SOURCE-LINKED INTELLIGENCE

Neural Approximation by Function Composition: Rigidity and Doubly Exponential Convergence

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

Deep neural networks approximate functions by composing affine maps with nonlinear activations, but how composition itself creates approximation power is not yet fully understood. We investigate a fundamental mechanism: geometrically weighted sums of iterates of a single scalar generator function. This mechanism underpins the classical tent-map construction of the function \(x - x^2\) and related recursive representations used by Yarotsky, W. E, et al., to analyze the approximation powers of deep neural networks. First, we establish a rigidity theorem: for continuous piecewise linear generator

Read original source ↗ Open in workspace

recordType

paper

region

Global