Beyond ICA: Identifiability by Symmetry Breaking

תקציר מקורי באנגליתarXiv:2607.23182v1 Announce Type: cross Abstract: We prove the identifiability of deep generative models (DGMs) with piecewise-affine (PWA) decoders and Gaussian mixture model (GMM) priors, in a purely unsupervised setting. We introduce three algebraic contrast principles for symmetry breaking: domain contrast, which trivializes the mixture symmetry group; mechanism contrast, which ensures every decoder branch is witnessed by a unique boundary; and interaction contrast, which forbids parameter conspiracies between latent components and decoder branches. Together they exploit the interplay between the discrete combinatorics of the PWA map and the continuous symmetry structure of the latent GMM. Continuity is replaced by algebraic symmetry conditions; injectivity is decoupled from structural