Develop formal statistical inference for Morse-skeleton methods

Develop a formal statistical inference framework for the Morse skeleton and the associated Morse-guided diffusion methodology, addressing the current absence of statistical inference for these topological representations.

Background

The paper introduces a Morse skeleton based on discrete Morse theory as a structural representation for graph diffusion. Although the method provides theoretical stability guarantees and empirical results, the authors identify the lack of formal statistical inference as a principal limitation. Such a framework would be needed to quantify uncertainty and establish inferential principles for Morse-skeleton representations, placing the problem at the interface of low-dimensional topology and mathematical statistics.

References

We find that one of the main current limitations of the proposed ideas on the Morse skeleton is the lack of formal statistical inference. However, this is a fundamental question at the interface of low dimensional topology and mathematical statistics, and we leave it a standalone future research direction.

— Graph Representation via Elements of Discrete Morse and Cobordism Theories  (2610.01937 - Rozenblit et al., 1 Oct 2026) in Appendix, Section "Limitations" (Section labeled "Limitations")