Best of Both Worlds: Advantages of Hybrid Graph Sequence Models
Authors: name: Ali Behrouz, name: Ali Parviz, name: Mahdi Karami, name: Clayton Sanford, name: Bryan Perozzi, name: Vahab Mirrokni

Modern sequence models (e.g., Transformers, linear RNNs, etc.) emerged as
dominant backbones of recent deep learning frameworks, mainly due to their
efficiency, representational power, and/or ability to capture long-range
dependencies. Adopting these sequence models for graph-structured data has
recently gained popularity as the alternative to Message Passing Neural
Networks (MPNNs). There is, however, a lack of a common foundation about what
constitutes a good graph sequence model, and a mathematical description of the
benefits and deficiencies in adopting different sequence models for learning on
graphs. To this end, we first present Graph Sequence Model (GSM), a unifying
framework for adopting sequence models for graphs, consisting of three main
steps: (1) Tokenization, which translates the graph into a set of sequences;
(2) Local Encoding, which encodes local neighborhoods around each node; and (3)
Global Encoding, which employs a scalable sequence model to capture long-range
dependencies within the sequences. This framework allows us to understand,
evaluate, and compare the power of different sequence model backbones in graph
tasks. Our theoretical evaluations of the representation power of Transformers
and modern recurrent models through the lens of global and local graph tasks
show that there are both negative and positive sides for both types of models.
Building on this observation, we present GSM++, a fast hybrid model that uses
the Hierarchical Affinity Clustering (HAC) algorithm to tokenize the graph into
hierarchical sequences, and then employs a hybrid architecture of Transformer
to encode these sequences. Our theoretical and experimental results support the
design of GSM++, showing that GSM++ outperforms baselines in most benchmark
evaluations.