  We propose a generalization of transformer neural network architecture for
arbitrary graphs. The original transformer was designed for Natural Language
Processing (NLP), which operates on fully connected graphs representing all
connections between the words in a sequence. Such architecture does not
leverage the graph connectivity inductive bias, and can perform poorly when the
graph topology is important and has not been encoded into the node features. We
introduce a graph transformer with four new properties compared to the standard
model. First, the attention mechanism is a function of the neighborhood
connectivity for each node in the graph. Second, the positional encoding is
represented by the Laplacian eigenvectors, which naturally generalize the
sinusoidal positional encodings often used in NLP. Third, the layer
normalization is replaced by a batch normalization layer, which provides faster
training and better generalization performance. Finally, the architecture is
extended to edge feature representation, which can be critical to tasks s.a.
chemistry (bond type) or link prediction (entity relationship in knowledge
graphs). Numerical experiments on a graph benchmark demonstrate the performance
of the proposed graph transformer architecture. This work closes the gap
between the original transformer, which was designed for the limited case of
line graphs, and graph neural networks, that can work with arbitrary graphs. As
our architecture is simple and generic, we believe it can be used as a black
box for future applications that wish to consider transformer and graphs.
