In this paper, we construct new models for the Anderson duals \( (I\Omega^G)^* \) to the stable tangential \(G\)-bordism theories and their differential extensions. The cohomology theory \( (I\Omega^G)^* \) is conjectured by Freed and Hopkins [Geometry & Topology, 25(3), (2021), 1165-1330] to classify deformation classes of possibly non-topological invertible quantum field theories (QFT's). Our model is made by abstracting certain properties of invertible QFT's, thus supporting their conjecture.