A central challenge in modern machine learning is learning generalizable procedures that remain effective on unseen, potentially out-of-distribution (OOD) data. Such generalization depends on a complex interplay among model architectures, task structures, data assumptions, and training methodologies. In this talk, I will focus on the interaction between model architecture and task structure in the context of graphs tasks or geometric problems. We are particularly interested in three questions: Do different neural networks learn fundamentally different algorithmic procedures? Can OOD generalization be achieved with only finite samples? How do we probe what's learned internally? How can we use obtained insights help design more effective neural models that can tackle (geometric) problems more efficiently? I will present some of our initial studies exploring these questions. This talk is based on joint work with several collaborators, whom I will acknowledge during the talk.