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.

Accelerated Image-Aware Generative Diffusion Modeling

We propose in this paper an analytically new construct of a diffusion model whose drift and diffusion parameters yield an exponentially time-decaying Signal to Noise Ratio in the forward process. In reverse, the construct cleverly carries out the learning of the diffusion coefficients on the structure of clean images using an autoencoder. The proposed methodology significantly accelerates the diffusion process, reducing the required diffusion time steps from around 1000 seen in conventional models to 200-500 without compromising image quality in the reverse-time diffusion. In a departure from conventional models which typically use time-consuming multiple runs, we introduce a parallel data-driven model to generate a reverse-time diffusion trajectory in a single run of the model. The resulting collective block-sequential generative model eliminates the need for MCMC-based sub-sampling correction for safeguarding and improving image quality, to further improve the acceleration of image generation. Collectively, these advancements yield a generative model that is an order of magnitude faster than conventional approaches, while maintaining high fidelity and diversity in generated images, hence promising widespread applicability in rapid image synthesis tasks.