HKAN: Hierarchical Kolmogorov-Arnold network without backpropagation.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Neural Networks

Background:

• Gradient-based methods like backpropagation are standard in neural networks.
• Existing models may face challenges in computational efficiency and interpretability.

Purpose of the Study:

• Introduce the Hierarchical Kolmogorov-Arnold Network (HKAN) as a backpropagation-free alternative.
• Evaluate HKAN's performance against established neural network architectures.

Main Methods:

• HKAN utilizes a randomized learning framework and hierarchical multi-stacking.
• Each layer refines approximations via convex optimization subproblems.
• A non-iterative training strategy is employed for efficiency and stability.

Main Results:

• HKAN achieves accuracy comparable to or exceeding standard KANs and Multi-Layer Perceptrons.
• The model demonstrates reduced training times.
• HKAN provides enhanced interpretability through input variable importance assessment.

Conclusions:

• HKAN offers a computationally efficient, numerically stable, and accurate alternative to gradient-based models.
• The framework bridges theoretical rigor with practical utility.
• HKAN enhances transparency in neural network modeling.