用核化方法让高阶信号模型更高效，同时保持可解释性。
Learning with Volterra Neural Networks: A System Theoretic Perspective
- 将伏特拉滤波的分阶结构与可学习多项式核结合，避免高阶张量参数化。
- 在视觉任务中实现精度与效率的平衡，无需显式高阶张量。
- 适合需要高阶交互建模且关注计算效率的研究者。
高阶交互成分对信号、图像和视频建模至关重要，但显式的高阶算子常伴随参数和计算成本的急剧增加。本文提出kVNN，一种可学习的核化伏特拉神经算子，用于紧凑的高阶滤波。其核心思想是通过核化提升伏特拉型神经算子的效率，同时提供高阶成分的结构化解释。该方法将伏特拉滤波的分阶结构与可学习的多项式核原子相结合，使不同交互阶次由独立的可学习中心和系数表示。这种分阶解耦表示避免了显式的高阶张量参数化，可实现为兼容卷积神经网络（CNN）的层。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。
原文摘要 · Abstract (English)
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.
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