Closing the certified-versus-accurate prediction gap

Develop a per-prediction certification guarantee for the accurate RBF-SVM head used with COMPLEX that narrows the gap between its high classification accuracy and the substantially weaker certified nearest-centroid or nearest-neighbor guarantees.

Background

The paper’s explicit per-prediction guarantees attach to nearest-centroid and nearest-neighbor rules, whereas the most accurate classifier is an RBF-SVM operating on the same COMPLEX embedding. The embedding certifies pairwise separation and kernel-induced separation for coherent pairs, but these results do not establish a useful margin guarantee for the fitted SVM. The authors identify connecting the certificate to the accurate head as the principal unresolved problem left by the study.

References

Narrowing that gap is the main open problem this paper leaves; the paragraph below reports how far a per-prediction reading of the same theorem goes toward it.

— COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modules  (2609.22012 - Majhi et al., 18 Sep 2026) in Section 5, “Certified selective classification”