In this work, we focus on an analogical reasoning task that contains rich compositional structures, Raven's Progressive Matrices (RPM). To discover compositional structures of the data, we propose the Scattering Compositional Learner (SCL), an architecture that composes neural networks in a sequence. Our SCL achieves state-of-the-art performance on two RPM datasets, with a 48.7% relative improvement on Balanced-RAVEN and 26.4% on PGM over the previous state-of-the-art. We additionally show that our model discovers compositional representations of objects' attributes (e.g., shape color, size), and their relationships (e.g., progression, union). We also find that the compositional representation makes the SCL significantly more robust to test-time domain shifts and greatly improves zero-shot generalization to previously unseen analogies.

Abstract reasoning refers to the ability to analyze information, discover rules at an intangible level, and solve problems in innovative ways. Raven's Progressive Matrices (RPM) test is typically used to examine the capability of abstract reasoning. In the test, the subject is asked to identify the correct choice from the answer set to fill the missing panel at the bottom right of RPM (e.g., a 3$\times$3 matrix), following the underlying rules inside the matrix. Recent studies, taking advantage of Convolutional Neural Networks (CNNs), have achieved encouraging progress to accomplish the RPM test problems. Unfortunately, simply relying on the relation extraction at the matrix level, they fail to recognize the complex attribute patterns inside or across rows/columns of RPM. To address this problem, in this paper we propose a Hierarchical Rule Induction Network (HriNet), by intimating human induction strategies. HriNet extracts multiple granularity rule embeddings at different levels and integrates them through a gated embedding fusion module. We further introduce a rule similarity metric based on the embeddings, so that HriNet can not only be trained using a tuplet loss but also infer the best answer according to the similarity score. To comprehensively evaluate HriNet, we first fix the defects contained in the very recent RAVEN dataset and generate a new one named Balanced-RAVEN. Then extensive experiments are conducted on the large-scale dataset PGM and our Balanced-RAVEN, the results of which show that HriNet outperforms the state-of-the-art models by a large margin.