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Title: Abstract Diagrammatic Reasoning with Multiplex Graph Networks

Paper content:
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.
Abstract reasoning has long been thought of as a key part of human intelligence, and a necessary component towards Artificial General Intelligence.
When presented in complex scenes, humans can quickly identify elements across different scenes and infer relations between them.
For example, when you are using a pile of different types of LEGO bricks to assemble a spaceship, you are actively inferring relations between each LEGO brick, such as in what ways they can fit together.
This type of abstract reasoning, particularly in the visual domain, is a crucial key to human ability to build complex things.
Many tests have been proposed to measure human ability for abstract reasoning.
The most popular test in the visual domain is the Raven Progressive Matrices (RPM) test (Raven (2000) ).
In the RPM test, the participants are asked to view a sequence of contextual diagrams, usually given as a 3 × 3 matrices of diagrams with the bottom-right diagram left blank.
Participants should infer abstract relationships in rows or columns of the diagram, and pick from a set of candidate answers the correct one to fill in the blank.
Figures 1 (a) shows an example of RPM tasks containing XOR relations across diagrams in rows.
More examples can be found in Appendix C. Another widely used test for measuring reasoning in psychology is Diagram Syllogism task (Sato et al. (2015) ), where participants need to infer conclusions based on 2 given premises.
Figure 1c shows an example of Euler Diagram Syllogism task.
Barrett et al. (2018) recently published a large and comprehensive RPM-style dataset named Procedurally Generated Matrices 'PGM', and proposed Wild Relation Network (WReN), a state-of-the-art neural net for RPM-style tasks.
While WReN outperforms other state-of-the-art vision models such as Residual Network He et al. (2016) , the performance is still far from deep neural nets' performance on other vision or natural language processing tasks.
Recently, there has been a focus on object-level representations (Yi et al. (2018) ; Hu et al. (2017) ; Hudson & Manning (2018) ; Mao et al. (2019) ; Teney et al. (2017) ; Zellers et al. (2018) ) for visual reasoning tasks, which enable the use of inductive-biased architectures such as symbolic programs and scene graphs to directly capture relations between objects.
For RPM-style tasks, symbolic programs are less suitable as these programs are generated from given questions in the Visual-Question Answering setting.
In RPM-style tasks there are no explicit questions.
Encoding RPM tasks into graphs is a more natural choice.
However, previous works on scene graphs (Teney et al. (2017) ; Zellers et al. (2018) ) model a single image as graphs, which is not suitable for RPM tasks as there are many different layers of relations across different subsets of diagrams in a single task.
In this paper we introduce MXGNet, a multi-layer multiplex graph neural net architecture for abstract diagram reasoning.
Here 'Multi-layer' means the graphs are built across different diagram panels, where each diagram is a layer.
'Multiplex' means that edges of the graphs encode multiple relations between different element attributes, such as colour, shape and position.
Multiplex networks are discussed in detail by Kao & Porter (2018) .
We first tested the application of multiplex graph on a Diagram Syllogism dataset (Wang et al. (2018a) ), and confirmed that multiplex graph improves performance on the original model.
For RPM task, MXGNet encodes subsets of diagram panels into multi-layer multiplex graphs, and combines summarisation of several graphs to predict the correct candidate answer.
With a hierarchical summarisation scheme, each graph is summarised into feature embeddings representing relationships in the subset.
These relation embeddings are then combined to predict the correct answer.
For PGM dataset (Barrett et al. (2018) (Zhang et al. (2019) ), MXGNet, without any auxiliary training with additional labels, achieves 83.91% test accuracy, outperforming 59.56% accuracy by the best model with auxiliary training for the RAVEN dataset.
We also show that MXGNet is robust to variations in forms of object-level representations.
Both variants of MXGNet achieve higher test accuracies than existing best models for the two datasets.
We presented MXGNet, a new graph-based approach to diagrammatic reasoning problems in the style of Raven Progressive Matrices (RPM).
MXGNet combines three powerful ideas, namely, object-level representation, graph neural networks and multiplex graphs, to capture relations present in the reasoning task.
Through experiments we showed that MXGNet performs better than previous models on two RPM datasets.
We also showed that MXGNet has better generalisation performance.
One important direction for future work is to make MXGNet interpretable, and thereby extract logic rules from MXGNet.
Currently, the learnt representations in MXGNet are still entangled, providing little in the way of understanding its mechanism of reasoning.
Rule extraction can provide people with better understanding of the reasoning problem, and may allow neural networks to work seamlessly with more programmable traditional logic engines.
While the multi-layer multiplex graph neural network is designed for RPM style reasoning task, it can be readily extended to other diagrammatic reasoning tasks where relations are present between multiple elements across different diagrams.
One example of a real-world application scenario is robots assembling parts of an object into a whole, such as building a LEGO model from a room of LEGO blocks.
MXGNet provides a suitable way of capturing relations between parts, such as ways of piecing and locking two parts together.

assistant: text: MXGNet is a multilayer, multiplex graph based architecture which achieves good performance on various diagrammatic reasoning tasks.