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arXiv Machine Learning By Zachary Morrow, Michael Penwarden, Brian Chen, Aurya Javeed, Akil Narayan, John D. Jakeman

SUPN: Shallow Universal Polynomial Networks for Efficient Function Approximation

Read the original on arXiv Machine Learning →

The paper introduces Shallow Universal Polynomial Networks (SUPNs), a single‑hidden‑layer architecture that replaces standard activations with learnable multivariate polynomials, thereby increasing expressivity per unit. SUPNs achieve universal approximation by either widening the network or increasing polynomial complexity, and the authors prove convergence rates and quasi‑optimal parameter choices. Empirical tests across a wide range of smooth, nonsmooth, and discontinuous functions in up to ten dimensions show that SUPNs often outperform deep neural networks and Kolmogorov‑Arnold networks in accuracy and variability while requiring fewer parameters and lower training cost.

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