In representation learning, there has been recent interest in developing algorithms to disentangle the ground-truth generative factors behind a dataset, and metrics to quantify how fully this occurs. However, these algorithms and metrics often assume that both representations and ground-truth factors are flat, continuous, and factorized, whereas many real-world generative processes involve rich hierarchical structure, mixtures of discrete and continuous variables with dependence between them, and even varying intrinsic dimensionality. In this work, we develop benchmarks, algorithms, and metrics for learning such hierarchical representations.
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