Learning unsupervised representations that are both semantically meaningful and stable across runs remains a central challenge in modern representation learning. We introduce entropy-ordered flows (EOFlows), a normalizing-flow framework that orders latent dimensions by their explained entropy, analogously to PCA's explained variance. This ordering enables adaptive injective flows: after training, one may retain only the top C latent variables to form a compact core representation while the remaining variables capture fine-grained detail and noise, with C chosen flexibly at inference time rather than fixed during training. EOFlows build on insights from Independent Mechanism Analysis, Principal Component Flows and Manifold Entropic Metrics. We combine likelihood-based training with local Jacobian regularization and noise augmentation into a method that scales well to high-dimensional data such as images. Experiments on the CelebA dataset show that our method uncovers a rich set of semantically interpretable features, allowing for high compression and strong denoising.

翻译：学习既具有语义意义又在多次运行中保持稳定的无监督表示，仍然是现代表示学习中的一个核心挑战。我们引入了熵排序流（EOFlows），这是一种归一化流框架，它通过潜在维度所解释的熵来对它们进行排序，类似于主成分分析（PCA）中的解释方差。这种排序实现了自适应单射流：训练完成后，可以仅保留前C个潜在变量以形成一个紧凑的核心表示，而其余变量则捕获细粒度的细节和噪声，其中C可以在推理时灵活选择，而非在训练期间固定。EOFlows建立在独立机制分析、主成分流和流形熵度量等工作的见解之上。我们将基于似然的训练与局部雅可比正则化和噪声增强相结合，形成了一种能够很好地扩展到高维数据（如图像）的方法。在CelebA数据集上的实验表明，我们的方法揭示了一组丰富的语义可解释特征，实现了高压缩率和强去噪能力。