# Hybrid Parallel Bessel KAN Model: a Kolmogorov Arnold Network: integrated framework for developing a novel architecture to reconstruct the fused-basis approach via a parameter free quadratic interaction

arXiv: https://arxiv.org/abs/2610.17779 · HTML: https://mlsanity.com/paper/2610.17779/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (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)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [FC-KAN: Function Combinations in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.01763/) (2024)
- [Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning](https://mlsanity.com/paper/2601.07760/) (2026)
- [Exploring Kolmogorov-Arnold Network Expansions in Vision Transformers for Mitigating Catastrophic Forgetting in Continual Learning](https://mlsanity.com/paper/2507.04020/) (2025)

## Abstract (arXiv)

The Kolmogorov-Arnold Network (KAN) challenges traditional MLPs by placing learnable activation functions on network edges. However, scaling KANs to spatial data exposes limitations in default B-Splines. While hybrid architectures mix multiple basis families on a single edge to resolve this, monolithic superposition causes geometric overlap, parameter explosion, and severe numerical ill-conditioning (kappa(G) ≈ 1016).To overcome this, we propose Parallel BesselKAN, which isolates B-Spline and low-order Bessel branches into parallel processing pipelines integrated via a parameter-free quadratic interaction. This decoupled architecture acts as an efficient internal ensemble, bypassing monolithic stability bottlenecks. It compresses the parameter footprint by 35% while achieving 97.99% accuracy on MNIST. Although standard MLPs retain a hardware speed advantage for pure vision tasks, Parallel BesselKAN provides a robust, parameter-efficient framework stabilizing mixed-basis networks and paving the way for scalable spatial adaptations like Convolutional KANs.