Array calibration is critical to achieving accurate beamforming in millimeter-wave (mmWave) antenna-in-package (AiP) phased arrays, where over-the-air (OTA) calibration in ALL-ON mode is a standard requirement. For practical calibration measurements, two core metrics are paramount: efficiency (defined by measurement time) and reliability (robustness, governed by the condition number of the phased array calibration codebook). In this work, we propose a neural network-enabled codebook generation method for phased array calibration compatible with arrays of arbitrary sizes. Codebooks generated via the proposed method achieve low condition numbers while requiring the minimum number of measurements, outperforming state-of-the-art calibration approaches. Practical measurements on a 26-GHz AiP phased array validate the effectiveness and robustness of the proposed method, with superior performance in both array calibration accuracy and beamforming quality.