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arXiv · 2602.20921

On the Generalization Behavior of Deep Residual Networks From a Dynamical System Perspective

Jinshu Huang·Mingfei Sun·Chunlin Wu
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Abstract

Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new mathematical insights into the structure and learning behavior of DNNs. In this work, we establish generalization error bounds for both discrete- and continuous-time residual networks (ResNets) by combining Rademacher complexity, flow maps of dynamical systems, and the convergence behavior of ResNets in the deep-layer limit. The resulting bounds are of order $O(1/\sqrt{S})$ with respect to the number of training samples $S$, and include a structure-dependent negative term, yielding depth-uniform and asymptotic generalization bounds under milder assumptions. These findings provide a unified understanding of generalization across both discrete- and continuous-time ResNets, helping to close the gap in both the order of sample complexity and assumptions between the discrete- and continuous-time settings.

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Jinshu Huang, Mingfei Sun, Chunlin Wu. 2026-02-24. On the Generalization Behavior of Deep Residual Networks From a Dynamical System Perspective. https://arxiv.org/abs/2602.20921

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