Fractional-Order Spiking Bayesian Neural Model for Cognitive Computations

Cognition under uncertainty can be formalized through Bayesian inference, but biologically plausible neural implementations remain a challenge. This study develops a Bayesian neural model for lifespan prediction that integrates fractional-order dynamics into classical Leaky Integrate-and-Fire and Izhikevich neuron models. The inclusion of fractional derivative introduces long-term memory, and thus enhancing both biological plausibility and representational capacity of the Bayesian neural model. Experimental results demonstrate that fractional-order neuron models consistently provide closer alignment with both human predictions and optimal Bayesian predictions. The large-scale fractional-order Izhikevich model shows the most robust convergence and cortical plausibility. These findings highlight the role of fractal neural dynamics in probabilistic cognition and bridging theoretical Bayesian models with realistic spiking behavior. The study demonstrates how biologically inspired spiking neuron models can approximate Bayesian inference, suggesting pathways for computational neuroscience to design models that learn, predict, and adapt with the efficiency of cortical computations. Further, in this study, neural populations represent priors from demographic lifetables. However, a uniform likelihood and posterior that yield median lifespan predictions as probability distributions within the Neural Engineering Framework have been retained from the previous study. To investigate the influence of neural population size on biological plausibility and Bayesian optimality, experimental conditions systematically increase the neural population size and compare the predictive outcomes.