# Beyond-Diagonal RIS Under Non-Idealities: Learning-Based Architecture Discovery and Optimization

arXiv: https://arxiv.org/abs/2510.15701 · HTML: https://mlsanity.com/paper/2510.15701/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 39 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive Beamforming](https://mlsanity.com/paper/1810.03961/) (2018)
- [Active RIS vs. Passive RIS: Which Will Prevail in 6G?](https://mlsanity.com/paper/2103.15154/) (2021)
- [Pay Less But Get More: A Dual-Attention-based Channel Estimation Network for Massive MIMO Systems with Low-Density Pilots](https://mlsanity.com/paper/2303.00986/) (2023)
- [Modeling and Architecture Design of Reconfigurable Intelligent Surfaces Using Scattering Parameter Network Analysis](https://mlsanity.com/paper/2011.11362/) (2020)
- [Beyond Diagonal Reconfigurable Intelligent Surfaces: From Transmitting and Reflecting Modes to Single-, Group-, and Fully-Connected Architectures](https://mlsanity.com/paper/2205.02866/) (2022)
- [Low-Overhead Channel Estimation via 3D Extrapolation for TDD mmWave Massive MIMO Systems Under High-Mobility Scenarios](https://mlsanity.com/paper/2406.08887/) (2024)
- [Discrete-Value Group and Fully Connected Architectures for Beyond Diagonal Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2110.00077/) (2021)
- [Reconfigurable Intelligent Surfaces Relying on Non-Diagonal Phase Shift Matrices](https://mlsanity.com/paper/2203.08184/) (2022)
- [Closed-Form Global Optimization of Beyond Diagonal Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2211.06117/) (2022)
- [Reconfigurable Intelligent Surfaces 2.0: Beyond Diagonal Phase Shift Matrices](https://mlsanity.com/paper/2301.03288/) (2023)
- [Beyond Diagonal Reconfigurable Intelligent Surfaces Utilizing Graph Theory: Modeling, Architecture Design, and Optimization](https://mlsanity.com/paper/2305.05013/) (2023)
- [Beyond Diagonal RIS in Multiuser MIMO: Graph Theoretic Modeling and Optimal Architectures with Low Complexity](https://mlsanity.com/paper/2502.16509/) (2025)
- [Lossy Beyond Diagonal Reconfigurable Intelligent Surfaces: Modeling and Optimization](https://mlsanity.com/paper/2504.19744/) (2025)
- [A Tutorial on Beyond-Diagonal Reconfigurable Intelligent Surfaces: Modeling, Architectures, System Design and Optimization, and Applications](https://mlsanity.com/paper/2505.16504/) (2025)
- [Pareto Frontier for the Performance-Complexity Trade-off in Beyond Diagonal Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2305.19773/) (2023)
- [A Universal Framework for Multiport Network Analysis of Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2311.10561/) (2023)
- [Localized and Distributed Beyond Diagonal Reconfigurable Intelligent Surfaces with Lossy Interconnections: Modeling and Optimization](https://mlsanity.com/paper/2402.05881/) (2024)
- [Global Optimal Closed-Form Solutions for Intelligent Surfaces With Mutual Coupling: Is Mutual Coupling Detrimental or Beneficial?](https://mlsanity.com/paper/2411.04949/) (2024)
- [A Novel Q-stem Connected Architecture for Beyond-Diagonal Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2411.18480/) (2024)
- [Non-reciprocal Beyond Diagonal RIS: Sum-Rate Maximization in Full-Duplex Communications](https://mlsanity.com/paper/2411.18523/) (2024)
- [A Novel Comprehensive Multiport Network Model for Stacked Intelligent Metasurfaces (SIM) Characterization and Optimization](https://mlsanity.com/paper/2501.02597/) (2025)
- [Out-of-Band Modality Synergy Based Multi-User Beam Prediction and Proactive BS Selection with Zero Pilot Overhead](https://mlsanity.com/paper/2506.15136/) (2025)

## Abstract (arXiv)

Beyond-diagonal reconfigurable intelligent surface (BD-RIS) has recently been introduced to enable advanced control over electromagnetic waves to further increase the benefits of traditional RIS in enhancing signal quality and improving spectral and energy efficiency for next-generation wireless networks. A significant issue in designing and deploying BD-RIS is the tradeoff between its performance and circuit complexity. While existing studies have explored optimal architectures to minimize circuit complexity in ideal BD-RIS, architecture discovery for non-ideal BD-RIS remains uninvestigated. Consequently, how non-idealities and circuit complexity jointly affect the performance of BD-RIS remains unclear, making it difficult to achieve the performance-circuit complexity tradeoff in the presence of non-idealities. Essentially, architecture discovery for non-ideal BD-RIS faces challenges from both the computational complexity of global architecture search and the difficulty in achieving global optima. To tackle these challenges, we propose a learning-based two-tier architecture discovery framework (LTTADF) consisting of an architecture generator and a performance optimizer to jointly discover optimal architectures for non-ideal BD-RIS given specific circuit complexities, which can effectively explore over a large architecture space while avoiding getting trapped in poor local optima and thus achieving near-optimal solutions for the performance optimization. Numerical results provide valuable insights for deploying non-ideal BD-RIS considering the performance-circuit complexity tradeoff.