  Foundation models that can perform inference on any new task without
requiring specific training have revolutionized machine learning in vision and
language applications. However, applications involving graph-structured data
remain a tough nut for foundation models, due to challenges in the unique
feature- and label spaces associated with each graph. Traditional graph ML
models such as graph neural networks (GNNs) trained on graphs cannot perform
inference on a new graph with feature and label spaces different from the
training ones. Furthermore, existing models learn functions specific to the
training graph and cannot generalize to new graphs. In this work, we tackle
these two challenges with a new foundational architecture for inductive node
classification named GraphAny. GraphAny models inference on a new graph as an
analytical solution to a LinearGNN, thereby solving the first challenge. To
solve the second challenge, we learn attention scores for each node to fuse the
predictions of multiple LinearGNNs. Specifically, the attention module is
carefully parameterized as a function of the entropy-normalized
distance-features between multiple LinearGNNs predictions to ensure
generalization to new graphs. Empirically, GraphAny trained on the Wisconsin
dataset with only 120 labeled nodes can effectively generalize to 30 new graphs
with an average accuracy of 67.26\% in an inductive manner, surpassing GCN and
GAT trained in the supervised regime, as well as other inductive baselines.
