KAN: Kolmogorov-Arnold Networks

Abstract

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.

Accepted by International Conference on Learning Representations (ICLR) 2025 (conference version: https://openreview.net/forum?id=Ozo7qJ5vZi). Codes are available at https://github.com/KindXiaoming/pykan

Cited by in corpus (19)

• Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks
• KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics
• Kolmogorov-Arnold Networks (KANs) for Time Series Analysis
• Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks
• Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)
• Kolmogorov-Arnold Recurrent Network for Short Term Load Forecasting Across Diverse Consumers
• SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions
• Tensor-decomposition-based A Priori Surrogate (TAPS) modeling for ultra large-scale simulations
• Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving Linear Elasticity Problems
• Machine Learning for Estimation and Control of Quantum Systems
• Accurate Surrogate Amplitudes with Calibrated Uncertainties
• Revisiting Medical Image Retrieval via Knowledge Consolidation
• ChemKANs for Combustion Chemistry Modeling and Acceleration
• A Survey of Spatio-Temporal EEG data Analysis: from Models to Applications
• Analysis of Structured Deep Kernel Networks
• EMK-KEN: A High-Performance Approach for Assessing Knowledge Value in Citation Network
• A Kolmogorov-Arnold Surrogate Model for Chemical Equilibria: Application to Solid Solutions
• XLSR-Kanformer: A KAN-Intergrated model for Synthetic Speech Detection
• Manipulating Vehicle 3D Shapes through Latent Space Editing