# Lookup multivariate Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2509.07103 · HTML: https://mlsanity.com/paper/2509.07103/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 72 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Conditional Computation in Neural Networks for faster models](https://mlsanity.com/paper/1511.06297/) (2015)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (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)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [Smooth, exact rotational symmetrization for deep learning on point clouds](https://mlsanity.com/paper/2305.19302/) (2023)
- [KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search](https://mlsanity.com/paper/2406.17630/) (2024)
- [PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets](https://mlsanity.com/paper/2410.10084/) (2024)
- [Hardware Acceleration of Kolmogorov-Arnold Network (KAN) for Lightweight Edge Inference](https://mlsanity.com/paper/2409.11418/) (2024)

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

- [InKAN: B-Spline KANs via Truncated Power Form](https://mlsanity.com/paper/2609.01956/) (2026)

## Abstract (arXiv)

High-dimensional linear mappings, or linear layers, dominate both the parameter count and the computational cost of most modern deep-learning models. We introduce a general-purpose drop-in replacement, lookup multivariate Kolmogorov-Arnold Networks (lmKANs), which deliver a substantially better trade-off between capacity and inference cost. Our construction expresses a general high-dimensional mapping through trainable low-dimensional multivariate functions. These functions can carry dozens or hundreds of trainable parameters each, and yet it takes only a few multiplications to compute them because they are implemented as spline lookup tables. Empirically, lmKANs reduce inference FLOPs by up to 6.0x while matching the flexibility of MLPs in general high-dimensional function approximation. In another feedforward fully connected benchmark, on the tabular-like dataset of randomly displaced methane configurations, lmKANs enable more than 10x higher H100 throughput at equal accuracy. Within frameworks of Convolutional Neural Networks, lmKAN-based CNNs cut inference FLOPs at matched accuracy by 1.6-2.1x and by 1.7x on the CIFAR-10 and ImageNet-1k datasets, respectively. Our code, including dedicated CUDA kernels, is available online at https://github.com/schwallergroup/lmkan.