# Kolmogorov-Arnold Networks

Jet taggers in high-energy physics are judged mainly by accuracy, yet it has been hard to say whether their decisions track the radiation structure inside a jet. Researchers fit a Kolmogorov-Arnold Network (KAN) locally to a trained model's perturbation response, then read two-body and three-body interaction scores from the surrogate's mixed partial derivatives and rank-correlate them with the dominant contributions to two-point and three-point energy correlation functions. On JetClass, the Particle Transformer shows clear positive two-body alignment while a standard multi-head attention baseline does not; three-body alignment is weaker for both, with ParT still stronger and its error bars excluding null correlation.

Jet taggers in high-energy physics are judged mainly by accuracy, yet it has been hard to say whether their decisions track the radiation structure inside a jet. Researchers fit a Kolmogorov-Arnold Network (KAN) locally to a trained model's perturbation response, then read two-body and three-body interaction scores from the surrogate's mixed partial derivatives and rank-correlate them with the dominant contributions to two-point and three-point energy correlation functions. On JetClass, the Particle Transformer shows clear positive two-body alignment while a standard multi-head attention baseline does not; three-body alignment is weaker for both, with ParT still stronger and its error bars excluding null correlation.

In power-system dynamic simulation, physics-informed neural networks built on multilayer perceptrons are limited by spectral bias toward smooth functions and struggle to capture electromechanical oscillations, while B-spline physics-informed Kolmogorov-Arnold networks are costly to train. mac-PIKAN embeds the closed-form modal response of the linearized swing equation as a fixed term in the trial solution and uses a Chebyshev-basis KAN to learn a nonlinear correction that vanishes at the initial time, so both initial rotor angle and speed hold exactly. On the single-machine infinite-bus benchmark its mean rotor-angle and frequency errors are 0.29% and 0.99%, against 1.59% and 5.26% for the PINN, and the advantage persists with less training data and at lower damping.

In power-system dynamic simulation, physics-informed neural networks built on multilayer perceptrons are limited by spectral bias toward smooth functions and struggle to capture electromechanical oscillations, while B-spline physics-informed Kolmogorov-Arnold networks are costly to train. mac-PIKAN embeds the closed-form modal response of the linearized swing equation as a fixed term in the trial solution and uses a Chebyshev-basis KAN to learn a nonlinear correction that vanishes at the initial time, so both initial rotor angle and speed hold exactly. On the single-machine infinite-bus benchmark its mean rotor-angle and frequency errors are 0.29% and 0.99%, against 1.59% and 5.26% for the PINN, and the advantage persists with less training data and at lower damping.