This work presents a novel paradigmatic revision of traditional neural networks, using network theoretic methods and Conformal Geometric Algebra. A unique theoretical framework called the ‘hyperfield cognition framework’ expands upon the mathematical foundations of neural networks in five-dimensional Conformal Geometric Algebraic space. This framework allows one to construct a novel theoretical computational engine, which is similar to a standard artificial neural network, but admits numerous added benefits: permits multiple training programs simultaneously, affords computational multiplicity in a single engine, reduces sensitivity to adversarial perturbations in training sets, affords broader capabilities and plasticity in the training of networks and produces robust and streamlined ‘neural networks’. We call this novel five-dimensional neural network a ‘hyperfield cognition network’ (HCN). This paper demonstrates the utility and merit of the proposed Hyperfield Cognition Network by presenting two case studies, the first of which investigates the fuel efficiency of various automobiles and the second of which models the residuary resistance per unit weight of displacement of ships.