4.5 LSBD-VAE: Learning LSBD Representations 71 correction to the encodings, which encourages the decoder to follow the required group structure. It only affects the reconstruction loss component of the ∆VAE. We remark that this is similar to the methodology in the Deep Convolutional Inverse Graphics Network (DC-IGN) (Kulkarni et al., 2015), but specifically adapted to our group-theoretic framework. dec. dec. dec. enc. enc. enc. Figure 4.3: Overview of the supervised part of LSBD-VAE. Figure 4.3 illustrates the supervised part of our method for a transformationlabelled batch{xm} M m=1. The loss function is the regular ELBO consisting of a reconstruction loss LRE and a KL loss LKL (but with adjusted decoder input as described above, and averaged over the batch) as used in ∆VAE plus an additional termγ · LLSBD, where γ is a weight hyperparameter to control the influence of the supervised loss component. By alternating unsupervised and supervised training (using the same encoder and decoder), we have a method that makes use of both unlabelled and transformation-labelled observations.
RkJQdWJsaXNoZXIy MjY0ODMw