In-Context Learning Is Provably Bayesian Inference
ICL-as-Bayesian-inference theory: the risk-decomposition identity and coupled p-N scaling of the Bayes gap verified numerically; the posterior-variance bound honestly inconclusive under finite precision.
3supported
2falsified
2inconclusive
0not audited
50model calls
109tool runs
18.8wall min
49failures kept
claims
7 audited · click a claim to open the auditor's own summary — metrics, notes, control status
auditor's noteClosed-form verification of Proposition 3.1 (R = RBG + RPV) on a two-family linear-task mixture (families distinguished by an intercept). MAIN predictor: task-1-only oracle (RBG_main > 0); CONTROL: Bayes predictor. Reviewer-provided reference implementation, executed by the audit pipeline.
R_main0.4891
RBG_main0.2882
RPV_main0.1990
rel_diff0.004006
R_ctrl0.1996
RPV_ctrl0.1990
rel_diff_ctrl0.003026
RBG_main_nonzerotrue
control_passtrue
M5000
p10.00
auditor's noteJoint R2=0.629, N-only R2=0.095, p-only R2=0.618. Criterion requires joint>0.8 and >0.1 above both single-variable models.
r2_joint0.6286
r2_n_only0.09538
r2_p_only0.6180
joint_a0.7133
joint_b14.48
joint_beta0.3215
joint_c-72.03
bg_values[1.909620166007698,1.6266746091631543,1.5864427176699258,1.0749929518957455,1.6698792569795113,1.5561045686113608,1.2763619554616676,1.134906320641344,1.4718270644863458,1.6167406594628477,1.3780500098689799,0.98726679838197,1.5211791175567937,1.601825030518865,1.2101026397469168,1.0523888687105654]
bg_mc_stderr_max0.09582
control_r20.9866
control_beta_recovered0.6177
control_beta_true0.5000
control_passtrue
auditor's noteClosed-form verification of the Theorem-3.3 mechanism on the paper's task-mixture class (linear vs degree-2 Hermite families, Definition 2.1): the mixture posterior concentrates on the true task and the Bayes-optimal mixture predictor converges to the true-family oracle, ratio(k) = excess_mix/excess_oracle >= 1 (Rao-Blackwell) decreasing to 1. The Transformer training experiment of Sec 4 needs GPU training and is out of CPU-audit scope; this verifies the Bayesian mechanism it demonstrates. Reviewer-provided reference implementation.
mean_p_true_50.7674
mean_p_true_150.9280
ratio_11.114
ratio_51.187
ratio_151.024
slope_ratio-0.02115
r_squared0.9016
control_ratio_is_1true
control_p_true_is_1true
control_passtrue
checks{"p_true_5_ge_0.7":true,"p_true_15_ge_0.9":true,"ratio_15_le_1.05":true,"p_true_in_01":true,"ratio_ge_1":true,"ratio_tail_decreasing":true,"ratio_tail_r2_gt_0.7":true,"control_pass":true}
auditor's notepN slope=-0.826, R2=0.995. m-fit R2=0.985, min_in_grid=True. Control pass=True.
slope_pN-0.8260
r2_pN0.9952
p_val_pN0.000008598
r2_fit0.9854
m_min13.71
min_in_gridtrue
control_slope-1.092
control_r20.9951
control_passtrue
auditor's notescript failed after 4 tries
script_exit_code1.000
attempts_used4.000
auditor's notePositive control failed; estimator unreliable.
C_chernoff0.3466
D_min2.000
minimax_risk1.000
excess_k10.6185
excess_k100.01520
excess_k300.000001033
frac_k_violating_C_bound0.000
max_ratio_excess_over_boundC0.2187
n_significant_increases0.000
tail_decay_rate_lambda_hat0.6779
control1_passtrue
control2_passfalse
control_passfalse
auditor's noteClaim falsified. Spearman rho=0.12, Mean CV=0.58.
spearman_rho0.1229
mean_within_pN_cv0.5758
control_spearman_rho-0.9358
control_mean_cv0.01167
control_passtrue
n_grid_points12.00
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 (6 claims), audit_report.json present
evidence6 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
trace267 events, 33 LLM calls, 95 tool runs, 15 failed attempts preserved
figure evidence
the trail
50 model calls · 109 tool runs · 18.8 min wall · append-only, failures preserved
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