Tensor Tests via High-Dimensional Expanders

Investigate whether tensor tests based on high-dimensional expanders, including coboundary-type expansion constructions, can provide the required low-rank guarantees without losing the covering property.

Background

The paper explores sparse graph structures and high-dimensional expanders as alternatives to the complete graph in the quadratic Grassmann encoding. These alternatives may restore the covering property, but localized tensor tests appear insufficient to enforce global low rank.

The authors explicitly state that one coboundary-type-expansion approach has not been thoroughly explored, leaving its potential unresolved.