Relational Learning in Pre-Trained Models: A Theory from Hypergraph Recovery Perspective
This work provides a mathematical framework for analyzing relational learning in pre-trained models, which is incremental as it integrates graph theory into existing pre-training paradigms.
The authors tackled the problem of understanding how foundation models learn relational dynamics by formalizing relational learning as hypergraph recovery, and they theoretically analyzed the feasibility and data efficiency of pre-trained models in recovering such hypergraphs with minimax near-optimal bounds.
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.