DAREK

Distance Aware Error for Kolmogorov Networks

Masoud Ataei

University of Maine

Masoud.Ataei@maine.edu

Mohammad Javad Khojasteh

Rochester Institute of Technology

mjkeme@rit.edu

Vikas Dhiman

University of Maine

Vikas.Dhiman@maine.edu

📄 Read Paper 💻 Code on GitHub

Abstract

We present DAREK, a method to compute tight, distance-aware, worst-case error bounds for Kolmogorov-Arnold Networks (KANs). Unlike probabilistic uncertainty estimation, DAREK uses Lipschitz continuity of true functions to derive analytical bounds that increase with distance from training data.

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

Tight, analytical, distance-aware error bounds for spline based neural networks
Efficient and interpretable uncertainty estimation
Outperforms Monte Carlo and traditional GP methods

Results

Multi-agent simulation when GP model fails.

Multi-agent simulation when DAREK model reaches goal.

Cite This Work

@inproceedings{ataei2025darek,
  title={DAREK-Distance Aware Error for Kolmogorov Networks},
  author={Ataei, Masoud and Khojasteh, Mohammad Javad and Dhiman, Vikas},
  booktitle={ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  pages={1--5},
  year={2025},
  organization={IEEE}
}