Logistic and logit functions play important roles in modern science, serving as foundational tools in various applications, such as artificial neural networks (ANN). While there are functions that could produce distinct logistic and logit curves, no single, unified framework has been developed to generate both logistic and logit curves. We introduce a Cannistraci–Muscoloni–Gu generalized logistic–logit function (CMG-GLLF) to fill this gap. CMG-GLLF provides four interpretable and trainable param