This work presents a novel creative approach to describe cognitive systems by combining differential geometry with reinforcement learning. We propose a mathematical approach primarily based on geometric properties of facts manifolds to improve cognitive models studying functionality. Differential geometry facilitates us to set up cognitive activities over curved surfaces. This allows us to depict the intellectual mechanisms concerned in learning and decision-making extra exactly. Considering they apply reinforcement mastering, those models might also adapt and enhance their behaviour relying on remarks from their surroundings. This hybrid model plays better in tests of challenging cognitive responsibilities such spatial navigation and sample reputation by using the use of the intrinsic geometric shape of the statistics. We carefully observe the convergence traits of the proposed models. The findings reveal that the geometric method not simplest clarifies cognitive techniques but additionally hastens mastering and guarantees elevated dependability of the models. Our results reveal that artificial cognitive systems with higher intelligence and efficiency might be produced from these mathematical models. This might have a significant impact on disciplines such robotics, self-driving automobiles, and the creation of intelligent systems