# Automatic Grid Updates for Kolmogorov-Arnold Networks using Layer Histograms

arXiv: https://arxiv.org/abs/2511.08570 · HTML: https://mlsanity.com/paper/2511.08570/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 57 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 30 of 40)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [Contrastive Training for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2007.05566/) (2020)
- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [Learning Deep Embeddings with Histogram Loss](https://mlsanity.com/paper/1611.00822/) (2016)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (2024)
- [Neural Mean Discrepancy for Efficient Out-of-Distribution Detection](https://mlsanity.com/paper/2104.11408/) (2021)
- [Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.17611/) (2024)

## Built on by (most cited first, 3 of 3)

- [SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks](https://mlsanity.com/paper/2603.18548/) (2026)
- [A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2601.18672/) (2026)
- [Clifford Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.05977/) (2026)

## Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) are a class of neural networks that have received increased attention in recent literature. In contrast to MLPs, KANs leverage parameterized, trainable activation functions and offer several benefits including improved interpretability and higher accuracy on learning symbolic equations. However, the original KAN architecture requires adjustments to the domain discretization of the network (called the "domain grid") during training, creating extra overhead for the user in the training process. Typical KAN layers are not designed with the ability to autonomously update their domains in a data-driven manner informed by the changing output ranges of previous layers. As an added benefit, this histogram algorithm may also be applied towards detecting out-of-distribution (OOD) inputs in a variety of settings. We demonstrate that AdaptKAN exceeds or matches the performance of prior KAN architectures and MLPs on four different tasks: learning scientific equations from the Feynman dataset, image classification from frozen features, learning a control Lyapunov function, and detecting OOD inputs on the OpenOOD v1.5 benchmark.