通过发现数据对称性，从混乱观测中无监督恢复隐藏结构和信号。
Blind Recovery of Latent Domains via Unsupervised Symmetry Discovery
- 基于数据分布对称性建模，用浅层群卷积网络学习隐式结构。
- 在随机过程、伊辛模型等多类数据上成功恢复隐含域与信号。
- 适合做无监督结构学习或盲反问题的科研人员参考。
盲反问题的核心挑战是：在未知退化机制的情况下，从被污染的观测中恢复感兴趣信号。当退化为卷积形式时，盲去卷积方法有效，但面对一般线性变换破坏域结构则不适用。本文提出一种无监督框架，通过发现数据分布的对称性来恢复隐含域与信号。模型将观测视为从隐式随机场采样的线性测量，通过在模型输出上施加平稳性和局部性正则化，优化一个浅层群卷积网络。该网络学习到隐含对称操作和合适滤波器，将无结构观测映射为基于对称性的表示，从而揭示隐藏信号。在随机过程、伊辛模型、乱序及位混淆图像、神经记录等数据上的实验表明，该方法能从无结构观测中有效恢复隐含域与信号，表明对称性发现是无监督结构学习与盲反问题的新方向。
原文摘要 · Abstract (English)
Primary motivation in blind inverse problems is to recover signals of interest from corrupted observations without knowing the obfuscating mechanism. Blind deconvolution is a prominent approach when the corruption is convolutional, but it is not applicable when general linear transformations obfuscate the domain structure. In this work, we propose an unsupervised framework for recovering latent domains and signals by discovering symmetries of the data distribution. Our framework models observations as linear measurements of signals sampled from a latent random field, and optimizes a shallow group-convolutional network by imposing stationarity and locality regularization at the model output. The model learns a latent symmetry action and an appropriate filter, thereby mapping unstructured observations to a symmetry-based representation that reveals latent signals. Experiments on stochastic processes, Ising models, shuffled and bit-scrambled images, and neural recordings show that the method recovers latent domains and signals from unstructured observations, suggesting symmetry discovery as a new direction for unsupervised structure learning and blind inverse problems.
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