Extension to tensor-clique contractions

Extend the tensor-contraction aggregation framework to contractions of tensor cliques, beginning with the $K_4$ contractions studied in the cited literature and determining whether the introduced embeddings and aggregation techniques yield useful constructions for these contraction graphs.

Background

The paper develops aggregation, centering, weighting, correction, and border-rank techniques for simultaneous matrix products and related tensor contractions. The authors explicitly identify extending these methods beyond the contraction patterns treated in the paper—particularly to tensor cliques and $K_4$ contractions—as an unresolved research direction.