Generalization Bounds for Transformer Channel Decoders

2026-01-11

arXiv.org

AI Summary

This work addresses the lack of theoretical guarantees for the generalization performance of Transformer-based channel decoders such as ECCT. From the perspective of statistical learning theory, it establishes the first upper bound on the generalization error of ECCT by analyzing bit-wise Rademacher complexity, thereby linking multiplicative noise estimation error to bit error rate. By incorporating covering number estimates, the analysis reveals that parity-check-matrix-guided masked attention induces sparsity and reduces model complexity, yielding a tighter generalization bound. The framework applies uniformly to both single- and multi-layer ECCT architectures and explicitly characterizes the dependence of generalization error on code length, model size, and training sample size. Theoretically, this confirms that sparse attention structures enhance generalization capability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Learning & Optimization for NLP
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Transformer channel decoders, such as the Error Correction Code Transformer (ECCT), have shown strong empirical performance in channel decoding, yet their generalization behavior remains theoretically unclear. This paper studies the generalization performance of ECCT from a learning-theoretic perspective. By establishing a connection between multiplicative noise estimation errors and bit-error-rate (BER), we derive an upper bound on the generalization gap via bit-wise Rademacher complexity. The resulting bound characterizes the dependence on code length, model parameters, and training set size, and applies to both single-layer and multi-layer ECCTs. We further show that parity-check-based masked attention induces sparsity that reduces the covering number, leading to a tighter generalization bound. To the best of our knowledge, this work provides the first theoretical generalization guarantees for this class of decoders.

Problem

• generalization
• Transformer
• channel decoding
• bit-error-rate
• Rademacher complexity

Innovation

• generalization bound
• Transformer decoder
• Rademacher complexity
• masked attention
• channel coding