Finding the Global Semantic Representation in GAN through Fréchet Mean

Disentangled Latent Perturbation • Consider a GAN-generator G ∶ 𝒵 ⟶ 𝒳 and an image transformation 𝑇. • The disentangled latent perturbation, i.e., Semantic Basis, 𝒗 𝒕 𝒛 on 𝒵 for 𝑻 is defined as follows: where 𝑥 = 𝐺 𝑧 . • 𝒗 𝒕 𝒛 is global if 𝑣 𝑡 𝑧 = 𝑣 𝑡 for all 𝑧 ∈ 𝒵, and is local otherwise.