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Deep-layer limit and stability analysis of the basic forward-backward-splitting induced network (II): learning problems
Xuan Lin, Ch · 2026-05-27 · via cs.LG updates on arXiv.org

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Abstract: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 $\Gamma$-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.
Comments: 38 pages, 1 figure
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2605.27133 [cs.LG]
  (or arXiv:2605.27133v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2605.27133

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Xuan Lin [view email]
[v1] Tue, 26 May 2026 15:03:34 UTC (78 KB)