Relational Learning in Pre-Trained Models: A Theory from Hypergraph Recovery Perspective

Yang Chen, Cong Fang, Zhouchen Lin, Bing Liu

Abstract: Foundation Models (FMs) have demonstrated remarkable insights into the relational dynamics of the world, leading to the crucial question: *how do these models acquire an understanding of world hybrid relations?* Traditional statistical learning, particularly for prediction problems, may overlook the rich and inherently structured information from the data, 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, the world is represented as a hypergraph, 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, 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, we extend the framework to entity alignment in multimodal learning.

Submission Number: 2734