Generalization across graph topologies and scales

Ascertain whether the observed implicit in-weights reasoning and geometric memory in Transformer and Mamba models extend beyond path-star and tree-star graphs to other graph topologies and to graphs of different sizes.

Background

The positive results in the paper are demonstrated primarily on path-star (and additionally tree-star) graphs, showing strong in-weights generalization on held-out leaves and large graphs. Whether this behavior persists on broader classes of graphs or at different scales is not yet established.

Clarifying this would define the scope of applicability of geometric memory in parametric models and inform the design of benchmarks and training protocols.