arXiv subjects

Sergii Kavun

Publications and source records attributed to Sergii Kavun.

5 recordsLinked to original sources

arXiv2026

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.

cs.LG↗

arXiv2025

Multi-Metric Algorithmic Complexity: Beyond Asymptotic Analysis

Traditional algorithm analysis treats all basic operations as equally costly, which hides significant differences in time, energy consumption, and cost between different types of computations on modern processors. We propose a weighted-operation complexity model that assigns realistic cost values to different instruction types across multiple dimensions: computational effort, energy usage, carbon footprint, and monetary cost. The model computes overall efficiency scores based on user-defined priorities and can be applied through automated code analysis or integrated with performance measurement tools. This approach complements existing theoretical models by enabling practical, architecture-aware algorithm comparisons that account for performance, sustainability, and economic factors. We demonstrate an open-source implementation that analyzes code, estimates multi-dimensional costs, and provides efficiency recommendations across various algorithms. We address two research questions: (RQ1) Can a multi-metric model predict time/energy with high accuracy across architectures? (RQ2) How does it compare to baselines like Big-O, ICE, and EVM gas? Validation shows strong correlations (\r{ho}>0.9) with measured data, outperforming baselines in multi-objective scenarios.

cs.PF↗

arXiv2025

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization

Activation functions are critical components in deep neural networks, directly influencing gradient flow, training stability, and model performance. Traditional functions like ReLU suffer from dead neuron problems, while sigmoid and tanh exhibit vanishing gradient issues. We introduce two novel hybrid activation functions: S3 (Sigmoid-Softsign) and its improved version S4 (smoothed S3). S3 combines sigmoid for negative inputs with softsign for positive inputs, while S4 employs a smooth transition mechanism controlled by a steepness parameter k. We conducted comprehensive experiments across binary classification, multi-class classification, and regression tasks using three different neural network architectures. S4 demonstrated superior performance compared to nine baseline activation functions, achieving 97.4% accuracy on MNIST, 96.0% on Iris classification, and 18.7 MSE on Boston Housing regression. The function exhibited faster convergence (-19 for ReLU) and maintained stable gradient flow across network depths. Comparative analysis revealed S4's gradient range of [0.24, 0.59] compared to ReLU's 18% dead neurons in deep networks. The S4 activation function addresses key limitations of existing functions through its hybrid design and smooth transition mechanism. The tunable parameter k allows adaptation to different tasks and network depths, making S4 a versatile choice for deep learning applications. These findings suggest that hybrid activation functions represent a promising direction for improving neural network training dynamics.

cs.LG↗

arXiv2025

Multiple data-driven missing imputation

This paper introduces KZImputer, a novel adaptive imputation method for univariate time series designed for short to medium-sized missed points (gaps) (1-5 points and beyond) with tailored strategies for segments at the start, middle, or end of the series. KZImputer employs a hybrid strategy to handle various missing data scenarios. Its core mechanism differentiates between gaps at the beginning, middle, or end of the series, applying tailored techniques at each position to optimize imputation accuracy. The method leverages linear interpolation and localized statistical measures, adapting to the characteristics of the surrounding data and the gap size. The performance of KZImputer has been systematically evaluated against established imputation techniques, demonstrating its potential to enhance data quality for subsequent time series analysis. This paper describes the KZImputer methodology in detail and discusses its effectiveness in improving the integrity of time series data. Empirical analysis demonstrates that KZImputer achieves particularly strong performance for datasets with high missingness rates (around 50% or more), maintaining stable and competitive results across statistical and signal-reconstruction metrics. The method proves especially effective in high-sparsity regimes, where traditional approaches typically experience accuracy degradation.

stat.ME↗

arXiv2025

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.

stat.ME↗