Learning Hierarchical Relational Representations through Relational Convolutions

TL;DR

This paper introduces relational convolutional networks, a neural architecture equipped with computational mechanisms that capture progressively more complex relational features through the composition of simple modules, a key component of this framework is a novel operation that captures relational patterns in groups of objects by convolving graphlet filters against subsets of the input.

Abstract

An evolving area of research in deep learning is the study of architectures and inductive biases that support the learning of relational feature representations. In this paper, we address the challenge of learning representations of hierarchical relations--that is, higher-order relational patterns among groups of objects. We introduce "relational convolutional networks", a neural architecture equipped with computational mechanisms that capture progressively more complex relational features through the composition of simple modules. A key component of this framework is a novel operation that captures relational patterns in groups of objects by convolving graphlet filters--learnable templates of relational patterns--against subsets of the input. Composing relational convolutions gives rise to a deep architecture that learns representations of higher-order, hierarchical relations. We present the motivation and details of the architecture, together with a set of experiments to demonstrate how relational convolutional networks can provide an effective framework for modeling relational tasks that have hierarchical structure.

Figures (19)

• Figure 1: A variant of a relational match-to-sample task.
• Figure 2: Proposed architecture for relational convolutional networks. Hierarchical relations are modeled by iteratively computing pairwise relations between objects and convolving the resultant relation tensor with graphlet filters representing templates of relations between groups of objects.
• Figure 3: A depiction of the relational convolution operation. A graphlet filter $\bm{f}$ is compared to the relation subtensor in each group of objects, producing a sequence of vectors summarizing the relational pattern within each group. The groups can be differentiably learned through an attention mechanism.
• Figure 4: Relational games dataset. Left Examples of objects from each split. Right Examples of problem instances for each task. The first row is an example where the relation holds and the second row is an example where the relation does not hold.
• Figure 5: Out-of-distribution generalization on hold-out object sets. Bar heights indicate the mean over 5 trials and the error bars indicate a bootstrap 95% confidence interval.