发表机构
North Carolina State University; Fayetteville State University（北卡罗来纳州立大学; 费耶特维尔州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对高阶算子成本过高问题，提出kVNN核化Volterra神经算子，通过阶次解耦设计实现高效高阶滤波，在视觉任务中取得良好的精度效率平衡。
AI 中文摘要
高阶交互组件对信号、图像和视频建模至关重要，但显式高阶算子常面临参数与计算成本快速增长的问题。本文提出kVNN，一种用于紧凑高阶滤波的可学习核化Volterra神经算子，其动机是利用核化提升Volterra型神经算子的效率，同时为其高阶组件提供结构化解释。所提公式结合了Volterra滤波的阶次结构与可学习多项式核原子，允许不同交互阶次由独立可学习中心和系数表示，这种阶次解耦表示避免了显式高阶张量参数化，可作为兼容CNN的层实现。在代表性视觉任务上的实验表明，kVNN实现了良好的精度-效率权衡。
英文摘要
Higher-order interaction components are important for signal, image, and video modeling, but explicit high-order operators often suffer from rapidly increasing parameter and computational costs. This paper presents kVNN, a learnable kernelized Volterra Neural operator for compact higher-order filtering. The motivation is to use kernelization to improve the efficiency of Volterra-type neural operators while providing a structured interpretation of their higher-order components. The proposed formulation combines the order-wise structure of Volterra filtering with learnable polynomial-kernel atoms, allowing different interaction orders to be represented by separate learnable centers and coefficients. This order-decoupled representation avoids explicit high-order tensor parameterization and can be implemented as a CNN-compatible layer. Experiments on representative vision tasks show that kVNN achieves a favorable accuracy--efficiency trade-off.
