Optimal Symbolic Basis Transformations for Term Deletion

Determine what constitutes an optimal choice of symbolic basis transformations for deleting one or more terms from an exact matrix-multiplication tensor decomposition to produce a lower-rank APA algorithm.

Background

The search framework applies symbolic De-Groote transformations to exact matrix-multiplication decompositions and deletes terms that become negligible in the evaluation parameter. The authors note that the transformations achieving this effect are nonunique and that hand-constructed transformations can perform better than the general construction used in the proof. The unresolved issue is to characterize or compute an optimal transformation, potentially improving the resulting APA decomposition.