AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
TL;DR
This paper introduces deep neural network operators based on a special class of sigmoidal functions, using a constructive approximation approach, and establishes Bernstein-type inequality for the derivative of a two-hidden-layer neural network operator.
The universal approximation property of dropout neural networks does not by itself describe the network size required for an accurate random realization. In this work, we study approximation of the unit ball of $W^{n,\infty}([0,1]^d)$ by ReLU networks whose edges are retained independently with probability $p$. The app...
The techniques share most of the high-level ideas presented in [Ruess et al., 2026], but there are also some minor differences which may be of interest for future research on this problem.
We investigate the best $L_2$ approximation of mixed Sobolev spaces by shallow neural networks with $n$ neurons and general activation functions. We first establish an activation-independent Fourier-block principle: if an activation has univariate approximation order $\rho$ in the sense of the Fourier-block property, t...
It is proved that quasi-Chebyshev parameter sets with univariate resolution $m$ generate fixed feature spaces attaining the sharp $H^r$-to-to-H^s$ approximation order for a class of analytic activations satisfying a quantitative non-cancellation condition on their Taylor coefficients.
A Banach space-valued approximation framework based on symmetrized neural network (SNN) operators generated by a deformation-dependent sigmoidal activation function, yielding a positive, even, normalized, and localized density kernel satisfying the partition of unity.
A rigidity theorem is established: for continuous piecewise linear generators with a finite number of segments, any \(C^3\) function that can be represented in this way is at most quadratic, which demonstrates how generator dynamics and remainder estimates govern depth allocation and approximation rates of deep neural...
We use cookies to run the site and, with your consent, for analytics and to show ads. See our Cookie Policy.