# Rao-Blackwellised Reparameterisation Gradients

arXiv: https://arxiv.org/abs/2506.07687 · HTML: https://mlsanity.com/paper/2506.07687/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 47 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference](https://mlsanity.com/paper/1703.09194/) (2017)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning](https://mlsanity.com/paper/2110.01515/) (2021)
- [Tighter Variational Bounds are Not Necessarily Better](https://mlsanity.com/paper/1802.04537/) (2018)
- [Variance reduction properties of the reparameterization trick](https://mlsanity.com/paper/1809.10330/) (2018)
- [Rao-Blackwellizing the Straight-Through Gumbel-Softmax Gradient Estimator](https://mlsanity.com/paper/2010.04838/) (2020)
- [Pathwise Derivatives Beyond the Reparameterization Trick](https://mlsanity.com/paper/1806.01851/) (2018)
- [Estimating Gradients for Discrete Random Variables by Sampling without Replacement](https://mlsanity.com/paper/2002.06043/) (2020)
- [DisARM: An Antithetic Gradient Estimator for Binary Latent Variables](https://mlsanity.com/paper/2006.10680/) (2020)
- [Rao-Blackwellized Stochastic Gradients for Discrete Distributions](https://mlsanity.com/paper/1810.04777/) (2018)
- [Generalized Doubly Reparameterized Gradient Estimators](https://mlsanity.com/paper/2101.11046/) (2021)

## Built on by (most cited first, 1 of 1)

- [Accelerating Evolutionary Strategy via Rao-Blackwellizing Realization of Uncertain Input](https://mlsanity.com/paper/2608.02073/) (2026)

## Abstract (arXiv)

Latent Gaussian variables have been popularised in probabilistic machine learning. In turn, gradient estimators are the machinery that facilitates gradient-based optimisation for models with latent Gaussian variables. The reparameterisation trick is often used as the default estimator as it is simple to implement and yields low-variance gradients for variational inference. In this work, we propose the R2-G2 estimator as the Rao-Blackwellisation of the reparameterisation gradient estimator. Interestingly, we show that the local reparameterisation gradient estimator for Bayesian MLPs is an instance of the R2-G2 estimator and Rao-Blackwellisation. This lets us extend benefits of Rao-Blackwellised gradients to a suite of probabilistic models. We show that initial training with R2-G2 consistently yields better performance in models with multiple applications of the reparameterisation trick.