universal-approximation

The paper provides a completeness theory proving that multi-layer message passing in graph neural networks achieves universal approximation for interatomic potentials, justifying common architectural practices in machine-learned potentials.

This paper develops constructive approximation and learning guarantees for shallow neural models with infinite-dimensional inputs, separating errors into coordinate-truncation, network width, and sample size components for a unified theoretical analysis.

This paper proves that EML trees, which represent elementary functions through composition, are universal approximators for continuous functions and other functional spaces. The proof constructs EML representations of basic operations and uses them as building blocks.

We propose hierarchical RBF-KAN and RBF-SKAN architectures for multidimensional function approximation and random field learning. The frameworks offer universal approximation properties and partially alleviate the curse of dimensionality, with empirical results showing improved accuracy over existing methods.

This paper proves the first universal approximation theorems for nonlinear operators and their derivatives in infinite-dimensional settings, extending classical results to operator learning architectures like DeepONet and PCA-Net.

The article explores the Universal Approximation Theorem in deep learning, analyzing the representation capacity of individual neurons and neural network layers using ReLU activation functions.