Certified Robustness of Antenna Selecting Neural Networks for Massive MIMO Wireless Communications

Future wireless systems with massive antennas must balance data rates and RF chain costs. Antenna selection activating only a subset of antennas addresses this challenge. Recently, neural network-based approaches have shown promise over traditional symbolic methods, offering fixed complexity in inference and suitability for hardware implementation. However, their closed-box nature raises concerns for safety-critical 6G applications like autonomous driving and drones, where reliable communication is vital. Specifically, it is often unclear how the neural network determines which antennas to select, making it difficult to interpret or trust the decision-making process. This paper investigates the robustness of neural networks for antenna selection in such contexts. While empirical robustness against finite random inputs sampled from a uniform distribution may suffice for general applications, certified robustness ensuring consistent inference under all possible perturbations is essential for safety-critical systems. Although certified robustness is well studied in vision and language tasks, we are the first, to our knowledge, to explore its application in telecommunications. We mathematically define robustness for antenna-selection networks and apply state-of-the-art linear relaxation-based perturbation analysis. Our findings show that pruned networks, beyond being more efficient, also exhibit superior certified robustness compared to their unpruned counterparts. We further compare certified and empirical robustness, identifying a significant gap that suggests the need for improved certification methods. Additionally, in our antenna selection setting, we observe that removing monotonic activations in the final layer improves certified robustness.