| { |
| "arxiv_revision": "2605.17126v1", |
| "counts": { |
| "balancedness_examples.csv": 3, |
| "glm_favorable_transfer.csv": 8, |
| "glm_grid.csv": 45, |
| "infinite_B_controls.csv": 256, |
| "intrinsic_fallback.csv": 600, |
| "linear_safety.csv": 216, |
| "literal_claim_evidence.csv": 6, |
| "objective_structures.csv": 4, |
| "optimization_diagnostics.csv": 373, |
| "outlier_radius_sweep.csv": 6, |
| "population_comparability.csv": 1200, |
| "source_pins.csv": 4, |
| "spectrum_collapse.csv": 6, |
| "transfer_delta_scaling.csv": 10, |
| "transfer_epsilon_scaling.csv": 6, |
| "transfer_m_scaling.csv": 6 |
| }, |
| "gates": { |
| "arbitrary_outlier_control": true, |
| "balancedness_without_rho": true, |
| "delta_squared_law": true, |
| "epsilon_squared_law": true, |
| "glm_direct": true, |
| "glm_mvt_exact": true, |
| "glm_transfer_direct": true, |
| "infinite_B_control": true, |
| "intrinsic_fallback_direct": true, |
| "joint_convexity": true, |
| "linear_safety_direct": true, |
| "nu_destructive_control": true, |
| "nuisance_blind": true, |
| "objective_prediction_space": true, |
| "one_over_m_law": true, |
| "optimizer_objectives_decrease": true, |
| "population_comparability_direct": true, |
| "registered_algorithm_executed": true, |
| "six_registered_claims_exact": true, |
| "source_assets_exact": true |
| }, |
| "paper_id": "D5Ijcnz1L9", |
| "registered_claims": [ |
| "Theorem 2 establishes an in-sample MSE bound for each task j that guarantees safety, \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 q\u00b2(d/n)\u03b6 regardless of the balancedness constant B, outlier fraction \u03b5, or heterogeneity \u03b4 (Section 5.1, Theorem 2).", |
| "Theorem 2 also shows a transfer guarantee for inlier tasks when B \u2272 min(1/\u03b5, m): \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 (Bd/mn + min(B\u03b4\u00b2, d/n) + B\u00b2\u03b5\u00b2d/n)\u03b6, achieved without knowing \u03b5, \u03b4, or the inlier set S (Section 5.1, Theorem 2).", |
| "Assumption 1 (Balancedness) replaces the classical Lower Boundedness of Second Moments condition \u03c1I \u2aaf \u03a3\u2c7c with the one-sided condition \u03a3\u2c7c \u2aaf B\u00b7\u03a3_S, accommodating rank-deficient or decaying covariate spectra where prior eigenvalue-lower-bound approaches (e.g. Duan & Wang 2023, depending on 1/\u03c1\u00b2) fail (Section 4, Assumption 1).", |
| "Theorem 3 extends the in-sample MSE guarantees of Theorem 2 to population risk via an empirical-to-population comparability constant \u03bd\u2c7c, retaining an intrinsic-dimension fallback for the safety guarantee (Section 5.2, Theorem 3).", |
| "Theorem 4 extends the same adaptive safety/transfer MSE guarantees to generalized linear models under bounded-domain assumptions (Section 6, Theorem 4).", |
| "Algorithm 1 solves a joint convex objective \u2112(\u0398)=\u03a3\u2c7c w\u2c7c(f\u2c7c(\u03b8\u2c7c)+\u03bb\u2c7c\u2016\u03b8\u2c7c-\u03b2\u2016_{\u03a3\u2c7c}) that penalizes disagreement in prediction space (via task-specific norms) rather than raw parameter space (Section 3, Algorithm 1)." |
| ], |
| "scope": "Direct finite Algorithm 1 experiments at the paper's native synthetic dimensions plus exact algebra; no finite run is presented as a universal proof.", |
| "summary": { |
| "convexity_violations": 0, |
| "degenerate_balancedness_pairs": 14197, |
| "delta_squared_r2": 1.0, |
| "delta_squared_slope": 1.9999999999999996, |
| "epsilon_squared_r2": 0.9992608122163799, |
| "epsilon_squared_slope": 2.1474761241097524, |
| "glm_configs": 45, |
| "intrinsic_fallback_pairs": 600, |
| "intrinsic_fallback_violations": 0, |
| "large_delta_mse": 3.1603965096785505, |
| "large_delta_over_safety_scale": 1.0611905374630106, |
| "linear_safety_configs": 216, |
| "linear_tasks_evaluated": 6480, |
| "m_scaling_r2": 0.9983439676342425, |
| "m_scaling_slope": -1.0086816250389234, |
| "max_balancedness_closed_form_error": 0.0, |
| "max_glm_mvt_ratio": 0.06192957643612639, |
| "max_glm_safety_ratio": 1.6494871421278146, |
| "max_linear_safety_ratio": 1.409812905125891, |
| "max_prediction_norm_identity_error": 1.1546319456101628e-14, |
| "median_glm_itl_over_mtlr": 17.234969116944626, |
| "naive_nu_one_failures": 1119, |
| "nullspace_checks": 3500, |
| "pooling_ratio_at_radius_100000": 3672340790.1570725, |
| "population_comparability_violations": 0, |
| "population_pairs": 1200 |
| } |
| } |
|
|
