KVNN: Learnable Multi-Kernel Volterra Neural Networks

2026-04-16

AI Summary

This work addresses the challenge of efficiently modeling high-order feature interactions in deep learning, which is often hindered by excessive model complexity and computational cost. To this end, the authors propose the kernelized Volterra Neural Network (kVNN), which leverages learnable multi-kernel polynomial representations to parallelly capture structured feature interactions of varying orders within a single layer. The method introduces order-adaptive, learnable polynomial kernel components that enable direct substitution of standard convolutional kernels, facilitating seamless integration into existing architectures. Despite significantly reducing both parameter count and computational complexity, kVNN maintains strong representational capacity. Experimental results demonstrate that kVNN achieves comparable or superior performance on video action recognition and image denoising tasks with fewer parameters and lower GFLOPs, without requiring large-scale pretraining.

Technology Category

• Machine Learning: Kernel Methods
• Computer Vision: Learning & Optimization for CV
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Higher-order learning is fundamentally rooted in exploiting compositional features. It clearly hinges on enriching the representation by more elaborate interactions of the data which, in turn, tends to increase the model complexity of conventional large-scale deep learning models. In this paper, a kernelized Volterra Neural Network (kVNN) is proposed. The key to the achieved efficiency lies in using a learnable multi-kernel representation, where different interaction orders are modeled by distinct polynomial-kernel components with compact, learnable centers, yielding an order-adaptive parameterization. Features are learned by the composition of layers, each of which consists of parallel branches of different polynomial orders, enabling kVNN filters to directly replace standard convolutional kernels within existing architectures. The theoretical results are substantiated by experiments on two representative tasks: video action recognition and image denoising. The results demonstrate favorable performance-efficiency trade-offs: kVNN consistently yields reduced model (parameters) and computational (GFLOPs) complexity with competitive and often improved performance. These results are maintained even when trained from scratch without large-scale pretraining. In summary, we substantiate that structured kernelized higher-order layers offer a practical path to balancing expressivity and computational cost in modern deep networks.

Problem

• higher-order learning
• model complexity
• computational efficiency
• feature interaction
• deep neural networks

Innovation

• learnable multi-kernel
• Volterra neural network
• higher-order interactions
• order-adaptive parameterization
• polynomial kernel