# Deep Complex-valued Neural-Network Modeling and Optimization of Stacked Intelligent Surfaces

## TL;DR

This paper introduces a complex-valued neural network framework for configuring stacked intelligent surfaces in multi-antenna systems, enabling adaptable, high-performance wavefront control that surpasses traditional methods.

## Contribution

It develops a novel CV-NN approach modeling SIS elements as complex neurons, allowing end-to-end optimization without channel orthogonality constraints, and demonstrates superior performance over existing schemes.

## Key findings

- Outperforms state-of-the-art in throughput and error rate.
- Enables rapid, near-online adaptation for high-dimensional channels.
- Recovers classical SVD solutions as a special case.

## Abstract

We propose a complex-valued neural-network (CV-NN) framework to optimally configure stacked intelligent surfaces (SIS) in next-generation multi-antenna systems. Unlike conventional solutions that separately tune analog metasurface phases or rely strictly on SVD-based orthogonal decompositions, our method models each SIS element as a unit-modulus complex-velued neuron in an end-to-end differentiable pipeline. This approach avoids enforcing channel orthogonality and instead allows for richer wavefront designs that can target a wide range of system objectives, such as maximizing spectral efficiency and minimizing detection errors, all within a single optimization framework. Moreover, by exploiting a fully differentiable neural-network formulation and GPU-based auto-differentiation, our approach can rapidly train SIS configurations for realistic, high-dimensional channels, enabling near-online adaptation. Our framework also naturally accommodates hybrid analog-digital beamforming and recovers classical SVD solutions as a special case. Numerical evaluations under Rician channels demonstrate that CV-NN SIS optimization outperforms state-of-the-art schemes in throughput, error performance, and robustness to channel variation, opening the door to more flexible and powerful wave-domain control for future 6G networks.