A Semi-amortized Lifted Learning-to-Optimize Masked (SALLO-M) Transformer Model for Scalable and Generalizable Beamforming

Abstract

We develop an unsupervised deep learning framework for real-time scalable and generalizable downlink beamforming in multi-user multiple-input single-output (MU-MISO) systems. The proposed semi-amortized lifted learning-to-optimize (SALLO) framework employs a multi-layer Transformer to iteratively refine an auxiliary variable and the beamformer solution, with a few projected gradient ascent steps at each layer. A key feature of our SALLO Transformer model is that it can handle varying numbers of users and antennas, enabled by a user-antenna dual tokenization and a structured sample/attention masking scheme, leading to generalization across different configurations without retraining. To improve convergence and robustness, we introduce three training strategies: (a) sliding-window training to stabilize gradient propagation, (b) curriculum learning with random masking to enable user-antenna configuration generalization and prevent poor early-stage convergence, and (c) sample replay to mitigate catastrophic forgetting during multi-stage training. Ablation studies validate several key architecture designs and show that the enhanced training scheme improves both generalizability and solution quality. Simulation results over both Gaussian and sparse channels show that the proposed scheme consistently outperforms existing deep learning baselines across diverse system configurations and channel conditions. The performance gain becomes more pronounced in overloaded regimes, highlighting improved robustness under challenging scenarios. Furthermore, our scheme surpasses the WMMSE benchmark in underloaded systems and even in overloaded systems when the overloading factor is below certain threshold. These gains are achieved with fast inference and a substantially more lightweight model than wireless foundation models.