ELBO with this optimal prior ℱ$%&'&() (𝜃, 𝜙) is always larger than or equal to original ELBO ℱ*+,- (𝜃, 𝜙): • That is, ℱ$%&'&() (𝜃, 𝜙) is also a better lower bound of the log-likelihood than ℱ*+,- 𝜃, 𝜙 . • This contributes to obtaining better representation for the improved performance on the target tasks. <latexit sha1_base64="cReRpIFFkHRHyAEW/aHr3JatyTY=">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</latexit> FProposed(✓, ) = FCVAE(✓, ) + DKL(q (z)kp(z)) FCVAE(✓, )