Neural behavior cloning compresses demonstrations into large models, making individual actions difficult to trace and policy updates costly. Retrieval policies retain access to demonstrations but struggle with mismatch between recorded and live behavior. We introduce Behavior Predictive Control (BPC), which synthesizes policies without end-to-end policy training by combining an action-aware retrieval metric, a Hankel-based action-continuation prior, and a closed-form one-step residual correction. Inspired by behavioral systems theory, BPC predicts future actions by blending stored observation-action data that best reconstructs the recent runtime observation--action history. Across simulated benchmarks and real-robot deployments, BPC is competitive with learned policies such as $π_{0.5}$ (surpassing it in some cases), while reducing policy fitting from hours to seconds on consumer GPUs and supporting closed-loop control upwards of 75 Hz on a Jetson Orin Nano. The retrieved demonstration windows and their coefficients also provide an intrinsic estimate of task progress. Retaining demonstrations within the deployed policy makes its predictions traceable to supporting trajectories and enables behavior revision through the demonstration bank.

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