  In analogy with the Gopakumar-Vafa conjecture on CY 3-folds, Klemm and
Pandharipande defined GV type invariants on Calabi-Yau 4-folds using
Gromov-Witten theory and conjectured their integrality. In this paper, we
propose a sheaf-theoretic interpretation of their genus zero invariants using
Donaldson-Thomas theory on CY 4-folds. More specifically, we conjecture genus
zero GV type invariants are $\mathrm{DT_{4}}$ invariants for one-dimensional
stable sheaves on CY 4-folds. Some examples are computed for both compact and
non-compact CY 4-folds to support our conjectures. We also propose an
equivariant version of the conjectures for local curves and verify them in
certain cases.
