  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. 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. However, they partly
ignore necessary inductive biases of RPM solver, such as order sensitivity
within each row/column and incremental rule induction. To address this problem,
in this paper we propose a Stratified Rule-Aware Network (SRAN) to generate the
rule embeddings for two input sequences. Our SRAN learns multiple granularity
rule embeddings at different levels, and incrementally integrates the
stratified embedding flows through a gated fusion module. With the help of
embeddings, a rule similarity metric is applied to guarantee that SRAN can not
only be trained using a tuplet loss but also infer the best answer efficiently.
We further point out the severe defects existing in the popular RAVEN dataset
for RPM test, which prevent from the fair evaluation of the abstract reasoning
ability. To fix the defects, we propose an answer set generation algorithm
called Attribute Bisection Tree (ABT), forming an improved dataset named
Impartial-RAVEN (I-RAVEN for short). Extensive experiments are conducted on
both PGM and I-RAVEN datasets, showing that our SRAN outperforms the
state-of-the-art models by a considerable margin.
