Abstract: Donaldson-Thomas invariants of Calabi-Yau 4-folds are defined through recently developed virtual Lagrangian cycles associated to (-2)-shifted symplectic derived moduli spaces. In this talk, we discuss various properties of these virtual Lagrangian cycles in the perspective of shifted symplectic geometry. We first provide a virtual pullback formula for Lagrangian correspondences and use it to compute Hilbert scheme invariants. We then construct reduced virtual cycles for counting surfaces via (-1)-shifted closed 1-forms and show that they can detect the variational Hodge conjecture. We also revisit cosection localization via virtual Lagrangian cycles for (-2)-shifted twisted cotangent bundles. We finally explain deformation invariance in terms of the exactness of the symplectic forms.