Kolmogorov–Arnold Networks
term_id: kolmogorovarnold_networks
Category: basic_concepts
Definition
Kolmogorov–Arnold Networks (KANs) are a recent class of neural networks inspired by the Kolmogorov-Arnold representation theorem, which states that any multivariate continuous function can be represented as a composition of continuous functions of one variable and addition. Unlike standard Multi-Layer Perceptrons (MLPs) that use fixed activation functions on weights, KANs place learnable activation functions on the edges (connections) of the network. This structure often leads to higher accuracy, better interpretability, and faster convergence during training, particularly in scientific machine learning applications.
Summary
Neural network architectures based on the Kolmogorov-Arnold representation theorem, offering an alternative to multi-layer perceptrons.
Key Concepts
- Kolmogorov-Arnold Theorem
- Learnable Activations
- Scientific Machine Learning
- Function Approximation
Use Cases
- Physics-informed neural networks
- Symbolic regression
- High-precision function approximation