Member-only story
Tropical Algebraic Kolmogorov-Arnold Network: Improving KAN Neural Networks
Introduction
In the ever-evolving field of artificial intelligence, the fusion of mathematical theorems with neural network technology presents an intriguing avenue for research and innovation. One such endeavor is the development of the Tropical Algebraic Kolmogorov-Arnold Network. This blog post will walk you through the creation of this novel network, from its theoretical foundations to its practical implementation in TensorFlow.
Understanding the Mathematical Foundations
1. Kolmogorov-Arnold Representation Theorem
The Kolmogorov-Arnold Representation Theorem is a foundational mathematical principle that states any multivariate continuous function can be represented as a superposition of continuous functions of one variable. Mathematically, it can be expressed as:
where Φ and ψ are continuous functions. This theorem suggests a method to decompose complex functions into simpler, manageable components, making it particularly suitable for modelling with neural networks.
