# Chebyshev Feature Neural Network for Accurate Function Approximation

arXiv: https://arxiv.org/abs/2409.19135 · HTML: https://mlsanity.com/paper/2409.19135/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2024.

## Built on by (most cited first, 4 of 4)

- [Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation](https://mlsanity.com/paper/2512.09165/) (2025)
- [FEKAN: Feature-Enriched Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.16530/) (2026)
- [SUPN: Shallow Universal Polynomial Networks for Efficient Function Approximation](https://mlsanity.com/paper/2511.21414/) (2025)
- [Spectral-Embedded Operator Learning for Three-Phase Interfacial Flow: A Ternary Cahn-Hilliard-Navier-Stokes Benchmark](https://mlsanity.com/paper/2608.29069/) (2026)

## Abstract (arXiv)

We present a new Deep Neural Network (DNN) architecture capable of approximating functions up to machine accuracy. Termed Chebyshev Feature Neural Network (CFNN), the new structure employs Chebyshev functions with learnable frequencies as the first hidden layer, followed by the standard fully connected hidden layers. The learnable frequencies of the Chebyshev layer are initialized with exponential distributions to cover a wide range of frequencies. Combined with a multi-stage training strategy, we demonstrate that this CFNN structure can achieve machine accuracy during training. A comprehensive set of numerical examples for dimensions up to 20 are provided to demonstrate the effectiveness and scalability of the method.