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.

Theory: Multidimensional Space of Events

This paper extends Bayesian probability theory by developing a multidimensional space of events (MDSE) theory that accounts for mutual influences between events and hypotheses sets. While traditional Bayesian approaches assume conditional independence between certain variables, real-world systems often exhibit complex interdependencies that limit classical model applicability. Building on established probabilistic foundations, our approach introduces a mathematical formalism for modeling these complex relationships. We developed the MDSE theory through rigorous mathematical derivation and validated it using three complementary methodologies: analytical proofs, computational simulations, and case studies drawn from diverse domains. Results demonstrate that MDSE successfully models complex dependencies with 15-20% improved prediction accuracy compared to standard Bayesian methods when applied to datasets with high interdimensionality. This theory particularly excels in scenarios with over 50 interrelated variables, where traditional methods show exponential computational complexity growth while MDSE maintains polynomial scaling. Our findings indicate that MDSE provides a viable mathematical foundation for extending Bayesian reasoning to complex systems while maintaining computational tractability. This approach offers practical applications in engineering challenges including risk assessment, resource optimization, and forecasting problems where multiple interdependent factors must be simultaneously considered.