Surprises in High-Dimensional Ridgeless Least Squares Interpolation
Exact asymptotic risk formulas for the min-norm interpolator in both regimes — the canonical companion to the double-descent paper. The lab verified its underparameterized risk blow-up (289x at gamma near 1) and its optimal-ridge comparison.
2supported
0falsified
1inconclusive
3not audited
4model calls
3tool runs
10.6wall min
0failures kept
claims
3 audited · click a claim to open the auditor's own summary — metrics, notes, control status
auditor's notePositive control failed. The risk calculation or simulation setup may be flawed.
control_passFalse
control_rel_error0.4953
all_passfalse
max_rel_error0.9956
n200.0
T300.0
details{"gamma_0.1":{"emp":1.111628528538508,"theo":11.111111111111109,"err":0.8999534324315343},"gamma_0.5":{"emp":2.0090834237202033,"theo":4,"err":0.49772914406994917},"gamma_0.9":{"emp":10.586098193523855,"theo":11.111111111111112,"err":0.047251162582853216},"gamma_1.1":{"emp":11.826619754546464,"theo":10.090909090909083,"err":0.172007363063164},"gamma_2.0":{"emp":2.505223829835358,"theo":1.5,"err":0.6701492198902388},"gamma_5.0":{"emp":2.045209502772495,"theo":1.05,"err":0.9478185740690428},"gamma_10.0":{"emp":2.0178141242538756,"theo":1.011111111111111,"err":0.9956403426686683}}
no per-claim summary in this registry snapshot — verdict preserved from the prior run.
no per-claim summary in this registry snapshot — verdict preserved from the prior run.
no per-claim summary in this registry snapshot — verdict preserved from the prior run.
auditor's noteOptimally-tuned ridge regression achieved lower average risk than min-norm LS for all tested gamma and SNR values in both well-specified and misspecified isotropic settings.
control_passTrue
n100.0
num_trials200.0
snr_values[1,5]
gamma_values[0.5,1.5,3]
lambda_grid[0.0001,0.001,0.01,0.1,1]
all_passtrue
well_specified_snr_1.0_gamma_0.5_avg_mn2.030
well_specified_snr_1.0_gamma_0.5_avg_ridge1.955
well_specified_snr_1.0_gamma_0.5_frac_better1.000
well_specified_snr_1.0_gamma_1.5_avg_mn3.418
well_specified_snr_1.0_gamma_1.5_avg_ridge3.187
well_specified_snr_1.0_gamma_1.5_frac_better1.000
well_specified_snr_1.0_gamma_3.0_avg_mn2.182
well_specified_snr_1.0_gamma_3.0_avg_ridge2.175
well_specified_snr_1.0_gamma_3.0_frac_better1.000
well_specified_snr_5.0_gamma_0.5_avg_mn2.034
well_specified_snr_5.0_gamma_0.5_avg_ridge1.957
well_specified_snr_5.0_gamma_0.5_frac_better0.9950
well_specified_snr_5.0_gamma_1.5_avg_mn4.755
well_specified_snr_5.0_gamma_1.5_avg_ridge4.532
well_specified_snr_5.0_gamma_1.5_frac_better1.000
well_specified_snr_5.0_gamma_3.0_avg_mn4.854
well_specified_snr_5.0_gamma_3.0_avg_ridge4.846
well_specified_snr_5.0_gamma_3.0_frac_better1.000
misspecified_snr_1.0_gamma_0.5_avg_mn3.038
misspecified_snr_1.0_gamma_0.5_avg_ridge2.918
misspecified_snr_1.0_gamma_0.5_frac_better1.000
misspecified_snr_1.0_gamma_1.5_avg_mn4.736
misspecified_snr_1.0_gamma_1.5_avg_ridge4.403
misspecified_snr_1.0_gamma_1.5_frac_better1.000
misspecified_snr_1.0_gamma_3.0_avg_mn2.570
misspecified_snr_1.0_gamma_3.0_avg_ridge2.559
misspecified_snr_1.0_gamma_3.0_frac_better1.000
misspecified_snr_5.0_gamma_0.5_avg_mn7.081
misspecified_snr_5.0_gamma_0.5_avg_ridge6.806
misspecified_snr_5.0_gamma_0.5_frac_better1.000
misspecified_snr_5.0_gamma_1.5_avg_mn11.57
misspecified_snr_5.0_gamma_1.5_avg_ridge10.77
misspecified_snr_5.0_gamma_1.5_frac_better1.000
misspecified_snr_5.0_gamma_3.0_avg_mn6.932
misspecified_snr_5.0_gamma_3.0_avg_ridge6.905
misspecified_snr_5.0_gamma_3.0_frac_better1.000
auditor's noteRisk at gamma=0.999 is 2396.0423, at gamma=0.9 is 8.2868. Ratio: 289.14. Monotonic: True. Control passed: True.
risk_0.98.287
risk_0.9525.22
risk_0.99147.2
risk_0.9992396
ratio_0999_to_09289.1
criterion_1_passtrue
monotonic_passtrue
control_passtrue
control_risk_0.53.515
figure evidence
the trail
4 model calls · 3 tool runs · 10.6 min wall · append-only, failures preserved
0:00