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

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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.