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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.27133 |
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| _version_ | 1866911720691204096 |
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| author | Lin, Xuan Wu, Chunlin |
| author_facet | Lin, Xuan Wu, Chunlin |
| contents | Deep unfolding neural networks derived from iterative optimization schemes and numerical ordinary/partial differential equations (ODEs/PDEs) have attracted much attention in data science over the last decade. Therein, numerous important network architectures were constructed from the basic forward-backward-splitting (FBS) algorithm. In this paper, we continue our research on the most basic FBS-induced network, an architecture unrolled from the original FBS algorithm by incorporating direct parameter relaxations. Following the difference/differential inclusion formulations in our previous forward system analyses, we here consider some theoretical aspects of corresponding learning problems. Under some mild assumptions, we establish a general convergence property of the training problem of the basic FBS-induced network to the learning problem of the deep-layer limit system, implying a $Γ$-convergence argument showing that any cluster point of the optimal learning parameters for the network is a solution to the learning problem of the deep-layer limit system. A qualitative analysis of perturbation stabilities of these learning problems is also presented. A simple numerical experiment is conducted to validate our main general convergence result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27133 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deep-layer limit and stability analysis of the basic forward-backward-splitting induced network (II): learning problems Lin, Xuan Wu, Chunlin Machine Learning Artificial Intelligence Deep unfolding neural networks derived from iterative optimization schemes and numerical ordinary/partial differential equations (ODEs/PDEs) have attracted much attention in data science over the last decade. Therein, numerous important network architectures were constructed from the basic forward-backward-splitting (FBS) algorithm. In this paper, we continue our research on the most basic FBS-induced network, an architecture unrolled from the original FBS algorithm by incorporating direct parameter relaxations. Following the difference/differential inclusion formulations in our previous forward system analyses, we here consider some theoretical aspects of corresponding learning problems. Under some mild assumptions, we establish a general convergence property of the training problem of the basic FBS-induced network to the learning problem of the deep-layer limit system, implying a $Γ$-convergence argument showing that any cluster point of the optimal learning parameters for the network is a solution to the learning problem of the deep-layer limit system. A qualitative analysis of perturbation stabilities of these learning problems is also presented. A simple numerical experiment is conducted to validate our main general convergence result. |
| title | Deep-layer limit and stability analysis of the basic forward-backward-splitting induced network (II): learning problems |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.27133 |