This repository provides foundational knowledge for understanding Kolmogorov-Arnold Networks (KANs), starting with Bézier curves, B-splines, and their role in function approximation. Building on these concepts, it explains the KAN architecture and its applications in approximating complex functions.
In this lecture, we will cover the following topics:
- Introduction to Bézier curves.
- Mathematical formulation and significance in curve modeling.
- Visualization and examples.
2. 📐 B-splines
- Overview of B-splines and their properties.
- Role of linear combinations in function approximation.
- Practical applications of B-splines in modeling.
- Understanding spline-based function approximation.
- Comparing splines with other function approximation methods.
- Challenges and advantages.
- Introduction to the KAN architecture.
- Theoretical foundations:
- Kolmogorov-Arnold representation theorem.
- Splines as building blocks in KANs.
- Applications of KANs in machine learning and function approximation.
- Benefits and limitations of KANs.
To supplement the lecture, explore these resources:
- 📄 KAN: Kolmogorov–Arnold Networks (Paper)
- 🌐 Beginner-friendly Introduction to KAN
- 🛠️ From-Scratch Implementation of KANs
- 🗂️ GitHub: Code for KAN Implementation
- 📘 KAN Tutorial Notebooks
- 🎥 Video: Kolmogorov-Arnold Networks Explained
- 📺 Video Series by Andrej Karpathy
- 🧠 How to Code a Neural Network with Backpropagation in Python
- 🖊️ MNIST From-Scratch Neural Network
- 📖 Backpropagation and Gradient Descent Simplified
- 🔨 Building a Neural Network From Scratch
For any issues or contributions, feel free to open an issue or submit a pull request. 🤝