Markov and lattice bases for Forman-Ricci curvature of graphs
arXiv:2608.01929
2026
Regularization
1 ideas extracted · analyzed Aug 31, 2026
What the math gives to ML
The paper develops integer-preserving local rewiring moves for traversing graph fibers with fixed vertex-degree and Forman-curvature statistics. The transferable asset is not curvature itself, but the construction of small, exactly constraint-preserving perturbations: a graph can be augmented while retaining prescribed structural marginals, while degree-three lattice moves provide a cheap move set even when indispensable Markov moves are large. This suggests a controlled graph-neural-network augmentation and topology-robustness method in which training views differ in connectivity but remain matched on degree and curvature distributions.
Ideas from this paper
Unverified
2026
Generate alternative graph views by applying small integer Markov moves to the joint degree matrix, while rejecting moves that violate nonnegativity or realizability as a simple graph. Train a GNN to produce consistent predictions across the original and rewired views, preserving degree frequencies and curvature-frequency statistics while forcing robustness to higher-order topology.
Useful6/10
Difficulty6/10
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