Decomposer Networks: Deep Component Analysis and Synthesis

We propose the Decomposer Networks (DecompNet), a semantic autoencoder that factorizes an input into multiple interpretable components. Unlike classical autoencoders that compress an input into a single latent representation, the Decomposer Network maintains N parallel branches, each assigned a residual input defined as the original signal minus the reconstructions of all other branches. By unrolling a Gauss--Seidel style block-coordinate descent into a differentiable network, DecompNet enforce explicit competition among components, yielding parsimonious, semantically meaningful representations. We situate our model relative to linear decomposition methods (PCA, NMF), deep unrolled optimization, and object-centric architectures (MONet, IODINE, Slot Attention), and highlight its novelty as the first semantic autoencoder to implement an all-but-one residual update rule.