Millimeter-wave (mmWave) beam alignment plays a critical role in next-generation wireless systems, yet its efficient implementation remains challenging. Meta-learning and transfer learning have been explored to enable deep learning-based beam prediction models to rapidly adapt to unseen environments; however, existing meta-learning approaches adapt the entire network and are trained from random initialization, leading to a large number of updated parameters and a high meta-training cost, while transfer learning approaches restrict adaptation to part of the network but do not exploit episodic meta-learning, which explicitly trains the model over multiple tasks, to optimize the adaptation process itself. To overcome these limitations, we propose MTL-BA, a meta-transfer learning framework for beam alignment in millimeter-wave multiple-input single-output (MISO) systems that freezes a pre-trained convolutional backbone and meta-learns only lightweight Scale-and-Shift (SS) adapters together with a classifier head. Warm-starting from the pre-trained model and restricting adaptation to the SS adapters and classifier head reduce both the adaptation cost and the meta-training budget without sacrificing prediction performance. Simulation results on the DeepMIMO ray-tracing dataset show that MTL-BA matches the accuracy and spectral efficiency of full fine-tuning across various SNR levels despite updating approximately $17\times$ fewer parameters than both full fine-tuning and Model-Agnostic Meta-Learning (MAML), outperforms last-layer fine-tuning while updating a comparable number of parameters, and approaches MAML's performance while requiring $60\%$ fewer meta-training epochs.

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