kVNN: Learnable Volterra Network Kernels

Higher-order learning exploits compositional features whose predictive value arises from nonlinear interactions beyond pairwise relations among variables, scales, or modalities. To address the complexity of modeling higher-order interactions in modern large-scale deep learning models, a kernelized Volterra Neural Network (kVNN) is proposed in this paper. Specifically, the proposed learnable multi-kernel representation models different interaction orders using distinct polynomial-kernel components with compact learnable centers, thereby yielding an order-adaptive parameterization. The resulting kVNN layers are composed of parallel order-specific branches and can readily replace standard convolutional kernels in existing learning architectures. Theoretical results are supported by experiments on video action recognition, image denoising, and image classification. The results show marked performance-efficiency trade-offs: kVNN consistently reduces model (parameters) and computational (GFLOPs) complexity while achieving competitive and often improved performance, even when trained from scratch without large-scale pretraining. In summary, structured kernelized higher-order layers offer a practical path to balancing expressivity and computational cost in modern deep networks.