  Abstract reasoning, particularly in the visual domain, is a complex human
ability, but it remains a challenging problem for artificial neural learning
systems. In this work we propose MXGNet, a multilayer graph neural network for
multi-panel diagrammatic reasoning tasks. MXGNet combines three powerful
concepts, namely, object-level representation, graph neural networks and
multiplex graphs, for solving visual reasoning tasks. MXGNet first extracts
object-level representations for each element in all panels of the diagrams,
and then forms a multi-layer multiplex graph capturing multiple relations
between objects across different diagram panels. MXGNet summarises the multiple
graphs extracted from the diagrams of the task, and uses this summarisation to
pick the most probable answer from the given candidates. We have tested MXGNet
on two types of diagrammatic reasoning tasks, namely Diagram Syllogisms and
Raven Progressive Matrices (RPM). For an Euler Diagram Syllogism task MXGNet
achieves state-of-the-art accuracy of 99.8%. For PGM and RAVEN, two
comprehensive datasets for RPM reasoning, MXGNet outperforms the
state-of-the-art models by a considerable margin.
