On the Dimension-Free Approximation of Deep Neural Networks for Symmetric Korobov Functions

arXiv:2511.12398v2 Announce Type: replace Abstract: Deep neural networks have been widely used as universal approximators for functions with inherent physical structures, including permutation symmetry. In this paper, we construct symmetric deep neural networks to approximate symmetric Korobov functions and prove that both the convergence rate and the constant prefactor scale at most polynomially with respect to the ambient dimension. This represents a substantial improvement over prior approximation guarantees that suffer from the curse of dimensionality. Building on these approximation bound

Source: arXiv cs.LG — read the full report at the original publisher.

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