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 have demonstrated remarkable insights into the relational dynamics of the world%2C leading to the crucial question: how do these models acquire an understanding of world hybrid relations%3F Traditional statistical learning%2C particularly for prediction problems%2C may overlook the rich and inherently structured information from the data%2C especially regarding the relationships between objects. We introduce a mathematical model that formalizes relational learning as hypergraph recovery to study pre-training of FMs. In our framework%2C the world is represented as a hypergraph%2C with data abstracted as random samples from hyperedges. We theoretically examine the feasibility of a Pre-Trained Model (PTM) to recover this hypergraph and analyze the data efficiency in a minimax near-optimal style. By integrating rich graph theories into the realm of PTMs%2C our mathematical framework offers powerful tools for an in-depth understanding of pre-training from a unique perspective and can be used under various scenarios. As an example%2C we extend the framework to entity alignment in multimodal learning.?quality=80&w=800)
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