Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model

arXiv:2610.00424v1 Announce Type: cross Abstract: Knowing how much a causal predictor could improve need not reveal the gain of the repair actually learned. We quantify this gap in a scalar Gaussian causal experiment with known intervention geometry: auxiliary data identify effect magnitude up to bounded contamination, while diagnostics identify direction. The target is the squared-loss gain of the realized trained repair relative to a fitted reference. Jointly optimizing the learner and assessor under uniform learning MSE eta avoids the trivial solution of making no repair. At the usual 1/k learning scale, every feasible learner incurs a k^{-2} assessment floor, even when oracle potential is estimable at a faster rate. In the magnitude-rich regime, we characterize a sharp leading-log frontier: the assessment exponent is min{ell_k,2keta_k/U} to first relative order, where ell_k=log(1/(k^2E_k)) and E_k is auxiliary precision. A diagnostic-abstention rule attains this exponent with unknown nuisance parameters. We also bound the critical allowance window and transfer the frontier to adaptive sampling by exact Gaussian simulation. Finite-grid experiments distinguish sign-tail suppression from total MSE and expose conservative finite-budget behavior. The result isolates how the assessment target changes information requirements in this experiment; it is not a general causal identifiability claim.

Related

• Emergent Causal-Geometric Dynamics Across Depth in Large Language Models
• Fourier Feature Methods for Nonlinear Causal Discovery: FFML Scoring, TRFF Scoring, and FFCI Testing in Mixed Data
• Conditional Co-Ablation: Recovering Self-Repair Backups in Transformer Circuits

Source: arXiv cs.AI | 2026-10-02