  We present a framework of Training Free Graph Matching (TFGM) to boost the
performance of Graph Neural Networks (GNNs) based graph matching, providing a
fast promising solution without training (training-free). TFGM provides four
widely applicable principles for designing training-free GNNs and is
generalizable to supervised, semi-supervised, and unsupervised graph matching.
The keys are to handcraft the matching priors, which used to be learned by
training, into GNN's architecture and discard the components inessential under
the training-free setting. Further analysis shows that TFGM is a linear
relaxation to the quadratic assignment formulation of graph matching and
generalizes TFGM to a broad set of GNNs. Extensive experiments show that GNNs
with TFGM achieve comparable (if not better) performances to their fully
trained counterparts, and demonstrate TFGM's superiority in the unsupervised
setting. Our code is available at
https://github.com/acharkq/Training-Free-Graph-Matching.
