发表机构
SANKEN, University of Osaka（大阪大学 SANKEN（大阪大学蛋白质研究所））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在纯无监督下证明带PWA解码器和GMM先验的DGM可识别性，引入三个代数对比原则，利用PWA与GMM结构作用，形成可识别性层次结构，允许不连续和非单射解码器，以代数对称性破缺为非线性可识别性引擎。
AI 中文摘要
我们在纯无监督设置下证明了具有分段仿射（PWA）解码器和高斯混合模型（GMM）先验的深度生成模型（DGM）的可识别性。引入了三个用于对称性破缺的代数对比原则：域对比使混合对称群平凡化；机制对比确保每个解码器分支由唯一边界见证；交互对比禁止潜在成分和解码器分支之间的参数共谋。它们共同利用了PWA映射的离散组合学与潜在GMM的连续对称结构之间的相互作用。连续性由代数对称条件取代；单射性与结构识别解耦，仅在逐点反演时需要。结果形成一个层次结构：从分布可识别性（LID）到映射可识别性（MID），再到后验和逐点可识别性。在对角成分协方差条件下出现ICA形式的模糊性。假设仅针对数据生成过程，除交互对比外不针对学习方法。据我们所知，这是首次将代数对称性破缺作为非线性可识别性的引擎，首次允许不连续解码器，首次处理完全非单射解码器，即每个观测值允许多个潜在代码。
英文摘要
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 identification and required only for pointwise inversion. Our results form a hierarchy: from law identifiability (LID; latent distribution up to a global affine map) through map identifiability (MID; decoder up to the same map) to posterior and pointwise identifiability. The ICA-form ambiguity emerges under conditions on diagonal component covariances. Assumptions are only on the data-generating process, not on learning methods, except for the interaction contrast. To our knowledge this is the first to make algebraic symmetry-breaking the engine of nonlinear identifiability, the first to admit discontinuous decoders, and the first to handle fully non-injective decoders, where every observation admits multiple latent codes.
