Fid

FID is an acronym that can refer to several terms across different disciplines. Notable meanings include Fréchet Inception Distance in machine learning, Free Induction Decay in magnetic resonance imaging, and Final Investment Decision in project finance.

Fréchet Inception Distance is a metric used to evaluate the quality of images produced by generative models, such as Generative Adversarial Networks. It compares the distributions of feature representations extracted from real and generated images using a pretrained Inception network. The distance is computed from the means and covariances of these features, typically expressed as FID = ||μ1 − μ2||^2 + Tr(C1 + C2 − 2(C1C2)^(1/2)). Lower FID values indicate closer similarity between the two distributions. FID is widely adopted because it correlates with perceptual quality on many datasets, but it relies on the chosen feature space, can be sensitive to preprocessing, and may be biased by sample size or dataset differences.

Free Induction Decay is the time-domain signal observed in nuclear magnetic resonance and magnetic resonance imaging after an excitation pulse. It represents the transverse magnetization that decays due to relaxation processes. The FID is Fourier-transformed to yield the frequency-domain spectrum, enabling analysis of chemical environments and molecular structures. In imaging, FID data are manipulated to reconstruct spatial information, and the quality of reconstruction depends on acquisition parameters and hardware.

Final Investment Decision is a term used in project finance and corporate investment to denote the formal approval to proceed with a project. Reaching the FID typically authorizes budget allocation, procurement, and construction activities, marking a transition from planning to execution and carrying with it significant risk and compliance considerations.