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Identifiable Deep Generative Models via Sparse Decoding

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arxiv 2110.10804 v2 pith:TCGW5W2B submitted 2021-10-20 stat.ML cs.LGstat.ME

Identifiable Deep Generative Models via Sparse Decoding

classification stat.ML cs.LGstat.ME
keywords datasparsedeepfactorsgenerativeidentifiablelatentmodels
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We develop the sparse VAE for unsupervised representation learning on high-dimensional data. The sparse VAE learns a set of latent factors (representations) which summarize the associations in the observed data features. The underlying model is sparse in that each observed feature (i.e. each dimension of the data) depends on a small subset of the latent factors. As examples, in ratings data each movie is only described by a few genres; in text data each word is only applicable to a few topics; in genomics, each gene is active in only a few biological processes. We prove such sparse deep generative models are identifiable: with infinite data, the true model parameters can be learned. (In contrast, most deep generative models are not identifiable.) We empirically study the sparse VAE with both simulated and real data. We find that it recovers meaningful latent factors and has smaller heldout reconstruction error than related methods.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. From Generalist to Specialist Representation

    cs.LG 2026-05 unverdicted novelty 8.0

    Task structure is identifiable across time steps and task-relevant representations are identifiable within steps in a nonparametric setting under sparsity regularization.

  2. The Linear Representation Hypothesis and the Geometry of Large Language Models

    cs.CL 2023-11 conditional novelty 8.0

    Linear representations of high-level concepts in LLMs are formalized via counterfactuals in input and output spaces, unified under a causal inner product that enables consistent probing and steering.

  3. Diverse Dictionary Learning

    cs.LG 2026-04 unverdicted novelty 7.0

    Diverse dictionary learning identifies intersections, complements, and dependency structures of latent variables from data X = g(Z) up to indeterminacies, and full identifiability when structural diversity is sufficient.

  4. Mechanistic Independence: A Principle for Identifiable Disentangled Representations

    cs.LG 2025-09 unverdicted novelty 7.0

    Mechanistic independence criteria yield identifiability of latent subspaces under nonlinear mixing by focusing on action-based independence rather than latent distributions, with a hierarchy and graph-theoretic view o...