Learning with Volterra Neural Networks: A System Theoretic Perspective

2026-09-01

AI Summary

本文提出kVNN，一种可学习的核化Volterra神经算子，用于高效高阶滤波，通过结合Volterra滤波结构和可学习多项式核原子来解决高阶运算成本问题。

Abstract

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.

Problem

• Higher-order interaction
• Volterra filtering
• parameter and computational costs

Innovation

• kernelized Volterra Neural operator
• higher-order filtering
• learnable polynomial-kernel atoms
• order-decoupled representation
• CNN-compatible layer