DeepGAR: Deep Graph Learning for Analogical Reasoning

TL;DR

DeepGAR introduces a deep learning framework for analogical reasoning based on Structure-Mapping Theory, effectively identifying relational correspondences in graphs while respecting cognitive constraints, and demonstrating superior performance on various datasets.

Contribution

It presents a novel deep learning approach that integrates cognitive theory-driven constraints into graph-based analogical reasoning, addressing previous computational challenges.

Findings

DeepGAR outperforms existing methods on synthetic datasets.

The framework effectively incorporates cognitive constraints into deep learning.

Experimental results validate the approach's efficiency and accuracy.

Abstract

Analogical reasoning is the process of discovering and mapping correspondences from a target subject to a base subject. As the most well-known computational method of analogical reasoning, Structure-Mapping Theory (SMT) abstracts both target and base subjects into relational graphs and forms the cognitive process of analogical reasoning by finding a corresponding subgraph (i.e., correspondence) in the target graph that is aligned with the base graph. However, incorporating deep learning for SMT is still under-explored due to several obstacles: 1) the combinatorial complexity of searching for the correspondence in the target graph; 2) the correspondence mining is restricted by various cognitive theory-driven constraints. To address both challenges, we propose a novel framework for Analogical Reasoning (DeepGAR) that identifies the correspondence between source and target domains by assuring cognitive theory-driven constraints. Specifically, we design a geometric constraint embedding space to induce subgraph relation from node embeddings for efficient subgraph search. Furthermore, we develop novel learning and optimization strategies that could end-to-end identify correspondences that are strictly consistent with constraints driven by the cognitive theory. Extensive experiments are conducted on synthetic and real-world datasets to demonstrate the effectiveness of the proposed DeepGAR over existing methods.