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Geodesic paths and distances are among the most popular intrinsic properties of 3D surfaces. Traditionally, geodesic paths on discrete polygon surfaces were computed using shortest path algorithms, such as Dijkstra. However, such algorithms have two major limitations. They are non-differentiable which limits their direct usage in learnable pipelines and they are considerably time demanding. To address such limitations and alleviate the computational burden, we propose a learnable network to approximate geodesic paths. The proposed method is comprised by three major components: a graph neural network that encodes node positions in a high dimensional space, a path embedding that describes previously visited nodes and a point classifier that selects the next point in the path. The proposed method provides efficient approximations of the shortest paths and geodesic distances estimations. Given that all of the components of our method are fully differentiable, it can be directly plugged into any learnable pipeline as well as customized under any differentiable constraint. We extensively evaluate the proposed method with several qualitative and quantitative experiments.