mlsanityData to 7 Oct 2026

Local Disentanglement in Variational Auto-Encoders Using Jacobian L1 Regularization

arXiv 2106.02923 ↗First posted 5 Jun 2021cs.LG cs.CVcited by 17

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Abstract (arXiv)

There have been many recent advances in representation learning; however, unsupervised representation learning can still struggle with model identification issues related to rotations of the latent space. Variational Auto-Encoders (VAEs) and their extensions such as β-VAEs have been shown to improve local alignment of latent variables with PCA directions, which can help to improve model disentanglement under some conditions. Borrowing inspiration from Independent Component Analysis (ICA) and sparse coding, we propose applying an L1 loss to the VAE's generative Jacobian during training to encourage local latent variable alignment with independent factors of variation in images of multiple objects or images with multiple parts. We demonstrate our results on a variety of datasets, giving qualitative and quantitative results using information theoretic and modularity measures that show our added L1 cost encourages local axis alignment of the latent representation with individual factors of variation.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Builds on 25 of its 43 references that are in the map. First posted on arXiv 5 Jun 2021.

Builds on

25 of 43 references.

References · 25

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 929
  3. 2018Disentangling by Factorisingcited by 614
  4. 2017Learning Sparse Neural Networks through L0 Regularizationcited by 571
  5. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 494
  6. 2019Multi-Object Representation Learning with Iterative Variational Inferencecited by 359
  7. 2017VAE with a VampPriorcited by 247
  8. 2020Weakly-Supervised Disentanglement Without Compromisescited by 237
  9. 2013Predicting Parameters in Deep Learningcited by 223
  10. 2013k-Sparse Autoencoderscited by 209
  11. 2018Hyperspherical Variational Auto-Encoderscited by 188
  12. 2018Isolating Sources of Disentanglement in Variational Autoencoderscited by 167
13 more
  1. 2019Robust Learning with Jacobian Regularizationcited by 127
  2. 2019Spatial Broadcast Decoder: A Simple Architecture for Learning Disentangled Representations in VAEscited by 116
  3. 2018Learning Deep Disentangled Embeddings with the F-Statistic Losscited by 101
  4. 2019On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Datasetcited by 100
  5. 2018Variational Autoencoders Pursue PCA Directions (by Accident)cited by 84
  6. 2018Bias and Generalization in Deep Generative Models: An Empirical Studycited by 83
  7. 2018Resampled Priors for Variational Autoencoderscited by 56
  8. 2020On Implicit Regularization in β-VAEscited by 34
  9. 2020Learning Flat Latent Manifolds with VAEscited by 33
  10. 2017Gradient Regularization Improves Accuracy of Discriminative Modelscited by 26
  11. 2019Independent Subspace Analysis for Unsupervised Learning of Disentangled Representationscited by 8
  12. 2020Epitomic Variational Graph Autoencodercited by 7
  13. 2021Improved Training of Sparse Coding Variational Autoencoder via Weight Normalizationcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 3; 2023: 4; 2024: 4; 2025: 3; 2026: 2.

17 papers.

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  1. 2022On the Identifiability of Nonlinear ICA: Sparsity and Beyondcited by 84
  2. 2022GlanceNets: Interpretabile, Leak-proof Concept-based Modelscited by 73
  3. 2021Identifiable Deep Generative Models via Sparse Decodingcited by 54
  4. 2023Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learningcited by 22
  5. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 17
  6. 2024Jacobian Regularizer-based Neural Granger Causalitycited by 9
  7. 2023PGODE: Towards High-quality System Dynamics Modelingcited by 7
  8. 20233D Generative Model Latent Disentanglement via Local Eigenprojectioncited by 6
  9. 2024The Gaussian Discriminant Variational Autoencoder (GdVAE): A Self-Explainable Model with Counterfactual Explanationscited by 5
  10. 2024Causal Representation Learning in Temporal Data via Single-Parent Decodingcited by 5
  11. 2025Diverse Influence Component Analysis: A Geometric Approach to Nonlinear Mixture Identifiabilitycited by 4
  12. 2025Mechanistic Independence: A Principle for Identifiable Disentangled Representationscited by 3
5 more
  1. 2025Nonparametric Identification of Latent Conceptscited by 3
  2. 2023Ensuring Topological Data-Structure Preservation under Autoencoder Compression due to Latent Space Regularization in Gauss--Legendre nodescited by 2
  3. 2022Subgroup Discovery in Unstructured Datacited by 1
  4. 2026Layer-Specific Lipschitz Modulation for Fault-Tolerant Multimodal Representation Learningcited by 0
  5. 2026Diverse Dictionary Learningcited by 0