  Can neural networks learn to compare graphs without feature engineering? In
this paper, we show that it is possible to learn representations for graph
similarity with neither domain knowledge nor supervision (i.e.\ feature
engineering or labeled graphs). We propose Deep Divergence Graph Kernels, an
unsupervised method for learning representations over graphs that encodes a
relaxed notion of graph isomorphism. Our method consists of three parts. First,
we learn an encoder for each anchor graph to capture its structure. Second, for
each pair of graphs, we train a cross-graph attention network which uses the
node representations of an anchor graph to reconstruct another graph. This
approach, which we call isomorphism attention, captures how well the
representations of one graph can encode another. We use the attention-augmented
encoder's predictions to define a divergence score for each pair of graphs.
Finally, we construct an embedding space for all graphs using these pair-wise
divergence scores.
  Unlike previous work, much of which relies on 1) supervision, 2) domain
specific knowledge (e.g. a reliance on Weisfeiler-Lehman kernels), and 3) known
node alignment, our unsupervised method jointly learns node representations,
graph representations, and an attention-based alignment between graphs.
  Our experimental results show that Deep Divergence Graph Kernels can learn an
unsupervised alignment between graphs, and that the learned representations
achieve competitive results when used as features on a number of challenging
graph classification tasks. Furthermore, we illustrate how the learned
attention allows insight into the the alignment of sub-structures across
graphs.
