Choosing splits in split-augmented flip graph searches

Develop principled heuristics or algorithms for selecting split operations during random or automated exploration of split-augmented flip graphs to efficiently discover low-rank tensor representations without incurring prohibitive branching.

Background

Augmenting flip graphs with split edges ensures strong connectivity, but it introduces a massive choice of possible splits at each step, rendering naive random exploration ineffective. The authors emphasize the lack of a clear strategy for choosing splits.

Addressing this question would improve practical search methods for low-rank decompositions across tensors, including matrix multiplication, by reducing search complexity and focusing exploration on promising transformations.