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[D] Why do disentangling methods not result in independent dimensions of the learned representation?

By disentangling methods I mean methods under the VAE framework such as factor-VAE and beta-TCVAE which explicitly regularize the total correlation of the aggregate posterior q(z) approx 1/N sum_n q(z | x_n).

Locatello et. al. in their large-scale study of disentanglement methods (1) show empirical evidence to demonstrate that the dimensions of the mean representation of q(z|x) (usually used for representation) are correlated, but it seems that the dimensions of the mean representation by definition are independent if we use a factorial distribution to represent the posterior such as a diagonal-covariance Gaussian. Also, averaging this representation over the data distribution should also be factorial if we assume that the aggregate posterior q(z) is factorial (proof in 2), so I think the claim in 1 is wrong.

submitted by /u/Tonic_Section
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Toronto AI is a social and collaborative hub to unite AI innovators of Toronto and surrounding areas. We explore AI technologies in digital art and music, healthcare, marketing, fintech, vr, robotics and more. Toronto AI was founded by Dave MacDonald and Patrick O'Mara.