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Shallow ReLU^k Networks: Geometry-Dependent Approximation and Stability Analyzed

By PulseAugur Editorial · [1 sources] ·

Researchers have published a paper detailing the approximation and stability properties of shallow ReLU$^k$ neural networks within bounded Euclidean domains. The study quantifies how the geometry of hidden parameters, specifically the fill distance ($h$) and antipodal separation distance ($\underline h$), influences network performance. The findings include geometry-dependent spectral estimates for conditioning and coefficient stability, as well as results on norm discretization and regularized recovery from function values. AI

IMPACT Provides theoretical insights into the behavior and stability of shallow ReLU networks, potentially informing future model architectures.

RANK_REASON The item is a research paper published on arXiv detailing theoretical properties of neural networks. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Shallow ReLU^k Networks: Geometry-Dependent Approximation and Stability Analyzed

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The item is a research paper published on arXiv detailing theoretical properties of neural networks. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Yuqing Liu, Tong Mao, Jinchao Xu ·

    Geometry-Dependent Approximation and Stability Properties of Shallow ReLU$^k$ Networks on Bounded Euclidean Domains

    arXiv:2611.13952v1 Announce Type: new Abstract: On bounded Euclidean domains, we study how hidden-parameter geometry affects shallow ReLU$^k$ networks through results on approximation rates, saturation-type lower bounds, Gram and stiffness matrix spectra, Bernstein and Marcinkiew…

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