What Makes Two Robot Failures the Same? Learning Recoverability Functions for Zero-Shot Robot Recovery

Robotic recovery depends on a question that semantic failure labels do not directly answer: which corrective intervention will restore task progress from the current failed state? We introduce the recoverability function $F_{\tau }(u)=P(\mathrm{success}\mid s_{t_0},u,{\pi }_c)$, which characterizes a natural failure trajectory $\tau$ by its response over a parameterized space of corrective interventions. RepairSpace learns an ordinal functional geometry in which nearby failures exhibit similar recoverability profiles, together with an intervention-conditioned predictor that estimates responses for unexecuted corrections. Recovery is performed by cost-constrained optimization over the predicted response surface. Across LIBERO-40 and RLBench-30, covering 70 tasks, 28,000 natural failures, three policy families, and 4.24M main-protocol recovery rollouts, RepairSpace reaches 0.824 success on unseen tasks and recovers 80.3% of failure-specific routing headroom. Under strictly matched supervision, the same 118M-parameter architecture improves unseen-task SR from 0.798 to 0.821 and cross-policy SR from 0.774 to 0.802. Its learned distance predicts held-out intervention transfer with correlation 0.842, compared with 0.694 for the matched full-trajectory response predictor. On held-out VLA-policy failures from unseen tasks, RepairSpace reaches 0.827 mean recovery success, compared with 0.784 for FLARE and 0.734 for REFLECT. The representation transfers across failure-generating policy families (0.806 success) and reaches 0.850 recovery success over eight real-robot failure configurations. Together, these results support recoverability as a functional coordinate system that connects failure representation to corrective action.