גאומטריה מוחלטת של תגובה אחת-צעד: תוקף-על-מסלול והתנאי-קרבורה-חתום

תקציר מקורי באנגליתarXiv:2609.36252v2 Announce Type: replace Abstract: Closed-form recourse moves a rejected user along the unit gradient $\hat g$ of the classifier score $f$ by the promised distance $d_p=|f(x)|/\|\nabla f(x)\|$, at which the linearized score reaches zero. We ask when this one-shot step succeeds and what additional model queries change. To leading order the step ends on the favorable side exactly when the path curvature $\kappa=\hat g^\top\nabla^2 f(x)\,\hat g$ is nonnegative. Across 80 shallow models, the fraction of rejected users whose step ends there and the fraction with $\kappa\ge0$ correlate at $r=0.985$, although on Fashion-MNIST the first falls below the second by 8.2 points on average. No rule that uses only the score value and gradient can be valid for every score with path curvat