English(EN) Boundary Geometry Determines Optimal Shallow ReLU Approximation under Weighted Coefficient Constraints

新研究探讨边界几何对浅层ReLU神经网络逼近的影响

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-28 04:00

本文研究了边界的几何特性如何影响浅层ReLU神经网络的逼近能力。研究在加权变差空间内为凸体上的逼近建立了上下界，将经典结果推广到更高维度和各种范数。它确定了决定最优逼近率的特定几何指数，并确定了维持经典逼近率的精确权重阈值。研究结果表明，即使在维度和误差范数等其他因素保持不变的情况下，边界几何也可以显著改变最优逼近指数。 AI

影响为ReLU网络的逼近能力提供了理论见解，可能为未来的模型架构提供信息。

排序理由该集群包含一篇详细介绍神经网络逼近理论研究的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv stat.ML 阅读 →

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arXiv stat.ML TIER_1 English(EN) · Jia-Qi Yang, Lei Shi · 2026-10-28 04:00

边界几何确定加权系数约束下最优浅层ReLU逼近

arXiv:2610.36854v1 Announce Type: new Abstract: We study how boundary geometry affects $L^q$ approximation by shallow ReLU neural networks on convex bodies $K\subset\mathbb R^d$. The target classes are unit balls of weighted variation spaces that can enlarge classical spaces by i…

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边界几何确定加权系数约束下最优浅层ReLU逼近

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