Economical certification conditions and algorithms

Develop more economical sufficient conditions or algorithms for certifying nonnegative tensor decomposition identifiability that avoid checking all nontrivial subsets of components and exploit additional structure.

Background

The main identifiability criteria require verifying a dimension–scattering inequality for every subset of components with at least two elements. Although the paper provides an exact procedure for computing the scattering term for a fixed subset, exhaustive subset enumeration can remain costly as the number of components grows. The authors explicitly leave open the development of more economical sufficient conditions or structurally specialized algorithms.

References

Several directions remain open. The full certificate still requires checking all nontrivial subsets of components, motivating the search for more economical sufficient conditions or algorithms that exploit additional structure.

— Identifiability of Nonnegative Tensor Decompositions via Positive Scattering  (2609.11606 - Wang et al., 10 Sep 2026) in Conclusion

Finally, the matrix specialization identifies two-sided separability as the exact boundary case of the present criterion, leaving open the question of which broader nonnegative matrix identifiability phenomena admit genuine higher-order analogues.

— Identifiability of Nonnegative Tensor Decompositions via Positive Scattering  (2609.11606 - Wang et al., 10 Sep 2026) in Conclusion