# asKAN: Active Subspace embedded Kolmogorov-Arnold Network

arXiv: https://arxiv.org/abs/2504.04669 · HTML: https://mlsanity.com/paper/2504.04669/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 7 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (2024)
- [On the approximation by single hidden layer feedforward neural networks with fixed weights](https://mlsanity.com/paper/1708.06219/) (2017)
- [EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials](https://mlsanity.com/paper/2410.10897/) (2024)
- [Multifidelity Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.14764/) (2024)

## Built on by (most cited first, 5 of 5)

- [Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning](https://mlsanity.com/paper/2603.23854/) (2026)
- [KAN-Dreamer: Benchmarking Kolmogorov-Arnold Networks as Function Approximators in World Models](https://mlsanity.com/paper/2512.07437/) (2025)
- [LUT-KAN: Segment-wise LUT Quantization for Fast KAN Inference](https://mlsanity.com/paper/2601.03332/) (2026)
- [Balance-Guided Sparse Identification of Multiscale Nonlinear PDEs with Small-coefficient Terms](https://mlsanity.com/paper/2604.18414/) (2026)
- [Structural Kolmogorov-Arnold Convolutions: Learnable Function on the Values or the Filter Shape as Parameter-Efficient Alternative to Per-Edge Convolutional KANs](https://mlsanity.com/paper/2606.24371/) (2026)

## Abstract (arXiv)

The Kolmogorov-Arnold Network (KAN) has emerged as a promising neural network architecture for small-scale AI+Science applications. However, it suffers from inflexibility in modeling ridge functions, which is widely used in representing the relationships in physical systems. This study investigates this inflexibility through the lens of the Kolmogorov-Arnold theorem, which starts the representation of multivariate functions from constructing the univariate components rather than combining the independent variables. Our analysis reveals that incorporating linear combinations of independent variables can substantially simplify the network architecture in representing the ridge functions. Inspired by this finding, we propose active subspace embedded KAN (asKAN), a hierarchical framework that synergizes KAN's function representation with active subspace methodology. The architecture strategically embeds active subspace detection between KANs, where the active subspace method is used to identify the primary ridge directions and the independent variables are adaptively projected onto these critical dimensions. The proposed asKAN is implemented in an iterative way without increasing the number of neurons in the original KAN. The proposed method is validated through function fitting, solving the Poisson equation, and reconstructing sound field. Compared with KAN, asKAN significantly reduces the error using the same network architecture. The results suggest that asKAN enhances the capability of KAN in fitting and solving equations in the form of ridge functions.