On the Generalization Behavior of Deep Residual Networks From a Dynamical System Perspective
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912923247443968 |
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| author | Huang, Jinshu Sun, Mingfei Wu, Chunlin |
| author_facet | Huang, Jinshu Sun, Mingfei Wu, Chunlin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_20921 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Generalization Behavior of Deep Residual Networks From a Dynamical System Perspective Huang, Jinshu Sun, Mingfei Wu, Chunlin Machine Learning 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. |
| title | On the Generalization Behavior of Deep Residual Networks From a Dynamical System Perspective |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.20921 |