arXiv:2603.08583cs.LGcs.CV2026-03

提出可独立控制输入输出非线性的双阶段KAN,显著减少参数量并提升训练稳定性。

DualFlexKAN: Dual-stage Kolmogorov-Arnold Networks with Independent Function Control

  • 分两阶段独立学习输入变换与输出激活函数,实现灵活的非线性建模
  • 在多个任务中用1-2个数量级更少参数达到更高精度和更快收敛
  • 支持多种基函数与正则化,适合科学计算中的小样本与可解释性需求

多层感知机(MLPs)依赖预设的固定激活函数,导致归纳偏置静态,需通过增加深度和宽度来逼近复杂拓扑。柯尔莫哥洛夫-阿诺德网络(KANs)通过边级可学习函数缓解此问题,但其架构存在参数量二次增长和结构僵化,难以融入常规正则化。本文提出双阶段可调KAN(DFKAN),通过解耦前线性输入变换与后线性输出激活,实现对非线性形式的独立控制。该设计支持正交多项式、B样条、径向基函数等多种基函数,并可配置正则化策略以稳定训练。在回归、物理信息任务及函数逼近等基准上,DFKAN在准确率、收敛速度和梯度保真度方面均优于传统MLP与KAN。其混合配置仅需标准KAN 1~2个数量级的参数即可实现更优性能,有效缓解参数爆炸问题,同时保持类KAN的表达能力。该框架为自适应非线性建模提供了系统化、可扩展的解决方案,特别适用于数据高效学习与科学领域的可解释函数发现。

原文摘要 · Abstract (English)

Multi-Layer Perceptrons (MLPs) rely on pre-defined, fixed activation functions, imposing a static inductive bias that forces the network to approximate complex topologies solely through increased depth and width. Kolmogorov-Arnold Networks (KANs) address this limitation through edge-centric learnable functions, yet their formulation suffers from quadratic parameter scaling and architectural rigidity that hinders the effective integration of standard regularization techniques. This paper introduces the DualFlexKAN (DFKAN), a flexible architecture featuring a dual-stage mechanism that independently controls pre-linear input transformations and post-linear output activations. This decoupling enables hybrid networks that optimize the trade-off between expressiveness and computational cost. Unlike standard formulations, DFKAN supports diverse basis function families, including orthogonal polynomials, B-splines, and radial basis functions, integrated with configurable regularization strategies that stabilize training dynamics. Comprehensive evaluations across regression benchmarks, physics-informed tasks, and function approximation demonstrate that DFKAN outperforms both MLPs and conventional KANs in accuracy, convergence speed, and gradient fidelity. The proposed hybrid configurations achieve superior performance with one to two orders of magnitude fewer parameters than standard KANs, effectively mitigating the parameter explosion problem while preserving KAN-style expressiveness. DFKAN provides a principled, scalable framework for incorporating adaptive non-linearities, proving particularly advantageous for data-efficient learning and interpretable function discovery in scientific applications.

KAN神经网络可解释性函数逼近

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。