  Graph Neural Networks (GNNs) are the predominant technique for learning over
graphs. However, there is relatively little understanding of why GNNs are
successful in practice and whether they are necessary for good performance.
Here, we show that for many standard transductive node classification
benchmarks, we can exceed or match the performance of state-of-the-art GNNs by
combining shallow models that ignore the graph structure with two simple
post-processing steps that exploit correlation in the label structure: (i) an
"error correlation" that spreads residual errors in training data to correct
errors in test data and (ii) a "prediction correlation" that smooths the
predictions on the test data. We call this overall procedure Correct and Smooth
(C&S), and the post-processing steps are implemented via simple modifications
to standard label propagation techniques from early graph-based semi-supervised
learning methods. Our approach exceeds or nearly matches the performance of
state-of-the-art GNNs on a wide variety of benchmarks, with just a small
fraction of the parameters and orders of magnitude faster runtime. For
instance, we exceed the best known GNN performance on the OGB-Products dataset
with 137 times fewer parameters and greater than 100 times less training time.
The performance of our methods highlights how directly incorporating label
information into the learning algorithm (as was done in traditional techniques)
yields easy and substantial performance gains. We can also incorporate our
techniques into big GNN models, providing modest gains. Our code for the OGB
results is at https://github.com/Chillee/CorrectAndSmooth.
