# PostHoc FREE Calibrating on Kolmogorov Arnold Networks

arXiv: https://arxiv.org/abs/2503.01195 · HTML: https://mlsanity.com/paper/2503.01195/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 14 of 14)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [A Review and Comparative Study on Probabilistic Object Detection in Autonomous Driving](https://mlsanity.com/paper/2011.10671/) (2020)
- [Calibration of Encoder Decoder Models for Neural Machine Translation](https://mlsanity.com/paper/1903.00802/) (2019)
- [Smooth ECE: Principled Reliability Diagrams via Kernel Smoothing](https://mlsanity.com/paper/2309.12236/) (2023)
- [Post-hoc Uncertainty Calibration for Domain Drift Scenarios](https://mlsanity.com/paper/2012.10988/) (2020)
- [Temperature Schedules for Self-Supervised Contrastive Methods on Long-Tail Data](https://mlsanity.com/paper/2303.13664/) (2023)
- [On Focal Loss for Class-Posterior Probability Estimation: A Theoretical Perspective](https://mlsanity.com/paper/2011.09172/) (2020)

## Abstract (arXiv)

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.