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 holds potential in building human-aligned and interpretable machine learning models. Despite its encouraging prospect%2C formalization and theoretical insights into this crucial task are still lacking. In this work%2C we formalize concepts as discrete latent causal variables that are related via a hierarchical causal model that encodes different abstraction levels of concepts embedded in high-dimensional data (e.g.%2C a dog breed and its eye shapes in natural images). We formulate conditions to facilitate the identification of the proposed causal model%2C which reveals when learning such concepts from unsupervised data is possible. Our conditions permit complex causal hierarchical structures beyond latent trees and multi-level directed acyclic graphs in prior work and can handle high-dimensional%2C continuous observed variables%2C which is well-suited for unstructured data modalities such as images. We substantiate our theoretical claims with synthetic data experiments. Further%2C we discuss our theory's implications for understanding the underlying mechanisms of latent diffusion models and provide corresponding empirical evidence for our theoretical insights.?quality=80&w=800)
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