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

arXiv: https://arxiv.org/abs/2601.10915 · HTML: https://mlsanity.com/paper/2601.10915/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Deep Learning Enabled Semantic Communication Systems](https://mlsanity.com/paper/2006.10685/) (2020)
- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [Tighter risk certificates for neural networks](https://mlsanity.com/paper/2007.12911/) (2020)
- [Learning Task-Oriented Communication for Edge Inference: An Information Bottleneck Approach](https://mlsanity.com/paper/2102.04170/) (2021)
- [Towards an Intelligent Edge: Wireless Communication Meets Machine Learning](https://mlsanity.com/paper/1809.00343/) (2018)
- [BottleNet++: An End-to-End Approach for Feature Compression in Device-Edge Co-Inference Systems](https://mlsanity.com/paper/1910.14315/) (2019)
- [Split Learning over Wireless Networks: Parallel Design and Resource Management](https://mlsanity.com/paper/2204.08119/) (2022)
- [Generalization Bounds: Perspectives from Information Theory and PAC-Bayes](https://mlsanity.com/paper/2309.04381/) (2023)
- [Communication-Computation Trade-Off in Resource-Constrained Edge Inference](https://mlsanity.com/paper/2006.02166/) (2020)
- [Data-dependent Generalization Bounds via Variable-Size Compressibility](https://mlsanity.com/paper/2303.05369/) (2023)
- [Robustness in Wireless Distributed Learning: An Information-Theoretic Analysis](https://mlsanity.com/paper/2401.17577/) (2024)
- [Take What You Need: Flexible Multi-Task Semantic Communications with Channel Adaptation](https://mlsanity.com/paper/2502.08221/) (2025)

## Abstract (arXiv)

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.