用局部参数化网络降低持续学习中的遗忘，效果显著优于传统方法。
KAN-CL: Per-Knot Importance Regularization for Continual Learning with Kolmogorov-Arnold Networks
- 基于KAN的分段样条结构，在每个节点粒度上做重要性加权正则化
- 在Split-CIFAR-10/5T和CIFAR-100/10T上遗忘率分别降低88%和93%
- 适合研究持续学习中参数重要性与模型架构协同设计的学者
灾难性遗忘仍是持续学习的核心难题：跨任务共享参数相互干扰，现有正则化方法如EWC和SI施加均匀惩罚，缺乏对参数服务输入区域的认知。本文提出KAN-CL，利用柯尔莫戈洛夫-阿诺德网络（KAN）的紧支集样条参数化，在节点粒度上实现重要性加权锚定。将KAN作为卷积主干的分类头，并在主干上采用标准EWC正则化（bbEWC），在Split-CIFAR-10/5T和Split-CIFAR-100/10T上相比仅头部KAN基线遗忘率分别降低88%和93%，且在两个基准上准确率均匹配或超越所有基线。进一步通过神经正切核（NTK）分析表明，KAN的样条局部性导致跨任务NTK存在结构秩缺陷，即使在特征学习阶段也成立遗忘上界。结果证明，结合具有天然参数局部性的架构（KAN头）与互补的主干正则化（bbEWC），可构成一种组合式、原理清晰的灾难性遗忘应对方案。
原文摘要 · Abstract (English)
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.
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