VexNet: Vector-Composed Feature-Oriented Neural Network

Extracting robust features against geometric transformations and adversarial perturbations remains a critical challenge in deep learning. Although capsule networks exhibit resilience through vector-encapsulated features and dynamic routing, they suffer from computational inefficiency due to iterative routing, dense matrix operations, and extra activation scalars. To address these limitations, we propose a method that integrates (1) compact vector-grouped neurons to eliminate activation scalars, (2) a non-iterative voting algorithm that preserves spatial relationships with reduced computation, and (3) efficient weight-sharing strategies that balance computational efficiency with generalizability. Our approach outperforms existing methods in image classification on CIFAR-10 and SVHN, achieving up to a 0.31% increase in accuracy with fewer parameters and lower FLOPs. Evaluations demonstrate superior performance over competing methods, with 0.31% accuracy gains on CIFAR-10/SVHN (with reduced parameters and FLOPs) and 1.93%/1.09% improvements in novel-view recognition on smallNORB. Under FGSM and BIM attacks, our method reduces attack success rates by 47.7% on CIFAR-10 and 32.4% on SVHN, confirming its enhanced robustness and efficiency. Future work will extend vexel representations to MLPs and RNNs and explore applications in computer graphics, natural language processing, and reinforcement learning.