בחירת נתונים משוקללת: צידוד עליון-חצי וחוקי-5 ממדים

תקציר מקורי באנגליתarXiv:2610.00101v1 Announce Type: cross Abstract: How much risk does a small reweighted training support retain? For finite weighted least squares with the minimum-norm learner, we prove the exact law $\Gamma_d(n)=3-n/d$ throughout $\lceil3d/2\rceil\leq n\leq2d-1$. The guarantee covers every observed feature rank and uses selections that preserve the full feature span. Balanced simplex anchors reduce dimension; positive-weight lifting and independent-line compression close the risk bound. Shifted coordinate pairs attain the matching lower bound. The complete dataset-level upper bound and sharpness construction are verified in Lean 4. At the smaller budget $(d,n)=(5,6)$, we also prove $\Gamma_5(6)=11/5$, matching the simplex-block prediction from $5=3+2$ over arbitrary interacting configura