A PAC-Bayesian Analysis of Channel-Induced Degradation in Edge Inference

TL;DR

This paper develops a PAC-Bayesian theoretical framework to analyze and bound performance degradation in edge neural network inference caused by wireless channel variability, proposing a channel-aware training method.

Contribution

It introduces a novel PAC-Bayesian bound for wireless inference error and a training algorithm that incorporates channel statistics for improved robustness.

Findings

The derived bound provides high-probability guarantees on inference performance.

The proposed training algorithm improves robustness across different wireless channel conditions.

Simulations confirm the effectiveness of the method in reducing inference degradation.

Abstract

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.