Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem
This addresses a fundamental problem in machine learning for high-dimensional data approximation, though it appears incremental as it builds on existing theoretical frameworks.
The paper tackles the curse of dimensionality in approximating multivariate functions by proving a theorem for deep ReLU networks based on the Kolmogorov-Arnold superposition theorem, resulting in error bounds that lessen this curse.
We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov--Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.