Catastrophic Forgetting in Kolmogorov-Arnold Networks

TL;DR

This paper investigates catastrophic forgetting in Kolmogorov-Arnold Networks (KANs), providing a theoretical framework and experimental validation, and introduces KAN-LoRA for efficient continual learning and knowledge editing.

Contribution

It offers the first comprehensive analysis of KANs' forgetting behavior, linking it to activation support overlap and data dimension, and proposes a novel adapter for parameter-efficient fine-tuning.

Findings

KANs show good retention in low-dimensional settings

KANs are vulnerable to forgetting in high-dimensional tasks

KAN-LoRA improves continual learning efficiency

Abstract

Catastrophic forgetting is a longstanding challenge in continual learning, where models lose knowledge from earlier tasks when learning new ones. While various mitigation strategies have been proposed for Multi-Layer Perceptrons (MLPs), recent architectural advances like Kolmogorov-Arnold Networks (KANs) have been suggested to offer intrinsic resistance to forgetting by leveraging localized spline-based activations. However, the practical behavior of KANs under continual learning remains unclear, and their limitations are not well understood. To address this, we present a comprehensive study of catastrophic forgetting in KANs and develop a theoretical framework that links forgetting to activation support overlap and intrinsic data dimension. We validate these analyses through systematic experiments on synthetic and vision tasks, measuring forgetting dynamics under varying model configurations and data complexity. Further, we introduce KAN-LoRA, a novel adapter design for parameter-efficient continual fine-tuning of language models, and evaluate its effectiveness in knowledge editing tasks. Our findings reveal that while KANs exhibit promising retention in low-dimensional algorithmic settings, they remain vulnerable to forgetting in high-dimensional domains such as image classification and language modeling. These results advance the understanding of KANs' strengths and limitations, offering practical insights for continual learning system design.