Act on the Low Frequencies: Prefix Execution of Vision-Language-Action Chunks

Vision-language-action policies predict chunks of robot controls and ship every chunk in full, and how much of a chunk a robot needs to finish its task has remained unmeasured in closed loop. We introduce frequency-prefix execution (FPE), a training-free scheme that transforms each finished chunk into a temporal cosine basis, transmits a fixed number of its lowest-frequency rows, and lets the robot reconstruct and execute the whole chunk under the unchanged policy, horizon and replanning schedule. The basis makes the discarded detail exactly accountable: the reconstruction error of a prefix equals the energy of the omitted rows, and under a contraction condition the accumulated state deviation stays within the largest single-chunk residual. On the official LIBERO protocol with OpenVLA-OFT, two cosine rows keep 98.8% success on Spatial against 98.6% for quantized full codes at 54% of the native payload, and four rows keep 92.6% against 92.2% on LIBERO-10 at 72% of the payload, both passing a registered non-inferiority test. On Goal the tolerance to truncation follows the task, which motivates PairGap, a shortest-path certificate that bounds, at a single restored state, the regret of executing a prefix against the best option in a fixed bank of prefixes and full codes. Together they show that a robot can act on a fraction of each predicted chunk, and they identify the tasks and states that call for the full code.