NOVAK: Unified adaptive optimizer for deep neural networks

This work introduces NOVAK, a modular gradient-based optimization algorithm that integrates adaptive moment estimation, rectified learning-rate scheduling, decoupled weight regularization, multiple variants of Nesterov momentum, and lookahead synchronization into a unified, performance-oriented framework. NOVAK adopts a dual-mode architecture consisting of a streamlined fast path designed for production. The optimizer employs custom CUDA kernels that deliver substantial speedups (3-5 for critical operations) while preserving numerical stability under standard stochastic-optimization assumptions. We provide fully developed mathematical formulations for rectified adaptive learning rates, a memory-efficient lookahead mechanism that reduces overhead from O(2p) to O(p + p/k), and the synergistic coupling of complementary optimization components. Theoretical analysis establishes convergence guarantees and elucidates the stability and variance-reduction properties of the method. Extensive empirical evaluation on CIFAR-10, CIFAR-100, ImageNet, and ImageNette demonstrates NOVAK superiority over 14 contemporary optimizers, including Adam, AdamW, RAdam, Lion, and Adan. Across architectures such as ResNet-50, VGG-16, and ViT, NOVAK consistently achieves state-of-the-art accuracy, and exceptional robustness, attaining very high accuracy on VGG-16/ImageNette demonstrating superior architectural robustness compared to contemporary optimizers. The results highlight that NOVAKs architectural contributions (particularly rectification, decoupled decay, and hybrid momentum) are crucial for reliable training of deep plain networks lacking skip connections, addressing a long-standing limitation of existing adaptive optimization methods.