Building confidence regions for Reeb graphs using the interleaving distance

What the math gives to ML

The paper provides an object-level metric for filtered graphs that distinguishes non-isomorphic Reeb structures, unlike barcode-only summaries, and gives a principled notion of confidence around an estimated filtered object. The transferable idea is to make a point-cloud or graph neural network invariant to perturbations at the level of connected-component topology across filter values, rather than only matching embeddings or outputs pointwise. A practical adaptation is a Reeb-consistency regularizer computed on two augmented views of the same input, with the interleaving scale set by augmentation or sampling uncertainty. The persistence bound supplies a cheaper fallback surrogate when exact interleaving computation is too expensive.