NeurIPS 2026 paper proves identifiability of nonlinear generative models via symmetry breaking
chaumian · x · 2026-09-30
Pengzhou Wu's paper "Beyond ICA: Identifiability by Symmetry Breaking" is accepted at NeurIPS 2026, which the author claims achieves three firsts.
- Core result: In a purely unsupervised setting, it proves identifiability of deep generative models with piecewise-affine (PWA) decoders and Gaussian mixture model (GMM) priors.
- Three algebraic contrast principles: domain contrast (trivializing the mixture symmetry group), mechanism contrast (each decoder branch witnessed by a unique boundary), and interaction contrast (forbidding parameter conspiracies between latent components and decoder branches).
- Methodological breakthroughs: algebraic symmetry conditions replace continuity assumptions; first to admit discontinuous decoders and fully non-injective decoders where every observation admits multiple latent codes.
- Hierarchy of identifiability: from law identifiability (LID) through map identifiability (MID) to posterior and pointwise identifiability, with conditions under which the ICA-form ambiguity emerges.
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