Spec${}^2$: Efficient VLA Control through Action Decoding and Propagation

Vision‑language‑action (VLA) models have demonstrated strong capabilities in language‑conditioned robotic manipulation, but their high inference cost limits the frequency and responsiveness of closed‑loop control. The computational burden stems from two components: sequential action generation within each VLA inference and repeated multimodal evaluation over successive observations. To address both sources of overhead, we present Spec${}^2$, a unified framework that reduces action‑decoding overhead and the frequency of redundant VLA inference while keeping the base VLA frozen. Verified Action Block Decoding first checks the previous VLA action as a complete candidate and, after the first mismatch, uses a separately trained noncausal proposal module to propose the unresolved suffix in parallel. The frozen VLA verifies all candidates with the same exact acceptance rule, reducing serial decoding overhead without relaxing token acceptance. Visuomotor‑Gated Action Propagation selectively propagates VLA actions across adjacent control steps according to visual consistency and motion mode consistency, without requiring an additional learned action model. Because propagation alters the physical trajectory, we introduce closed‑loop recoverability to characterize whether subsequent feedback can preserve the task outcome. Extensive experiments show that \method achieves a 2.7$\times$ mean inference speedup on LIBERO, with an average success rate 1.6 percentage points below OpenVLA. Paired closed‑loop evaluations observe successful recovery in more than 92% of evaluated futures. The propagation mechanism also generalizes to the continuous‑action CogACT policy, yielding about 1.7$\times$ acceleration on SimplerEnv. Moreover, in real‑robot evaluations, \method achieves a 2.6$\times$ inference speedup and improves aggregate success from 73.3% to 81.3%.