KVNN: Learnable Multi-Kernel Volterra Neural Networks

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.

Proximal Vision Transformer: Enhancing Feature Representation through Two-Stage Manifold Geometry

The Vision Transformer (ViT) architecture has become widely recognized in computer vision, leveraging its self-attention mechanism to achieve remarkable success across various tasks. Despite its strengths, ViT's optimization remains confined to modeling local relationships within individual images, limiting its ability to capture the global geometric relationships between data points. To address this limitation, this paper proposes a novel framework that integrates ViT with the proximal tools, enabling a unified geometric optimization approach to enhance feature representation and classification performance. In this framework, ViT constructs the tangent bundle of the manifold through its self-attention mechanism, where each attention head corresponds to a tangent space, offering geometric representations from diverse local perspectives. Proximal iterations are then introduced to define sections within the tangent bundle and project data from tangent spaces onto the base space, achieving global feature alignment and optimization. Experimental results confirm that the proposed method outperforms traditional ViT in terms of classification accuracy and data distribution.