English(EN) ReLU Neural Network Approximation to Smooth Functional Operator: Dimensional Decay and Error Analysis

新研究探索神经网络逼近复杂函数算子 · 已追踪3个来源

作者 PulseAugur 编辑部 · [3 个来源] · 2026-09-15 04:00

研究人员正在探索用于逼近复杂函数的高级神经网络架构。一篇论文详细介绍了深度ReLU网络如何在无限维希尔伯特空间上逼近光滑泛函，并根据坐标衰减和敏感性建立误差界限。另一项研究引入了使用浅层神经网络算子的分形插值函数，以保持函数的平滑性，并通过Python实验进行了验证。第三篇论文研究了再生核希尔伯特空间上非线性泛函的神经算子，使用点评估而非积分来简化架构，并推导了逼近率和学习保证。 AI

影响这些理论进展可能带来更高效、更准确的AI模型，用于复杂数据分析和函数逼近。

排序理由该集群包含三篇在arXiv上发表的学术论文，详细介绍了神经网络逼近技术的理论进展。

在 arXiv cs.LG 阅读 →

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报道来源 [3]

arXiv cs.LG TIER_1 English(EN) · Shuhao Jiao · 2026-09-15 04:00

ReLU神经网络逼近光滑函数算子：维度衰减与误差分析

arXiv:2609.15355v1 Announce Type: cross Abstract: We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by deep ReLU neural networks. Writing the functional input as $X(t)=\sum_{d\geq1}\xi_d\nu_d(t)$, we quantify…
arXiv cs.LG TIER_1 English(EN) · Aaqib Ayoub Bhat, Asif Khan, M. Mursaleen · 2026-09-15 04:00

基于神经网络算子的分形逼近：光滑性保持与收敛性分析

arXiv:2505.06229v2 Announce Type: replace Abstract: This paper introduces the construction of fractal interpolation functions (FIFs), whose graphs are the attractors of an iterated function system (IFS). Integrating concepts from approximation theory, $\alpha$-fractal functions a…
arXiv cs.LG TIER_1 English(EN) · Tian-Yi Zhou, Namjoon Suh, Guang Cheng, Xiaoming Huo · 2026-09-15 04:00

RKHS 上的非线性泛函的神经算子

arXiv:2403.12187v2 Announce Type: replace-cross Abstract: Motivated by the abundance of functional data, such as time series and images, we study the approximation and statistical learning of nonlinear functionals defined on reproducing kernel Hilbert spaces (RKHSs) using neural …

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报道来源 [3]

ReLU神经网络逼近光滑函数算子：维度衰减与误差分析

基于神经网络算子的分形逼近：光滑性保持与收敛性分析

RKHS 上的非线性泛函的神经算子

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