Theoretical Mechanism for Scaling Behavior in Normalized Residual Networks

Researchers from the machine learning community have published a new theoretical framework addressing the scaling behavior of normalized residual networks in deep learning. The study investigates how inserting new residual blocks into trained models affects test risk, aiming to provide a rigorous mathematical basis for the empirical observation that performance improves with increased model size and data. The authors decompose the problem into representational gain, optimization gain, and generalization transfer. They prove that under specific conditions, such as first-order descent near zero initialization, the expanded hypothesis class contains models with strictly lower population risk. Additionally, they establish norm-based Rademacher complexity bounds tailored to post-normalized architectures. These findings offer two complementary guarantees for test-risk improvement, suggesting that scaling is a joint effect where depth creates improvement directions, width enhances signal observability, and data controls statistical costs. This work contributes significantly to the theoretical understanding of deep learning scalability.