In the emerging paradigm of edge learning, neural networks (NNs) are partitioned across distributed edge devices that collaboratively perform inference via wireless transmission. However, deploying NNs for edge inference over wireless channels inevitably leads to performance degradation, as the exact channel realizations in the inference stage are not known in the training stage. In this paper, we establish a theoretical framework to evaluate and bound this performance degradation. Inspired by statistical learning theory, we define a wireless generalization error to characterize the gap between the empirical performance during training and the expected inference performance under the true stochastic channel. To enable theoretical analysis, we introduce an augmented NN model that incorporates channel statistics directly into the weight space. Leveraging the PAC-Bayesian framework, we derive a high-probability bound on this error, which provides theoretical guarantees for wireless inference performance. Furthermore, we propose a channel-aware training algorithm that minimizes a tractable surrogate objective based on the derived bound. Simulations demonstrate that the proposed algorithm effectively improves wireless inference performance and model robustness under various channel conditions.

翻译：在边缘学习的新兴范式下，神经网络通过分布式边缘设备进行分区部署，这些设备通过无线传输协同执行推理任务。然而，将神经网络部署于无线信道上的边缘推理不可避免地会导致性能退化，这是因为推理阶段确切的信道实现在训练阶段是未知的。本文建立了一个理论框架来评估并限定这种性能退化。受统计学习理论的启发，我们定义了一种无线泛化误差，用以刻画训练过程中的经验性能与真实随机信道下期望推理性能之间的差距。为便于理论分析，我们引入了一种增强型神经网络模型，该模型将信道统计数据直接融入权重空间。借助PAC-贝叶斯框架，我们推导出该误差的一个高概率上界，为无线推理性能提供了理论保证。此外，我们提出了一种信道感知训练算法，该算法基于所推导的上界最小化一个易处理的替代目标函数。仿真结果表明，所提出的算法在各种信道条件下有效提升了无线推理性能及模型鲁棒性。