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Shallow ReLU-s Networks Approximation and Generalization Explored

By PulseAugur Editorial · [2 sources] ·

Researchers have published a paper detailing approximation bounds for shallow ReLU-s networks within L^p-type and Sobolev spaces. The study utilizes spherical harmonic analysis to establish these bounds, showing improvements over existing random-feature rates for certain parameter ranges. Additionally, the paper presents minimax-optimal generalization bounds for path-norm-regularized networks in nonparametric regression scenarios. AI

IMPACT Provides theoretical insights into the approximation capabilities and generalization properties of shallow neural networks, potentially informing future model design.

RANK_REASON Academic paper published on arXiv detailing theoretical advancements in neural network approximation and generalization.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Shallow ReLU-s Networks Approximation and Generalization Explored

COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Weizhao Li, Fanghui Liu, Lei Shi ·

    Shallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization

    arXiv:2605.18468v1 Announce Type: new Abstract: We study approximation by shallow ReLU$^s$ networks, $\sigma_s(t)=\max{0,t}^s$, and the generalization behavior of such networks under $\ell_1$ path-norm control. For the $L^p$-type integral spaces $\widetilde{\mathcal{F}}_{p,\tau_d…

  2. arXiv stat.ML TIER_1 English(EN) · Lei Shi ·

    Shallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization

    We study approximation by shallow ReLU$^s$ networks, $σ_s(t)=\max{0,t}^s$, and the generalization behavior of such networks under $\ell_1$ path-norm control. For the $L^p$-type integral spaces $\widetilde{\mathcal{F}}_{p,τ_d,s}$, $1\le p\le2$, we establish approximation bounds fo…

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