# Enhancing Neural Function Approximation: The XNet Outperforming KAN

arXiv: https://arxiv.org/abs/2501.18959 · HTML: https://mlsanity.com/paper/2501.18959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Reinforcement Learning in Healthcare: A Survey](https://mlsanity.com/paper/1908.08796/) (2019)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.11833/) (2023)
- [ExSpliNet: An interpretable and expressive spline-based neural network](https://mlsanity.com/paper/2205.01510/) (2022)
- [Kolmogorov-Arnold Network for Online Reinforcement Learning](https://mlsanity.com/paper/2408.04841/) (2024)
- [Cauchy activation function and XNet](https://mlsanity.com/paper/2409.19221/) (2024)

## Abstract (arXiv)

XNet is a single-layer neural network architecture that leverages Cauchy integral-based activation functions for high-order function approximation. Through theoretical analysis, we show that the Cauchy activation functions used in XNet can achieve arbitrary-order polynomial convergence, fundamentally outperforming traditional MLPs and Kolmogorov-Arnold Networks (KANs) that rely on increased depth or B-spline activations. Our extensive experiments on function approximation, PDE solving, and reinforcement learning demonstrate XNet's superior performance - reducing approximation error by up to 50000 times and accelerating training by up to 10 times compared to existing approaches. These results establish XNet as a highly efficient architecture for both scientific computing and AI applications.