Formal Verification for Deep Learning-based Power Control in Massive MIMO

A rigorous robustness framework for neural network power allocation under adversarial input perturbations

Thanh Le; Takeshi Matsumura; Yusheng Ji; John C. S. Lui· 2026· DOI 10.48550/arXiv.2607.14500

The core problem

Deep learning has emerged as a promising approach to optimize wireless communication by simplifying the search for near-optimal solutions. Prior studies on deep learning-based wireless communication optimization have explored supervised learning approaches that map raw user information, such as location or channel state information, to optimal power allocation vectors. While this approach demonstrates competitive performance, it is susceptible to adversarial attacks via input perturbations. Current defense mechanisms primarily rely on empirical methods, which do not provide formal guarantees of robustness. This paper fills this gap by proposing a formal verification framework to evaluate the robustness of deep learning-based power allocation in multi-cell massive multiple-input multiple-output (MIMO) systems against a wide range of potential adversarial input manipulations. To the best of our knowledge, this is the first attempt to formally verify deep neural networks in a regression setting with non-linear output constraints.

Evaluation on publicly available datasets for power allocation in multi-cell massive MIMO indicates that a well-trained model can guarantee the local robustness under location perturbation by \pm 1 m while retaining a maximum 1% optimality gap. The authors report that the formal verification framework successfully certifies robustness for a range of perturbation magnitudes, and the computed bounds are tight enough to provide meaningful guarantees. Specifically, for perturbations up to \pm 1 m in user location, the worst-case sum rate degradation is bounded, and the optimality gap remains below 1%. The results also show that the DeepPoly-based approach scales to networks with multiple layers and hundreds of neurons, making it practical for real-world massive MIMO systems.

Deep learning has emerged as a promising approach to optimize wireless communication by simplifying the search for near-optimal solutions. Prior studies on deep learning-based wireless communication optimization have explored supervised learning approaches that map raw user information, such as location or channel state information, to optimal power allocation vectors. While this approach demonstrates competitive performance, it is susceptible to adversarial attacks via input perturbations. Current defense mechanisms primarily rely on empirical methods, which do not provide formal guarantees of robustness. This paper fills this gap by proposing a formal verification framework to evaluate the robustness of deep learning-based power allocation in multi-cell massive multiple-input multiple-output (MIMO) systems against a wide range of potential adversarial input manipulations. To the best of our knowledge, this is the first attempt to formally verify deep neural networks in a regression setting with non-linear output constraints.

The authors model the adversary's capabilities using hyper-rectangle constraints on their perturbation. Formally, for an input x and perturbation δ, the adversary can choose any δ such that ∥ δ ∥_{\infty} \leq ϵ, which defines a hyper-rectangle [x - ϵ, x + ϵ] . The goal is to verify that for all inputs within this region, the neural network's output (allocated powers) satisfies certain performance requirements.

The paper presents the first formal verification framework for deep learning-based power allocation in multi-cell massive MIMO, addressing a critical gap in robustness guarantees. By leveraging DeepPoly bound propagation, the authors provide a sound over-approximation of the neural network's output range, enabling certification of performance under adversarial input perturbations. The use of hyper-rectangle constraints for adversary modeling is both realistic and computationally tractable. The results demonstrate that formal verification can be achieved with a modest optimality gap, suggesting that deep learning models for power control can be made robust without significant performance loss. However, the approach has limitations: the bound propagation may become loose for very deep networks, and the verification is specific to the considered perturbation model. Future work could extend the framework to other types of perturbations (e.g., channel estimation errors) and to more complex neural architectures. Overall, this work bridges the gap between empirical defenses and formal guarantees, paving the way for trustworthy AI in wireless communications.

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