K-DAREK

Distance Aware Error for Kurkova Kolmogorov Networks

Masoud Ataei

University of Maine

Masoud.Ataei@maine.edu

Vikas Dhiman

University of Maine

Vikas.Dhiman@maine.edu

Mohammad Javad Khojasteh

Rochester Institute of Technology

mjkeme@rit.edu

📄 Read Paper 💻 Code on GitHub 📄 DAREK page

Abstract

K-DAREK is a novel extension of DAREK that introduces distance-aware error bounds for more robust function approximation. By measuring uncertainty based on the distance to training data, it produces tighter and more meaningful confidence estimates. Evaluations on safe control tasks show K-DAREK is faster, more scalable, and safer than methods like Gaussian Processes, Deep Ensembles, and earlier versions such as DAREK.

Interactive Demo of Newton Polynomial

Lipschitz constant

Knots

Newton
Polynomial

Interpolate
Error

GP-mean

GP-std

Click and drag any circle. Newton polynomial and interpolation error bounds.

Highlights

Distance-aware uncertainty: Provides tighter, data-dependent error bounds that improve reliability in prediction.
High computational efficiency: ~4× faster and ~10× more efficient than Deep Ensembles.
Better scalability: ~8.6× more scalable than Gaussian Processes as data size grows.
Enhanced safety: Achieves 50% greater safety over the original DAREK method in control tasks.
Built on KKAN: Leverages a streamlined architecture combining MLPs and Spline transformations for stable and efficient learning.

Results

Multi agent simulation.

Cite This Work

      @INPROCEEDINGS{ataei2025kdarek,
  author={Ataei, Masoud and Dhiman, Vikas and Khojasteh, Mohammad Javad},
  booktitle={2025 59th Asilomar Conference on Signals, Systems, and Computers}, 
  title={K-DAREK: Distance Aware Error for Kurkova Kolmogorov Networks}, 
  year={2025},
  pages={1336-1342},
  keywords={Training;Uncertainty;Computational modeling;Neural networks;Training data;Computer architecture;Systems modeling;Reliability theory;Computational efficiency;Splines (mathematics);Error bounds;neural networks;worst-case analysis;KKAN},
  doi={10.1109/IEEECONF67917.2025.11443822}}