Zero-Shot Beamforming for RIS Systems via Differentiable RZF

Reconfigurable Intelligent Surfaces (RIS) are an effective solution for improving wireless coverage under severe blockage. However, existing deep learning-based methods usually require extensive offline training and suffer from limited generalization, while conventional optimization approaches may incur high computational complexity. This paper proposes a model-driven online gradient descent (MD-OGD) method for RIS-assisted multiple-input single-output (MISO) systems. A joint design framework is considered, where the active beamforming is computed via a closed-form regularized zero-forcing (RZF) solution, and the passive RIS beamforming is optimized online to maximize the system sum-rate under Rician fading channels. By embedding a differentiable regularized zeroforcing (RZF) layer into the optimization process, the proposed approach enables a training-free and interpretable beamforming framework. A manifold-based parameterization is adopted to satisfy the unit-modulus constraint of RIS elements. Simulation results show that the proposed method outperforms random phase configurations and non-RIS benchmarks. At a transmit power of 30 dBm, a sum-rate of $21.48 \text{bps} / \text{Hz}$ is achieved, demonstrating the potential effectiveness of the proposed zero-shot beamforming approach.