Efficient Approximation to Analytic and $L^p$ functions by Height-Augmented ReLU Networks

ArXi:2603.11128v1 Announce Type: cross This work addresses two fundamental limitations in neural network approximation theory. We nstrate that a three-dimensional network architecture enables a significantly efficient representation of sawtooth functions, which serves as the cornerstone in the approximation of analytic and $L^p$ functions. First, we establish substantially improved exponential approximation rates for several important classes of analytic functions and offer a parameter-efficient network design.