Break The Spell Of Total Correlation In betaTCVAE

This paper proposes a way to break the spell of total correlation in betaTCVAE based on the motivation of the total correlation decomposition. An iterative decomposition path of total correlation is proposed, and an explanation for representation learning ability of VAE from the perspective of model capacity allocation. Newly developed objective function combines latent variable dimensions into joint distribution while relieving independent distribution constraint of the marginal distribution in combination, leading to latent variables with a more manipulable prior distribution. The novel model enables VAE to adjust the parameter capacity to divide dependent and independent data features flexibly. Experimental results on various datasets show an interesting relevance between model capacity and the latent variable grouping size, called the "V"-shaped best ELBO trajectory. Additional experiments demonstrate that the proposed method obtains better disentanglement performance with reasonable parameter capacity allocation. Finally, we design experiments to show the limitations of estimating total correlation with mutual information, identifying its source of estimation deviation.