Fractional Quantum Chaotic Maps for Neural Network Enhancement

This paper presents a novel framework for enhancing neural network performance through the integration of fractional and quantum chaotic maps. We introduce a fractional hierarchical rational chaotic map alongside quantum adaptations of the logistic and tent maps, analyzing their dynamic properties via bifurcation and time series diagrams. These chaotic mechanisms are embedded into gradient-based learning algorithms—batch, mini-batch, and stochastic gradient descent—to improve training efficiency and predictive accuracy. Empirical evaluations on three real-world regression tasks (housing prices, bike sharing, and concrete strength) demonstrate consistent performance gains across all models. The inclusion of chaotic maps notably accelerates convergence, reduces training error, and improves weight distribution within networks. Our findings underscore the transformative potential of fractional and quantum chaos in optimizing neural learning systems for complex, real-world applications.