mlsanityData to 7 Oct 2026

Pathwise Derivatives Beyond the Reparameterization Trick

arXiv 1806.01851 ↗First posted 5 Jun 2018stat.ML cs.LGcited by 36

Not on the map. Why?

Abstract (arXiv)

We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability distributions not directly amenable to the reparameterization trick: Gamma, Beta, and Dirichlet. We further observe that when the reparameterization trick is applied to the Cholesky-factorized multivariate Normal distribution, the resulting gradients are suboptimal in the sense of optimal transport. We derive the optimal gradients and show that they have reduced variance in a Gaussian Process regression task. We demonstrate with a variety of synthetic experiments and stochastic variational inference tasks that our pathwise gradients are competitive with other methods.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Jun 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 10; 2022: 6; 2023: 10; 2024: 5; 2025: 3; 2026: 2.

36 papers.

Sort:

  1. 2021Is Automated Topic Model Evaluation Broken?: The Incoherence of Coherencecited by 74
  2. 2022Visual Attention Methods in Deep Learning: An In-Depth Surveycited by 37
  3. 2023Identifiable Latent Polynomial Causal Models Through the Lens of Changecited by 23
  4. 2022Gradient Estimation with Discrete Stein Operatorscited by 22
  5. 2022Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flowscited by 22
  6. 2021Learning PAC-Bayes Priors for Probabilistic Neural Networkscited by 21
  7. 2021Auto-FedAvg: Learnable Federated Averaging for Multi-Institutional Medical Image Segmentationcited by 19
  8. 2021Differentiable Particle Filtering without Modifying the Forward Passcited by 18
  9. 2021Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Boundcited by 16
  10. 2023Synthetic optical coherence tomography angiographs for detailed retinal vessel segmentation without human annotationscited by 16
  11. 2021A unified view of likelihood ratio and reparameterization gradientscited by 12
  12. 2021Progress in Self-Certified Neural Networkscited by 10
24 more
  1. 2022Reinforcement Learning in Presence of Discrete Markovian Context Evolutioncited by 9
  2. 2023Continual Learning with Dirichlet Generative-based Rehearsalcited by 7
  3. 2022Variational Sparse Coding with Learned Thresholdingcited by 6
  4. 2023Sample Average Approximation for Black-Box VIcited by 6
  5. 2021BaLeNAS: Differentiable Architecture Search via the Bayesian Learning Rulecited by 5
  6. 2024Fast and Unified Path Gradient Estimators for Normalizing Flowscited by 5
  7. 2022Sparse Conditional Hidden Markov Model for Weakly Supervised Named Entity Recognitioncited by 4
  8. 2021Hierarchical Variational Auto-Encoding for Unsupervised Domain Generalizationcited by 3
  9. 2021Scalable Marked Point Processes for Exchangeable and Non-Exchangeable Event Sequencescited by 2
  10. 2023Reparameterized Variational Rejection Samplingcited by 2
  11. 2023Learning Interpretable Deep Disentangled Neural Networks for Hyperspectral Unmixingcited by 2
  12. 2024Differentiable and Stable Long-Range Tracking of Multiple Posterior Modescited by 2
  13. 2025BN-Pool: Bayesian Nonparametric Pooling for Graphscited by 2
  14. 2025Large Language Models Struggle to Describe the Haystack without Human Help: Human-in-the-loop Evaluation of Topic Modelscited by 2
  15. 2023Bayesian sparsification for deep neural networks with Bayesian model reductioncited by 1
  16. 2023Variational Autoencoders for Feature Exploration and Malignancy Prediction of Lung Lesionscited by 1
  17. 2025Rao-Blackwellised Reparameterisation Gradientscited by 1
  18. 2026Retry Policy Gradients in Continuous Action Spacescited by 1
  19. 2023Likelihood-based inference and forecasting for trawl processes: a stochastic optimization approachcited by 0
  20. 2023Geometry-Aware Normalizing Wasserstein Flows for Optimal Causal Inferencecited by 0
  21. 2024A VAE-based Framework for Learning Multi-Level Neural Granger-Causal Connectivitycited by 0
  22. 2024Analytical Approximation of the ELBO Gradient in the Context of the Clutter Problemcited by 0
  23. 2024Soft Actor-Critic with Beta Policy via Implicit Reparameterization Gradientscited by 0
  24. 2026SLP-ProbHard: Probabilistic Hard-Constrained Learning via Structural Latent Parameterizationcited by 0