Data to 7 Oct 2026

Variational Autoencoders and Nonlinear ICA: A Unifying Framework

arXiv 1907.04809 ↗First posted 10 Jul 2019stat.ML cs.LGcited by 494

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Abstract (arXiv)

The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model's marginal distribution over observed variables fits the data. Often, we're interested in going a step further, and want to approximate the true joint distribution over observed and latent variables, including the true prior and posterior distributions over latent variables. This is known to be generally impossible due to unidentifiability of the model. We address this issue by showing that for a broad family of deep latent-variable models, identification of the true joint distribution over observed and latent variables is actually possible up to very simple transformations, thus achieving a principled and powerful form of disentanglement. Our result requires a factorized prior distribution over the latent variables that is conditioned on an additionally observed variable, such as a class label or almost any other observation. We build on recent developments in nonlinear ICA, which we extend to the case with noisy, undercomplete or discrete observations, integrated in a maximum likelihood framework. The result also trivially contains identifiable flow-based generative models as a special case.

Key facts. Cited by 494 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Jul 2019.

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Citing papers per year: 2021: 50; 2022: 65; 2023: 102; 2024: 84; 2025: 88; 2026: 105.

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2023The Linear Representation Hypothesis and the Geometry of Large Language Modelscited by 679
2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 308
2023A Cookbook of Self-Supervised Learningcited by 248
2021Contrastive Learning Inverts the Data Generating Processcited by 220
2021Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalizationcited by 220
2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 158
2022Weakly supervised causal representation learningcited by 140
2022Interventional Causal Representation Learningcited by 140
2022CITRIS: Causal Identifiability from Temporal Intervened Sequencescited by 132
2022Disentangled Representation Learningcited by 111
2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
2021Independent mechanism analysis, a new concept?cited by 96

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2021Learning Temporally Causal Latent Processes from General Temporal Datacited by 96
2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
2022On the Identifiability of Nonlinear ICA: Sparsity and Beyondcited by 84
2022Temporal Attention Unit: Towards Efficient Spatiotemporal Predictive Learningcited by 84
2022Linear Causal Disentanglement via Interventionscited by 84
2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
2021Desiderata for Representation Learning: A Causal Perspectivecited by 76
2024On the Origins of Linear Representations in Large Language Modelscited by 76
2022GlanceNets: Interpretabile, Leak-proof Concept-based Modelscited by 73
2021Unsupervised Learning of Compositional Energy Conceptscited by 71
2024ObjectDrop: Bootstrapping Counterfactuals for Photorealistic Object Removal and Insertioncited by 71
2022Identifiability of deep generative models without auxiliary informationcited by 70
2024Causal Representation Learning from Multiple Distributions: A General Settingcited by 67
2025Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Modelscited by 67
2021Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICAcited by 64
2022Weakly Supervised Representation Learning with Sparse Perturbationscited by 64
2023Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcutscited by 63
2021Visual Representation Learning Does Not Generalize Strongly Within the Same Domaincited by 60
2022Temporally Disentangled Representation Learningcited by 59
2023Concept Algebra for (Score-Based) Text-Controlled Generative Modelscited by 59
2022ZIN: When and How to Learn Invariance Without Environment Partition?cited by 58
2023Identifiability of latent-variable and structural-equation models: from linear to nonlinearcited by 58
2023Identifiability Results for Multimodal Contrastive Learningcited by 58
2023Posterior Collapse and Latent Variable Non-identifiabilitycited by 57
2021Beyond Trivial Counterfactual Explanations with Diverse Valuable Explanationscited by 56
2023Causal Component Analysiscited by 56
2023Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolationcited by 56
2021Learning latent causal graphs via mixture oraclescited by 55
2021Identifiable Deep Generative Models via Sparse Decodingcited by 54
2022Function Classes for Identifiable Nonlinear Independent Component Analysiscited by 53
2023High Fidelity Image Counterfactuals with Probabilistic Causal Modelscited by 53
2022Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systemscited by 50
2022Mechanistic Mode Connectivitycited by 50
2022A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awarenesscited by 49
2023Score-based Causal Representation Learning with Interventionscited by 49
2022CLEAR: Generative Counterfactual Explanations on Graphscited by 48
2023Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learningcited by 48
2021Learning Disentangled Representations in the Imaging Domaincited by 46

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