Conformable Fractional Deep Neural Networks (CFDNN) for high-speed cyber-attack detection

Abstract

Abstract The growing sophistication of cyber-attacks exposes the limitations of conventional deep neural networks, which often suffer from slow convergence and high computational costs. This paper introduces the Conformable Fractional Deep Neural Network (CFDNN), a framework that replaces standard backpropagation with conformable fractional gradient descent. By operating in the super-integer regime ( $$\alpha \in [1.2, 1.8]$$ ), the model smooths the loss landscape to accelerate training. Evaluated on NSL-KDD and CIC-IDS2018 using cross-validation, the CFDNN achieves 99.42% and 99.86% accuracy, respectively. It attains these results in just 30 epochs–a 40% reduction in training time. On the large-scale CIC-IDS2018 dataset, the model converged in approximately 24.2 minutes on a system equipped with an standard CPU. The CFDNN thus provides a computationally efficient, high-performance alternative to classical methods, offering a robust solution for modern cyber-defense.