  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.
