General learnability guarantees for shared memories and ordinary GNN training

Establish general learnability guarantees for directly optimized graph-specific shared memories in nonlinear multilayer Graph Transformers and for ordinary local graph neural network training.

Background

The experiments show that directly optimized shared-memory states can perform comparably to memories generated by the original writer on several fixed transductive tasks. The theoretical analysis establishes exact recovery and optimization relations only in restricted settings, including affine readers and affine writers.

The paper explicitly leaves unresolved whether comparable guarantees hold for nonlinear multilayer models and for the training of ordinary message-passing GNNs.

References

More general learnability guarantees for nonlinear multilayer models and ordinary GNN training remain open.

— Global Communication or Graph-Specific Memory?  (2610.05874 - Shirzad et al., 5 Oct 2026) in Section 3, paragraph “Optimization perspective”

While this is possible, it is not clear if the model will learn a generalizable memory there from a single graph.

— Global Communication or Graph-Specific Memory?  (2610.05874 - Shirzad et al., 5 Oct 2026) in Section 3, paragraph “How generalizable is the writer against changes in the input?”

We have not established this condition for the experimental architectures.

— Global Communication or Graph-Specific Memory?  (2610.05874 - Shirzad et al., 5 Oct 2026) in Appendix, Section “Theoretical Support,” subsection “Optimization Perspective,” paragraph following Proposition 3

However, it has not been established for the nonlinear Graph Transformers considered here.

— Global Communication or Graph-Specific Memory?  (2610.05874 - Shirzad et al., 5 Oct 2026) in Appendix, Section “Theoretical Support,” subsection “Optimization Perspective,” paragraph “A local extension beyond affine readers”