# KAN-CL: Per-Knot Importance Regularization for Continual Learning with Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2605.12306 · HTML: https://mlsanity.com/paper/2605.12306/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 18 of 18)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Rotate your Networks: Better Weight Consolidation and Less Catastrophic Forgetting](https://mlsanity.com/paper/1802.02950/) (2018)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix](https://mlsanity.com/paper/2010.04003/) (2020)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent](https://mlsanity.com/paper/2006.11942/) (2020)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)
- [Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Tasks](https://mlsanity.com/paper/2406.14916/) (2024)
- [Kolmogorov-Arnold Networks: A Critical Assessment of Claims, Performance, and Practical Viability](https://mlsanity.com/paper/2407.11075/) (2024)
- [PowerMLP: An Efficient Version of KAN](https://mlsanity.com/paper/2412.13571/) (2024)
- [A preliminary study on continual learning in computer vision using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.13550/) (2024)

## Abstract (arXiv)

Catastrophic forgetting remains the central obstacle in continual learning (CL): parameters shared across tasks interfere with one another, and existing regularization methods such as EWC and SI apply uniform penalties without awareness of which input region a parameter serves. We propose KAN-CL, a continual learning framework that exploits the compact-support spline parameterization of Kolmogorov-Arnold Networks (KANs) to perform importance-weighted anchoring at per-knot granularity. Deployed as a classification head on a convolutional backbone with standard EWC regularization on the backbone (bbEWC) KAN-CL achieves forgetting reductions of 88% and 93% over a head-only KAN baseline on Split-CIFAR-10/5T and Split-CIFAR-100/10T respectively, while matching or exceeding the accuracy of all baselines on both benchmarks. We further provide a Neural Tangent Kernel (NTK) analysis showing that KAN's spline locality induces a structural rank deficit in the cross-task NTK, yielding a forgetting bound that holds even in the feature-learning regime. These results establish that combining an architecture with natural parameter locality (KAN head) with a complementary backbone regularizer (bbEWC) yields a compositional and principled approach to catastrophic forgetting.