Vision-language-action (VLA) policies have demonstrated strong generalization in robotic manipulation, yet processing dense visual tokens often incurs high inference latency. Visual token pruning offers a practical way to reduce this cost, but identifying a compact set of tokens that preserves reliable action generation remains challenging. Existing methods largely rely on static or immediate heuristic cues to estimate token importance. We introduce APS-VLA, a framework that learns visual token selection from robot demonstrations while keeping the pretrained VLA backbone frozen. A lightweight Decision Influence Estimator scores tokens conditioned on current visual observations, language instructions, and robot proprioception. Its training combines two complementary signals: action supervision matches both the full-input policy predictions and demonstrated actions, while an auxiliary visual transition objective uses demonstrated actions to predict subsequent visual features from the selected representation. At deployment, the estimator performs a single hard selection and packing step before the policy's native action-generation procedure; the auxiliary predictor is removed. Experiments with OpenVLA-OFT on LIBERO and with $π_{0.5}$ and XR-1 on RoboCasa365 demonstrate inference acceleration with modest changes in task success. Across five real-world tasks on two dual-arm platforms, APS-VLA reduces mean policy inference latency from 137.25 to 93.25 ms, achieving a $1.47\times$ speedup with an average success rate of 61%, compared with 60% for the unpruned baseline. Together, these results support APS-VLA as a modular, plug-in framework for efficient robotic control across VLA architectures, preserving the underlying policy parameters and native action-generation procedure.

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