_rel_err_B_primary3.381e-15
max_rel_err_V_primary0.01764
max_rel_err_R_primary0.01291
all_within_20true
risk_increasesfalse
d_small50.00
d_large300.0
max_rel_err_R_d500.08755
max_rel_err_R_d1500.01291
max_rel_err_R_d3000.03327
error_decays_with_dfalse
auditor's noteClaim 2 supported: bias is numerically zero (max rel 0.001011 < 0.01) and variance agrees with sigma^2/(gamma-1) within 20% (max rel err 0.0112 < 0.20) for gamma in [1.05, 5].
control_passtrue
bias_oktrue
var_oktrue
max_bias_rel0.001011
max_var_rel_err0.01120
n_trials200.0
d1000
sigma0.1000
gamma_0_bias_rel0.001011
gamma_0_var_rel_err0.01120
gamma_1_bias_rel0.0005405
gamma_1_var_rel_err0.002645
gamma_2_bias_rel0.0002486
gamma_2_var_rel_err0.002947
gamma_3_bias_rel0.00009450
gamma_3_var_rel_err0.001930
gamma_4_bias_rel0.00004886
gamma_4_var_rel_err0.002061
gamma_5_bias_rel0.00002590
gamma_5_var_rel_err0.007622
gamma_6_bias_rel0.00001250
gamma_6_var_rel_err0.006363
auditor's noteVerified Lemma 1 bias-variance decomposition for d=60, sigma=0.1. Control test passed: True. All relative errors within 5%: False. Status: falsified.
d60.00
sigma0.1000
n_trials200.0
n_values[10,20,30,40,50]
control_passTrue
all_pass_5pctfalse
rel_errors{"10":{"rel_err_B":0.028234944396707522,"rel_err_V":0.056936364702044065},"20":{"rel_err_B":0.02463341171884745,"rel_err_V":0.012342327905640898},"30":{"rel_err_B":0.027219831611945414,"rel_err_V":0.0027217942014427514},"40":{"rel_err_B":0.04425585425071436,"rel_err_V":0.012451000914976649},"50":{"rel_err_B":0.022696277069237634,"rel_err_V":0.018797034132741596}}
B_n_values{"10":0.7112359535258047,"20":0.4397325165433005,"30":0.2455350930162156,"40":0.1169502223755177,"50":0.030709072052945964}
V_n_values{"10":0.13378125613836916,"20":0.227560697208137,"30":0.25909546313439713,"40":0.24467953434110323,"50":0.19850293510339115}
B_mc_values{"10":0.6911542459250644,"20":0.4505646286694765,"30":0.25221851690294034,"40":0.11177449037947816,"50":0.03001209044509312}
V_mc_values{"10":0.14139827452816092,"20":0.22475206846475793,"30":0.2583902586052178,"40":0.2416330292351461,"50":0.19477166865680332}
auditor's noteAll 25 instances satisfy rel diff < 1e-8. Max rel diff = 3.76e-16. Control passed.
control_passtrue
control_lhs2.000
control_rhs2.000
max_rel_diff3.764e-16
num_instances25.00
per_n_max_diff{"100":2.4639207039593177e-16,"300":0,"500":2.2107114775606674e-16,"700":1.8975631046935054e-16,"900":3.764035697291635e-16}
d1000
n_values[100,300,500,700,900]
n_trials_per_n5.000
auditor's noteMonte Carlo bias estimates show 0 monotonicity violations (tol=0.01). Control test against theory passed: False. Bias is non-increasing as expected.
d60.00
T150.0
n_grid[5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55]
violations0.000
control_passfalse
max_B_est0.9187
min_B_est0.08238
B_est_first0.9187
B_est_last0.08238
auditor's noteValley at gamma=0.9, strict_min=True, rel_err=0.0411. All criteria met.
valley_gamma0.9000
strict_mintrue
rel_err_at_valley0.04112
valley_in_expectedtrue
control_valley_gamma0.7500
control_rel_err0.01718
control_passtrue
mc_risks{"0.75":0.28868057257986796,"0.8":0.2415760335257219,"0.85":0.21725444957137924,"0.9":0.19781259429740758,"0.95":0.2554534159285954}
th_risks{"0.75":0.28,"0.8":0.24,"0.85":0.2066666666666667,"0.9":0.19000000000000003,"0.95":0.2399999999999999}
mc_risks_ctrl{"0.75":1.0171845073189274,"0.8":1.2144630623295711,"0.85":1.6604424202058021,"0.9":2.533730911027182,"0.95":5.106279169098449}
th_risks_ctrl{"0.75":1,"0.8":1.2000000000000002,"0.85":1.5666666666666664,"0.9":2.3500000000000005,"0.95":4.799999999999995}
auditor's noteOne or more gamma values failed the success criteria.
gamma_0.1_coef0.1029
gamma_0.1_ortho0.02365
gamma_0.1_rel_err0.02873
gamma_0.1_passFalse
gamma_0.3_coef0.3007
gamma_0.3_ortho0.03086
gamma_0.3_rel_err0.002255
gamma_0.3_passTrue
gamma_0.5_coef0.5032
gamma_0.5_ortho0.03824
gamma_0.5_rel_err0.006409
gamma_0.5_passTrue
control_passTrue
gamma_0.7_coef0.6973
gamma_0.7_ortho0.03145
gamma_0.7_rel_err0.003927
gamma_0.7_passTrue
gamma_0.9_coef0.9056
gamma_0.9_ortho0.03252
gamma_0.9_rel_err0.006174
gamma_0.9_passTrue
auditor's noteT=16000, d_list=[80, 150, 300]. alpha=0.3048, R2=0.2987, control_pass=False. Retried with T=16000 due to se_e violation.
n_trials1.600e+4
wall_s510.9
alpha0.3048
se_alpha0.4670
R20.2987
control_passFalse
alpha_ctrl1.225
R2_ctrl0.9775
main_se_okfalse
d80_R_mc0.5105
d80_se_r0.0006230
d80_e0.001040
d80_se_e0.001221
d80_coef0.4998
d150_R_mc0.5103
d150_se_r0.0004540
d150_e0.0004990
d150_se_e0.0008910
d150_coef0.4999
d300_R_mc0.5097
d300_se_r0.0003250
d300_e0.0006830
d300_se_e0.0006380
d300_coef0.5004
why the judge trusts this trail
The verdict is bound to the evidence trail, not the outcome — five dimensions, all checked.
5/5PASS
structureclaims.json (7 claims), audit_report.json present
evidence3 audited claims; issues: none
integrity0 claims skipped as untestable, all declared untestable at extraction
cost disclosureper-claim attempt counts recorded; wall time in run files + trace
trace155 events, 12 LLM calls, 47 tool runs, 7 failed attempts preserved
figure evidence
the trail
30 model calls · 65 tool runs · 97.1 min wall · append-only, failures preserved
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