The non-Markovian characteristics of NE-FGR become more prominent for the population dynamics starting from the lower polariton. In this case, the dynamics are dominated by the k -→D rate, since the corresponding transfer starts from the lower polariton and the rate scales with N . Further, the |-⟩ → |D⟩ being energetically unfavorable leads to a large difference between transient NE-FGR rates and the E-FGR rate, and the resulting NE-FGR population dynamics differ significantly from E-FGR in both non-collective and collective cases. Comparison to the numerical exact result shows a clear advantage of using NE-FGR over E-FGR to simulate the |-⟩ ← {|D} process. This advantage of NE-FGR is likely to exist for dynamics where the transient process is dominated by a transfer process from a polariton state to a higher-energy dark state. In this work, a Brownian form of the single-site bath spectral density is used, which has the following expression