The Signed Geometry of One-Shot Recourse: On-Path Validity and the Signed-Curvature Criterion
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 $κ=\hat g^\top\nabla^2 f(x)\,\hat g$ is nonnegative. Across 80 shallow models, the fraction of rejected users whose step ends there and the fraction with $κ\ge0$ 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 ...
| Authors | Hazar Yueksel |
|---|---|
| Primary category | cs.LG |
| Published | 28 September 2026 |
| Last updated at source | 6 October 2026 |
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