# Want to train KANS at scale? Now UKAN!

arXiv: https://arxiv.org/abs/2408.11200 · HTML: https://mlsanity.com/paper/2408.11200/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [Deep Learning for Computational Chemistry](https://mlsanity.com/paper/1701.04503/) (2017)
- [FlashFFTConv: Efficient Convolutions for Long Sequences with Tensor Cores](https://mlsanity.com/paper/2311.05908/) (2023)

## Built on by (most cited first, 1 of 1)

- [ChemKANs for Combustion Chemistry Modeling and Acceleration](https://mlsanity.com/paper/2504.12580/) (2025)

## Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) have recently emerged as a powerful alternative to traditional multilayer perceptrons. However, their reliance on predefined, bounded grids restricts their ability to approximate functions on unbounded domains. To address this, we present Unbounded Kolmogorov-Arnold Networks (UKANs), a method that removes the need for bounded grids in traditional Kolmogorov-Arnold Networks (KANs). The key innovation of this method is a coefficient-generator (CG) model that produces, on the fly, only the B-spline coefficients required locally on an unbounded symmetric grid. UKANs couple multilayer perceptrons with KANs by feeding the positional encoding of grid groups into the CG model, enabling function approximation on unbounded domains without requiring data normalization. To reduce the computational cost of both UKANs and KANs, we introduce a GPU-accelerated library that lowers B-spline evaluation complexity by a factor proportional to the grid size, enabling large-scale learning by leveraging efficient memory management, in line with recent software advances such as FlashAttention and FlashFFTConv. Performance benchmarking confirms the superior memory and computational efficiency of our accelerated KAN (warpKAN), and UKANs, showing a 3-30x speed-up and up to 1000x memory reduction compared to vanilla KANs. Experiments on regression, classification, and generative tasks demonstrate the effectiveness of UKANs to match or surpass KAN accuracy. Finally, we use both accelerated KAN and UKAN in a molecular property prediction task, establishing the feasibility of large-scale end-to-end training with our optimized implementation.