PostHoc FREE Calibrating on Kolmogorov Arnold Networks
This work addresses the reliability of probabilistic predictions in spline-based neural networks, offering actionable design insights and a robust loss solution, though it appears incremental as it builds on existing KAN architectures with a specific calibration improvement.
The paper tackles the problem of miscalibrated confidence estimates in Kolmogorov Arnold Networks (KANs), which cause overconfidence in dense data regions and underconfidence in sparse areas, by introducing a novel TemperatureScaled Loss (TSL) that integrates a temperature parameter into the training objective to dynamically adjust predictive distributions, resulting in significantly reduced calibration errors as demonstrated through theoretical analysis and empirical evaluations on standard benchmarks.
Kolmogorov Arnold Networks (KANs) are neural architectures inspired by the Kolmogorov Arnold representation theorem that leverage B Spline parameterizations for flexible, locally adaptive function approximation. Although KANs can capture complex nonlinearities beyond those modeled by standard MultiLayer Perceptrons (MLPs), they frequently exhibit miscalibrated confidence estimates manifesting as overconfidence in dense data regions and underconfidence in sparse areas. In this work, we systematically examine the impact of four critical hyperparameters including Layer Width, Grid Order, Shortcut Function, and Grid Range on the calibration of KANs. Furthermore, we introduce a novel TemperatureScaled Loss (TSL) that integrates a temperature parameter directly into the training objective, dynamically adjusting the predictive distribution during learning. Both theoretical analysis and extensive empirical evaluations on standard benchmarks demonstrate that TSL significantly reduces calibration errors, thereby improving the reliability of probabilistic predictions. Overall, our study provides actionable insights into the design of spline based neural networks and establishes TSL as a robust loss solution for enhancing calibration.